Principles of Instrumental Analysis Douglas A. Skoog Stanford Universi~}·
F James Holler University of KentuckJ'
Stanley R. Crouch Michigan State University
THOMSON BROOKS/COLE
'"
Australia. Brazil. Canada· Mexico· United Kingdom· United States
Singapore.
Spain
THOIVISON
Contents Overvie,v
+;
BROOKS/COLE
Pr;/lr;p!('.t; of !w,lrllmt'1l1al Skoog.
Holler.
Alla( •..•,is ,"'ii.rill Editio(l and Cront'h
Publisher: David Harris Development Editor: Sandra Kiselica Editorial Assistant: Lauren Oliveira Technology Project Manager: Lisa Weber Marketing Manager: Amee Mosley Project Manager, Editorial Production: Belinda Krohmer Creative Director: Rob Hugel Art Director: John Walker Print Buyer: Rebecca Cross
Permissions Editor: Roberta Broyer Production Service: Ncwgen-Austin Tcxt Designer: Ellen Pettengell Photo Researcher: Terri Wright Copy Editor: Mary Ann Short Cover Designer: Irene Morris Cover Image: Photo Researchers, Inc. Cover Printer: Phoenix Color Corp. Compositor: Newgen Printer: Quebecor World Versailles
© 2007.1998. Thomson Brooks/Cole, a part of The Thomson Corporation. Thomson, the Star logo, and Brooks/Cole arc trademarks used hercin under license.
Thomson
Higher
Instrumental Analysis in ActionMonitoring i\lercuf) :__ t31
Education
10 Da"is DriVt' Belmont, CA 94002-:3093
CHAPTER TWO
lISA
Circuits
Electrical
Components
and
:2()
Molecular Spectroscopy An Introductioll to ldtravlo[clAbsorption Spectrollwlry ;_-nh
CHAPTER THIRTEEN
ALL RIGHTS RESERVED. No part of this work covered by the copyright hereon may bc reproduced or used in any form or by any means - graphic, electronic, or mechanical, including photocopying, recording, taping, web distribution, information storage and retrieval systems, or in any other manner ~ without the written permission of the publisher.
CHAPTER THREE
Operati(H1al Amplifiers
in Chemical
sq
Instrumentation
For permission to use material from this text or product, submit a request online at http://www.thomsonrights.com. Any additional questions about permissions can be submitted bye-mail to thomson righ
[email protected].
ApplicatiollS of l i1tra\ioletAbsorption Spectrolllt'try ;Hi?
CHAPTER FOURTEEN
ISBN-13: 978-0-495-01201-6 ISBN-lO: 0-495-01201-7
Digital Electronics
CHAPTER FOUR
Computers
and
Visible i\lolecular
80 CHAPTER FIFTEEN
Signals and Noise 110
CHAPTER FIVE
Instrumental Anal)'sis in ActiooElectronic Analytical Laboratory
Sprctrometry The 127
Printed in Canada. 1 2 3 4 5 6 7 11 10 09 08 07 For more information about our products, contact us at: Thomson Learning Academic Resource Center 1-800-423-0563
Visible ~rolccular
'\-lolecular LuminesCf'IlCe
:39C)
CHAPTER SIXTEEN
Spectrometry
An Introduction
10 Illfrarrd
4:lO Applications
CHAPTER SEVENTEEN
Spectrometry
of Infrared
457>
Atomic Spectroscopy CHAPTER SIX
\[eth",b
An Introduction
to Spectrometric
]:12
CHAPTER NINETEEN
Spectro~copy
CHAPTER SEVEN
C()mpoJH~nr:'i of
Optical
CHAPTER
Nudear
B(,:-;oW:Hln~
TWENTY
.\-Ioircillar
:\Ias-'i
SllC('tnllll('lr~
;");-){)
16;.
III;;;truments
CHAPTER TW"ENTY-ONE CHAPTER
\-lagllHic
4gB
EIGHT
Spectrometry
:::!
to Optical Atomic
Atomic Ab:-iorptioll and Atomic Slwi'tronwtr~ 230
CHAPTER NINE flU(IH'SCt'IH'(,
An Introduction 1;)
Sprctroscnpy
Charadnizal "~8q
.'-illrLict'
and l\licros('op~
ion h~
In!'itrumeutal Analvsi:"O in AdionAssessin~ the Al1tl;enticit~· of tht~ ,"iulan.1 'lap: Surfact~ .~nalysis ill the S.'n"if'e of Ifistoq-. Art. and Forensics (l~-t
Instrtllllental Anah'sis
A"IJ·lamide
E leet roallal,·rieal Chemistry
in .-\dion-()iscon~rin(J'
890"
~
Contents
():2"7
CHAPTER TWENTY-TWO
Elt~nrfJallalytical
.\ll
Chf'lIIi . ;,tr~
~liscellaneous !\lethods 89.3
11Irrndl!I.,ti()[\ In
(I~(l
CHAPTER
Instrumental
Analysis in .\ction-i\lt·asuring-
the Parts to hlrophysiometer
,-) CHAPTER ONE
Separation
Instrumental Analysis in Action- The John Vollman Case 964
1\1ethocls :\11 IllrroJlt(_~tion to Separarion.:; '0:2
CHAPTER TWENTY-SIX
Chromatographic
CHAPTER TWENTY-SEVEN CHAPTER TWENTY-EIGHT
ChrolllJ.wgraphr
APPENDIX TWO
Activity CoefficicIlb
APPENDIX THREE
APPENDIX SUf1t'fcriti,'al
and Extraction
Fillill
R")()
Capillary EIt:'ctrupllOfC:3i::i. (:apillary Elcctnwhromatography. and Ficld-FIO\\ Fractionation 367
CHAPTER THIRTY
....33
Evaluation of Aualytical Data
Electrode Potentials
Liquid
8th
CHAPTER TWENTY-NINE
Chromarography
Cas ChnlllliHngraphy
APPENDIX ONE
Preparation
Elements
Some Standard 997
96~
9(H
and Furmal
Intl"odlletion IA 18 IC ID IE
Classification of Analytical Methods Types of Instrumental Methods 2 Instruments for Analysis 3 Calibration of Instrumental Methods Selecting an Analytical Method 17 Questions and Problems 22
CHAPTER FOUR
Bigital Electronics and Computel"s 11
Compuunds RecollllnendeJ for tile of Stant lard Solutions of Some Common
FOUR
1001 CHAPTER TWO
Eleetl"ieal Components and CiI"ellils 2A Direct-Current Circuits and Measurements 28 Alternating Current Circuits 32 2C Semiconductors and Semiconductor ·Devices 43 2D Power Supplies and Regulators 49 2E Readout Devices 51 Questions and Problems 54
SO
4A Analog and Digital Signals 81 4B Counting and Arithmetic with Binary Numbers 81 4C Basic Digital Circuits 83 4D Computers and Computerized Instruments 4E Components of a Computer 92 4F Computer Software 95 4G Applications of Computers 103 4H Computer Networks 104 Questions and Problems 108
26
90
CHAPTER FIVE
26
Signals and Noise
110
5A The Signal-to-Noise Ratio 110 58 Sources of Noise in Instrumental Analyses 5C Signal-to-Noise Enhancement 113 Questions and Problems 124 Instrumental Analysis in AdionThe Electronic Analytical Laboratory
111
127
CHAPTER THREE
Opentlional Amplifiers in Chemieal hlStl"lImentation ;");
TWENTY-SEVEN
Chl'Omatogmphy
788
27A Principles of GLC 788 27B Instruments for GLC 789 27C Gas Chromatographic Columns and Stationary Phases 800 270 Applications of GC 806 27E Advances in GC 808 27F Gas-Solid Chromatography 810 Questions and Problems 811 CHAPTER
29A Properties of Supercritical Fluids 856 29B Supercritical Fluid Chromatography 857 29C Supercritical Fluid Extraction 862 Questions and Problems 865 THIRTY
30A 30B 30C 300 30E
An Ovcrview of Electrophoresis 867 Capillary Electrophoresis 868 Applications of CE 875 Packed Column Electrochromatography Field-Flow Fractionation 884 Questions and Problems 888 Instrumental Analysis in AdionDiscovering Aerylamide 890
'\/liscellaneous
Methods
816
Scope of HPLC 816 Column Efficiency in LC 817 LC Instrumentation 818 Partition Chromatography 828 Adsorption Chromatography 837 Ion Chromatography 839 Size-Exclusion Chromatography 844
894
Thermogravimetric Analysis 894 Differential Thermal Analysis 897 Differential Scanning Calorimetry 900 Microthermal Analysis 904 Questions and Problems 906
CHAPTER
THIRTY-TWO
l{ad ioehemical 'Ietlwds 32A Radioactive Nuclides 909 32B Instrumentation 916
THIRTY-FOUR
Pal,tiele Size Determination
883
Cl29
Overview 929 Flow Injection Analysis 931 Micronuidics 940 Discrete Automatic Systems 942 Questions and Problems 948
9.50
34A Introduction to Particle Size Analysis 950 34B Low-Angle Laser Light Scattering 951 34C Dynamic Light Scattering 955 34D Photosedimentation 958 Questions and Problems 962 Instrumental Analysis in AdionThe John Vollman Case 964 1 E,"aillation of Analytical Data 9h7 Precision and Accuracy 967 Statistical Treatment of Random Errors 971 Hypothesis Testing 983 Method of Least Squares 985 Questions and Problems 988
APPENDIX
alA alB alC aID
2 Actiyity Coefficients 444 a2A Properties of Activity Coefficients 994 a2B Experimental Evaluation of Activity Coefficients 995 a2C The Debye-HUckel Equation 995
CH.!\PTER THIRTY-ONE
31A 31B 31C 31D
33A 33B 33C 33D
APPENDIX
893
Thcl'mal \Iethods
THIRTY-THREE
Automated :\Iethods of Analysis
CHAPTER
Capilhll'y Electrophoresis. Capillary E1ectl"Oehromatography, and Field-Flow fmctionation 867
TWENTY-EIGHT
Li1luid Chl'onJatognlphy 28A 28B 28C 28D 28E 28F 28G
TWENTY-NINE
Supercritical Fluid Chl"Olllatography and Extraction 856
9()9
APPENDIX
Potentiab
3
80me Standard 9'J7
amI Formal Electrode
4 COltll'olll"b Heconllllen,kd for the Pn:'paralion of Standard Solutions of SOIll(' Coltlluon E"'merlts 100 I
APPENDIX
Preface
Today, there is a wide and impressive array of powerful and elegant tools for obtaining qualitative and quantitative information about the composition and structure of matter. Students of chemistry, biochemistry, physics, geology, the life sciences, forensic science, and environmental science must develop an understanding of these instrumental tools and their applications to solve important analytical problems in these fields. This book is addressed to meet the needs of these students and other users of analytical instruments. When instrument users are familiar with the fundamental principles of operation of modern analytical instrumentation, they then will make appropriate choices and efficient use of these measurement tools. There are often a bewildering number of alternative methods for solving any given analytical problem, but by understanding the advantages and limitations of the various tools, users can choose the most appropriate instrumental method and be attuned to its limitations in sensitivity, precision. and accuracy. In addition, knowledge of measurement principles is necessary for calibration, standardization. and validation of instrumental methods. It is therefore our objective to give readers a thorough introduction to the principles of instrumental analysis. including spectroscopic. electrochemical, chromatographic, radiochemical, thermal, and surface analytical methods. By carefully studying this text, readers will discover the types of instruments available and their strengths and limitations.
• Section 1 contains four chapters on basic electrical circuits, operational amplifiers, digital electronics and computers, signals, noise, and signal-to-noise enhancement. • Section 2 comprises seven chapters devoted to various atomic spectrometric methods, including an introduction to spectroscopy and spectroscopic instrumentation, atomic absorption, atomic emission, atomic mass spectrometry, and X-ray spectrometry. • Section 3 treats molecular spectroscopy in nine chapters that describe absorption, emission, luminescence, infrared, Raman, nuclear magnetic resonance, mass spectrometry, and surface analytical methods. • Section 4 consists of four chapters that treat electroanalytical chemistry, including potentiometry, coulometry, and voltammetry. • Section 5 contains five chapters that discuss such analytical separation methods as gas and liquid chromatography, supercritical fluid chromatography, electrophoresis, and field-flow fractionation. • Section 6 consists of four chapters devoted to miscellaneous instrumental methods with emphasis on thermal, radiochemical, and automated methods. A chapter on particle size analysis is also included in this final section. Since the first edition of this text appeared in 1971. the field of instrumental analysis has grown so large and diverse that it is impossible to treat all of the modern instrumental techniques in a one- or even twosemester course. Also, instructors have differing opinions on which techniques to discuss and which to omit in their courses.
This text is organized in sections similar to the fifth edition. After the brief introductory chapter. the hook is divided into six sections.
Because
of this. we have
included
more material in this text than can bc covered in a single instrumental analysis course, and as a result. this comprehensive text will also be a valuable reference
for years to come. An important advantage of organizing the material into sections is that instructors have flexibility in picking and choosing topics to be included in reading assignments. Thus, as in the previous edition, the sections on atomic and molecular spectroscopy, clectrochemistry, and chromatography begin with introductory chapters that precede the chapters devoted to specific methods of each type. After assigning the introductory chapter in a section, an instructor can select the chapters that follow in any order desired. To assist students in using this book, the answers to most numerical problems are provided at the end of the book.
• We have included a new chapter on particle size determination (Chapter 34). The physical and chemical properties of many research materials and consumer and industrial products are intimately related to their particle size distributions. As a result, particle size analysis has become an important technique in many research and industrial laboratories. • Exciting new Instrumental Analysis in Action features have been added at the end of each of the six sections. These case studies describe how somc of the methods introduced in each section can be applied to a specific analytical problem. These stimulating examples have been selected from the forensic, environmental, and biomedical areas. • ~ Spreadsheet applications have been included throughout to illustrate how thesc powerful programs can be applied to instrumental methods. Problems accompanied by this icon ~ encourage thc use of spreadsheets. When a more detailed approach is required or supplemental reading is appropriate, readers are referred to our companion book, Applications of Microsoft') Excel in Analytical Chemistry (Belmont, CA: Brooks/Cole, 2(04), for assistance in understanding these applications. • The hook is now printed in two colors. This particularly aids in understanding the many figures and diagrams in the text. The second color clarifies graphs; aids in following the data flow in diagrams; provides keys for correlating data that appear in multiple charts, graphs, and diagrams; and makes for a more pleasing overall appearance. • An open-ended Challenge Problem provides a capstone research-oriented experience for each chap-
ter and requires reading the original literature of analytical chemistry, derivations, extensive analysis of real experimental data, and creative problem solving. • All chapters have been revised and updated with recent references to the literature of analytical chemistry. Among the chapters that have been changed extensively are those on mass spectrometry (Chapters II and 20), surface characterization (Chaptcr 21), voltammetry (Chapter 25), chromatography (Chapters 26 and 27), and thermal analysis (Chapter 31). Throughout the hook, new and updated methods and techniques arc described, and photos of specific commercial instruments have been added where appropriate. Some of these modern topics include plasma spectrometry, fluorescence quenching and lifetime measurements, tandem mass spectrometry, and hiosensors. • Many new and revised charts, diagrams, and plots contain data, curves, and waveforms caleulaied from theory or obtained from the originalliteratuce to providc an accurate and rcalistic representation. • Throughout the text, we have attempted to present material in a student-friendly style that is active and engaging. Examples are sprinkled throughout each chapter to aid in solving relevant and interesting problems. The solutions to the problems in each example are indicated so that students can easily separate the problem setup from the problem solution.
· IIIThe
book's companion wensite at www.thom son ••du,corn/chemistr}'/skoog includes more than 100 interactive tutorials on instrumental methods, simulations of analytical techniques, exercises, and animations to help students visualize important concepts. In addition, Excel filcs containing data and sample spreadsheets are available for download. Selected papers from the chemical literature are also availanle as PDF files to engage student interest and to provide background information for study. Throughout the book, this icon alerts and encourages students to incorporate the wensite into their studies. • An Instructor's Manual containing the solutions to all the text problems and online images from the text can he found at www.thomsonedu.com/
bll
('hclllis(ry/skoog.
We wish to acknowledge the many contributions ofreviewers and critics of all or parts of the manuscnpt. Those who offered numerous helpful suggestions and corrections include: Larrv Bowman, University of Alaska, Fairbanks John'Dorsey, Florida State University Constantinos E. Efstathiou, University of Athens Dale Ensor, Tennessee Tech University Doug Gilman, Louisiana State University . Michael Ketterer, Northern Arizona UniverSity Robert Kiser, University of Kentucky Michael Koupparis, University of Athens David Rvan, University of Massachusetts-Lowell Alexand~r Scheeline, University of Illinois at UrbanaChampaign Dana Spence, Wayne State University Apryll Stalcup, University of Cincinnati Greg Swain, Michigan State UnIvcrslty Dragic Vukomanovic, UniverSity of MassachusettsDartmouth Mark Wightman, University of North Carolina Charles Wilkins, University of Arkansas Steven Yates, University of Kentucky We are most grateful for the expcrt assistance of Professor David Zellmer, California State UniverSity, Fresno, who reviewed most of the chapters and served as the accuracy reviewer for the entire manuscnpt. HIS efforts are most heartily appreciated. We owe special thanks to Ms. Janette Carver, head of the University of Kentucky Chemistry/PhysIcs LIbrarv, who, in addition to serving as a superb reference libr;rian, provided essential library scrvices and tech-
nieal assistance in the use of the many electronic resources at our disposal. Numerous manufacturers of analytical instruments and other products and services related to analytical chemistrv havc contributed by providing diagrams, application' notes, and photos of their products. We are particularly grateful to Agilent TechnologIes, BlOanaIvtical Svstems, Beckman Coulter, Inc .. Bnnkman Ins'trume;ts, Caliper Life Sciences, Hach Co., Hamamatsu Photonics, InPhotonics, Inc., Kaiser Optical Svstems, Leeman Labs, LifeScan, Inc., MettlerToledo, Inc., National Instruments Corp .. Ocean Optics, Inc., Pcrkin-Elmer Corp., Post nova Analytics, Spectra Analytical Instruments, T. A. Instrume~ts, Thermo-Electron Corp., and Varian, Inc. for provldmg photos. We are cspecially indebted to the many members of the staff of Brooks/Cole-Thomson Learning who provided excellent support during the production of this text. Our development editor, Sandra Kiselica: did a wonderful job in organizing the project, in keepmg the authors on task, and in making many important comments and suggestions. We also thank the many people involved in the production of the book. We arc grateful to Katherine Bishop, who served as the project coordinator, and to Belinda Krohmer, the project manager at Brooks/Cole. Finally, we wish to acknowledgc the support and assistance of our publtsher DaVid Harris. His patience, understanding, and guidance were of great assistance in the completion of the project. Douglas A. Skoog F. J ames Holler Stanley R. Crouch
1A
Introduction
.•.•
A
determining the chemic(ll composition
of
,s~rnples 0fl!lfltter. A IJu.alitative'flethod
yields in[c:;mation alJeut the id~fltity of alfJmic or molecular~pecies
or the functi~nfl
sample. Ilguantitativt.
groups in the
method: in contrast,
providesn,merical.informatio~as
to the r~lative
(lmount of (me or more of thes(niomponenls.
r7l lQ.J
OF ANALYTICAL
Analytical methods are often classified as being either classical or i/lstrumelltal. Classical methods, so';;etimes called wet-chemieal methods, preceded instrumental methods by a century or more.
n.... a./y.tical. Ch.e..... ~.istry d.e...a...ls with methods for
.
CLASSIFICATION METHODS
Throughout the book, this logo indicates an opportunity for online self-study. Visit the book's cOfilpanion website at www.thomsonedu.com/ ehemistrylskoog to view interactiVe tutorials, guided simulations, and exercises.
In the early years of chemistrv, most analvses were carried out by separating the c'omponents ~f interest (the analytes) in a sample by precipitation. extraction, or distillation. For qualitative analyses, the separated components were then treated with reagents that yielded products that could be recognized by their colors, their boiling or melting points, their solubilities in a series of solvents, their odors, their optical activities, or their refractive indexes. For quantitative analyses, the amount of analyte was determined by gravimetrie or by volumetric measurements. In gravimetric measurements, thc mass of the analytc or some compound produced from the analyte was determined. In volumetric, also called titrimetric, procedures, the volume or mass of a standard reagent required to react completely with the analyte was measured. These classical methods for separating and determining analytes are still used in many laboratories. The extent of their general application is, however, decreasing with the passage of time and with the advent of instrumental methods to supplant them.
Early in the twentieth century, scientists began to exploit phenomena other than those used for classical methods for solving analytical problems. Thus, measurements of such analyte physical properties as conductivity, electrode potential, light absorption or cmission, mass-to-charge ratio, and fluorescence began to be used for quantitative analysis. Furthermore, highly efficient chromatographic and electrophoretic techniques began to replace distillation, extraction, and precipitation for the separation of components of complex mixtures prior to their qualitative or quantitative determination. These newer methods for separatiilg and determining chemical species are known collectively as instrume/ltal methods of a/lalrsis.
Many methods
of the phenomena
underlying
have
for a century
been
known
Their
application
by most scientists,
layed
by lack of reliable
In fact, the growth
the
or more.
howe;'er,
and simple
of modern
instrumental was de-
instrumentation.
instrumental
application
of
of the elec-
teractions
of the analyte
by the analyte; teraction
TYPES OF INSTRUMENTAL METHODS us first consider
then follow. grouped
some of the chemical
and physical
characteristics
that are useful for qualitative
tative analysis.
Table
properties
that
analysis. require
a source from
Finally,
emission
for instrumental
excited-state magnetic
the atoms atoms
then
radiation,
the instrument. of a rapid
For gaseous
to higher emit
thermal
change radiation
in the table
a measurable
example,
of the analyte
energy
classical
eombinations mental
states.
The
a gravimetric
electro-
measured
bv
may -take the for~ example;
a selected
region
of
Be aware method
Thus.
violet
and
properties
of elements
method
are
ratio, reaction
or volumetric
are not. With
approach
in-
counterparts.
or compounds,
than
tal methods space assume
that
these
through output
produced
sented
the applications.
of time are equally
diffi-
true that instrumensophisticated
or more
tion ahout and
procedures
because
we
studied
these
nature spectroscopy:
and magnitude
mation
Turhidimetry; nephelometry; Raman spectroscopy Refractometry; interferometry
is contained
the interaction miliar
X-ray and electron diffraction methods
example
lengths
an analytical device
which is usuallv
electrical,
mcchanical,
in Figure
the system
The measurement dcvices
process
that convert
and physics.
investigating
how instruments how information
is passing
voltage,
1-2. data domains may be broadly classified nonelectrical dornaifls and electrical domains.
understanding
As shown
study
whose
a sample
that result from band
of
A fa\\ia\'e~
to measure
measurement
electrical
infor-
with thc analyte.
The
the
mation
that
resides
in these
acteristics
The data
Electrical
('onductometry
The intensity
of
It is possible
comparison
Gravimetry (ljuartz crystal microbalance) l\fass spec[fOmetr~/ Sptcrn
Kindic methods Thermal gravimetry and titrimctry; differential analyses: thermal conductometric methods Acti\"ation and isotope dilution methods
s into
gives. after rearrangement,
To determine changes
how
as a function
tion 2-32 with respect constant. Thus, dl-; = 0
= ~
+ iR
the
current
the charging
plots
are
presented
shape
of the curves
of time, to time,
-"eft.;
-_. -wultllTItrS/second circuit
we differentiate remembering
Equathat
V, is
The product circuit pacitor
C
dt
to charge
ponent
dt
Here.
again,
we have used lowercase charge
and current.
letters
to repre-
=
is moved
to position
of the time
2-37. Because
sidered
required
Example
change
for a caof the
from the form -I
determines
of the voltage
2-2 illustrates
were Just derived.
for the
This dependence
the ratio
Re
from
across
iRC is the exthe r;-ttc of exthe capacitor.
the use of the equations
that
=
0.0067
When
across
Inputs
the con-
i assume
v Rand
in Figure instant,
becomes
ultimately after
a capacitor five time
At this point,
however,
in Figure a source
v, is described
signal
Phase Chang-9$ in Capacitive [fthe
switch and battery
ure 2-l'>a are replaced capacitor
2-24;
a con-
causing
a current
changes
continuously.
constants
the current
has
5 H('Re
=
Circuits
with a sinusoidal stores that
alternates
A phase
and voltage
capacitor (see Figure We Olav determine
and
between
as a consequence and discharge
the
2-8b and c). the magnitude
of the phase
shift
a capacitor
from the circuit
and the
no resistance.
We first combine
fiow of
2-30 tel give. after
direction
the thus
to charge
by consid~ring
The
charge,
in direction
difference
is introduced
of the finite time required
in Fig-
ac source,
and releases
to posi-
Thus,
sig-
by Equation
in the [(C circuit shown
continuously
is con-
the current
of current.
the response ac voltage
that is,
2-8a is moved
will be in the opposite
what it was during. charging.
to a sinusoidal
2-l'>a
increases
approaches
purposes,
is removed
RC circuits
their on the
the capacitor
that follow, we investigate
These
= O.O!).
the switch
tion 2. the batterv capacitor charge,
across
and
elapsed.
that oc-
of the time
to less than 1% of its initial value (e
decayed
e-
zero
Vc
because
1. At the same
For practical
havc
units
the switch
to be fully charged
(5RC) 5
that
the instant
the voltage
value.
and
cycle of an RC circuit.
Note
values
hand,
VR.
is independent
of the circuit.
stant
seconds
the lillle wflstalli
or discharge.
in this equation.
ponential sent instantaneous
.--1.'011
time on RC can be rationalized
of Equation
cl \0"):
to
(Z, ~ 10' to 1015 Il); (3) low
(2) high input impedances
common
proper-
(Z" ~ 0.001 to Ill):
output
impedanccs
output
voltage
plifiers
do m fael exhihit
for Z.ero input.
Most
and nearly zero operational
a small output
am-
voltage
with
consequence,
all voltages
with respect
to the circuit
tronic
is not
which
is symbolized
the circuit
common
recognize
that circuit
same potential cuit comm0n
quired
to pruduce
sured
tional
amplifiers
lrim ,alue
adjustment
in thl-' manufacturing
amplifiers
arc provided
to n.:duce
(see Figure
tvlndern
opera-
have less than :i mV offset
often
cause of laser trimming Some operational
voltage.
the offset
directly
with an off,el to a negligible
.'-2c).
As shown in Figure that the h'/o Input voltages
\'
and \
amplifiers
More detail than usual
as well as the output
voltage
IS
prOVided In ta) Note
\ '-' are measured
with'
respect to the CirCUitcommon, which IS usually at or near earth ground potential. (bl The usual way of representlllg an operational amplifier In Circuit diagrams. (c) Representation of typical commerCial 8-plll operational amplifier.
as \\-,'ell as the output
Inverting
3-2a, each of the two input \'olta~t.:~. uf a typical
and {losirit'£' ill!'{/{I
operational
depending negative
to realize
output
the other
angle
n·). Circuit
a common
I'd
common
is a conouctnr
urn fur all currl'nts
tri-
that pruvide"
to tlll:il' sources.
afe mea-
Inpuis
that in Figure
signs indicate
"rthe
the it/I'crtiflg and do
amplitier
A:-. a
vl,rting
is connected
of the amplilicr
()f
and llollin\'crl-
Uf
signals. negative
of the circuit.
Either signals
Thus.
if a
to the inverting
input, the
is (lusiti\'(.· with respect
to it: if. on
the amplifier.
An ac signal connected
:'-2 the negatire
imply that they are
and negative
hand, a pnsiti\-e voltage input
1101
to positive
on thG application \ultage
which is symholiz.ed
open
to
at the
to it.
may h~ connected
ampli lief arc I11cdsurc:.,J wi th rL'SpL'ct h) cireui t common. hv a downward-pOInting
is not necessarily
hut you may aSSUn1l' that
and f\ioninverting
It is important illg
\'o!tage.
signifi-
hut it is important
he-
process.
input for operational
howe,·er,
not differ
and that all voltages
to be conneclt:d to positi\'l:
FiGURi: 3-2 Symbols
elec-
to earth
Nolc that in Figure 3-2b a cir-
commun
with respect
docs
common
is not shown,
thert..' is a circuit
connected
potential,
as ground.
are measured
Ordinarily,
hy ~. Usually,
potential
from the ground
zero input due to circuit characteristics or component instabilities. The o.th'!'l vultage is the input voltage rezeru output
common.
equipment
ground, cantly
in till' circuit
is conneckd
to the in-
a nCf'-dtive output
results.
tu the in\'ertin~
input yields an
thar is ISO degrees Ollt of phase with the signal at
output
the input. The noninverting other
hand, yidds
input of an amplifier,
an in-phase
signal at the noninvcrting input. the output signal of the same polarity as the input.
Operational modes: mode,
amplifiers
the
are
comparator
on the
=-:{>'-
used
mode,
and the ClInent follol\'er,
will be a dc
in three thc
-~-
~
signaL in the case of a dc
~
0
.
\'-,-
different
vo!tilge
or opera/iuna!,
Linear
mode,
operatmg
FlOUR I: 3-5 Voltage follower. The amplifier output is connected directly back to the amplifier inverting Input. The input voltage ", is connected to the noninverting Input. The output voltage is the sum of the input voltage and the difference voltage ",. If the output voltage is not at limit, v, is very small. Therefore, I'" = 1', and the output voltage follows the input voltage.
range
I
38-1 Comparators [n the comparator used open!oap,
mode, without
ure 3-4a, [n this mode,
the operational any feedback
the amplifier Usually,
the
are connected
directly
to the two 01' amp
The
amplifier
A(v_ - 1'_). If A supply
always at
:'::15-V supplies).
compared inputs.
is almost
is
in Fig-
limits
output
is givcn
106, for example,
=
were:'::
-13IJV in Figure
put voltage
+ 13
to 1'0
1'0
=
be at
where
V, 2-
v, is in the
tells us whether
1'_
> v _ or
< v __ If the output is 1'+
> v_by more than 13IJV, for example, at positive limit (+ 13 V in our case). [n contrast, than
13 IJV. the output
FKmRE 3-4 (a) Comparator mode. Note that the , operational amplifier has no feedback and is thus an open-loop amplifier. (b) Output voltage v" of operational amplifier as a function of input difference voltage ",. Note that only a very small voltage difference at the two inputs causes the amplifier output to go to one limit or the other.
>
if v.
is at negative
( -13 V). Some applications of comparator given in Sections 31" and 4C.
limit
circuits
are
A typical
operational
shown in Figure amplifiers have and output voltage
amplifier
follower
impedances
of less than 1 fl. Therefore,
connected
by circuits
to the amplifier
to the noninverting
source
the
and distorting
vent such loading, device
the inherent
circuit
internal
the voltage
ternal
resistance,
its output
of loading
To pre-
larger
of the voltage
is a transducer
than
source.
with high in-
such as a glass pH electrode
or pion
electrodc, it is necessary to introduce a circuit known a I'()!wge follol\'('r to prelent the loading error.
When
or measuring
output
1'0-
devices
Furthermore,
as the input,
as
put signal is connected
limih [u whIch Ih~ op dmp .:-an be dri\,;'n ,He \Jtlcn slightly ks~ than rilL' pO\\cr sllrply \olt;)g~~!:: L'i \. ) bcc which
Ie =
For the voltage
cor-
A similar
relate
I
I kHz, which
line, and so on for other
might
we see that
required
3-8. The bandwidth
of the upper
10 then has a bandwidth
response
is characterized
rale can be calculated
3-7
=
that
to 90% of the total change.
of Figure
1 MHz/1000
input
for this am=
the amplifier
parameters
.1f of an amp Iitier are illustrated
a dB,
Rf/ R, = WOO, as indicated
line in Figure
is then
by the lower dashed
inside
diagram, such as that shown in Figure 3-8 (see also Section
;\, =
small capaciresponse
the time
10 Hz. This characteristic
gain A
dashed
the amplitier
of
amplitier
in the same
at which A = 1, or
of the bandwidth
As an example,
other
ure 3-'1. The output step
configuration. with a signal
operational
point
105, or 100 dB;
of the operational
above
Two
10 Hz, the open-
the gain bandwidth product at I MHz, which stant
R, because
=
tilter (Section
The
and
or dB, where
A
above
the unily-gain bandwidth,
is called plitier
Time
FIGURE 3-9 Response of an operational amplifier to a rapid step change in input voltage. The slope of the changing portion of the output signal is the slew rate, and the time required for the output to change from 10% to 90% of the total change is the rise time.
bandwidth
increases
ion as in a low-pass
are log scales
in decibels,
frequencies,
but as the frequency
with the open-loop
typical
if the input
given
Response
The gain of a typical
is small
mode can be used to make
amplifier
on how ac-
and not on the amplitier.
voltage
is a possibility
2 to
Voltage Amp/ifier
follower
voltage
Vi'
end, the out(typically
6
FIGURE 3-8 A Bode diagram showing the frequency response of a typical operational amplifier. Solid line: operational amplifier open-loop gain without negative feedback; dashed line: inverting amplifier configuration as in Figure 3-7 with A, ~ RrfR, = 1000 and A, = R,/R, = 10.
the upper 3B-4 Frequency
operational The Inverting
X
3-6 re-
of the amplifier,
less. On the high current
capability
-10
=
3-7 is often called an invert-
of Figure
that there
1'0
of the gain depends
the two resistances
voltage 1', because current drawn from the source. When
lOll 0
range from de to the frequency
10 kD, the gain would
however,
bias current
10'
were
case
by the input
20
loop gain rolls off at - 20 dBldecade
amplifier
ing amplifier or an inverter when Ri
limited
10'
closed-loop gain, R,/Ri, can be made quite accurate. For example, if R, were 100 kD and R, the
The amplifier
duces
vi~mul-
by the ratio of two resistors,
open-loop gain, A, of the operational
3-4. Measurement
~
gain
~O
that both
I
i
tiplied
100 MD, for example, resistance
3-4, we obtain
. Rf -IR, = -v-R
site polarity. factor
this result into Equation
I
R=, A
the effective
Closed-loop
S is at virtual
is con-
Thus, the output
of R, on the circuit
10'
60
0
3-4 ii = - vol R" we can write
effect
10'
Inverting voltage amplifier. Here, the input current into the summing poinl S comes from the input voltage v, and input resistance R,.
and point S is kept
R,
The loading
W
FIGURE 3-7
R, is the error voltage v; divided by the ii; that is, Ri = v,li,. Because v; = -volA
and from Equation
10'
lJ
an output
of the current
current
the input-signal at its output
100
ClIrrent, the current
effect
the input
JO
""
an output
a clIrrent-IO-I'ollage converter.
point S and common
ally zero resistance
if that
to i,. If, for ex-
would
120
the opera-
it produces
is very little loading
lower circuit. nected
input
voltage
proportional
There
i, and
100 MD (la' 0) and
measured.
follower
the Slll/lInin,~
current
proportional
cur-
interacting
that
a feedback
current
is directly
A), the output
is readily
here without
Point S is thus called junction .
amplifier
fol/ow,
(!), several
common
can be connected
Simulation: response.
Learn more ahout op amp frequen('~
amplification
amplitiers
tind general
and measuremc:nt
nals frol11 transducers.
Such
application
of the electrical
transducers
in the sig:~
can produce
voltage outputs. current outputs. or charge outputs. The signals from transducers are often related to con-
the photocathode
centration.
a potential
This section
presents
operational ampliliers type of signal.
basic applications
to the
measurement
of
of each
the
cathode
that
ode (cathode t:jected
measurement
tant to such analytical metry.
photometry.
out in Chapter all physical ment.
methods
and chromatography.
measurements.
significantly error.
including being
negative
cess will perturb
a system
that the quantity
actually
original
value
therefore kept small. suring
device
be minimized
significantly.
in Section device.
3B-3
The
of a current
transducer
tensity
into
follower
is a phototube
a related
current,
in such
proa wav
We
I
must
with a high degree As shown
I, provided
the current currents
presented
being used to meain Figure
in-
Ie- Radiation
striking
Assume
that R, in Figure
sistance
of the phototube
3-1. an operation'al
amplifier
current
R,
output
follower
for measuring
phe-
is an in-
the small
currents
FIGURE 3-11
A high-,mpedance and measurement.
circuit for voltage
Measurements
transducers
concentration example.
perturbation
produce
is 5.0 X LO'
n, and
gain is 1.0 X lO'- Calculate
in the current
the presence
}-10 is I MD. the internal
measurement
of the measuring
re-
the amthe rela-
that results
from
circuit.
output
larly those
based
Equation surements
2·19
R, R =, A
1
resistance
of the current
10"
X
in a current
measurement rei error
=
loading
error
(rei
is given hy
-~_!?~
which typically
order
of tens
where
resistance R" is the current follower Ri and RL is the internal rcsistancL' of
the meter
input resistance the phototubc.
Thus.
rei error
I¢
~ (:i0
instrument
p!lo(onu.'(cr.
shown
A photometer
in Figure
can he combined of Figure
device
follower. in excess
of
10'-
amplities
n.
+-IM l!
3-10 is calleJ
can h~ used to measure
a the
designed
sion measurements.
a very
of the glass
for conductomctric
ient means
for measurement
ductance
of a transducer.
amplification
as
shown
control
or convoltage
is substituted
R, or R, in the circuit. The amplified
for either voltage
a conven-
a constant
is used for Vi and the transducer l'"
is then measured
with a suitable
or a computerized
of Equation
in a
output
meter.
data-acquisition
posys-
for R, in Fig-
is substituted
as can he seen from rearrangement
3-8. is
of a voltage
an input impedance
inverting output
amplifier
circuit
by R,f R,. or 20 in
such as this with a resistance called
in
and emis-
of the resistance Here.
or
signal.
and ther-
absorption
and for temperature
ure 3-7, the output,
yoltagc-
to an analytical
for infrared
ex-
resistance
variety of analytical applications_ The circuit shown in Figure 3-7 provides
source
voltage
are used
titrations.
tem. Thus. if the transducer
an ilTIOt\i:3 A.r'-~PL!F!ER3 TO
31"
Another
important
erational
and widespread
amplifiers
Such circuits log timers,
circuits,
circuits
tween
the digital
and analog
mode
of operational
tion 3B-1. Figure
common,
with a reference
voltage in Figure
whether
I)
- Limit
is compared
a zerovoltage
is often
voltage
is greater
If v, > 0 by more
is at negative
"0 is at
plifier
is very rapid,
positive
than
limit. If
ll;
limit. Because such
a detector
< 0 by a
FJf3UFFE. 3~'J 7 Operational
the am-
detector
time the sine wave crosses
scope
state.
Such circuits
triggering.
hy connecting
the noninverting input to common. In Figure ll;
>
the opposite of comparator
input
output
detec-
the
to
inverting
system. might
output
is between
is at positive
and
10(') and very fast rise times.
a lellel detee/or. It can he
interfacing
and other
whether
coolant
the pH has
triggering
amplifiers
campara/aI's are often
\~d'
when
amplifier
specialized
ll,
the tempera-
level and to supply base. The level
is also used in oscilloscope
the comparator
such a level de-
when
value and to supply
This type
when
to determine a certain
ll,
limit. whereas
can be part of a feedback
In a chemical
he used to determine
Although
is often called
h"s exceeded
tector
in oscillo-
zero-crossing
and connecting
limit is reached
used. for example.
used
the sine wave signal
3-17b, the comparison
V;", the
side.
zero, the comparator
A noninverting
tor can he made
V;". If
on the right
are often
at the end of the book
amplifier
used with a :'C 15 \" power
has output supply.
switching
(b) 500.00n X
10"
for problems
used
error
voltage
due to (a) the finite gain of the amplifier
voltage
source. show that the output ll"
=
cirCUIt of Figure
3-5.
of 2.0 V and a source in the follower
and (b) the loading
voltage
resis-
output of the
v" and the input voltage
\',
\"(&R+, R2).
Why is this circuit "3-6 For the circuit
3-7 In the following a function
divider,
a voltage
in Prohlcm
follower
with gain')
3-5, it is desired
that
R, + R, is to equal 10.0 kn, find suitahle
resistance
"0 as
called
shown
Perform
the feedback
circuit. of
V;
R is a variable
resistor.
llo
=
Derive
3.51',. If the total
for Rj and R,_
values
an equation
that descrihes
x of the movable contact of the voltage such that x is zero if there is zero resistance in
and the position
the derivation
loop.
These
in computer
applications.
marked
mltage
to be used in a current
j
(ai
Design
a current
follower
follower
has an open-loop
gain A
of 2.5 nA.
that will produce
a 1.0 \" output
for a 10.0 flA input
current.
limits of -+ 13 Vand
-14
l'_
(hi
Y when
is used as a comparator.
have to exceed
amplifier
of 2 X 10 and an input bias current
with an asterisk.
using spreadsheets.
If the amplifier
amount does v_ have to exceed l'_ ancll at limit if th~ open-loop gain A is (a) 200.000
15
follower
relative
by
5.0 flY'?
gain of 1.0 X I oj and an input
with a voltage
arc related
iv, i s
voltage
in Fig-
with this icon are best solved
*3-1 An operational
(C)
value of the difference
tance of 10.0 kll. Find the percentage
3-8 An operational arc provided
Q~ Problems
volt-
of 500 mV what is
limits of ::,.
C;lrnhrid~t:' . .\1.-\: l\f1T
48 COUNTING AND ARITHMETIC WITH BINARY NUMBERS In a typical tronic
3rd ed" purt'r
HalL
DC J.nd R. E. Hohun. SdlJr1dL'r~.
Errl,'rilllt'llr,lfiuIL
!al"lfilfOn
!y,,;l)
~c.:c
If. \', :\l;lll!l~tadt
and Elt'c£r(>/Iic
\\·d~hil1gt'ln.
Phlbdclphl[
0~8
'0"
0~6
~
0.4
fIl .c
I I I
02 00
L~-
r i
--
+---
800
900
1000
1100
I
'"
ot-· l:
'c:" .c
I
~
1200 _~ Vb~r, em
.,
-t--
-7
I
1300 .14._00 '500
'"00 I
oJl
A R_
CI \Hj~'h
(1101111:1\
snft\\~lre
ur mort.' cornpkk
can be Linne with spreadsheets. JILl! lIl!drllLl1 lUll
t I. oIkr_-i.{J!" Ikiln,)nr.(·-\ Br,,\,I..J
and analy-
include basic statistical functions.
stanoard
\-ariuus distribution functions.
to their spre~~d-
Excel now contallls
that can ht.' used to s,
H ~:::.
c:
Change I
Do.)
I
Elt'\ator
HourI
10'
10' Envimnrnenlal nOise 1 10-'
10
b
10-'
la'
10-2
Shot Noise
Shot noise is encountered wherever electrons or other charged particles cross a junction. [n typical electronic CirCUits,these junctions arc found at pn interfaces; in photocells and vacuum tubes, the junction consists of the evacuated space between the anode and caihode. The currents comprise a series of quantized evdnts, the transfer of individual electrons across the junction. These events occur randomly, however, and the rate at which they occur is thus subject to statistical fluctuations, which are described by the equation 1m" =
V2/~-s.7
where i,m, is the root-mean-square current fluctuation associated with the average direct current, I; c is thecharge on the electron of 1.60 x 10 19 C; and J.fis agam the bandwidth of frequencies being considered. LIke thermal noise, shot noise is white noise and is thus the same at any frequency. Equation 5-5 suggests that shot noise in a current measurement can be minimized only by reducing handwidth. Flicker Noise
As shown by Equation 5-3, thermal noise can also be reduced by lowering the electrical resistance of
I
Frequency, Hz --
Solution
If we assume that the response time is approximatelv cqual to the rise time, we find that the bandwidth ha~ been cha"..ged from I Hz to 10' Hz. According to EquatIOn )-3, such a change will cause an increase in the noise by (106/1) I!2,or IOOO-fold.
Power line 611ISIl-
Temp.
Flicker noise is characterized as having a magnitude that IS Inversely proportional to the frequency of the SIgnal bemg ohserved; it is sometimes termed IIf(oneover-fJ nOISe as a consequence. The causes of flicker noise are not totally understood; it is ubiquitous, howe_ver,and is recognizable bv its frequency dependence. Fhcker noise hecomes significant at frequencies lower than about 100 Hz. The long-term drift observed in de amplifiers, light sourecs, voltmeters, and current meters is an example of flicker noise. Flicker noise can be reduced significantly in SOffit: cases by using wire-wound
FIGURE 5-3 Some sources of environmental noise in a universIty laboratory. Note the frequency dependence and regions where various types of interference occur. (From T. Coor, J. Chem. Educ., 1968,45, A540. With permission.)
or metallic-film resistors rather than the more common carbon-composition type. Environmental
Noise
Environmenta[ noise is a composite of different forms of noise that arise from the surroundings. Figure 5-3 suggests typical sources of environmental noise in a university laboratory. Much environmental noise occurs because cach conductor in an instrument is potentially an antenna capable of picking up electromagnetic radiation and converting it to an electrical signal. There are numerous sources of electromagnetic radiation in the em·ironment. induding ac power lines, radio and TV stations, gasoline-engine ignition systems, arcing switches, brushes in electric motors, lightning, and ionospheric disturbances. Note that some of these sources, such as power lines and radio stations, cause noise with relatively narrow frequency bandwidths. Note that the noise spectrum shown in Figure 5-3 contains a large, continuous noise region at low frequencies. This noise has the properties of flicker noise: its sources arc not fully known. Superimposed on the flicker noise are noise peaks associated with yearlv and daily temperature fluctuations and other periodic phenomena associated with the use of a laboratory building. Finally, two quiet-frequency regions in which environmental noise is low are indicated in Figure 5-3: the region extending from about 3 Hz to almost 60 Hz and
the region from about f kHz to about 500 kHz, or a frequency at which AM radio signals arc prevalent. Often, signals arc converted to frequencies in these regions to reduce noise during signal processing.
Many laboratory measurements require only minimal effort to maintain the signal-to-noise ratio at an acceptable level. Examples include the weight dcterminations made in the course of a chemical synthesis or the color comparison made in determining the chlorine content of the water in a swimming pool. For both examples, the signal is large relative to the noise and the requirements for precision and accuracy are minimal. When the need for sensitivity and accuracy increases, however, the signal-to-noise ratio often becomes the limiting factor in the precision of a measurement. Both hardware and software methods are available for improving the signal-to-noise ratio of an instrumental method. Hardware noise reduction is accomplished hy incorporating into the instrument design components such as filters, choppers, shields, modulators, and synchronous detectors. These devices remove or attenuate the noise without affecting the analytical signal significantlv. Software methods are based on "arious computer algorithms that permit extraction of signals from noisy data. As a minimum. software methods require sufficient hardware to condition the output
signal from the instrument and convert it from analo to digital form. Typically, data arc collected by using; computer equipped with a data·acquisition module'as described in Chapter 4. Signals may then be extracted from noise by using the data-acquisition computer or another that ISconnected to it via a network.
Narrow-band electronic filters are also available to attenuate noise outside an expected band of signal frequencies. We have pointed out that the magnitude of fundamental noise is directly proportional to the square root of the frequency bandwidth of a signal. Thus, significant noise reduction can be achieved by restricting the input signal to a narrow band of frequencies and using an amplifier that is tuned to this band. It is important to note that the bandpass of the filter must be sufficiently wide to include all of the signal frequencies.
5C-1 Some Hardware Devices for NOise Reduction We briefly describe here some hardware devices and techniques used for enhancing the signal-to-noise ratio.
FIGURE 5-4 An instrumentation amplifier for reducing the effects of nOIsecommon to both inputs. The gain of the CirCUitIS controlled by resistors R,Ia and KR,.
Grounding and Shielding
Noise that arises from environmentally generated electromagnetic radiation can often be substantially reduced by shleldmg, grounding, and minimizing the lengths of conductors within the instrumental system. Shleldmg consists of surrounding a circuit, or the most CrItical conductors in a circuit, with a conducting material that is attached to earth ground. Electromagnetic radiation is then absorbed by the shield rather than by the enclosed conductors. Noise pickup and pOSSibly amplification of the noise by the instrument CirCUItmay thus be minimized. It may be somewhat surprIsmg that the techniques of minimizing noise through grounding and shielding are often more art than science, particularly in instruments that involve both analog and digital circuits. The optimum configuralion IS often found only after much trial and error4 Shielding becomes particularly important when the output of a high-resistance transducer, such as the glass electrode, is being amplified. Here, even minuscule randomly induced currents produce relatively large voltage fluctuations in the measured signal. Difference
and Instrumentation
Amplifiers
Any noise generated in the transducer circuit is particularly CrItical because it usually appears in an amplified form in the instrument readout. To attenuate this type of noise, most instruments employ a difference amplIfier, such as that shown in Figure 3-13, for the first stage of amplification. Common-mode noise in the
~For an excelkm discussion of groundlllQ. and shielding see H \/ M' I _ stadt, C. G. Enke, and S. R. Crouch. ,V/;rncompulen- a'nd Ele~lr~ni;~~_ Hr~meflIQI/()n: ,'-lakmg the Right Connections, pp . .tOl --9, W<e;hinglon, ?C: American Chemical Society. 1994. A valuahle reference is R Morri~on, Groundlllg arid Shielding Tf'chniql~es in Instrumentation. 4th ed., Nev. York: Wiley, 199cS.
transducer circuit generally appears in phase at both the inverting and non inverting inputs of the amplifier and IS largely canceled by the circuit so that the noise at its output is diminished substantially. For cases in which a difference amplifier is insufficient to remove the noise, an instrumentation amplifier such as,the one shown in Figure 5-4 is used. r Instrumentation amplifiers are composed of three op amps configured as shown in Figure 5-4. Op amp A and op amp B make up the input stage of the instrumentation amplifier in which the two op amps are cross-coupled through three resistors R" R11a,and R,. The second stage of the module is the difference amplIfier of op amp C. The overall gain of the circuit is given by' Vo
=
K(2a + l)(v,
-
(5-6)
VI)
Equation 5-6 highlights two advantages of the instrumentation amplifier: (1) the overall gain of the amplIfier may be controlled by varying a single resistor Rlla, and (2) the second difference stage rejects common-mode signals. In addition, op amps A and Bare voltage followers with very high input resistance, so the Instrumentation amplifier presents a negligible load to Its transducer circuit. The combination of the two stages can proVide rejection of common-mode noise by a fac6 tor of 10 or more while amplifying the signal by as much as lOOO. These devices are used often with low-level signals in nOIsy enVlfonments such as those found in biological orgaOisms In which the organism acts as an antenna.
j~.
v. r-.~almstadt,
c. G. Enk.::. and S. R. Crouch, Microcomputers
L~.t'Cl~/}mc IflStrumenrI.11:fm-
\\''1'~ ~1;!~~=;'"
particularly
cal industry, government
_~-~Qi195r-=.~ __J.1.Q
'"
can be manipuiated
and
Data can be entered in electronic
automatically.
In paper-based
to be entered manually into notebooks
systems, data had and chart recordings
or photographs had to be stored. Another positive effect of an electronic laboratory
system. In some cases, information
data system or notebook
Several of these components
are discussed in this case study.
Electronic Laboratory Notebooks Electronic
laboratory
notebooks
(ELNs) first became avail·
able in the mid-1990s. They promised to revolutionize is in-
collection
and dissemination
of laboratory
cently though, ELNs were not in widespread
cally, sharing data and information
trial, governmental,
among many coworkers
can be accomplished
workers who need information
quite readily. Those
have nearly immediate
ac-
cess so that decisions can be made much more rapidly than with paper-based laboratories. A third benefit is to speed the throughput analytical laboratories.
Here, lahoratory
regulations
automation
and
or academic laboratories.
use in indus· With new
and the desire to enhance efficiency has come
the realization
that capturing
information
about new prod-
ucts or analytical samples as soon as possible and making that information
of samples in
the
data.' Until re-
creased efficiency. With the availability of data electroniin an organization
from the
flows directly into archival storage.
available to others in the organization
is an
idea with a good deal of merit. Hence, the ELN has been making a comeback
in the last few years, particularly
in the
ses of samples more rapidly so that those who need analyti-
pharmaceutical industry. The ELN consists of laboratory
cal results can receive them quickly. This can help alleviate
a research worker can enter data and graphics or import the
production
data from instruments,
the electronic manipulation
of data help to complete analy-
problems, assist in studies of the efficacy of new
notebook
pages in which
data systems. or software like
products, or speed up the release of new materials to the marketplace.
25. Piper, Am. Phann Rev. 2005. 8 (1). 10 (\WWw.americanpharmaceutical review. com). 3p. Rees, Scienti.fic Computing
World 2004. 79. 10 (~v,:w.scientilic-
computing. com Iscwnovdcc04lab _notebooks.htmll.
"""'"
..•..
~ ••••••. ••••
FIGURE IA 1-3 Laboratory FileMaker, Inc.)
spreadsheets
and scientific packages. [n one ELN, a library
card is first issued by a librarian.
With the type of notebook
Once a user has a library card, ID number, and pass· word, the ELN can be opened and pages observed. A typi·
shown in Figure IA ).), a librarian gives a library card to
callaboratory
each user of the notebook. The library card contains per-
Here, the author of the page is required
sonal information about the user such as that shown in Figure IA)·2.
electronically
notebook page is illustrated
in Figure IA)·3.
to sign the page
by posting it with a picture and statement.
The electronic signature is a unique, nonhandwritten means
[1]-".I.lItlk
lniTJGOS lO;S4)4AU Jl2l1.lOOJ IOJlj)f AJ,I JJ2l12OOJ 10'" 04 AM
notebook
•
: 14lJJOOS .". 'OJ'" AM
page showing author, witness,
and validator. (Courtesy
of identifying a person that remains with the individual so
idates the notebook
that other users cannot apply it. These usually include an ID
of security when the library card is issued.
number and password, a bar code, and a personal 10 code or a retinal, voice, or fingerprint scan. A witness must then
of
page. Users are assigned various levels
The ELN is searchable
electronically
by any registered
user, This feature allows a user to quickly find data and to
sign in with a valid ID number and password and electroni-
share it with coworkers who have the appropriate
cally witness the page. Likewise, a validator signs in and val-
clearance.
security
The ELN does not depend on the penmanship
of
the user as does a conventional notebook. It can be accessed remotely from home, a meeting in another location, or a worker's office. The ELN can be backed up by normal procedures
so that it cannot be lost or destroyed
searcher. Notebook
by a re-
pages can be printed for use in reports.
It is anticipated integrated
that in the future we will see more closely
electronic laboratory
pharmaceutical
Many laboratory
notebooks
are networked
governmental,
tories will also become paperless.
to LlMSs or to
and academic labora-
Scientists often have addi-
tional electronic devices such as laptop computers
archival storage systems. The LIMS handles sample tracking
sonal digital assistants to support
and management
we should see these devices communicating
along with scheduling and data archiving
(see Figure 4-21). Some ELNs communicate the LIMS or data-archiving
wirelessly with
system, and others are part of a
instruments
ciency and productivity.
Although
havc been driving the adoption
ments, data systems, and LIMSs is often a formidable
the pharmaceutical
Although
it is difficult to fully integrate older laboratories,
with ELNs,
to further increase effigovernment
regulations
of electronic laboratories
in
industry, the benefits of increased pro-
ductivity, reduced paper work, and lower costs will eventu-
new or redesign"ed laboratories can incorporate electronic
ally be the most important
laboratory
less, electronic laboratories.
principles from the beginning.
and per-
their work. Increasingly,
LIMSs, and laboratory
wired local area network. Integration of existing instru~ task.
in the
switch. As the benefits become more generally recognized, many other industrial,
Connecting to LlMS and Archival Storage
systems. Companies
industry have already begun making the
reasons for implementing
paper-
The image
~hl.)\nlcontains
the optical emission spectra of a Each spectrulll provides a unique fingerprint of the corresponding ::iuhstallce that may be lIsed to iJelllify it. From top to hottom. the sullstances afe hromint'_ deuterium. helium, hydrogen. krypton. mercury. neOll, water vapor. and XPUOIl. Note tilt" similarities bf't\vPCIl hydrogen. dellnumber
of gaseous
tt"rllllll_
and
sub::Olances.
water
vapor.
As we shall
lines ill the ::ipeClnl yield informatioIl tioIls of the elemenl:-i. .-ipe(·tru:--copic
S
methods
Optical
the
sef'_
spectroscopy
that we shall
of the
illtelisities
regarding: tilt' ('Ollcentrais just
explore
(lIlt'
uf
in Seetioll
nHUI~
~.
,.,ction:2 co. mprise .• the jilllliamental principles
01111
met/wds of atomic spectroscopy. Chapter 6
investigates the nature of light and its interac-
tion with maUer, Will Chapler 7 introdaces the optical, electronir, and mechanical componcnts of oplical instruments. nzcs" ta'o chapters also present cmzcepts and instrument components that are IlSf:!iL! in our discussioll ofrrzolcclliar speclroscop.l' in See/ion .J. The general naaspects (!(iatroduc-
lure ,,( atomic spcctru and pmctical
irig atomic srlfflples into a :''1)(xfrorneler are addressed
ill
Clzapter S. Chapter 9 e.lplores Ihe pructic!' of atomic absolptioll
and atomic .flu.orescence spectroscopy,
and
Chapter 10 proridcs a similar treatment Ii/atomic emissioll sppr:lroscopy .. \fass
spec/romrtry
Chupter 11. as arc descnfJliolls ulld
methods (~(atumic
tion
({atomic
is introducrd
l'uriuu.s illslnunents
IIWSS speclrUlIletl:L
"jH'C/nJllletly
in
r~r
is cOIllIJ/eted
Ollr
IJ.,·
(J
presentadiscu.ssifJll
ulS-ray speclroml'tlT in Chapler 1:2.In the Instrumental llla~n·i.s in Actioll 10 /IIUflito,.
ulld
S!U{{\'.
speciale
ire
P.l'Onl,·IlC
lIlerClll:"
ill
(Jlul~\"icaL methods
Llw PllrirOlUnl'lll.
:~~~~>;, ~,,"F'
AnIn~pd,cti~P toSpe~trofetlc Methoas~!~'~f~:7;
{(~~';~-~ ~l: '
;;ft:V,;~ ::;:-:~tl:;' ,;/.:_~,'{,~
.-:";I'.~-.
'-,,'?!
J;
;->~;gi;
:~~g },,:j:'-~:'
:~~~~:; :rii~~~""
.~·i'·'" /i'"
.~-~/,'
his chaputk'treats
T
':~'S~:-/';'
i~~'~eneral
teractions()lelectro'Jfg~netic
atomic and molec
introduction
pp
six chapters describe spectro&}tric
meth;ods used
element.'; present invarious forms of mafli3r. Chapters 13 through 21 theTl-~ifcuss th¢ uses
arc used for their quantitative
r71 [Q.J
A~
I
Direction of propagation
FIGURE 6-1 Wave nature of a beam of single-frequency electromagnetic radiation. In (a). a plane-polarized wave is shown propagating along the i-axis. The electric field oscillates in a ptane perpendicular to the magnetic field. Ifthe radiation were unpolarized, a component of the electric field would be seen in all planes. In (b), only the electric field oscillations are shown. The amplitude of the wave is the length of the electric field vector at the wave maximum, while the wavelength is the distance between successive maxima.
68 6A
GENERAL PROPERTIES OF ELECTROMAGNETIC RADIATION
aq~ determir:ing the
molecular species and descrifjhow
I-'~----Wavelength.
I
in-
ds,/t!;enext
of spectrometry forstructur{l[~eterminqtion
I
with
'.' ecies. Alter this
to spec,'tromet
by scientists for ide0tifying
t1ay the ~,es
Spectrometric methods are a large group of analytical methods that are based on atomic and molecular spectroscopy, Spectroscopy is a general term for the science that deals with the interactions of various types of radiation with matter. Historically, the interactions of interest were between electromagnetic radiation and matter, but now spectroscopy has been broadened to include interactions between matter and other forms of energy. Examples include acoustic waves and beams of particles such as ions and electrons. Spectrometry and spectrometric methods refer to the measurement of the intensity of radiation with a photoelectric transducer or other type of electronic device. The most widely used spectrometric methods are based on electromagnetic radiation, which is a type of energy that takes several forms, the most readily recognizable being light and radiant heat. Less obvious manifestations include gamma rays and X-rays as well as ultraviolet, microwave, and radio-frequency radiation.
of
these methods
determination.
Throughout this chapter, this logo indicates an opportunity for online self-study at www .thomsooedu.com/chemistrylskoog, linking you to interactive tutorials, simulations;and exercises.
Many of the properties of electromagnetic radiation are conveniently described by means of a classical sinusoidal wave model, which embodies such characteristics as wavelength, frequency, velocity, and amplitude. In contrast to other wave phenomena, sueh as sound, electromagnetic radiation requires no supporting medium for its transmission and thus passes readily through a vacuum. The wave model fails to account for phenomena associated with the absorption and emission of radiant energy. To understand these processes, it is necessary to invoke a particle model in which electromagnetic radiation is viewed as a stream of discrete particles, or wave packets, of energy called photons. The energy of a photon is proportional to the frequency of the radiation. These dual views of radiation as partieles and as waves arc not mutually exclusive but, rather, complementary. Indeed, the wave-particle duality is found to apply to the behavior of streams of electrons. protons . and other elementary particles and is completely rationalized by wave mechanics.
WAVE PROPERTIES ELECTROMAGNETIC
OF RADIATION
For many purposes, electromagnetic radiation is conveniently represented as electric and magnetic fields that undergo in-phase, sinusoidal oscillations at right angles to each other and to the direction of propagation. Figure 6-1a is such a representation of a single ray of plane-polarized electromagnetic radiation. The term plane polarized implies that all oscillations of eithei' the electric or the magnetic field lie in a single plant:. Figure 6-1b is a two-dimensional representation of the electric component of the ray in Figure 6-1a. The electric Held strength in Figure 6-1 is represented as a vector whose length is proportional to its magnitude. The abscissa of this plot is either time as the radiation passes a fixed point in space or distance when time is held constant. Throughout this chapter and most of the remaining text, only the electric component of radiation will be considered because the electric field is responsible for most of the phenomena that are of interest to us, including transmission, retlection, refraction, and absorption. Note, however, that the magnetic component of electromagnetic radiation is responsible for absorption of radio-frequency waves in nuclear magnetic resonance.
In Figure 6-1b, the amplitude A of the sinusoidal wave is shown as t~e length of the electric vector at a maximum in the wave. The time in seconds required for the passage of successive maxima or minima through a fixed point in space is called the period p of the radiation. The frequency v is the number of oscillations of the lield that occur per second I and is equal to lip. Another variable of interest is the wavelength A, which is the linear distance between any two equivalent points on successive waves (e.g., successive o13xima or minima).' Multiplication of the frequency in cycles per second by the wavelength in meters per cycle gives the velocity of propagation V, in meters per second:
It is important to realize that the frequency of a beam of radiation is determined by the source and lThe common unit of fr~quenc)' is the reciprocal second (5 I), or hertz (Hz). which corresponds to one cycle per second. :The units commonly used for describing wavelength differ considerably in the v,HidUS spectral regions. For example, the angstrom unit, A (10--10 m). is convenient for X-ray and short ultraviolet radialion; the nanomder, om (to "mj, is employed with visible and ultraviolet radiation; lhe micromeler. /lrn {In of, m), is useful for the infrared region. (The micrometer was called miu()fl in the early literature: use of this term is discouraged.l
3X
3 X 108
10'0
10"
3 X 10'
3 x 10'
3 x 10'
10"
10"
1015
101.1
I
I
I
I
I
3
3 x 10'
3xlO-'
10"
10'
10'
I
I
I
100
X
Vv'avenumher,
Frequency.
cm-l
Hz
H Visible
f------1 Ultraviolet
FIGURE 6-2 Change in wavelength as radiation passes from air into a dense glass and back to air. Note that the wavelength shortens by nearly 200 nm, or more than 30%. as it passes into glass; a reverse change occurs as the radiation again enters air.
remains invariant. In contrast, the velocity of radiation depends upon the composition of the medium through which it passes. Thus, Equation 6-] implies that the wavelength of radiation also depends on the medium. The subscript i in Equation 6-1 indicates these dependencies. In a vacuum, the velocity of radiation is independent of wavelength and is at its maximum. This velocity, given the symbol c, has been determined to he 2.99792 x ]08 m/s. It is significant that the velocity of radiation in air differs only slightly from c (about 0.03% less); thus, for either air or vacuum, Equation 6-1 can he written to three significant figures as c
=
vA = 3.00 x 108 mls
=
3.00 x W\() cmls
(6-2)
In any medium containing matter, propagation of radiation is slowed by the interaction between the electromagnetic field of the radiation and the hound electrons in the matter. Since the radiant frequency is invariant and fixed by the source, the wavelength must decrease as radiation passes from a vacuum to another medium (Equation 6-2). This effect is illustrated in Figure 6-2 for a monochromatic heam of visihle radiation.' Note that the wavelength shortens nearly 200 nm, or more than 30~/~, as it passes into glass~a reverse change occurs as the radiation again enters air. The wavenumber v. which is defined as the reciprocal of the wavelength in centimeters, is vet another way of describing electromagnetic radiation. The unit for v is cm--'. Wavenumber is widely used in infrared spec)A mOrJlJchromuric beam is a beam of radiation whose rays have identical wavelengths -\ poil'chromaflc beam is made up (It r;:1~S of differeJlt wavelengths
troscopy. The wavcnumber is a useful unit because, in contrast to wavelength, it is directly proportional to the frequency, and thus the encrgy, of radiation. Thus, we can write
Usual Wavelength Range' Gamma-ray
where the proportionality constant k depends on the medium and is equal to the reciprocal of the velocity (Equation 6-1). The power P of radiation is the energy of the beam that reaches a given area per second, whereas the intensity I is the power per unit solid angle. These quantities are related to the square of the amplitude A (see Figure 6-1). Although it is not strictly correct to do so, power and intensity are often used interchangeahly.
emission
Type or
Range, cm-1
Quautum Transition
A
0.005-1.4
Nuclear
A
Inner electron
X-ray absorption, emission, fluorescence, and diffraction
0.1-100
Vacuum ultraviolet absorption Ultraviolet-visible absorption.
10-180 nm
1 X 106 to 5 x 10'
180-780 nm
5 X 10' to 1.3 x 10'
Bonding electrons Bonding electrons
emission, and fluort'scence
Infrared absorption and
Rotation/vibration of
Raman scattering
molecules
Microwave absorption
0.75-375 mm
13-0.03
Rotation of molecules
Electron spin resonance
3cm
0.33
Spin of electrons
in a
magnetic field Spin of nuclei in a magnetic field *1 A.~JO-lOm 1 nm
As shown in Figure 6-3, the electromagnetic spectrum encompasses an enormous range of wavelengths and frequencies (and thus energies). [n fact, the range is so great that a logarithmic scale is required. Figure 6·3 also depicts qualitatively the major spectral regions. The divisions are based on the methods used to generate and detect the various kinds of radiation. Several overlaps are cvident. Note that the portion of the spectrum visible to thc human eye is tiny when compared with other spectral regions. Also note that spectrochemical methods emploving not only visihle hut also ultraviolet and infrared radiation are often called optical methods despite the human eye's inability to sense either of the latter two tvpes of radiation. This somewhat ambiguous terminology arises from the many common features
Usual Wavenumber
=
\o-y
m ""
lllm=-1O-6m::;
1O-8cm 10
7
em
10-4 em
of instruments for the three spectral regions and the similarities in how we view the interactions of the three types of radiation with matter. Table 6·] lists the wavelength and frequency ranges for the regions of the spectrum that are important for analytical purposes and also gives the names of the various spectroscopic methods associated with each. The last column of the table lists the types of nuclear. atomic, or molecular quantum transitions that serve as thc basis for the various spectroscopic techniques.
f"'Jl
Exercise: Learn more ahout the electromagnetic
lQj spectrum.
68-3 Mathematical Description of a Wave With time as a variable, the wave in Figure 6-lb can be descrihed by the equation for a sine wave. That is,
where y is the magnitude of thc electric field at time t. 1> is the phase angle, a term defined in Section 2B-I, page 34. The angular velocity of the vector w is related to the frequency of the radiation v by the equation
A is the amplitude or maximum value for y, and
FIGURE 6-4 Superposition of sinusoidal wave: (a) Al < A" (1)1 - 1>,) = 20', VI = V,; (b) Al < A" (1)1 - 1>,) ~ 200', VI = v,. In each instance, the black curve results fro~ the combination of the two other curves.
Substitution yields
68-4
of this relationship
Superposition
into Equation
6-4
of Waves
The principle of superposition states that when two or more waves traverse the same space, a disturbance occurs that is the sum of the disturbances caused by the individual waves. This principle applies to electromagnetic waves, in which the disturbances involve an electric Held, as well as to several other types of waves, in which atoms or molecules are displaced. When n electromagnetic waves differing in frequcncy, amplitude, and phase angle pass some point in space simultaneously, the principle of superposition and Equation 6-5 permit us to write y
=
Pb
Al sin(21Tl'lt + dJI) + A, sin(21Tv2t + 0)
S -I
ki
:.:: -2
-3
-4 -WCu
-5
0
10
5 v
X
15
20
10-14, Hz
Tutorial: Learn more about the photoelectric
6-14 Maximum kinetic energy of photoelectrons emitted from three metal surtaces as a function of radiation frequency. The y-intercepts (-w) are the work functions for each metal. If incident photons do not have energies of at least hv = w, no photoelectrons are
effect.
emitted from the photocathode.
FIGURE
energy, or stopping energy, KErn = el-;, of the photoelectrons is plotted against frequency for photocathode surfaces of magnesium, cesium, and copper. Other surfaces give plots with identical slopes, h. but different intercepts. w. The plots shown in Figure 6-14 are described by the equation
Calculate the energy of (a) a 5.3-A X-ray photon and (b) a 530-nm photon of visible radiation. E
hv
=
= ~
A
In this equation, the slope h is Planck's constant, which is equal to 6.6254 X 10-34 joule second, and the intercept -w is the work function, a constant that is characteristic of the surface material and represents the minimum energy binding electron in the metal. Approximately a decade before Millikan's work that led to Equation 6-16, Einstein had proposed the relationship between frequency v of light and energy E as embodied by the now famous equation
E
(6.63 ~ 10-34 l· s) x (3.00
=
5.30 A
E
=
h~A
=
KE
rn
- w
Note that although photon energy is directly proportIonal to frequency, it is a reciprocal function of wavelength.
(I0"om/A)
The energy of radiation in the X-ray region is commonly expressed in electron volts, the energy acquired by an electron that has been accelerated through a potential of one volt. In the conversion table inside the front cover of this book, we see that 1 1 = 6.24 X 10'" e V. E
E
lOR m/s)
= 3.75 X 10-16 1
By substituting this equation into Equation 6-16 and rearranging, we obtain
This equation shows that the energy of an incoming photon is equal to the kinetic energy of the ejected photoelectron plus the energy required to eject the photoelectron from the surface being irradiated. The photoelectric effect cannot bc explained by a classical wave model but requires instead a quantum model, in which radiation is viewed as a stream of discrete bundles of energy, or photons as depicted in Figure 6-13. For example, calculations indicate that no single electron could acquire sufficient energy for ejection if the radiation striking the surface were uniformly distributed over the face of the electrode as it is in the wave model; nor could any electron accumulate enough energy rapidly enough to establish the nearly instantaneous currents that arc observed Thus it is necessary to assume that the energy is n~t uni: formly distributed over the beam front but rather is concentrated in packets, or bundles of energy. Equation 6-18 can be recast in terms of wavelength by substitution of Equation 6-2. That is.
X
X
3.75
2.34 x 10' eV
X
10'10 1
(6.6~~'''l·s)
=
=
= =
3.75
X
X
(6.24
X
10" eVil)
x (3.00 x 108m/s)
or emits an amount of energy exactly equal to the energy difference between the states. 2. When atoms. ions. or molecules absorb or emit radiation in making the transition from one energy state to another, the frequency v or the wavelength A of the radiation is related to the energy difference between the states by the equation E, - E" = hv =
=
A
where E1 is the energy of the higher state and Eo the energy of the lower state. The terms e and h are the speed of light and the Planck constant, respectively. For atoms or ions in thc elemental state, the energy of any given state arises from the motion of electrons around the positively charged nucleus. As a consequence the various energy states are called electronic states. In addition to having electronic states, molecules also have quantized vibrational states that are associated with the energy of interatomic vibrations and quantized rotational states that arise from the rotation of molecules around their centers of mass.
Spectroscopists use the interactions of radiation with matter to obtain information about a sample. Several of the chemical elements were discovered by spectroscopy. The sample is usually stimulated by applying energy in the form of heat, electrical energy, light, particles, or a chemical reaction. Prior to applying the stimulus, the analyte is predominantly in its lowest energy state, or ground state. The stimulus then causes some of the analyte species to undergo a transition to a higher energy, or excited state. We acquire information about the analyte by measuring the electromagnetic radiation emitted as it returns to the ground state or by measuring the amount of electromagnetic radiation absorbed or scattered as a result of excitation. Figure 6-15 illustrates the processes involved in emission a~ chemiluminescence spectroscopy. Here,
530 nm x (10 - 0 m/nm) 10-19 1
Energy of radiation in the visible region is often expressed in kllmol rather than kl/photon to aid in the discussion of the relationships between the energy of absorbed photons and the energy of chemical bonds. E
he
The lowest energy state of an atom or molecule is its ground state. Higher energy states are termed excited states. Generally. at room temperature chemical species are in their ground state.
Emitted radiation
PE f ...-.-
3.75 x 10'19 __ 1_ photon (6.02 X 1023 photons) x ------.----mol
X
10-3-
E2
=
hV2
=
he/A2
£1
=
hVI
=
he/A
I
kJ 1
~ 226 kllmol
6C-2 Energy States
of Chemical
Species
The quantum theory was first proposed in 1900 bv Max Planck, a German physicist, to explain the properties of radiation emitted by heated bodies. The theorv was later extended to rationalize other types of emission and absorption processes. Two important postulates of 4uantum theory include the following: 1. Atoms, ions, and molecules can exist only in certain discrete states, characterized by definite ~mounts of energy. When a species changes its state. it absorbs
Emission or chemiluminescence processes. In (a), the sample is excited by the application of thermal, electtical, ot chemical energy. These processes do not involve radiant enetgy and are hence called nonradiative processes. In the enetgy level diagtam (b), the dashed lines with upwatd-pointing arrows symbolize these nonradiative excitat,on processes, while tbe solid lines with downward-pointing atrows indicate that the analyte loses its energy by emission of a photon. In (c), the resulting spectrum is shown as a measurement of the radiant power emitted Pc as a function of wavelength, A.
FIGURE 6-15
the analyte is stimulated
by heal or electrical
energy
processes are possible. For example, the radiation can
When radiation is scattered, the interaction
Electromagnetic
radiation
incoming
When some of the inci-
elastic. In elastic scattering, the wavelength 01 the scat-
particles (atoms, ions, or molecules) relax 10 lower en-
electrical energy, and chemiluminescence
dent radiation
ergy levels by giving up their excess energy as photons.
refers to excitation
spectroscopy
of the analyte by a chemical reac-
tion. In both cases, measurement of the radiant power
is absorbed, it promotes some of the
tered radiation is the same as that of the source radIa-
analyte species to an excited state, as shown in Fig-
tion. The intenSity of the elastically scattered radWlIon
Excitation
ure 6-16. In ahsorption spectroscopy,
is used to make measurements in nephelometry
including (1) bombardment with electrons or other ele-
we measure the
The results of such a measurement are often expressed graphically
by a spectrum, which is a plot of the emit-
ted radiation as a function of frequency or wavelength. When the sample is stimulated an external electromagnetic
--.
by application
radiation
of
source, several
can be brought about by a variety of means.
mentary
spec-
cussed in detail in Chapter IS, uses inelastic scattering
rent, an ac spark. or an intense heat source (flame, dc
t,,)Scopy (Figure 6-17), the emission of photons is mea-
to produce a vibrational spectrum of sample molecules,
are, or furnace), producing ultraviolet,
sured after absorption.
as illustrated
red radiation;
amount of light absorbed as a function of wavelength. This can give both qualitative
and concentration.
and
wrhidimecrr. and particle sizing. RanulII spectroscopv, which is mentioned brietly in Section 6B-1O and IS d,s-
emitted as the analyte returns to the ground state can give information
about its identity
or in-
is produced when excited
be reflected (Section 68-9), scattered (Section 68-10).
lTIay
he ela:tic
of Radiation
or absorbed (Section 6C-5).
f~mi.,si{)n 1peclroscopy usu-
reaction.
with the sample
6C-4 Emission
ally involves methods in which the stimulus is heat or
or by a chemical
radiation
of the
and quantitative
mation about the sample. In pholOluminescence
photoluminescence
The most important
infor-
forms of
for analytical purposes are fluores-
cence and phosphorescence spectroscopy.
particles, which generally leads to the. emIS-
sion of X-radiation:
in Figure 6-IS. In thIS lype of spectro-
(2) exposure to an electric
(3) irradiation
cur-
visible, or infra-
with a heam of electro-
scopic illlalysis, the intensity of the scattered radiation
magnetic radiation, which produces tluorcseence radi-
is recorded as a function of the frequency shllt of the
ation; and (4) an exothermic
incident
produces chemiluminescence. . Radiation from an excited source is conven,ently
radiation.
The intensity
related to the concentration
of Raman peaks [s
of the analvte.
chemical reaction that
characterized by means of an emission spectrum, which usually takes the form of a plot of the relative power 01 Simulation:
Inciden[ radiation
of
the e~itled
FIGURE 6-16 Absorption methods. Radiation of incident radiant power Pocan be absorbed by the analyle, resulting in a transmitted beam of lower radiant power P. For absorption to occur, the energy of the incident beam must correspond to one of the energy differences shown in (b). The resulting absorption spectrum is shown in (c).
hi' e\
2mF:" ~ I
I
I
, '..
~ ~ \
Line Spectra
1.0
A
metal.
E,
are superimposed on this continuum. The source of the continuum is described on page 152. Figure 6-20 is an X-ray em~sion spectrum produced by bombarding a piece of molybdenum with an energetic stream of electrons. Note the line spectrum superImposed on the continuum. The source of the continuum is described in Section 12A-I.
0.8
0.6 Wavelength.
FIGURE 6-19 Emission spectrum of a brine sample obtained with an oxyhydrogen flame. The spectrum consists of the supenmposed line, band, and continuum spectra of the constituents of the sample. The characteristic wavelengths of the species contributing to the spectrum are listed beside each feature. (R. Hermann and C . T" J Alkema d e, Ch'emlcal AnalysIs. by Flame Ph t o orne try, 2nd ed., p. 484. New York:Interscience, 1979.)
frequency. Figure 6-19 illustrates a typical emission spectrum, which was obtained by aspirating a brine solulton Into an oxyhydrogen flame. Three types of spectra appear In the figure: lines, bands. and a continuum The line spectrum is made up of a series of sharp, well~ defined peaks caused by excitation of individual atoms. The band spectrum consists of several groups of lines so closely spaced that they are not completely resolved. The source of the bands consists of small molecules or radicals. Finally, the continuum portion of the spectrum IS responSible for the increase in the background that is evident above about 350 nm. The line and- band spectra
= (E, - Eo)/h
Al = hd(E, - Eo)
Eo
A,
(a)
Band Spectra
Band spectra are often encountcred in spectral sources when gaseous radicals or small molecules are present. For example, in Figure 6-19 bands for OH, MgOH, and MgO are labeled and consist of a series of closely spaced lines that are not fully resolved by the instrument used to obtain the spectrum. Bands arise from numerous quantized vibrational levels that are superimposed on the ground-state electronic energy level of a molecule. Figure 6-21b is a partial energy-level diagram for a molecule that shows its ground state Eo and two of its excited electronic states, E, and E,. A few of the many vibrational levels associated with the ground state are also shown. Vibrational levels associated with the two excited states have been omitted because the lifetime of an excited vibrational state is brief compared with that of an electronically excited state (about 10-15 s versus 10- 8 s). A consequence of this tremendous difference in lifetimes is that when an electron is excited to one of the higher vibrational levels of an electronic state, relaxation to the lowest vibrational level of that state occurs before an electronic transition to the ground state can occur. Therefore, the radiation produced by the electricalor thermal excitation of polyatomic species nearly always results from a transition from the lowest vibrational level of an excited electronic state to any of the several vibrational levels of the ground state. The mechanism by which a vibrationally excited species relaxes to the nearest electronic state involves a transfer of its excess energy to other atoms in the system through a series of collisions. As noted, this process takes place at an enormous speed. Relaxation from one electronic state to another can also occur by collisional transfer of energy, but the rate of this p,,;_ cess is slow enough that relaxation by photon release is favored. The energy-level diagram in Figure 6-21b illustrates the mechanism by wbieh two radiation bands that consist of five closely spaced lines are emitted by a molecule excited by thermal or electrical energy. For a real molecule. the number of individual lines is much larger because in addition to the numerous vibrational states, a multitude of rotational states would be superimposed On each. The differences in energy among the rotationa I levels is perhaps an order of magnitude smaller than that for vibrational states. Thus. a real molecular band would be made up of many more lines than we have shown in Figure 6-2Ib. and these lines would be much more closely spaced.
Continuum
Spectra
As shown in Figure 6-22, truly continuum radiation is produced when solids are heated to incandescence. Thermal radiation of this kind, which is called blackbody radiation, is characteristic of the temperature of the emitting surface rather than the material of which that surface is composed. Blackbody radiation is produced by the innumerable atomic and molecular oscillations excited in the condensed solid by the thermal energy. Note that the energy peaks in Figure 6-22 shift to shorter wavelengths with increasing temperature. It is clear that very high temperatures are needed to cause a thermally excited source to emit a substantial fraction of its energy as ultraviolet radiation. As noted earlier, part of the continuum background radiation exhibited in the flame spectrum shown in Figure 6-19 is probably thermal emission from incandescent particles in the flame. Note that this background decreases rapidly as the ultraviolet region isapproached. Heated solids are important sources of infrared, visible, and longer-wavelength ultraviolet radiation for analytical instruments.
According to quantum theory, atoms, molecules, and ions have only a limited number of discrete energy levels; for absorption of radiation to occur, the energy of the exciting photon must exactly match the energy difference between the ground state and one of the excited states of the absorbing species. Since these energy differences are unique for each species, a study of the frequencies of absorbed radiation provides a means of characterizing the constituents of a sample of matter. For this purpose, a plot of absorbance as a function of wavelength or frequency is experimentally determined (absorbance, a measure of the decrease in radiant powcr, is defined by Equation 6-32 in Section 6D-2). Typical absorption spectra are shown in Figure 6-23. The four plots in Figure 6-23 reveal that absorption spectra vary widely in appearance; some are made up of numerous sharp peaks, whereas others consist of smooth continuous curves. In general, the nature of a spectrum is influenced by such variables as the complexity, the physical state, and the environment of the absorbing species. More fundamental, however, are
6C-5 Absorption of Radiation When radiation passes through a layer of solid, liquid, or gas, certain frequencies may be selectively removed by absorption, a process in which electromagnetic energy is transferred to the atoms, ions, or molecules composing the sample. Absorption promotes thcse particles from their normal room temperature state, or ground state, to one or more higher-energy excited states.
{",'"""]Ml 588
589
590
10'
>.
103
~ ~ " 10' ~ 0;
.. : ~"-I -~-fungs-t~nfamp ..
spectra for atoms
Atomic Absorption
The passage of polychromatic ultraviolet or visible radiation through a medium that consists of mono atomic particles, such as gaseous mercury or sodium, results in the absorption of but a few well-defined frequencies (see Figure 6-23a). The relative simplicity of such spectra is due to the small number of possible energy states for the absorbing particles. Excitation can occur only by an electronic process in which one or more of the electrons of the atom are raised to a higher energy leveL For example, sodium vapor exhibits two closely spaced, sharp absorption peaks in the yellow region of the visible spectrum (5H9.0 and 589.6 nm) as a result of excitation of the 3s electron to two 3p states that differ only slightly in energy. Several other narrow absorption lines, corrcsponding to other allowed electronic t;ansitions, are also observed. For example, an ultraviolet peak at about 285 nm results from the excitation of t~e 3s electron in sodium to the excited 5p state, a process that requires significantly greater energy than docs excitation to the 3p state (in fact, the peak at 285 nm is also a doublet; the energy difference between the two peaks is so small, however, that most instruments cannot resolve them). Ultraviolet and visible radiation have enough energy to cause transitions of the outermost, or bonding, electrons only. X-ray frequencies, on the other hand, are several orders of magnitude more energetic (see Example 6-3) and are capable of interacting with electrons that are closest to the nuclei of atoms. Absorption peaks that correspond to electronic transitions of these innermost electrons are thus observed in the X-ray region. Molecular Absorption
xe.n ..o..n.. ,arc Carbon arc
Absorption spectra for polyatomic molecules, particularly in the condcnsed state, are considerably more complex than atomic spectra because the number of energy states of molecules is generally enormous when compared with the number of energy states for isolated atoms. The energy E associated with the bands of a moleculc is made up of three components. That is,
Nerrist glower
>
"
the differences between absorption and those for molecules.
10
FIGURE 6·23
spectra.
Some typical ultraviolet absorption
where Eelectmoic describes the electronic energy of the molecule that arises from the energy states of its several bonding electrons. The second term on the right refers
to the total energy associated with the multitude of interatomic vibrations that are prescnt in molecular species. Generally, a molecule has many more quantized vibrational energy levels than it does electronic levels. Finally. Em""o",' is the energy caused bv various rotational motions within a molecule; again the number of rotational states is much larger than the number of vibrational states. Thus, for each electronic energy state of a molecule, there are normally several possible vibrational states. For each of these vibrational states, in turn, numerous rotational states are possible. As a consequence, the number of possible energy levels for a molecule is normally orders of magnitude greater than the number of possible energy levels for an atomic particle. Figure 6-24 is a graphical representation of the energy levels associated with a few of the numerous electronic and vibrational states of a molecule. The heavy line labeled Eo represents the electronic cnergy of the molecule in its ground state (its state of lowest elec-
tronic energy); the lines labeled E, and E, represent the energies of two excited electronic states. Several of the many vibrational energy levels (eo, e" ... , en) are shown for each of these electronic states. Figure 6-24 shows that the energy difference between the ground state and an electronically excited state is large relative to the energy differences between vibrational levels in a given electronic state (typically, the two differ by a factor of 10 to 100), The arrows in Figure 6-24a depict some of the transitions that result from absorption of radiation. Visible radiation causes excitation of an electron from Eo to any of the n vibrational levels associated with E, (only five of the n vibrational levels are shown in Figure 6-24), Potential absorption frequencies are then given by n equations, each with the form =
Vi
I h(E,
-~,~-~--
Excited £2
electronic
2
Slate
;
;
::l
Excited £1
, Visihle
'
energy
IT'I !
e, CJ,
e1# R
t tI
electronic state I
Vibrational
__
i !
!
~ e
i~
,.,.-
-
--- -----
_
__ I• ' ... _~ __
t,
t,
;
Ground Eo
electronic state
(al
(h)
where i = 1,2, 3, ... , m. Finally, as shown in Figure 6-24a, the less energetic near- and mid-infrared radiation can bring about transitions only among the k vibrational levels of the ground state. Here, k potential absorption frequencies are given by k equations, which may be formulated as
(e)
FIGURE 6-24 Partial energy-level diagrams for a fluorescent organic molecule.
I
Figure 6-23d. Solvent effects are considered in later chapters. Pure vibrational absorption is observed in the infrared region, where the energy of radiation is insufficient to cause electronic transitions. Such spectra exhibit narrow, closely spaced absorption peaks that result from transitions among the various vibrational quantum levels (see the transition labeled IR at the bottom of Figure 6-24a). Variations in rotational levels may give rise to a series of peaks for each vibrational state; but in liquid and solid samples rotation is often hindered to such an extent that the effects of these small energy differences are not usually detected. Pure rotational spectra for gases can, however, be observed in the microwave region. Absorption
+ e; - Eo)
where i = 1,2,3, ... , n.
!
Similarly, if the second electronic state has m vibrational levels (four of which are shown), potential absorption frequencies for ultraviolet radiation are given by m equations such as
where i = 1,2,3, ... , k. Although they are not shown, several rotational energy levels are associated with each vibrational level in Figure 6-24. The energy difference between the rotational energy levels is small relative to the energy difference between vibrational levels. Transitions between a ground and an excited rotational state are brought about by radiation in the 0.01- to l-cm-wavelength range, which includes microwave and longer-wavelength infrared radiation. fn contrast to atomic absorption spectra, which consist of a series of sharp, well-defined lines, molecular spectra in the ultraviolet and visible regions are ordinarily characterized by absorption regions that often encQmpass a substantial wavelength range (see Figure -6-23b, c). Molecular absorption also involves electronk transitions. As shown by Equations 6-23 and 6-24, however, several closely spaced absorption lines will be associated with each electronic transition, because of the existence of numerous vibrational states. Furthermore, as we have mentioned, many rotational energy levels are associated with each vibrational state. As a result, the spectrum for a molecule usually consists of a series of closely spaced absorption lines that constitute an absorption band, such as those shown for benzene vapor in Figure 6-23b. Unless a high-resolution instrument is employed, the individual peaks may not be detected, and the spectra will appear as broad smooth peaks such as those shown in Figure 6-23c. Finally, in the condensed state, and in the prcsence of solvent molecules, the individual lines tend to broaden even further to give nearly continuous spectra such as that sh()\vn in
Induced by a Magnetic Field
When electrons of the nuclei of certain elements are subjected to a strong magnetic field, additional quantized energy levels can be observed as a consequence of the magnetic properties of these elementary particl,,,. The differences in energy between the induced states are small, and transitions between the states are brought about only by absorption of long-wavelength (or low-frequency) radiation. With nuclei, radio waves ranging from 30 to 500 MHz (A = 1000 to 60 em) are generally involved; for electrons, microwaves with a frequency of about 9500 MHz (A = 3 em) are absorbed. Absorption by nuclei or by electrons in magnetic fields is studied by nuclear magnetic resonance (NMR) and electron spin resonance (ESR) techniques, respectively; NMR methods are considered in Chapter 19.
Ordinarily, the lifetime of an atom or molecule excited by absorption of radiation is brief because there are several relaxation processes that permit its return to the ground state. Nonradiative
Relaxation
As shown in Figure 6-24b, non radiative relaxation involves the loss of energy in a series of small steps, the excitation energy being converted to kinetic energy by collision with other molecules. A minute increase in the temperature of the system results. As shown by the blue lines in Figure 6-24c, relaxation can also occur by emission of fluorescence radia· tion. Still other relaxation processes arc discussed in Chapters IS, 18, and 19.
Fluorescence Relaxation
and Phosphorescence
Fluorescence and phosphorescence are analytically important emission processes in which species are excited by absorption of a beam of electromagnetic radiation: radiant emission then occurs as the excited species return to the ground state. Fluorescence occurs more rapidly than phosphorescence and is generally complete after about 10 -5 S from the time of excitation. Phosphorescence emission takes place over periods longer than 10 -5 S and may indeed continue for minutes or even hours after irradiation has ceased. Fluorescence and phosphorescence are most easilv observed at a 90° angle to the excitation beam. . Molecular fluorescence is caused by irradiation of molecules in solution or in the gas phase. As shown in Figure 6-24a, absorption of radiation promotes the molecules into any of the several vibrational levels associated with the two excited electronic levels. The lifetimes of these excited vibrational states are, however, only on the order of 10-15 s, which is much smaller than the lifetimes of the excited electronic states (10-8 s). Therefore, on the average, vibrational relaxation occurs before electronic relaxation. As a consequence, the energy of the emitted radiation is smaller than that of the absorbed by an amount equal to the vibrational excitation energy. For example, for the absorption labeled 3 in Figure 6-24a, the absorbed energy is equal to (£2 - £0 + whereas the energy of the fluorescence radiation is again given by (£2 - £0)' Thus, the emitted radiation has a lower frequency, or longer wavelength, than the radiation that excited the fluorescence. This shift in wavelength to lower frequencies is sometimes called the Stokes shift as mentioned in connection with Raman scattering in Figure 6-1K Phosphorescence occurs when an excited molecule relaxes to a metastable excited electronic state (called the triplet state), which has an average lifetime of greater than about 10-5 s. The nature of this type of excited state is discussed in Chapter 15.
Section 68-4. Applications of this principle will be found in several later chapters that deal with spectroscopic methods.' Let us suppose that we wish to determine the frequency VI of a monochromatic beam of radiation by comparing it with the output of a standard clock, which is an oscillator that produces a light beam that has a precisely known frequency of 1'2' To detect and measure the difference between the known and unknown frequencies, tJ.v = VI - V" we allow the two beams to interfere as in Figure 6-5 and determine the time interval for a beat (A to B in Figure 6-5). The minimum time tJ.t required to make this measurement must be equal to or greater than the period of one beat, which as shown in Figure 6-5, is equal to lItJ.v. Therefore, the minimum time for a measurement is given by
Note that to determine tJ.v with negligibly small uncertainty, a huge measurement time is required. If the observation extends over a very short period, the uncertainty will be large. Let us multiply both sides of Equation 6-25 by Planck's constant to givc
e'; - e;,),
6C-7 The Uncertainty Principle The uncertainty principle was first proposed in 1927 by Werner Heisenberg, who postulated that nature places limits on the precision with which certain pairs of physical measurements can be made. The uncertainty principle, which has important and widespread implications in instrumental analysis, is readily derived from the principle of superposition, which was discussed in
60
c (Pe gives
QUANTITATIVE ASPECTS OF SPECTROCHEMICAL MEASUREMENTS
As shown in Table 6-2, spectrochemical methods fall into four major categories. All four require the measurement of radiant power P, which is the energy of a beam of radiation that reaches a given area per second. In modern instruments, radiant power is determined with a radiation detector that converts radiant cnergy into an electrical signal S. Generally 5 is a voltage or a current that ideally is directly proportional to radiant power. That is,
where k is a constant. Many detectors exhibit a small, constant response, known as a dark current, in the absence of radiation. In those cases, the response is described by the relationship
where kd is the dark current, which is generally small and constant at least for short periods of time. Spectrochemical instruments are usually equipped with a compensating circuit that reduces kd to zero whenever measurements are made. With such instruments, Equation 6-27 then applies.
=
kc). Combining this equation with Equation 6-27
where k' is a constant that can be evaluated by exciting analyte radiation in one or more standards and by measuring S. An analogous relationship also applies for luminescence and scattering methods. 60-2 Absorption Methods As shown in Table 6-2, quantitative absorption methods require two power measurements: one before a beam has passed through the medium that contains the analyte (Po) and the other after (P). Two terms, which are widely used in absorption spectrometry and are related to the ratio of Po and P, are transmittance and absorbance. Transmittance
Figure 6-25 depicts a beam of parallel radiation before and after it has passed through a medium that has a thicl«less of b cm and a concentration c of an absorbing species. As a consequence of interactions between the photons and absorbing atoms or molecules, the power of the beam is attenuated from Po to P. The transmittance T of the medium is then the fraction of incident radiation transmitted by the medium: T
From Equation 6-17, it is apparent that tJ.E = htJ.v
Equation 6-26 is one of several ways of formulating the Heisenberg uncertainty principle. The meaning in words of this eq uation is as follows. If the energy E of a particle or system of particles - photons, electrons, neutrons, or protons, for example - is measured for an exactly known period of time tJ.t, then this energy is uncertain by at least hi tJ.t. Therefore, the energy of a particle can be known with zero uncertainty only if it is observed for an infinite period. For finite periods. the energy measurement can never be more precise than hltJ.t. The practical consequences of this limitation will appear in several of the chapters that follow.
60-1 Emission, Luminescence, and Scattering Methods
Transmittance
As sncopy and Spectrometry, Vols. 1-3. San Diego: Acad~mic Press. 2000: J. \\:. Robillslm, cd., Pracliwl Handhook ufSpectroscoP:I', Buca Raton, fL: eRr Press. 1\)91; E, J. ~1cchan, in Trelllise on AnalvIlc,ll Chemistry, P. 1. Elving. E. 1. Meehan. and L M. Kolthll(f. eds" Part!. Vol. 7. Chap. 3. New York:-\\,iky, 19,s1; 1. D, Ingle Jr. and S. R. Crouch. SpeC/l'Oellemlwl Arwlrsls. Chaps. J and~. Upper S 100 flm) of photosensitive material sandwiched between two transparent layers as shown on the right in Figure 7-14a. The thick-volume film assembly is placed at the plane of intersection of the two laser beams as before, and the interference fringes arc formed throughout the volume of the film laycr rather than just at its surface. When the two beams intersect at equal angles to the surface normal of the film, a sinusoidally modulated fringe pattern such as the one shown in Figure 7-14c is formed within the film, and the entire volume of the film is sensitized with this pattern. The film is then developed chemically to "fix" the
pattern, which produces a corresponding pattern of variation of the refractive index within the film material. By making the angle of incidence of the two beams asymmetric about the film normal, the resulting refractive-index modulation pattern can be tilted as illustrated in Figure 7-14d, By controlling the laser wavelength and angle of incidence of the beam, the frequency of the refractive-index modulation may be tailored to the requirements of the device. These devices are also used as gratings and as filters for removing undesirable radiation such as plasma lines and sidebands from laser radiation. Perhaps the most useful volume holographic device is formed when the transparent back face of the thick film is replaced by a mirror, and the film is illuminated by a single laser beam. The beam enters the front surface of the film, is reflected from the interface between the back of the film and the mirror, and forms an interference pattern within the film that is parallel to its face as illustrated in Figure 7-14e. These devices are called cOllformal reflection holograms, and their characteristics make them nearly ideal for use as Ilotchjilters. The transmission characteristics of a typical holographic notch filter are compared to those of a dielectric interference filter in Figure 7-15a. Note that the holographic filter provides extremely fiat transmission at all wavelengths except at the notch, where it blocks more than 99.99% of the incident radiation, corresponding to an optical density (absorbance) of 4. The effective band-
FIGURE7-14 (a) Experimental arrangement for fabricating holograms. A laser beam is split into two beams, which are directed by mirrors to recombine at the surface of a photosensitive film.The apparatus as shown is used to produce holographic reflection gratings. By replacing the surface object with a thick-volume photosensitive filmshown on the right, a volume transmission hologram results. (b) Interference pattern at the surface of the photosensitive film, which produces a corresponding refractive-index pattern on the film. (c) Untilled fringe pattern, (d)tilted fringe pattern, (e) conformal fringe pattern produced by making the back surface of the thick-volume filma mirror, (f) nonconformal fringe pattern. Holographic
Filters
Holographic optical devices and, in particular, holographic filters 11 are among a growing repertoire of optical devices and materials that have resulted from the
hroad availability of laser technology. Figure 7-14a is a schematic diagram of a typical experimental arrangement for producing holograms. The coherent radiation of a laser heam impinges on a heamsplitter, where it is divided into two heams. I and 2. shown in the figure. The two beams are redirected bv the two front-surface
FIGURE 7-15 (a) Comparison of the bandwidths of a typical holographic notch filler and an interference filter.(b) Tilt-tuningof a holographic notch filter by l' increments from perpendicular to the incident laser beam. The rejection band can be finely adjusted by altering the angle of the notch filter relative to the laser. (Courtesy of Kaiser Optical Systems, Inc., Ann Arbor. MI. with permission.)
width of the filter is less than 10 nm and its edgewidth, or the wavelength range O'er which its optical density ranges from 0.-' to 4, is less than 4 nm. Figure 7-I'ib shows how the rejection band of a notch filter may be fine-tuned by tilting it with respect to incoming radiation. These filters are available in a wide varietv of sizes and rejection bands tuned to the most common laser lines in the range of 350 to 1400 nm. The commercial availability of holographic notch filters has initiated a revolution in the use of Raman spectroscopy (see Section 18B-3) by virtually eliminating the need for costly high-resolution double monochromators for routine work. The refractive-index modulation characteristics of nonconformal holographic optical elements are shown in Figure 7-14f. Because there is some modulation of the refractive index at the surface of the device, it acts in principle both as a notch filter and as a grating.
Glass filters with transmittance maxima throughout the entire visible region are available commercially. Clltofffillen' have transmittances of nearly ]()O% over a portion of the visible spectrum but then rapidly decrease to zero transmittance over the remainder. A narrow spectral band can be isolated by coupling a cutoff filter with a second filter (see Figure 7-17). Figure 7-1 h shows that the performance characteristics of absorption filters are significantly inferior to those of interference-type filters. Not only are the bandwidths of absorption f,lters greater than those of interference filters, but for narrow bandwidths the fraction of light transmitted by absorption tilters is also smaller. Nevertheless, absorption tilters arc adequate for some applications.
Absorption
For many spectroscopic methods, it is necessary or desirable to be able to continuously vary the wavelength of radiation over a broad range. This process is called scan ninE( a spectrum. Monochromators are designed for spectral scanning. Monochromators for ultraviolet, visible, and infrared radiation arc all similar in mechanical const ruction in the sense that they use slits, lenses, mirrors, windows, and gratings or prisms. The materials from which these components are fabricated depend on the wavelength region of intended use (see Figure 7-2).
Filters
Absorption filters, which are generally less expensive than interference filters, have been widely used for band selection in the visible region. These filters function by absorbing selected portions of the spectrum. The most common type consists of colored glass or of a dye suspended in gelatin and sandwiched between glass plates. Colored glass filters have the advantage of greater thermal stability. Absorption filters have effective bandwidths that range from30to 250 nm (see Figures 7-16 and 7-17). Filters that provide the narrowest bandwidths also absorb a significant fraction of the desired radiation and may have a transmittance of 10% or less at their band peaks.
Components
ation is focused on the focal plane A B where it appears as two rectangular images of the entrance slit (one for Al and one for A,). By rotating the dispersing element, one band or the other can be focused on the exit slit. In the past, most monochromators were prism instruments. Currently, however, nearly all commercial monochromators arc based on reflection gratings because they are cheaper to fabricate, provide better wavelength separation for the same size dispersing element, and disperse radiation linearly along the focal plane. As shown in Figure 7-19a, linear dispersion means that the position of a band along the focal plane for a grating varies linearly with its wavelength. For prism instruments, in contrast, shorter wavelengths are dispersed to a greater degree than are longer ones, which complicates instrument design. The nonlinear dispersion of two types of prism monochromators is illustrated by Figure 7-19b. Because of their more general use, we will focus most of our discussion on grating monoehromators.
(2) a collimating lens or mirror that produces a parallel beam of radiation, (3) a prism or a grating that disperses the radiation into its component wavelengths, (4) a focusing element that reforms the image of the entrance slit and focuses it on a planar surface called a focal plane, and (5) an exit slit in the focal plane that isolates the desired spectral band. In addition, most monochromators have entrance and exit windows designed to protect the components from dust and corrosive laboratory fumes. As shown in Figure 7-18, two types of dispersing elements are found in monochromators: re"ection gratings and prisms. For purposes of illustration, a beam made up of just two wavelengths, Al and A2 (AI> A,), is shown. This radiation enters the monochromators via a narrow rectangular opening, or SUI; is collimated; and then strikes the surface of the dispersing element at an angle. For the grating monochromator, angular dispersion of the wavelengths results from diffraction, which occurs at the reflective surface; for the prism, refraction at the two faces results in angular dispersion of the radiation, as shown. In both designs, the dispersed radi-
~
Exerc~e:
Learn more about monochromators.
of Monochromators
Figure 7-18 illustrates the optical elements found in all monochromators, which include the following: (I) an entrance slit that provides a rectangular optical image,
/"
(
Hnlographic
~nterfcrencc
mlh:h lilter
filter
~ 60
g
I
40
Orange cutoff filter
Effective handwidth \bsorpllOri
-10 nm
L/~ ~~ z~7
__
~~-~"A~
filter
Entrance ~ht
Collimating lens
Prism
.I
Focusing lens
FIGURE 7-17 Comparison of various types of absorption filters for visible radiation.
~~a~~
~~R
A~ / A
/' Ex.it silt
FIGURE 7-18 Two types of monochromators: (a) Czerney-Tumer grating monochromator and (b) Bunsen prism monochromator. (In both instances, Al > A,.)
Grating 200
300
400
500
600
A,nm
700
800
Diffracted
----------,
reflected
beam at angle
r 2
la}
200 A,nm
Absorption
200
r..1onochromatic
Glass prism
350
J
Quartz
400
500
600800
--i-.--H
prism
250
300
- -+-------
A,nm
450
beams at angle
350
400 I
3
incident j
500 600800 i
i
,
(b}
A I 0
B 5.0
10.0
15.0
20.0
25.0
FIGURE 7-19 Dispersion for three types of monochromators. The points A and B on the scale in (c) correspond to the points shown in Figure 7-18.
Prism Monochromators
Prisms can be used to disperse ultraviolet, visible, and infrared radiation. The material used for their construction differs, however, depending on the wavelength region (see Figure 7-2b). Figure 7-20 shows the two most common types of prism designs_ The first is a 60° prism, which is usually fabricated from a single block of material. When crystalline (but not fused) quartz is the construction material, however, the prism is usually formed by cementing two 30° prisms together, as shown in Figure 7-20a; one is fabricated from right -handed quartz and the second from left-handed quartz_ [n this way, the optically active quartz causcs no net polarization of the emitted radiation; this type of prism is called a Cornu prism. Figure 7-18b shows a Bunsen monochromator, which uscs a 60° prism, likewise often made of quartz. As shown in Figure 7-20b, the !.iUra", prism, which permits more compact monochromator designs, is a 30° prism with a mirrored back. Refraction in this type of prism takes place twice at the same interface so that the performance characteristics are similar to those of a 600 prism in a Bunsen mount.
FIGURE 7-20 Dispersion by a prism: (a) quartz Cornu type and (b) Litlrowtype.
mon type_ Replica gratings, which are used in most monochromators, are manufactured from a master grating.'] A master grating consists of a hard, optically flat, polished surface that has a large number of parallel and closely spaced grooves, made with a diamond tool. A magnified cross-sectional view of a few typical grooves is shown in Figure 7-2L A grating for the ultraviolet and visible region typically has from 300 to 2000 grooves/mm, with 1200 to 1400 being most common. For the infrared region, gratings typically have 10 to 200 grooves/mm; for spectrophotometers designed for the most widely used infrared range of S to IS Ilm.
Grating Monochromators
Dispersion of ultraviolet, visible, and infrared radiation can be brought about by directing a polychromatic beam through a transmission grating or onto the surface of a reflection grating; the latter is by far the more COIll-
,; For an interesting and informative discu);sion u1' the manufacture, testing, and performance characteristics of gratings, see Diffraction Grating Handbook, 6th cd" Irvine. CA: Newport Corp .. ~005 (v,.'ww.newport,com l For a historical pt:rspecti\'c nil the imparlance of gratings in the' aJ\'anccmenl of science. see A. G. Ingalls. Sd. Amer .. 195!. 186 (6), 45
a grating with about 100 grooves/mm is suitable. The construction of a good master grating is tedious, timeconsuming, and expensive because the grooves must be of identical size, exactly parallel, and equally spaced over the length of the grating (3 to 10 cm). Replica gratings are formed from a master grating by a liquid-resin casting process that preserves virtually perfectly the optical accuracy of the original master grating on a clear resin surface. This surface is usually made reflective by a coating of aluminum, or sometimes gold or platinum. The Echellette Grating, Figure 7-21 is a schematic representation of an echelieue-type grating, which is grooved, or blazed, such that it has relatively broad face~ from which reflection occurs and narrow unused face~_This geometry provides highly efficient diffraction of radiation, and the reason for blazing is to concentrate the radiation in a preferred direction_I' Each of the broad faces can be considered to be a line source of radiation perpendicular to the plane of the page; thus interference among the reflected beams 1,2, and 3 can occur. For the interference to be constructive, it is necessary that the path lengths differ by an integral multiple n of the wavelength A of the incident beam. [n Figure 7-21, parallel beams of monochromatic radiation I and 2 are shown striking the grating at an incident angle i to the grating normal. Maximum constructive interference is shown as occurring at the re-
f1ected angle r. Beam 2 travels a greater distance than beam 1 and the difference in the paths is equal to (CB + BD) (shown as a blue line in the figure). For constructive interference to occur, this difference must equal nA_ That is,
where n, a small whole number, is called the diffraction order. Note, however, that angle CAB is equal to angle i and that angle DAB is identical to angle r. Therefore, from trigonometry, we can write
where d is the spacing between the rellecting surfaces_ It is also seen that
Substitution of the last two expressions into the first gives the condition for constructive interference. Thus.
Equation 7-6 suggests that there are several values of A for a given diffraction angle r. Thus, if a first-order line
(n = I) of 900 nm is found at r, second-order (4S0-nm) and third-order (300-nm) lines also appear at this angle. The flfSt-order line is uo;ually the most intense; indeed, it is possible to design gratings with blaze angles and sh:lpes that concentrate as much as 90% of the incident intensity in this order. Filters can generally remove the higher-order lines. For example, glass, which absorbs radiation below 3S0 nm. eliminates the higher-order spectra associated with first-order radiation in most of
e visible
region.
The example
that follows
illustrates
Holographic
lese points.
gratings,
tion with rcspect
hecause
spectra that arc relatively ghosts I douhle images). In the -\n echellette rradiated angle
grating
1450 blazesimm was
thatcontams
with a polychromatic
48' to the grating
lengths
of radiation
beam
normal.
that would
Calculate appear
of + 20, + 10, and 0' (angle
reflection
at an incident the wave-
at an angle
of
r. Figure 7 -21).
preparation
toresist.
angles
heams
sensitize
solved,
leaving
a reflection
d in Equation
7-6. we write
altered
d =~~
X 10" _~m_ = 6li9.7 nm mm blaze
1450 blazes
=
A
689.7 nm . ~-n~' (sin 48 + sm 20)
order
reflections
Further lowing
for thc lirst-, secondo, of a similar
kind yield the fol-
Nearly
n= 2
741\
374
249
316
2!!
0
513
256
171
The quality
width. Gratings.
cave surface
in much
face. A concave chromator mirrors
or lenses
hecause
the energy
Holographic pearing
a concave Gratings. even
in numhcr
some
sur-
of a monoand focusing
the concave
throughput
in ever-incrcasing
instruments,
collimating
is advantageous
the rcduction
that contains
the design
surface
both
it on the exit slit. in terms of optical
of cost: surfaces
of a monochromator
grating.
Holographic gracings'; are apof the
output,
given by drldA, where
of a thin
gratings
to
The last property
or refraction
The angular
usually
Purity.
in this way replica grating.
dispersion
bv differentiating
contaminated
El\uation
dr dA
dcpends
can he related
wave-
power, and its spectral
band-
in Section
7C-3.
A more
useful
mcasure
are reflections
m modern
less expensive
optical ones.
selling.
tical parts
of the beam
introduced parts
are minimi7Cd
radiation
these sources optical
Reflections during
also causes
of Monochromators.
10
separate
adjacent
in wavelength.
A is the average
where
hench-top
from
dcosr
to the angular
linear dispersion D
-I
hy
of f)
By suhstituting have
the
are often
-I
that the resolving
when n is the diffraction hlazes
order
illuminated
slit. Thus. better
resolution
gratings,
blaze spacings,
smaller
orders.
This el\uation
letle and echellc
nm/mm
or A/mOl in
tcctor
7-7 into Equation
lincar
dispersion
for
7-'1 we a grating
"ower
the signal-to-noise
necessary
baffles in appro-
applies
and higher to both
echel-
of Monochromators,
that the radiant
be as large as possible. a mcasure
To in
ratio of a spectrometer, energy
that reaches
The {"umber
of the ahility
it i the d,
F. or spec,
of a monochromat'
Il' collect the radiation that emerges slit. The f.numbcr is defined hj'
from the enlran
mirror
The light-gathering
po'
or all optical device increases as the iO\'t:rsc squar, that the angular
tance
d Od\\'ccn
lines per millimeter
I'For
di_~ClJ_'i-;lOlJ tlf
dispersion
rulings
A/hit
increases
as thc dis-
decreases. as th~ number
increases.
the Jd,;dion.
raJi;llil)O. sc,' W K;Jw Chem __t91U.)',.'.N,.-\
of dif-
gratings.
where lis the focal length of the collimating
Note
of
the en-
monochromator:
or on the to
from
is a characteristic
(see later discussion)
lens} and d is its diameter.
ra-
of a grat-
and N is the number
by radiation
longer
crease
manufacture. radiation
of typranges
power
trance
provides
Equation
reciprocal
power
monochromators
where
.r
region.
of thc two images
The rcsolving
R = .~ = nN 1,1
Ught-Gathering
the UV -visible
have a slight
ing is given bv the exprcssion
fraction is thc reciprocal
= d,,- = 1 dA dy dr
The dimcnsions
that
10' to 10'-
7-18. If
dispcrsion
the limit of its
by definition
wavelength
liV -visihle
the lincar
Idr dA
di.
images
Here.
resolving
The
describes
and t.A is tbeir ditference.
in Figure
is
monochro-
..\A
i con-
holding
par-
the effects of spurious
by introducing
stray
parts
from op-
imperfections,
in the atmosphere
reach the exit slit. Generally. diation
from various
housing.
by dust particles of optical
Among
from mechanical
in gratings.
Scattering surfaces
result
This unwanted
sources.
from
ability
ical
as shown
simplifies
A R = ~~~-
n
of dispersion
is
of scattered
far different
Power
polI'er R of a monochromator
grating
D =
that greatly
can be obtained
of the monochromator.
r is small.
if the angle
design.
It can be shown"
on the purity
with small amounts
and the monochromator
in wavelength
linear dispersion D refers to the variation in wavelength as a (unction of y, the distance along the
dispersion
adjacent
a properly
difference
The
the focal lcngth
purposes,
7-20 and 7-21.
7-6 while
dl'
is discussed
to several
of
thc relationship
with wavelengths
that of the instrument can be traced
in the angle
of a grating
line AS of the focal planes
grating.!h
for all practical
Rcsoh'ing
wavelengths
stant. Thus, at any given angle of incidence,
I is
The exit beam of a monochromator
or stray radiation
in Figures
(7-11)
ability
angular dispersion is
with a change
D' Spectral
different
=.d.
1
the linear dispersion of a gratin!: nl0nochronlalOr
certain
The
dr is the change
dA. The angle r is defined
with as
holographic
its ahility to resolve
its light-gathering
ticularly
numhers
to separate
on its dispersion. The
such as alu-
holographic
Monochromators.
1
=
nf Thus.
can have serious under
[)
(,Oll.l'/anl,
of Gratin!:
r
approximately
still
mator Dispersion
7 -I 0 becomes
thcse
radiation
measurements
(> 2()"), cos
At small angles of dilIraction
and E4uation
the slits
conditions."
on a con-
way as on a plane
and focuses
Such an arrangement increases
permits
auxiliary
the radiation
in addition.
can he formed
the same
grating
without
disperses
Gratings
absorption
heams
Characteristics
of a monochromator
of its radiant
over
the
Despitc
spurious
we shall see that its presence on
of Grating Monochromators
lengths, Concave
some
of a monochromator
test that can distinguish
and a replica
with windows
creases.
by coating
In addition.
The grat-
can be manufactured
no optical
a mastcr
Performance 632
substance
can be cast from a master is apparently
however,
depends
is developed
large (~50cm)
and
of dust and fumes.
can be
in Fig-
low cost. As with ruled gratings.
n=3
20 lIJ
perfect.
appears:
is sealed
entrance
precautions, effects
monochromator
with flat hlack paint.
monochromator
by gener-
of the grating.
with a reflective
many as 6000 lines/mm at a relatively
which
structure
in the
surfaces
reflection 7C-l and illustrated
material.
the grooved
between n= 1
of thc two laser
on the surface
There
r,O
to produce
pattern
gratings
data:
substance
of the grooves
ating
an interference
spots
interior
it can be dis-
that can be coated
are produced
film of photosensitive
and third-
from the two
gratings
minum.
to bear
with pho-
ure 7-14. holographic
provide
nm
are 748, 374, and 244 nm, respectively.
calculations
the angle
in Section
ing is then coated and the wavelengths
reflecting
the
to one another.
As descrihed
748.4
= ~'.;-'
so that
structure
The spacing
by changing
coated
fringes
the photoresist a grooved
gratings.
lasers are hrought
interfercnce
or other
and
priate
to prevent
on a glass surface
grating.
with respect
perfecprovidc
radiation
of holographic
The resulting
with aluminum To obtain
free of stray
beams from a pair of identical at suitable
of their greater
to line shape and dimcnsions,
the
or as the focallcngth
IllC;JSIH.'nwnl,
(,heln ..
llJfH,q.
alll\
22HL
Ihl.'dlc,\~
~t
R
of in-
il\ ....tLI\
ShMpc, And!
the f-number.
Thus. an f/2 lens gathers
light than an ('4 lens. Thc {numbers chromalurs
lii: in the 1 ID 10 f:.lngc'.
four times n for m"ny
ill
cning.
A,
Exil 4
is
is
mator
power
setting.
along the focal plane,
resolve
A,
A,
width
that exit the mono-
where Il.A and Il.y are now finite intervals
AJ
Al
arc identical,
to the reciprocal
Equation
and linear
effective ~tonochrnillator
the two slit widths
by writing
A,
slit
effecrive bandwidrh (also called the spectral bandpass or spectral slit width), which is one half the when
A,
Relati\'t'
The
bandwidth
A,
(in units
in units of cm '1) needed
or sometimes
St'ttlllg
from the exit slit for a given
in width.
the slit as a function
as the span of monochromator
of wavelength,
sent the span of wavelengths monochromator setting.
fills the exit slit.
to a setting
Note
!\:lonochromatl)[
slit across the exit slit. If
were used, it would also repre-
of wave-
7-24 shows a plot of the ra-
through
radiation
the monochroma-
slit just
in the image being moved
polychromatic
persion
tor is set for A2 and the two slits are identical The
move the image of the entrance
slits so that the effective
The use of the minimal
when narrow
absorption
On the other
power decreases
significantlv
slit
or emission
hand,
the avail-
when the slits
ent materials listed in Figure 7-2 may also be used for this purpose.
7E-1 Introduction The detectors for early spectroscopic instruments were the human eye or a photographic plate or film. Transducers that convert radiant energy into an electrical signal have almost totally replaced these detection devices. We will confine our discussion to modern transducers. properties
of the Ideal Transducer
The ideal transducer would have a high sensitivity, a high signal-to-noise ratio, and a constant response over a considerable range of wavelengths. In addition, it would exhibit a fast response time and a zero output signal in the absence of illumination, Finally, the electrical signal produced by the ideal transducer would be directly proportional to the radiant power P. That is,
where S is the current or voltage output of the transducer,and k is the calibration sensitivity (Section IE-2). Many real transducers exhibit a small, constant response, known as a dark current in the absence of radiation. For these transducers, the response is described by the relationship
(e)
FIGURE 7-26 Effect of bandwidth on spectral detail for benzene vapor: (a) 0.5 nm, (b) 1.0 nm, (c) 2.0 nm. (From V, A. Kohler,Amer. Lab., 1984, 11,132. Copyright 1984 International Scientific
Communications Inc. Reprinted with permission.)
where kd represents the dark current, which is usually con~ant over short measurement periods. Instruments'with transducers that produce a dark current are Often equipped with a compensating circuit that reduces k" to zero; Equation 7-18 then applies. Types of Radiation
are narrowed, and it becomes more difficult to measure the power accurately. Thus, wider slit widths mav be used for quantitative analysis rather than for qualit~tive work, where spectral detail is important.
Sample containers are required for all spectroscopic studies except emission spectroscopy. Like the optical elements of monochromators, the cells, or cuvettes, that
hold the samples must be made of material that is transparent to radiation in the spectral region of interest. Thus, as shown in Figure 7-2, quartz or fused silica is required for work in the UV region (below 350 nm). Both of these substances are transparent in the visible region and up to about 3 11min the infrared region as well. Silicate glasses can be used in the region between 350 and 2000 nm. Plastic containers have also been used in the visible region. Crystalline sodium chloride is the most common substance used for cell windows in the [R region: the other infrared transpar-
Transducers
As indicated in Figure 7-3b, there arc two general types of radiation transducers.2o One type responds to photons, the other to heat. All photon transducers (also called photoelectric or quantum detectors) have an active surface that absorbs radiation. [n some types, ~
Tutorial: L~arn more about radiation transducers.
~"For a discussion of optical radiation detectors, "tee 1. D, Ingk Jr. and S. R. Crouch. Spectrochemical Ana/pis, pp. 106 -17, Upper Saddle Ri\er. ~J: Prnl.. 1993,24.59: 1. V. Sweedkr. R. B. Bilhorn, P. \1. Epperson G. R. Sims. and \1. R. Denton, Anal. Chem., 1988,60. 2S2A, 327A
On-chip preamp
Optical
input
Metallic electrode
(gate)
Insulator
(SiO,)
temperature rise is measured. The radiant power level 7 from a typical infrared beam is extremely small (10to 10-' W), so that the heat capacity of the absorbing element must be as small as possible if a temperature change is to be detected. The size and thickness of the absorbing element is minimized and the entire infrared beam is concentrated on its surface so that, under optimal conditions, temperature changes are limited to a few thousandths of a kelvin. The problem of measuring infrared radiation by thermal means is compounded by thermal noise from the surroundings. For this reason, thermal detectors are housed in a vacuum and are carefully shielded from thermal radiation emitted by other nearby objects. To further minimize the effects of extraneous heat sources, the beam from the source is generally chopped. In this way, the analyte signal, after transduction, has the frequency of the chopper and can be separated electronically from extraneous noise, which usually varies slowly withtime. Thermocouples
(b)
FIGURE 7-37 .A CCO array: (a) arrangement of 512 x 320 pixels and (b) schematic showing four of the IUdlvldualdetectors.
hardware and software issues associated with the acquisition and use of these devices. 7E-4 Photoconductivity Transducers The most sensitive transducers for monitoring radiation 10 the near-infrared region (0.75 to 3 /Jm) are semiconductors whose resistances decrease when thev absorb radiation within this range. The useful range df photoconductors can be extended into the far-infrared region by cooling to suppress noise that arises from thermally induced transitions among closely lying energy levels. ThIS application of photoconductors is important in infrared Fourier transform instrumentation. Crystalline semiconductors are formed from the sulfides, selenides, and stibnides of such metals as lead cadmium, gallium, and indium. Absorption of radia: tlOn by these materials promotes some of their bound electrons into an energy state in which they are free to conduct electricity. The resulting change in conductivIty can then be measured with a circuit such as that shown in Figure 3-lOa. . Lead sulfide is the most widely used photoconductive material that can be used at room temperature.
Lead sulfide transducers are scnsitive in the region between 0.8 and 3/Jm (12,500 to 3300 cm-I). A thin laycr of thIS compound is deposited on glass or quartz plates to form the cell. The entire assembly is then sealed in an evacuated container to protect the semiconductor from reaction with the atmosphere. The sensitivity of cadmIUm sulfide, cadmium selenide, and lead sulfide transducers is shown by curves B, D, and G in Figure 7-27. 7E-5 Thermal Transducers The convenient phototransducers just considered are generally not applicable in the infrared because photons 10 thIS region lack the energy to cause photoemisSlon of electrons. Thus, thermal transducers or photoconducllve transducers (see Section 7E-4) must be used. Neither of these is as satisfactorv as photon transducers. . In thermal transducers,27 the radiation impinges on and IS absorbed by a small blackbody; the resultant
a good discussion of optical radiation transdUCers of alllvpc-s 10c1udlO~ thermal dC-lectors. see E. L. Dercniak and G D. Grov.'c: Op;ical Detectors. Ne .••• ' York: Wiley. 19.s~
n:;'>"3
the instrument to another. Fiber optics have added a new dimension of utility to optIcal mstrument designs."
pies of their application to conventional struments in the chapters that follow.
analytical in-
7G.2 Fiber-Optic Sensors
7G-1 Properties of Optical Fibers Optical fibers are fine strands of glass or plastic that transmit radiation for distances of several hundred feet or more. The diameter of optical fibers ranges from 0.05 pm to as large as 0.6 em. Where images are to be transmitted, bundles of fibers, fused at the ends, are used. A major application of these fiber bundles has been in medical diagnoses, where their flexlblhty permits transmission of images of organs through tortuous pathways to the physician. Fiber optics are used not onlv for observation but also for Illummation of objects.~ In such applications, the ability to Illumillate without heating is often very important. Light transmission in an optical fiber takes place by total internal reflection as shown IIIFIgure 7-39. For total internal reflections to occur. it is necessary that the transmitting fiber be coated with a material that has a refr~c~ive index that is somewhat smaller than the refract;ve index of the tiber material. Thus, a typIcal glass fiber has a core with a refractive index of about 1.6 and has a glass coating with a refractive index of approx.lmately 1.5. Typical plastic tibershave a polym~thylmethacrylate core with a refractIve mdex of I.) and have a polymer coating with a refractIve mdex of 1.4. A liber (Figure 7-39) will transmIt radIatIOn contained in a limited incident cone with a half angle shown as e in the ligure. The numerical aperture of the fiber provides a measure of the magnitude of the socalled acceptance cone. . . By suitable choice of construction matenals. libers that will transmit ultraviolet, visible. or mfrared radIation can be manufactured. You will find several exam-
Fiber-optic sensors, which are sometimes called optrades, consist of a reagent phase immobilized on the end of a fiber optic30 Interaction of the analyte WIth the reagent creates a change in absorbance, reflectance, fluorescence, or luminescence, whIch IS then transmitted to a detector via the optical fiber. Flberoptic sensors are generally simple, inexpensIve deVIces that are easily miniaturized. They are used extensIvely for sensing biological materials, where they are often called biosensors. In fact, such sensors have been miniaturized to the nanometer scale. These devices are called nanobiosensors.J1
In this section, we define the terminology we us~ to describe various types of optical instruments. It ISImportant to understand that the nomenclature proposed here is not agreed upon and used by all scientists; it is simply a common nomenclature and the one that WIll be encountered throughout this hook. A spectroscope is an optical instrumentused for the visual identification of atomic emission hnes. It consists of a monochromator, such as one of those shown in Figure 7-18, in which the exit slit is replaced hy an eyepiece that can be moved along the focal plane. The wavelength of an emission line can then be determmed
'\)~1..-\...\rnold, Anal. C~t'm .. 1992. 64. to15A; R. E.Dcssy, Anal. C~mi' 1989.61. 1079A: W. R. Seltz, AnaL. Chern., 1984, 56, loA: S. Borman. na. Chern. 1987.59. 1161A; lbid., 1986,58. 76tJA r V~-Dinh. in t;nqclopedia of N'ano\'cicnce and Xan()lt'chll~,lo~y, Stevenson Ranch. CA: America.n Scientific Publi5her'i. 2004. 6, )3-)9: \j
~"For d re\"i~w of applications fiber ()~!ii.:s.see L Cha~a\ 1982.54.1071.-\ and 1. K. Cru!TI. A,wl. Cht'm __1969. -JI. ,-0.-\ \.)f
.-\ruzf Chen!"
T Vo-Dinh.
J.
Cell. Biochem. Supp!., 2002. 39, 154
from the angle between the incident and dispersed beams when the line is centered on the eyepiece. We use the term colorimeter to designate an instrument for absorption measurements in which the human eye serves as the detector using one or more COlor-comparison standards. A phOfOrr~eterconsists of a source. a filter. and a photoelectric transducer as well as a signal processor and readout. Note that some scientists and instrument manufacturers refcr to photometers as calorimeters or photoelectric colorimeters. Filter photometers are commercially available for absorption measurements in the ultra~iolct. visibk and infrared regions, as well as emission and Iluorescence in the first two wavelength regions. Photometers designed for fluorescence measurements arc also called fluorometers. A spectro!(raph is similar in construction to the two monoehromators shown in Figure 7-18 except that the sht arrangement is replaced with a large aperture that holds a detector or transducer that is continuously exposed tn the entire spectrum of dispersed radia-tion. HlStoncally. the detector was a photographic film or plate. Currently. however. diode arrays or CTDs are often used as transducers in spectrographs. A spectrometer is an instrument that provides informatIOn about the intensity of radiation as a function of wavelength or frequency. The dispersing modules in some spectrometers are multichannel so that two or mare frequencies can be viewed simultaneously. Such instruments are sometimes called polychrollla;ors. A spectrophotometer is a spectrometer equipped with one or more exit slits and photoelectric transducers that permit the determination of the ratio of the radiant power of two beams as a function of wavelength as in absorption spectroscopy Aspect rophotomctcr for fluorescence analysis is sometimes called a spec! roflllO
r( J1llele r.
All of the instruments named in this section thus far use filters or monochromators to isolate a portion of the spectrum for measurement. A mllitiplex instrument. IIIcontrast. obtains spectral information without lirst dispersing or tiltering the radiation to provide wavelengths of interest. The term mulriplex comes from communication theory. where it is used to describe systems in which many sets of information are transported simultaneously through a single channel. Multiplex analytical instruments are single-channel devices in which all components of an an'alvtical response are collected simultlilleolllly. To deter'mine the magnitude of each of these signal components. it is
necessary to modulate the analyte signal so that. subsequently, it can be decoded into its components. tvIost multiplex analytical instruments depend on the fOllner rransform (FT) for Signal decoding and arc thus often called Fourier transform spectr~meters. Such IIlstruments are by no means confined to optical spectroscopy. Fourier transform devices have been described for nuclear magnetic resonance spectrometry, mass spectrometry, and microwave spectroscopy. Several of these IIlstruments are discussed in some detail in SUbsequent chapters. The section that follows describes the principles of operation of Fourier transform optical spectrometers.
1
06 .
..=
O.-l
/
Cr(Il)
Fourier transform spectroscopy was first developed by astronomers in the early 19505 to study thc infrared spectra of distant stars: only by the Fourier technique could the very weak signals from these sources be isolated from environmental noise. The first chemical apphcatlons of Fourier transform spectroscopy, which were reported approximately a decade later, were to the energy-starved far-infrared rcgion; by the late I 960s. IIlstruments for chemical studies in both the farmfrared (10 to 400 cm J) and the ordinary infrared regHJIlS were available commercially. Descriptions of Founer transform instruments for the ultraviolet and VISIblespectral regions can also be found in the literature, but their adoption has been less widespread. 12 of Fourier
The use of Fourier transform instruments has several major advantages. The first is the throll!(hput, or }iI£l"ltlO1. adnlfllagc. which is rcalized because Fourier transform instruments have few optical elements and
l:h'r
IllUf O. From a practical standpoint, only a finite-sized sampling interval can be summed over a finite retardation range of a few centimeters. These constraints have the effect of limiting the i"e~olution of a Fourier transform instrument and restricting its frequency range.
(il
FIGURE 7-44 Formation of interferograms at the output of the Michelson interferometer.
(a) Interference pattern at the output of the interferometer resulting from a monochromatic source. (b) Sinusoidally varying signal (interferogram) produced at the detector as the pattern in (a) sweeps across the detector. (c) Frequency spectrum of the monochromatic light source resulting from the Fourier transformation of the signal in (b). (d) Interference pattern at the output of the interferometer resulting from a two-frequency source. (e) Complex signal produced by the interference pattern of (d) as it falls on the detector. Zero retardation is indicated by point A. (f) Frequency spectrum of the two-frequency source. (g) Interference pattern resulting from a broad emission band. (h) Interferogram of the source in (f). (I) Frequency spectrum of the emission band. useful to introduce a new variable, B(v), which depends on P(V) but takes these factors into account. We can then rewrite the equation in the form 1'(0)
=
B(v)cos hft
=
B(v)cos47TV"vt
of this relationship
into Equation
7-28
(7-27)
Substitution of Equation 7-24 into Equation 7-27 leads to 1'(0)
Substitution gives
(7-28)
But the mirror velocity can be expressed in terms of retardation or
which expresses the magnitude of the interferogram signal as a function of the retardation factor and the wavenumber of the source. The interferograms shown in Figure 7-44b, e, and h can be described by two terms, one for each wavenumber. Thus,
This equation means that resolution in wavenumbers will improve in proportion to the reciprocal of the distance that the mirror travels.
What length of mirror drive will provide a resolution of 0.1 cm-'?
01 cm-' =.t. . 0
Resolution The resolution of a Fourier transform spectrometer can be described in terms of the difference in wavenumber between two lines that can be just separated by the instrument. That is,
The mirror motion required is one half the retardation, or 5 cm.
Instruments where V, and V, are wavenumbers for a pair of barely resolvable lines. It is possible to show that to resolve two lines, the time-domain signal must be scanned long enough so that one complete cycle, or beat, for the two lines is
Details about modern Fourier transform optical spectrometers are found in Section 16B-1. An integral part of these instruments is a state-of-the-art computer for controlling data acquisition, for storing data, for signal averaging, and for computing the Fourier transforms.
*Answers are provided at the cnd of the book for problems marked with an asterisk. ~
Problems with this icon are best solved using spreadsheets.
*7-13 Consider an infrared grating with 84.0 lines per millimeter and 15.0 mm of illuminated area. Calculate the first-order resolution (A/JlA) of this grating. How far apart (in cm -I) must two lines centered at 1200 cm I be if they are to be resolved" 7-14 For the grating in Problem 7-13, calculate the wavelengths of first- and secondorder diffraction at reflective angles of (a) 25 and (b) 0". Assume the incident angle is 45". 0
7-1 Why must the slit width of a prism monochromator be varied to provide constant effective bandwidths but a nearly constant slit width provides constant bandwidth with a grating monochromator? 7-2 Why do quantitative and qualitative analyses often require different monochromator slit widths? *7-3 The Wicn displacement law states that the wavelength maximum in micrometers for blackbody radiation is given by the relationship
where T is the temperature in kelvins. Calculate the wavelength maximum for a blackbody that has been heated to (a) 5000 K, (b) 3000 K, and (c) 1500 K. *7-4 Stefan's law states that the total energy E, emitted by a blackbody per unit time and per unit area is given by E, = aT', where a has a value of 5.69 x 10" Wm-2 K -4 Calculate the total energy output in W/m2 for each of the blackbodies described in Problem 7-3. *7-5 Relationships described in Problems 7-3 and 7-4 may be of help in solving the following. (a) Calculate the wavelength of maximum emission of a tungsten filament bulb operated at the usual temperature of 2870 K and at a temperature of 3500 K. (b) Calculate the total energy output of the bulb in terms of W/cm2• 7-6 Contrast spontaneous and stimulated emission. 7-7 Describe the advantage of a four-level laser system over a three-level type. 7-8 Define the term effective bandwidch of a filter. *7-9 An interference filter is to be constructed for isolation of the nitrobenzene absorption band at 1537 cm l (a) If it is to be based on first-order interference, what should be the thickncss of the dielectric layer (refractive index of 1.34)" (b) What other wavelengths would be transmitted" 7-10 A 1O.0-cm interference wedge is to be built that has a linear dispersion from 400 to 700 nm. Describe details of its construction. Assume that a dielectric with a refractive index of 1.32 is to be used. 7-11 Why is glass better than fused silica as a prism construction material for a monochromator to be used in the region of 400 to SOOnm ry *7-U For a grating, how many lines per millimeter would be required for the first-order diffraction line for A = 400 nm to he ohserved at a reflection angle of 5° when the angle of incidence is 45°')
7-15 With the aid of Figures 7-2 and 7-3, suggest instrument components and materials for constructing an instrument that would be well suited for (a) the investigation of the fine structure of absorption bands in the region of 450 to 750 nm. (b) obtaining absorption spectra in the far infrared (20 to 50 flm). (c) a portable device for determining the iron content of natural water based on the absorption of radiation by the red Fe(SCN)2+ complex. (d) the routine determination of nitrobenzene in air samples based on its absorption peak at 11.8 flm. (e) determining the wavelengths of flame emission lines for metallic elements in the region from 200 to 780 nm. (f) spectroscopic studies in the vacuum ultraviolet region. (g) spectroscopic studies in the near infrared, *7-16 What is the speed (f-number) of a lens with a diameter of 5.4 cm and a focal length of 17.6 em? 7-17 Compare the light-gathering power of the lens described in Problem 7-16 with one that has a diameter of 37.6 cm and a focal length of 16.8 em. *7-18 A monochromator has a focal length of 1.6 m and a collimating mirror with a diameter of 3.5 cm. The dispersing device was a grating with 1500 lines/mm. For first -order diffraction, (a) what is the resolving power of the monochromator if a collimated beam illuminated 3.0 cm of the gratingry (b) what are the first- and second-order reciprocal linear dispersions of the monochromator? 7-19 A'monochromator with a focal length of 0.78 m was equippcd with an echellette grating of 2500 blazes per millimeter. (a) Calculate the reeiprocallinear dispersion of the instrument for first-order spectra. (b) If 2.0 em of the grating were illuminated, what is the first-order resolving power of the monochromator" (c) At approximately 430 nm, what minimum wavelength difference could in theory be completely resolved by the instrument" 7-20 Describe the basis for radiation detection with a silicon diode transducer. 7-21 Distinguish among (a) a spectroscope, (b) a spectrograph, photometer.
and (c) a spectro-
*7-22 A Michelson interferometer had a mirror \'elocity of 2.75 cm/s. What would be the frequency of the interferogram for (a) UV radiation of 350 nm, (b) visible radiation of 575 nm, (c) infrared radiation of 5.5 f,m. and (d) infrared radiation of 25 flm?
*7-23 What length a resolution (a) infrared (b) infrared
Ii] Challenge
of mirror drive in a Michelson interferometer sufficient to separate peaks at 500.6 and 500.4 em-I.) peaks at 4002.1 and 4008.8 cm-I?
is required to produce
Problem
7-24 The behavior of holographic filters and gratings is described by coupled wave theory.35 The Bragg wavelength Ab for a holographic optical clement is given by Ab
=
2ndcos Ii
where n is the refractive index of the grating material; d is the grating period, or spacing; and Ii is the angle of incidence of the beam of radiation. (a) Create a spreadsheet to calculate the Bragg wavelength for a holographic grating with a grating spacing of 17.1 flm and a refractive index of 1.53 at angles of incidence from 0 to 90°. (b) At what angle is the Bragg wavelength 462 nm? (c) The Bragg wavelength is sometimes called the "playback wavelength." Why? (d) What is the historical significance of the term "Bragg wavelength?" (e) A tunable volume holographic filter has been developed for communications applications.'6 Thc filter is said to be tunable over the wavelength range 2nd to 2d~. If the filter has a Bragg wavelength of 1550 nm and a grating spacing of 535 nm, calculate the angular tuning range of the filter. (f) Find the Bragg wavelength for a grating with a spacing of 211.5 nm, assuming that the grating is made of the same material. Find the wavelength range over which this grating may be tuned. (g) Discuss potential spectroscopic applications of tunable holographic filters. (h) When a volume grating is created in a holographic film, the refractive index of the film material is varied by an amount t1n, which is referred to as the refractive-index modulation. In the ideal case, this quantity is given by :in = ~ 2t where A is the wavelength of the laser forming the interference pattern, and t is the thickness of the film. Calculate the refractive-index modulation in a film 38 flm thick with a laser wavelength of 633 nm. (i) For real gratings, the refractive-index modulation is Asin-IV7)~
:in = -----
7Tt
An Introduction to Optical Atomic
.Spectrometry
"I'
n this chapter, we first present a theoretical dis-
..y....•;
cussion. o.if the sou.r.ces and properties of optical
'.,
atomic~pectra.
);i~'producinga.toms ./§fs.
We.then lISt methods usedfor frolfl;samplesfor
elemental analy-
Finally, we descdke in some detail the various
:'7f.chniquetased
for introducing
Jlevices thaf.are usedfor
samples into the
opticalabsorption,
':sion, andf!l1orescencespectrometry . melfl, ~lnd':0 .. -\. \l,lnta~er anJ D, W. Golightly,
~ "
'0
~
l.O
6
FIGURE9-3 Temperature profiles in degrees Celsius for a natural gas-air flame. (From B. Lewis and G. van Elbe, J. Chem. Phys., 1943, 11,94. With permission.)
acetylene-nitrous oxide sources. Because free atoms are prevalent in the interzonal region, it is the most widely used part of the flame for spectroscopy. In the secondary reaction zone. the products of the inner core are converted to stable molecular oxides that are then dispersed into the surroundings. A flame profile provides useful information aoout the processes that go on in different parts of a flame; it is a contour plot that reveals regions of the flame that have similar values for a v'ariable of interest. Some of these variaoles include temperature. chemical composition. absorbance. and radiant or fluorescence intensity. Temperature Profiles. Figure 9-3 shows a temperature profile of a typical flame for atomic spectroscopy. The maximum temperature is located in the flame about 2.5 em aoove the primary combustion zone. It is important - particularly for emission methods (Section JOe-I)-to focus the same part of the flame on the entrance slit for all calibrations and analytical measurements. Flame Absorption Profiles. Figure 9-4 shows typical absorption profiles fm three elements. Magnesium exhibits a maximum in absorbance at aoout thc mid-
die of the flame because of two opposing effects. The initial increase in ahsorhancc as the distance from the oase increases results from an increased numoer of magnesium atoms produced by the longer exposure to the heat of the flame. As the secondary com oust ion zone is approached. howe\'er. appreciable oxidation of the magnesium begins. This process evcntuallv leads to a decrease in absorbance because the OXide particles formed do not absorb at the ooservation wa\'e1ength. To achieve maximum analytical sensitivity. then. the flame must be adjusted up and down with respect to the beam unt il the region of maximum absorbance is located. The behavior of silver. which is not easily oxidized. is quite different; as shown in Figure 9-4. a continuous increase in the number of atoms, and thus the aosorbance, is ooserved from the oase to the periphery of the flame. By contrast, chromium. which forms very staole oxides, shows a continuous decrease in absorbance beginning close to the ourner tip; this ooservation suggests that oxide formation predominates from the start. These ooservations suggest that a different portion of the flame should oe used for the dctermination of each of these clements. The more sophisticated instruments for flame spectroscopy are equipped with monochromators that sample the radiation from a relatively small region of the flame, and so a critical step in the optimization of signal output is the adjustment of the position of the flame with respect to the entrance slit. Flame Atomizers
Flame atomizers arc used for atomic absorption. fluorescence. and emission spcctroscopy. Figure 9-5 is a diagram of a typical commercial laminar-flow burner
~ To
\\'ask
Nebulizu oxidanl
that uses a concentric-tube neoulizer, such as that shown in Figure 8-1 la. The aerosol.formed oy the flow of oxidant, is mixed with fuel and passes a series of baffles that remove all but the finest solution droplets. The baffles cause most of the sample to collect in the bottom of the mixing chamber where it drains to a waste container. The aerosol, oxidant, and fuel are then burned in a slotted ourner to provide a 5- to llJ-cm high flame. Laminar-flow burners produce a relatively quiet flame and a long path length for maximizing absorptio~. These properties tend to enhance sensitivity and reproducioility in AAS. The mixing chamber in this typ~ of burner contains a potentially explosive mixture that can flash oack if the tlow rates are too low. Note that the laminar-flow burner in Figure 9-5 is equipped with pressure relief vents for this reason. Other types of laminar-flow burners and turbulent-flow burners arc availaole for atomic emission spectrometry and AFS. Fuel and Oxidant Regulators. An important varia ole that requires close control in flame spectroscopy is the flow rate of both oxidant and fuel. It is desirable to be aole to varv each over a broad range so that optimal atomization conditions can oe determined experimentally. Fuel and oxidant arc usually comoined in approximately stoichiometric amounts. For the determination of metals that form stable oxides, however, a l1ame that
FIGURE9-5 A laminar-flow burner. (Courtesy of Perkin-Elmer Corporation, Norwalk, CT.)
contains an excess of fuel is often desirablc. Flow rates arc usually controlled by means of double-diaphragm pressure regulators followed oy needle valves in the instrument housing. A widely used device for measuring flow rates is the rotameter. which consists of a tapered, graduated, transparent tube that is mounted vertically with the smaller end down. A lightweight conical or spherical float is lifted by the gas flow; its vertical position is determined by the tlow rate. Performance Characteristics of Flame Atomizers. Flame atomization is the most reproducible of all liquid-sample-introduction methods that have been developed for atomic absorption and fluorescence spectrometry to datc. The sampling efficiency of other atomization methods and thus the sensitivity. however, are markedly beller than in flame atomization. There are two primary reasons for the lower sampling efficiency of the flame. First, a large portion of the sample flows down the drain. Second. the residence time of individual atoms in the optical path in the flame is brief (-10-·5).
Electrothermal atomizers, which licst appeared on the market in the earlv 1970s. generally provide enhanced sensiti\'ity oecause the entire sample is atomiz.ed in a short period, and the average residence time of the
atoms in the optical path is a second or more.' Elec. trothermal atomizers are used for atomic absorption and atomic fluorescence measurements but have not been generally applied for direct production of emis. sion spectra. They are used for vaporizing samples in inductively coupled plasma emission spectroscopy. however.
Experiments show that reducing the natural poros· itv of the graphite tube minimizes some sample mat;ix effects and poor reproducibility associated with graphite furnace atomization. During atomization, part of the analyte and matrix apparently dlfluse Into the surface of the tube, which slows the atomIzatIOn process, thus giving smaller analyte signals. To over· come this effect, most graphite surfaces are coated WIth a thin layer of pyrolytic carbon, which seals the pores of the graphite tube. Pyrolytic graphite is a type of graphite that is deposited layer by layer from a highly homogeneous environment. It is formed by passing a mixture of an inert gas and a hydrocarbon such as methane through the tube while it is held at an elevated temperature .
In electrothermal atomizers, a few microliters of sample is first evaporated at a low temperature and then ashed at a somewhat higher temperature in an elec· trically heated graphite tube similar to the one in Figure 9·6 or in a graphite cup. After ashing, the current is rapidly increased to several hundred amperes, which causes the temperature to rise to 2000"C to 3000°C; atomization of the sample occurs in a period of a few mil· liseconds to seconds. The absorption or fluorescence of the atomic vapor is then measured in the region immediately above the heated surface. Electrothermal
Figure 9·6a is a cross-sectional view of a commercial electrothermal atomizer. In this device, atomization occurs in a cylindrical graphite tube that is open at both ends and that has a central hole for introduction of sample by means of a micropipette. The tube is about 5 em long and has an internal diameter of some· what less than 1 em. The interchangeable graphite tube fits snugly into a pair of cylindrical graphite electrical contacts located at the two ends of the tube. These contacts are held in a water-cooled metal housing. Two inert gas streams are provided. The external stream prevents outside air from entering and incinerating the tube. The internal stream flows into the two ends of the tube and out the central sample port. This stream not only excludes air but also serves to carry away vapors generated from the sample matrix during the first two heating stages. Figure 9·6a illustrates the so-called L'vov platform, which is often used in graphite furnaces such as that shown in the figure. The platform is also made of graphite and is located beneath the sample entrance port. The sample is evaporated and ashed on this plat· form. When the tube temperature is increased rapidly, however. atomization is delayed because the sample is
:F,lr detailed dlSCU'isionsof d.:ctwlhL·rmal ElectrmhcmUl! York:
Wiley.
Aromizmiofl J999: A. Varma.
51!fpriofJ SpcctroscOpL
Boca
for
atomi.zCf
c~r: r-r-J ~
Analyte
hollow·
Deuterium lamp
n
!
~fi' ~-:"Vy/ ~/ ,~
Rotaling chopper
~
C
/1
11/\/
D
_~,,"--Tomono~
j\J;;
chromator Electrothermal
szrq// ~agnel
(J+
//}// //>/ / '1))'-1
E
Y
~~~C==1 / 8
//
n_n_ /
J.LU,;U.LUL/
(J
/ Background
Schematic of a continuum-source background correction system, Note that the chopper car be eliminated by alternately pulsing each lamp, FIGURE
9-14
The slit width is kept sufficiently wide so that the fraction of the continuum source that is absorbed by the atoms of thc samplc is negligible, Therefore, thc attenuation of the continuum source as it passes through the atomized sample reflects only the broadband absorption or scattcring hy the sample matrix components, A background correction is thus achieved, Unfortunately, although most instrument manufacturers offer continuum-source background correction systems, the performance of thcse devices is often less than ideal, which leads to undercorrection in some systems and overcorrection in others, One of the sources of error is the inevitable degradation of signal-to-noise ratio that accompanies the addition of the correction system, Another is that hot gaseous media are usually highly inhomogeneous both in chemical composition and in particulate distribution; thus if thc two lamps are not in perfect alignment, an erroneous correction will result that can cause either a positive or a negative error. Finally, the radiant output of the deuterium lamp in thc visible region is low enough to preclude the use of this correction procedure for wavelcngths longer than about 350 nm, Background
Correction Based
on the Zeeman Effect When an atomic vapor is exposed to a strong magnetic field (-10 kG), a splitting of electronic energy levels of the atoms takes place that leads to formation of several absorption lines for each electronic transition, These lines are separatcd from one another bv about 0,01 nm, with the sum of the absorhances for th~ lines being exactly equal to that of the original line from which they
F=r1
only
F
\ Background atomic
plus
absorption
Schematic of an electrothermal atomic absorption instrument that provides a background correction based on the Zeeman effect. (Courtesy of Hitachi Scientific Instruments, Mountain View,CA,)
FIGURE
9-15
were formed, This phenomenon, which is termed the Zeeman effect, i9 is general for all atomic spectra, Several splitting patterns arise depending on the type of electronic transition that is involved in the absorption process. The simplest splitting pattern, which is observed with singlet (Section SA-I) transitions, leads to a central, or 7f,line and two equally spaced satellite a lines, The central line, which is at the original wavelength, has an absorbance that is twice that of each a line, For more complex transitions, further splitting of the 7f and a lines occurs, Application of the Zceman effect to atomic absorption instruments is based on the diffcring response of the two types of absorption lines to polarized radiation, The 7f line absorbs only that radiation that is plane \polarized in a direction parallel to the external magnetic field; thc a lines, in contrast, absorb only radiation polarized at 90" to the field, Figure 9-15 shows details of an electrothermal atomic absorption instrument, which uscs the Zeeman effect for background correction, Un polarized radiation from an ordinary hollow-cathode source A is passcd through a rotating polarizer B. which separates the beam into two components that are plane-polarized at 90' to one another C. These beams pass into a tubetype graphite furnace similar to the one shown in Fig-
I)For a detailed discussion of the_ applicatIOn of the Zeeman effect to atomiC ahsorption, see D. 1. Butcher and 1. Sneddon. A Practical Gllide to Graphltf' Furnuce Atomic Absorption Spectrometry. :\ew York: Wiley, 19Yk, pro 7,-8-l: F 1. Fernanda. S. A. Myers, and \\". Slavin. Anal. Chern .. 1980,5':. 7-lL S. D. Rr'Win. Anal. Chem., 1977.49 \ l-l), 12fi9A
ure 9-6a, A permanent II-kG magnet surrounds the furnace and splits the cnergy levels into the three absorption peaks shown in D, Notc that the central peak absorbs only radiation that is plane polarized with the field, During that part of the cycle when the source radiation is polarized similarly, absorption of radiation by the analyte takes place, During the other half cycle, no analyte absorption can occur. Broadband molecular absorption and scattering by the matrix products occur during both half cycles, which leads to the cyclical absorbance pattern shown in F. The data-acquisition system is programmed to subtract the absorbance during the perpendicular half cycle from that for the parallel half cycle, thus giving a background corrected value, A second type of Zeeman effect instrumcnt has been designed in which a magnet surrounds the hollow-cathode sourcc, Here, it is the emission spectrum of the source that is split rather than the absorption spectrum of the sample, This instrument configuration provides an analogous correction, To date, most instruments are of the type illustrated in Figure 9-15, Zeeman effcct instruments provide a more accurate correction for hack ground than the mcthods described earlier. These instruments are particularly useful for electrothermal atomizers and permit the direct determination of elements in samples such as urinc and blood, The decomposition of organic material in these samples leads to large background corrections (background A > I) and, as a result. susccptibility to significant error. ~
Tutorial: Learn more ahout the Zeeman effect.
Background
Correction
Based
Protective agents prevent interference by forming stable but volatile species with the analytc. Three common reagents for this purpose are ethylenediaminetetraacetic acid (EDTA). 8-hydroxyquinoline, and APCD, which is the ammonium salt of I-pyrroIidinecarbodithioic acid. The presence of EDTA has been shown to eliminate the interference of aluminum, silicon, phosphate, and sulfate in the determination of calcium. Similarly. 8-hydroxyquinoline suppresses the interference of aluminum in the determination of calcium and magnesium.
on Source Self-Reversal
A remarkably simple means of background correction appears to offer most of the advantages of a Zeeman effect instrument. 2
·----6500 ---6800
.c
8000 -'-'---'-
100()()
FIGURE10-4 Temperatures in a typicallCP source. (From V.A. Fassel, Science, 1978,202,186. With permission. Copyright 1978 by the American Association for the Advancement of Science.) 2 to 30 with ultrasonic nebulization). The disadvantages are that the cool plasma tail must be removed from the light path to prevent interference from oxides and that it is more difficult to prevent thermal and contaminant degradation of the spectrometer optics in the axial configuration than in the radial arrangement.' The decision as to which viewing arrangement to use depends on the chemical behavior of the analyte in the plasma, the spectral line chosen for the analysis, the quality of the data required, and the detailed nature of the cxperiment. For example, the axial arrangement is especially useful in ICPMS, which is described in Section lie Analyte Atomization
and Ionization
Figure 10-4 shows temperatures in the plasma using isothcrmal contours. Sample atoms reside in the plasma for about 2 ms before they reach thc observation point. During the residence time they experience temperatures ranging from 5500 to 8000 K. The time and temperatures are roughly two to three times greater than those found in the holiest combustion flames (acetylene-nitrous oxide) used in flame spectroscopic methods. As a result, atomization is more complete in "L. H. 1. Lajunen and P. Peramaki. SpenrochcmlcI11 Anafvsis hl- Atomic Ahsorptlon and Frninion, 2nd cd. pr- 2S3-5-t. C;Jmhridgc: Royal SOCid~ of Chemistry. 20(}4
plasmas than in flames. and fewer chemical interferences occur. Surprisingly, ionization interference effects are small, probably because the large electron concentration from ionization of the argon maintains a fairly constant electron conccntration in the plasma. Several other advantages are associated with the plasma source. First, atomization occurs in a chemically inert environment, which tends to enhance the lifetime of the analyte by preventing oxide formation. In addition, and in contrast to arcs, sparks, and flames, the temperature cross section of the plasma is relatively uniform; as a consequence, self-absorption and selfreversal effects do not occur as often. Thus, calibration curves are usually linear over several orders of magnitude of concentration. Finally, the plasma produces significant ionization. which makes it an excellent source for ICPMS.
DCP sources were first described in the 1920s and were systematically investigated as sources for emission spectroscopy for several decades. III It was not until the 1970s, however, that the first commercial DCP emission source was introduced. The source became quite popular, particularly among soil scientists and geochemists for multielement analysis. Figure 10-5 is a schematic of a commercially available DCP source that is well suited for excitation of emission spectra for a wide variety of elements. This plasma jet source consists of three electrodes configured in an inverted Y A graphite anode is located in each arm of the Y and a tungsten cathode at the inverted base. Argon flows from the two anode blocks toward the cathode. The plasma jet is formed by bringing the cathode into momentary contact with the anodes. Ionization of the argon occurs and a current develops (~14 A) that gcnerates additional ions to sustain the current indefinitely. The temperature at the arc core is more than 8000 K and at the viewing region about 5000 K. The sample is aspirated into the area between the two arms of the Y, whcre it is atomized, excited, and detected. Spectra produced by the DCP tend to have fewer lines than those produced by the ICP, and the lines l'IFor additional details. Set: G. \V. Johnson. H. E. Taylor, and R. K Skllgahoe. Anal. Chem, 1979.5/.2-1.03; Specrrochim. ACII1. Part B. 1979, 14.197: R. 1. DeckeL Specrrochim. ACla. Part B, 1980.35, 2t
~ lQj
Lxercise: Learn more about the OCP.
TABLE10-1 Desirable Properties of an Emission Spectrometer L 2. 3. 4.
High resolution (0.01 nm or A/j,). > 100,(00) Rapid signal acquisition and recovery Low stray light Wide dynamic range (> 106)
5. Accurate and precise wavelength identification and selection
6. Precise intensity readings «1 % relative standard deviation at 500 X the detection limit) 7. High stability with respect to environmental changes 8. Easy background corrections 9. Computerized operation: readout, storage data manipulation, etc. Anode
block
FIGURE10-5 Diagram of a three-electrode DCP source. Two separate DCPs have a single common cathode. The overall plasma burns in the form of an upside-down Y. Sample can be introduced as an aerosol from the area between the two graphite anodes. Observation of emission in the region beneath the strongly emitting plasma core avoids much of the plasma background emission. (Courtesy of Spectrametrics, Inc. Haverhill, MA.l
formed in the DCP are largely from atoms rather than ions. Sensitivities achieved with the DCP range from an order of magnitude lower than those obtainable with the ICP to about the same as the ICP's. The reproducibilities of the two systems are similar. Significantly less argon is required for the DCP, and the auxiliary power supply is simpler and less expensive. The DCP is able to handle organic solutions and aqueous solutions with a high solids content better than the ICP. !iample volatilization is often incomplete with the DCP, however, because of the short residence times in the high-temperature region. Also, the optimum viewing region with the DCP is quite smalL so optics have to be carefully aligned to magnify the source image. In addition, the graphite electrodes must be replaced every few hours, whereas the ICP requires little maintenance. 10A-3 Plasma Source Spectrometers
Table 10-1 lists the most important properties of the ideal instrument for plasma emission spectroscopy. The idcal spectrometer is not available today, partly because some of these properties are mutually exclusive. For example, high resolution requires the use of
narrOw slits, which usually reduces the signal-to-noise ratio and thus the precision of intensity readings. Nevertheless, instruments developed recently approach many of the ideals listed in the table." A dozen or more instrument manufacturers currently offer plasma emission spectrometers. The designs, performance characteristics, and wavelength ranges of these instruments vary substantially. Most encompass the entire ultraviolet-visible spectrum, from 170 to 800 nm. A few instruments are equipped for vacuum operation, which extends the ultraviolet to 150 to 160 nm. This short-wavelength region is important because elements such as phosphorus, sulfur, and carbon have emission lines in this range. Instruments for emission spectroscopy are of three basic types: sequential, simultaneoliS multichannel, and Fourier transform. Fourier transform instruments have not been widely used in emission spectroscopy. Sequential instruments are usually programmed to move from the line for one element to that of a second, pausing long enough (a few seconds) at each to measure line intensities with a satisfactory signal-to-noise ratio. In contrast, multichannel instruments are designed to measure simultaneously, or nearly so, the intensities of emission lines for a large number of elements (sometimes as many as fifty or sixty). When several elements are determined, sequential instruments require significantly greater time for samples to be introduced than is required with the other two types. Thus, these instruments. although simpler, are costly in terms of sample consumption and time.
10-6 Optical diagram of a sequential ICP optical emission spectrometer. Allmoving parts are under computer control, and their modes of motion are indicated by the threedimensional arrows. Moving parts include the grating, a mirror for transducer selection, a refractor plate for optimizing signal throughput, and a viewing mirror to optimize the plasma viewing position. The spectrometer contains a mercury lamp for automatic wavelength calibration. Notice the axial viewing geometry. (Courtesy of VarianAnalyticalInstruments.) FIGURE
Both sequential and multichannel emission spectrometers are of two general types, one using a classical grating spectrometer and the other an echelle spectrometer, such as that shown in Figure 7-23. Sequential Instruments
Sequential instruments often incorporate a grating monochromator such as that shown in Figure 10-6. Usually, the grating is a holographic type having 2400 or 3600 grooves per millimeter. With some instruments of this type. scanning involves rotating the grating with a digitally controlled stepper motor so that different wavelengths are sequentially and precisely focused on the exit slit. In some designs, however_ the grating is fixed and the slit and photomultiplier tube are moved along the focal plane or curve. Instruments such as the one shown in Figure 10-6 have two sets of slits and photomultiplier tuhes, one for the ultraviolet region and one for the visible. In such instruments, at an appropriate wavelength. the exit beam is switched from one photomultiplier to the other by movement of the plane mirror located between the two transducers. Slew-Scan Spectrometers. With complex spectra made up of hundreds of lines, scanning a significant wavelength region takes too long and is thus imprac-
tical. To partially overcome this problem, slew-scan spectrometers were developed in which the grating (see Figure 10-6), or the transducer and slit, is driven by a two-speed (or multispeed) motor. In such instruments. the monochromator scans very rapidly, or slews, to a wavelength near a line of interest. The scan rate is then quickly reduced so that the instrument scans across the line in a series of small (0.01 to 0.001 nm) steps. With slew seanning, the time spent in wavelength regions containing no useful data is minimized. but sufficient time is spent at analyte lines to obtain satisfactory signal-to-noise ratios. In spectrometers, such as the one illustrated in Figure 10-6, in which the grating movement is under computer control, slewing can be accomplished very efficiently. For example. the spectrometer shown can slew to lines corresponding to fifteen elements and record their intensities in less than 5 minutes. Generally, however, these instruments are slower and consume more sample than multichannel instruments. Scanning Echelle Spectrometers. Figure 10-7 is a schematic of an echelle spectrometer that can he operated either as a scanning instrument or as a simultaneous multichannel spectrometer. Scanning is accomplished by moving a photomultiplier tuhe in both x and
y directions to scan an aperture plate located on the fo-
cal plane of the monochromator. The plate contains as many as 300 photo-etched slits. The time required to move from One slit to another is typically 1 s. The instrument can be operated in a slew-scan mode. This instrument can also be converted to a multichannel polychroma tor by mounting several small photomultiplier tubes behind appropriate slits in the aperture plate. Multichannel
Spectrometers
Simultaneous multichannel instruments are of two general typ\,s: polychromators and spectrographs. Polychroma tors contain a series of photomultiplier tubes for detection, but spectrographs use two-dimensional charge-injection devices (CIDs) or charge-coupled devices (CCDs) as transducers. Older instruments used photographic emulsions as transducers. Polychromators. In some multichannel emission spectrometers, photomultipliers are located behind fixed slits along the focal curve of a grating polychromator such as the Paschen-Runge design shown in Figure 10-8. In these instruments. the entrance slit, the exit slits, and the grating surface are located along the circumference of a Rowland circle. the curvature of which corresponds to the focal curve of the concave grating. Radiation from each of the fixed slits impinges on the photomultiplier tubes. The slits are factory configured to transmit lines for selected elements. In such instru-
ments. the pattern of lines can be changed relatively inexpensively to accommodate new elements or to delete others. The signals from the photomultiplier tubes are integrated, the output voltages are then digitized and converted to concentrations, and the results are stored and displayed. The entrance slit can be moved tangentially to the Rowland circle by means of a stepper motor. This device permits scanning through peaks and provides information for background corrections. Polychromator-based spectrometers with photomultipliers as transducers have been used both with plasma and with arc and spark sources. For rapid routine analyses, such instruments can be quite useful. For example, in the production of alloys, quantitative determinations of twenty or more elements can be completed within 5 minutes of receipt of a sample; close control over the composition of a final product is then possible. In addition to speed, photoelectric multichannel spectrometers often exhibit good analytical precision. Under ideal conditions reproducibilities of the order of 1% relative to the amount present have been demonstrated. Because other instrument components (such as the source) exhibit lower precision than the spectrometer. such high precision is not often achieved in the overall measurement process. however. Multichannel instruments of this type arc generally more expensive than the sequential instruments described in the previous section and not as versatile.
Concave diffraction grating
Mercury
FIGURE 10-9 Optical diagram of an echelle spectrometer with a charge-injection device. (From R. B. Bilhorn and M. B. Denton, Appl. Spectrosc., 1990, 44,1615. With permission.)
calibnHion lamp
cQ
A toroidal the
camera
transducer
in the liquid
transducer nitrogen
of 135 K.
mirror
surface.
focuses
elements, cryostat
the slit images
To eliminate that
the
unit
maintains
dark
onto
currents
is housed
in a
a temperature
A set of 39 transducer
elements,
dow, is used to monitor Figure image
lO-lOa. of one
window,"
Normally,
as shown
of the windows
the spectral
called
each spectral
"examination on the 9 center
FIGURE 10-8 Direct-reading ICP emission spectrometer. The polychromator is of the PaschenRunge design. It features a concave grating and produces a spectrum around a Rowland circle. Separate exit slits isolate each spectral line, and a separate photomultiplier tube converts the optical information from each channel into an electrical signal. Notice the radial viewing geometry. PMT ~ photomultiplier tube. (From J. D.lngle Jr. and S. R. Crouch, Spectrochemical Analysis, p. 241, Upper Saddle River, NJ: Prentice-Hall, 1988, with permission.)
A Charge-Injection of companies trometers
based
dimensional replaced meters
Device
offer
on echelle
array devices.
other
Instrument.
multichannel
A number
simultaneous
spectrometers
specand
two-
This type of instrument
has
types of multichannel
emission
spectro-
in many applications.
Figure spectrometer
10-9 is an optical thai
diagram
has a charge
of an echelle
injection
device
for
simultaneous prism formed The
operation."
to sort the spectral by the echelle
transducer
6.6 mm
It uses a calcium orders grating
and containing
94,672
fluoride
that are subsequently (see also Figure
is a elD (Section
7E-3)
transducer
7-21).
8.7 mm by elements.
in
by the projected
labeled
line is focused
a read win-
line as shown
FIGURE 10-10 (a) Schematic representing the surface of a CID. The short horizontal lines represent the read windows. A magnified image of one of the read windows is also shown. The nine central elements form the examination window. where a line is positioned. (b) Intensity profile for an iron line. All of the radiation from the line falls on the 3 x 3 examination Window. (From R. B. Bilhorn and M. B. Denton, Appl. Spectrose .. 1990, 44, 1540. With penmission.)
lnterface logic
FIGURE 10-12 Schematic of an array segment
showing phototransducers, storage and output registers, and readout circuitry. (From T. W. Barnard et ai., Anal. Chern., 1993,65,1231. Figure 3, p. 1232. Copyright 1993 American Chemical Society.)
FIGURE 10-11 An echelle spectrometer with segmented array of CCOs. (From T. W. Barnard et ai., Ana/. Chern., 1993,65,1231. Figure 1, p. 1232. Copyright 1993 American Chemical Society.)
elements of the window, and the 15 elements on either side of the central set provide background intensity data. Figure 1O-lOb shows the intensities recorded for the read window for the iron 297.32 nm line. Note that most of the iron radiation falls on the central elements of the window. One of the useful features of the CID, in contrast to the CCD discussed next, is that the amount of charge accumulated in an element at any instant can be monitored nondestructively; that is, no charge is lost in the measurement process. To make the measurement of line intensity as rapid and efficient as possible, only the charge accumulated in the 9 central elements of the window are read initially to determine when sufficient charge has accumulated to provide a satisfactory signalto-noise ratio. Only then are the remaining elements in the two 15-element sets read to correct the observed line intensity for the background radiation. This process goes on simultaneously at the read windows for each element. With an intense line, the time required to accumulate the desired charge is brief. With weak lines. the charge accumulated in a brief period is often used to estimate the integration time required to yield a satisfactory signal-to-noise ratio. In some cases integration times of 100 s or more are required.
Periodic wavelength calibration of the spectrometer just described is maintained through reference to the 253.65 nm mercury line from a small mercury lamp. Data files for line positions for more than 40 elements have been developed. The file for each element contains the wavelengths of up to ten lines and the x and y coordinates of each of these spectral lines with respect to the coordinates for the mercury line. Database reealibration is seldom necessary unless something perturbs the optics of the system significantly. Identification of elements in samples is done by visual inspection with the use of a video monitor and interactive markers. With an ICP excitation source, detection limits that rangc from a few tenths of a nanogram to 10 flg/mL have been reported for most elements. For nonmetals such as phosphorus and arsenic, detection limits are larger by a factor of 100. A Charge-Coupled Device Instrument, Figure 10-11 is an optical diagram of a commercial spectrometer with two echdle systems and two CCDs, one system for the 160-375-nm region and the other for the 375782-nm range." Radiation from the plasma enters the
spectrometer via a slit and is then dispersed by an echelle grating. The radiation falls on a Schmidt crossdisperser element that separates the orders of the ultraviolet radiation and also separates the ultraviolet and visible optical beams. The Schmidt element consists of a grating ruled on a spherical surface with a hole in the center to pass the visible radiation to a prism where order separation takes place as shown in Figure 7-23. The two dispersed beams are then focused onto thc surface of transducer clements as shown. Note that a schematic representation of the surface of the ultraviolet transducer is shown as an insert in Figure 10-11. These unique detector systems consist of numerous subarrays, or array segments, fabricated on silicon chips, with each subarray being custom positioned so that three to four major emission lines for each of 72 clements fall on its surface. Each array segment consists of a linear (rather than two-dimensional) CCD tha~ i~ made up of twenty to eighty pixels. Figure 10-12 is a' s~hematic of one of these array segments, which is n{ade up of the individual photo~ensitive registers, storage and output registers, and output electronics. Because each array segment can be addressed separately, charge-integration times can be varied over a wide enough range to provide dynamic ranges of 105 or greater. Although there are only 224 (235 in the current production version) of these array segments in the system, multiple lines fall on many of the subarrays so that about 6000 lines can be monitored simultaneously. In the production version of this spectrometer, one of the mirrors that guides the radiation into the optical system is under computer control so that plasma viewing may be axial. radial, or mixed. This arrangement also permits optimization of the spectrometer signal. The entire optical system is contained within a purged
temperature-controlled enclosure and is protected from the intense UV radiation of the plasma between samples by a pneumatically operated shutter to extend the life of the input mirror. In addition, a mercury lamp is built into the shutter mechanism to calibrate the spectrometer periodically. Different models of the spectrometer are available that cover the spectral range of 163-782 nm or segments thereof, depending on whether one or both arrays are installed. A Combination Instrument. An interesting and useful application of both the Paschen-Runge polychromator and modular array detectors is the spectrometer shown in the photo of Figure lO-13a. Fifteen or sixteen linear CCD array modules (eight are visible) are arranged along the circumference of the Rowland circle to provide nearly complete coverage of the range from 140 to 670 nm. Each detector module (see Figure 1O-13b) contains a mirror to reflect the radiation to the CeD array, which is arranged parallel to the plane of the Rowland circle. The modules are easily exchanged and positioned in the optical path. Because of its relalively compact design (115 em wide X 70 em deep), this spectrometer is particularly well suited to benchtop operation and routine use in industrial and environmental laboratories. Fourier Transform
Spectrometers
Since the early 1980s, several workers have described applications of Fourier transform instruments to the ultraviolet-visible region of the spectrum by using instruments that are similar in design to the infrared instruments discussed in detail in Section 16B-1." 14
A. P. Thorne, Anal. Chem., 1991, 63. 57 A; L. M. Faires, Anal. Chern., 1013A
1986,58,
~
Tllloria/: Learn more abOU1ICP spectrometers.
~3-6 .10-30
30-1000100-300
FIGURE10-14 Periodic table characterizing the detection power and number of useful emission lines of ICP by using a pneumatic nebulizer. The color and degree of shading indicate the range of detection limits for the useful lines. The area of shading indicates the number of useful lines. (Adapted from Inductively
(a)
FIGURE10-13 Components of a simultaneous CCD-ICP spectrometer: (a) Photo of the optical system. Note the Rowland circle with the grating in the rear, the slit in the front, and the detector array modules along the circle. (b) Array detector module containing a 1024-pixel linear CCD. (Courtesy of Spectro A. I. Inc., Marlborough, MA.) Much of this work has been devoted to the use of such instruments for multielement analyses with ICr sources. The advantages of Fourier transform instruments include their wide wavelength coverage (170 nm to > 1000 nm), speed, high resolution, highly accurate wavelength measurements, large dynamic range, compact size, and large optical throughput. In contrast to Fourier transform infrared instruments, however, ultraviolet-visible instruments of this type often exhibit no multiplex advantage and indeed under some circumstances show a multiplex disadvantage (see Section 71-1). The reason forthis difference is that the performance of infrared instruments is usually limited by transducer noise, whereas ultraviolet-visible spectrometers are limited by shot and flicker noise associated with the source. An ultraviolet-visible Fourier transform instrument first appeared on the market in the mid- I980s.15 The mechanical tolerances required to achieve good resolution with this type of instrument arc very demanding, however. Consequently, these spectrometers are quite expensive and arc generally used for research projects rather than for routine analytical applications.
Plasma sources produce spectra rich in characteristic emission lines, which makes them useful for both qual-
itative and quantitative elemental analysis.16 The IC? and the DC? yield significantly better quantitative analytical data than other emission sources, The quality of these results stems from their high stability, low noise, low background, and freedom from interferences when operated under appropriate experimental conditions. The performance of the IC? source is somewhat better than that of the DC? source in terms of detection limits. The DC?, however, is less expensive to purchase and operate and is entirely satisfactory for many applications. Sample Preparation
IC? emission spectroscopy is used primarily for the qualitative and quantitative analysis of samples that are dissolved or suspended in aqueous or organic liquids. The techniques for preparation of sueh solutions arc similar to those described in Section 90-1 for flame absorption methods. With plasma emission, however, it is possible to analyze solid samples directly, These procedures include incorporating electrothermal vaporization, laser and spark ablation, and glowdischarge vaporization, all of which were described in Section 8C-2. Suspensions of solids in solutions can
For useful dis..:u~si(1nsof the appli
~
-UJO
'"
Spectroscopy on a sample
is power-
the pulse),
not only
(-1 c;W em -, during and
resolved
composition.
laser beam focused
can solid samples superheated
of on
of single
to obtain
of surface
Laser-Induced
ful enough
the surface
is then focused
areas in alloys. The laser can be scanned
a surface
If th~ pulsed
ions, of the
a pair of small
above
radiation
it has been
element
sentation
up of atoms,
between
of
it is a con-
the contents
monochromator-detection
type of source,
across
is made
immediately
The resulting
amount
of whether
by a spark
located
on a 5- to
a small
In the microprobe,
arc excited
electrodes
is focused
surface,
regardless
trace
contaminants
over the period
of similar
the pre-integration
III F.le",enIJI
illustrated.
was thus chosen
of the composition the nature
times during
3% relative
II' This period
The
Dur-
to the compo-
is best determined
cess. For the sample
inhave
as a function
surface
here
in
spectroscopy
spectroscopy
the solid is vaporized
plume
of 60 s, the signals
material.
period
to be an-
The plots show
level corresponding
of the signal at various
spot
in the curves
clements
period,
relatively
bulk
50-flm
of the glow discharge.
volatilize,
of the
laser
excita-
RF modes
of brass.
monitored
of time from the initiation
sition
their
a powerful
in some commercial
is illustrated
10-19 for a sample
ing the pre-integration
Sources
When
useful
We consider
laser microprobe
Laser Microprobe
line intensities."
profiling
for seven
(RF)
materials
de and pulsed
spectroscopy.
techniques:
very
by colli-
and emit
Radio-frequency
has become
breakdown
surface,
excited
the laser
and laser-induced
of 40-
at a current
AI
:":~,~~"..""'''"::-,,~:'''':':''',,::'''':':',,.,,~.'''''''''.:''.±.'''.:~~:'',,.:::~"'''::'::'.::~:::~':'''. . ".,,=,,-,.,'''.
laser-based solid
--' 13
of each layer.'o
FIGURE 10·18
of the
I:.
in each successive
and thickness
limits on the order
typical
O-ring
spark
sputtering
!t-.........,......•...----'->"I'f''''-~__
~
__ Waler circulation
or a band contained
sigcom-
integrated
with RF excitation.
of the elements
layer of the circuit
uniform
In Figure
of an electronic
with time of a peak
indicate
constant
indicate
the sample.
profile
using GDOES
pearance -O-nng Insulator
The relatively
for all of the elements
but the plume
converted
into
can become
a highly
luminous
T. A. Ndis dOJ R. A. Payling. r;lm,,· Di.Kharge Optiml Emission. Spl'Cpp. 23- 2-1, New York: Springer. ~OO~ !~N. hkuhowskl, A. BOg:d~rt~.anti \'. Hoffmann, .·lton/i,' SpCcrW5l'OP} in F./emet/fal AIlaIJ'iIJ'. M. Culkn. ~d., p. 120, Bo·0
I
. j~ l;..c
~Iagnetic
III II:.
\
I
\
I
analyzer /
\ \
-c=- ud\: \ \
Electrostatic analyzer
\
\
~90°
"
\.-
I,
_
-\--\-Photographic plate or array transducer
11-11 Mattauch-Herzog-type double-focusing mass spectrometer. Resolution> has been achieved with instruments based on this design.
FIGURE
analyzers function is in Section 20C-3. As shown in Table 11-1, analyzers of this type find use in several types of atomic mass spectrometry. 11C
INDUCTIVELY COUPLED MASS SPECTROMETRY
PLASMA
Since the early 1980s, ICPMS has grown to be one of the most important techniques for elemental analysis because of its low detection limits for most elements, its high degree of selectivity, and its reasonably good precisi,in and accuracyII In these applications an ICP torch serves as an atomizer and ionizer. For solutions, sample introduction is accomplished by a conventional or an ultrasonic nebulizer. For solids, one of the other sample-introduction techniques discussed in Section 8C-2, such as spark or laser ablation or glow discharge, are used. Commercial versions of instruments for these various techniques have been on the For detailed descriptions of this technique. see R. A. Thomas. Pracrical Guide to iep-AtS, Vol. 33, New York: Dekker, 2003: H. E. Taylor, inductively Coupled Plasma-A/ass Spectromerry: PraClices and Techniques, San Diego. CA: Elsevier. 200t: Inductively Coupled Plasmll Muss Specrrome(n.~A. E ~Iontaser, ed. Hoboken, Nl: \\/iley-VCH. i9Y8; K. E. Jarvis. .-\_ L Grav. and R. S. Houk. Handbook of llld/.l.cti~'dy Coupled Plm;rna Ha.H 5pec~rome(ry. New York: Chapman & I £all, 1992. \l
f71.
'"
[qJ
10 5
market since 1983. In these instruments, positive metal ions, produced in a conventional ICP torch, are sampled through a differentially pumped interface linked to a mass analyzer, usually a quadrupole. The spectra produced in this way, which are remarkably simple compared with conventional ICP optical spectra, consist of a simple series of isotope peaks for each element present. These spectra are used to identify the elements present in the sample and for their quantitative determination. Usually, quantitative analyses are based on calibration curves in which the ratio of the ion count for the analyte to the count for an internal standard is plotted as a function of concentration. Analyses can also be performed by the isotope dilution technique, which is described in detail in Section 32D.
Figure 11-12 shows schematically the components of a commercial ICPMS systemI2 A critical part of the instrument is the interface that couples the ICP torch, which operates at atmospheric pressure with the mass 4 spectrometer that requires a pressure of less than 10torr. This coupling is accomplished by a differentially pumped interface coupler that consists of a sampling cone, which is a water-cooled nickel cone with a small
Simulation: Learn more about double-focusing
,2For a re\icw of available instruments.
mass analyzers.
2004. 76. 35A
see K. Cottingham.
Anl1l. Chon ..
Coolant flow Auxiliar) I Sampling tlo\', I cone
Skimmer cone
Quadrupole
I
/
Ion !enses
/ Beam-shaping optics
\
!
FIGURE11-12 Schematic of an ICPMS system: Dotted lines show introduction of gaseous samples; solid lines show introduction of liquid samples. HPLC = high-performance liquid chromatography, SFC = supercritical fluidchromatography. (From N. P. Vela, L. K. Olson, and J. A. Caruso, Anal. Chern., 1993, 65, 585A. Figure 1, p. 587A. Copyright 1993 American Chemical Society.) orifice «1.0 mm) in its center. The hot plasma gas is transmitted through this orifice into a region that is maintained at a pressure of about 1 torr by means of a mechanical pump. In this region, rapid expansion of the gas occurs, which results in its being cooled. A fraction of the gas in this region then passes through a small hole in a second cone called a skimmer and into a chamber maintained at the pressure of the mass spectrometer. Here, the positive ions are separated from electrons and molecular species by a negative voltage, are accelerated, and are focused by a magnetic ion lens onto the entrance orifice of a quadrupole mass analyzer. Performance specifications for typical commercial atomic mass spectrometers equipped with an ICP torch include a mass range of 3 to 300, the ability to resolve ions differing in m/z by I, and a dynamic range of six orders of magnitude. More than 90% of the elements in the periodic table have been determined by ICPMS. Measurement times of 10 s per element, with detection limits in the range of 0.1 to 10 ppb for most elements, are achieved. Relative standard deviations of 2% to 4% for concentrations in the middle regions of calibration curves are reported. In recent years, laser ablation has come into its own as a method of solid-sample introduction with minimal
III
Tillorial: Learn more about ICPl\tS.
preparation for ICPMS.13 In this technique, shown in Figure 11-13, a pulsed laser beam is focused onto a few square micrometers of a solid, giving power densities of as great as 10 11 W/cm 2 This high-intensity radiation rapidly vaporizes most materials, even refractory ones. A flow of argon then carries the vaporized sample into an ICP torch where atomization and ionization take place. The resulting plasma then passes into the mass spectrometer. Instruments of this type are particularly well suited for semiquantitative analysis (or quantitative analysis if the internal standard can be used) of samples that are difficult to decompose or dissolve, such as geological materials, alloys, glasses, gemstones, agricultural products, urban particulates, and soils. Figure 11-14 is a mass spectrum of a standard rock sample obtained by laser ablation-ICPMS. To obtain this spectrum, the rock was ground into a fine powder and formed into a small disk under pressure. After ablation with the laser beam. the resulting vapor was introduced into an ICP torch by injector gas flow, where ionization took place. The gaseous ions were then analyzed in a quadrupole mass spectrometer.
I'See B. Hattendorf. C. Lalkoczy. D. Gunther,Anal. Chern.,ZOO3. 75. 341A: A. y...-lontascr ct al.. in Induc1il'ely Coupled PlasmJ Mass Specrromelry. A.1\tontaser. ed_. Hoboken. NJ: Wiky-VCH. 1998, pp.194-21R
FIGURE11-13 Laser ablation sample-introduction system for mass spectrometry. The device is similar to most commercially available instruments for spatially resolved elemental analysis. CCD = charge-coupled device. (Reprinted from B. Hattendorf, C. Latkoczy, and D. Gunther, Anal. Chem., 2003,75, 341A. Figure 1, p. 342A. Copyright 2003 American Chemical Society.)
200
x
3 8
1O0
]
;
-c U
0
FIGURE11-14 Spectrum of a standard rock sample obtained by laser ablation-ICPMS. Major components (%): Na, 5.2; Mg, 0.21; AI,6.1; Si. 26.3; K, 5.3; Cu, 1.4; Ti, 0.18; Fe, 4.6. (From Inorganic Mass Spectrometry. F.Adams, R. Gijbek, and R. Van Grieken. eds., p. 297, New York:Wiley.1988. With permission.)
Although detection limits for laser ablation in ICPMS depend on a broad range of experimental variables, including instrument variables as well as sample type and quality, typical limits arc below the microgram-per-gram level: under certain experimental conditions, for certain elements such as thallium and uranium, detection limits are in the nanogramper-gram range, Standard deviations on the order of a few percent relative are typical, A major advantage of laser ablation is that the beam can be directed at various locations on the sample to provide mass spectra with spatial resolution, Accessories that permit use of most of the other ion sources listed in Table I I-I in conjunction with an ICP torch are available commercially, 11 C-2 Atomic
Mass Spectra
and Interferences
One of the advantages of using mass spectrometric detection with ICPs as opposed to optical detection is that mass spectra are usually much simpler and easier to interpret than corresponding optical spectra, This property is especially true for those elements such as the rare earths that may exhibit thousands of emission lines, Figure 11-15 illustrates this advantage for a solution containing cerium, Figure 11-15a is the optical emission spectrum of a solution containing lOO ppm cerium; the lower plot is the mass spectrum of a solution having a concentration of 10 ppm of the element The optical spectrum contains a dozen or more strong cerium lines and hundreds of weak lines for the element, all of which are superimposed on a complicated background spectrum, The optical background is made up of molecular bands from atmospheric contaminants, such as NH, OH, N" and H" and a continuum from the recombination of argon and other ions with electrons, In contrast, the mass spectrum for cerium, shown in Figure 11-15b, is simpler, consisting of two isotope peaks for !'oCe' and I
1. H. Huhbt'lJ.
/fU{'fIlalUm,J!
'
••
0'
R
in the atoms of the matter to produce scattering. When X-rays are scattered by the ordered environment in a crystal, constructive and destructive interfercnce occurs among the scattered rays because the distances between the scattering centers are of the same order of magnitude as the wavelength of the radiation. Diffraction is the result. Bragg's Law
When an X-ray beam strikes a crystal surface at some angle 8. part of the beam is scattered by the layer of atoms at the surface. The unscattered part of the beam penetrates to the second layer of atoms where again a fraction is scattered, and the remainder passes on to the third layer (Figure 12-6), and so OIl. The cumulative effeet of this scattering from the regularly spaced centers of the crystal is diffraction of the beam in much the same wav as visible radiation is diffracted by a reflection grating (Section 7C-2). The requirements for X-ray diffraction are (I) the spacing between layers of atoms must be roughly the same as the wavelength of the radiation and (2) the scattering centers must be spatially distributed in a highly regular way. In 1912, W L Bragg treated the diffraction of X-rays by crystals as shown in Figure 12-6. Here, a narrow beam of radiation strikes the crystal surface at angle 8; scattering occurs as a result of interaction of the radiation with atoms located at O. P, and R. If the distance
where n is an integer, the scattered radiation will be in phase at OeD, and the crystal will appear to rellect the X-radiation. But
erated at significantly lower power than formerly. op 'bl eyeb th This reduction- in power .IS made POSSI greater sensitivity of modern X-ray transducers,
where d is the interplanar distance of the crystal. Thus, the conditions for constructive interference of the beam at angle 0 are
Emission
sin 0
=
Metal target
nA
-..........
(anode)
2d
Tungsten filament (cathode)
Focusing
cup
Evacuated tube
Absorption, emission, fluorescence, and diffraction of X-rays are all applied in analytical chemistry, Instruments for these applications contain components that are analogous in function to the five components of instruments for optical spectroscopic measurement; these components include a source, a device for restricting the wavelength range of incident radiation, a sample holder, a radiation detector or transducer, and a signal processor and readout. These components differ considerably in detail from the corresponding optical components. Their functions, however, are the same, and the ways they combine to form instruments are often similar to those shown in Figure 7-1. As with optical instruments, both X-ray photometers and spectrophotometers are encountered, the first using filters and the second using monochromators to transmit radiation of the desired wavelength from the source, In addition, however, a third method is available for obtaining information about isolated portions of an X-ray spectrum. Here, isolation is achieved electronically with devices that discriminate among various parts of a spectrum based on the energy rather than the wavelength of the radiation, Thus, X-ray instruments are often described as wavelength-dispersive instruments or energy-dispersive instruments, depending on the method by which they resolve spectra.
Three types of sources are used in X-ray instruments: tubes, radioisotopes, and secondary fluorescence sources.
High voltage
The X-ray Tube
The most common source of X-rays for analytical work is the X-ray tube (sometimes called a Coolidge tube), which can take a variety of shapes and forms; one design is shown schematically in Figure 12-7. An X-ray source is a highly evacuated tube in which is mounted a tungsten filament cathode and a massive anode. The anode generally consists of a heavy block of copper with a metal target plated on or embedded in the surface of the copper. Target materials include such metals as tungsten, chromium, copper, molybdenum, rhodium, scandium, silver, iron, and cobalt. Separate circuits are used to heat the filament and to accelerate the electrons to the target. The heater circuit provides the means for controlling the intensity of the emitted X-rays, whereas the accelerating voltage determines their energy, or wavelength. For quantitative work, both circuits must be operated with stabilized power supplies that control the current or the voltage to 0.1 % relative, The production of X-rays by electron bombardment is a highly inefficient process, Less than I % of the electrical power is converted to radiant power, the rcmainder being dissipatcd as heat. As a result, until relatively recently, water cooling of the anodes of X-ray tubes- was required. With modern equipment, howevcr, cooling is often unnecessary because tubes can be
A varietv of radioactivc substances have been used as sourc~s in X-ray fluorescence and absorption methods (see Table 12-2). Generally, the radioisotope IS encapsulated to prevent contamination of the laboratory and shielded to absorb radiation in all but certam directions. Manv of the best radioactive sources provide simple line sp~ctra; others produce a continuum (see Table 12-2). Because of the shape of X-ray absorption curves, a given radioisotope will be suitable for excitatIOn of fluorescence or for absorption studies for a range of elements. For example, a source producing a line in the region between 0.30 and 0.47 A is suitable for fluorescence or absorption studies involving the K absorption edge for silver (see Figure 12-5), Sensitivity improves as the wavelength of the source line approache~ th~ absorption edge. Iodine-125 with a line at 0.46 A is ,deal for determining silver from thiS standpomt. Secondary Fluorescent
--_
target
Radioisotopes
Equation 12-6 is the fundamentally important Bragg equation. Note that X-rays appear to be reflected from the crystal only if the angle of incidence satisfies the condition
by
molybd~num
Sources
In some applications, the fluorescence spectrum of an element that has been excited by radiation from an X-ray tube serves as a source for absorption or fluorescence studies. This arrangement has the advantage of eliminating the continuum emitted by the primary source, For example, an X-ray tube with a tungsten target (Figure 12-1) could be used to excite the Ka and K/3 lines of molybdenum (Figure 12-2), The resultmg fluorl\scence spectrum would then be similar to the spectrum in Figure 12-2 except that the contmuum would be absent.
0.4 Wavelength,
06
A
12-8 Use of a filter to produce monochromatic radiation,
FIGURE
isolate one of the intense lines of a target element. Monochromatic radiation produced in this way is widely used in X-ray diffraction studies. Thechoice of wavelengths available by this techOlque IS limited by the relatively small number of target-filter combmations that are available. Filtering the continuum from an X-ray tube is also feasible with thin strips of metal. As with glass filters for visible radiation, relatively broad bands are transmitted with a significant attenuation of the desired wavelengths. 12B-3 X-ray Monochromators
12B-2 Filters for X-rays In many applications, it is desirable to use an X-ray beam ;ith a narrow wavelength range. As in the VISIble region, both filters and monochromators are used for this purpose. . Figure 12-8 illustrates a common techOlque for produci;g a relatively monochromatic beam by use of a lilter. ~Here. the Kf:l line and most of the continuum emitted from a molybdenum target is removed by a zirconium tiller having a thickness of about 0.01 em. The pure Ka line is then available for analytical purposes. Several other target-filter combmatlons of thIS type have been developed, each of whICh serves to
Figure 12-9 shows the essential components of an X-ray spectrometer. The monochromator consists of a pair of beam collimators, which serve the same purpose as the slits in an optical instrument, and a dISpersing element. The latter is a single crystal mounted on a goniometer, or rotatable table, that permIts vanation and precise determination of the angle 0 between the crystal face and the collimated incident beam. From Equation 12-6, it is evident that, for any given angular setting of the goniometer. only a few wavelengths are diffracted (A, A/2, A/3, ... , AIR, where A=2d sm 0). To produce a spectrum. it is necessarv that the exit beam collimator and the detector be mounted on a
Lattice Spa~ng
d,A
Cry.ial
Wavelengtb Range,' A.
A...,
A ••••
Topaz
1.356
2.67
0.24
LiF
2.014
3.97
NaCl
2.820
EDDTb ADP'
4.404 5.325
5.55 8.67
0.35 0.49
10.50
0.77 0.93
'Based on the assumption that the measurable 16Cf for Amax to 1O~ for AmiQo
Dispersion, 0/ A at
ARlO:
atARti1I
0.37
2.12 1.43
0.25
Photon Counting
1.02
0.18
0.65 0.54
0.11
In contrast to the various photoelectric detectors we have thus far considered, X-ray detectors are usually operated as photon counters. [n this mode of operation, individual pulses of charge are produced as quanta of radiation, are absorbed by the transducer, and are counted; the power of the beam is then recorded digitally as the number of counts per unit of time. Photon counting requires rapid response times for the transducer and signal processor so that the arrival of individual photons may be accurately transduced and recorded. In addition, the technique is applicable only to beams of relatively low intensity. As the beam intensiiy increases, photon pulses begin to overlap and only a steady-state current, which represents an average number of pulses per second, can be measured. If the response time of the transducer is long, pulse overlap occurs at relatively low photon intensities. As its response time becomes shorter, the transducer is more capable of detecting individual photons without pulse overlap.' For weak sources of radiation, photon counting generally provides more accurate intensity data than are obtainable by measuring average currents. The improvement can be traced to signal pulses being generally substantially larger than the pulses arising from background noise in the source, transducer, and associated electronics; separation of the signal from noise can then be achieved with a pulse-height discriminator, an electronie device that is discussed further in Section 12B-5. Photon counting is used in X-ray work because the power of available sources is often low. In addition, photon counting permits spectra to be acquired without using a monochromator. This property is considered in the section devoted to energy-dispersive systems.
0.09
range 0[28 is from
bEDDT = Ethylenediamine d-tartrate "ADP ::. Ammonium dihydrogen phosphate.
20 greater than about 160° cannot be measured because the location of the source unit prohibits positioning of the detector at such an angle (sec Figure 12-9). The minimum and maximum values for A in Table 12-3 were determined from these limitations. Table 12-3 shows that a crystal with a large lattice spacing, such as ammonium dihydrogen phosphate, has a much greater wavelength range than a crystal in which this variable is small. The advantage of large values of d is offset, however, by the resulting lower dispersion. This effect can be seen by differentiation of Equation 12-6, which leads to
FIGURE 12-9 An X-ray monochromator and detector. Note that the angle of the detector with respect to the beam (20) is twice that of the crystal face. For absorption analysis, the source is an X-ray tube and the sample is located in the beam as shown. For emission measurements, the sample becomes a source of X-ray fluorescence as shown in the insert.
second table that rotates at twice the rate of the first: that is, as the crystal rotates through an angle 0, the detector must simultaneously move through an angle 20. Clearly, the interplanar spacing d for the crystal must be known precisely (Equation 12-6). Many modern X-ray monochromators have computer-controlled motors to drive the crystal and the detector independently without a gear-based mechanical connection. These units arc capable of scanning at very rapid rates (ca. 240 Imin). Some instruments feature slew-scan operation, in which the monochromator can be slewed to the wavelength region of interest (ca. 1400 lmin) and then slowly scanned over analyte peaks. The collimators for X-ray monochromators ordinarily consist of a series of closely spaced metal plates or tubes that absorb all but the parallel beams of radiation. X-radiation longer than about 2 A is absorbed b\ constituents of the atmosphere. Therefore, provision is usually made for a continuous flow of helium through the sample compartment and monochromator when longer wavelengths are required. Alternatively. these areas can be evacuated by pumping. 0
0
The loss of intensity is high in a monochromator equipped with a flat crystal because as much as 99% of the radiation is sufficiently divergent to be absorbed in the collimators. Increased intensities, by as much as a factor o[ 10, have been achieved by using a curved crystal surface that acts not only to diffract but also to focus the divergent beam from the source on the exit collimator. As illustrated in Table 12-1, most analytically important X-ray lines lie in the region between about 0.1 and 10 A. The data in Table 12-3, however, lead to the conclusion that no single crystal satisfactorily disperses radiation over this entire range. As a result, an X-ray monochromator must be provided with at least two (and preferably more) interchangeable crystals. Thc useful wavelength range [or a crystal is determined by its lattice spacing d and the problems associated with detection of the radiation when 20 approaches zero or 180'. When a monochromator is set at angles of 20 that are much less than 10", the amount of polychromatic radiation scattered [rom the crystal surface becomes prohibitively high. Generally, values of
dO - ---~n dA 2dcosO Here, dO/dA, a measure of dispersion, is seen to be inversely proportional to d. Table 12-3 provides dispersion,Jiata for the various crystals at their maximum and minim'um wavelengths. The low dispersion of ammonium dihydrogen phosphate prohibits its use in the region of short wavelengths; here, a crystal such as topaz or lithium fluoride must be substituted. 128-4 X-ray Transducers and Signal Processors Early X-ray equipment used photographic emulsions for detection and recording of radiation. For convenience, speed, and accuracy, however, modern instruments are generally equipped with transducers that convert radiant energy into an electrical signal. Three types of transducers arc used: gas-filled transducers, scintillation counters, and semiconductor transducers. Before considering the function of each of these de~
vices, it is worthwhile to discuss photon counting, a signal-processing method that is often used with X-ray transducers as well as detectors of radiation from radioactive sources (Chapter 32). As was mentioned earlier (Section 7F-1), photon counting is also used in ultraviolet and visible spectroscopy.
Exercise: Learn more about X~ray spectrometers.
Gas-Filled Transducers
When X-radiation passes through an inert gas such as argon, xenon, or krypton, interactions occur that produce a large number of positive gaseous ions and
electrons (ion pairs) for each X-ray quantum. Three types of X-ray transducers. ionization chambers, proportional counters. and Geiger tubes, are based on the enhanced conductivity of the gas resulting from this phenomenon. A typical gas-filled transducer is shown schematically in Figure 12-10. Radiation enters the chamber through a transparent window of mica, beryllium, aluminum, or Mylar. Each photon of X-radiation that interacts with an atom of argon causes it to lose one of its outer electrons. This photoelectron has a large kinetic energy, which is equal to the difference between the X-ray photon energy and the binding energy of the electron in the argon atom. The photoelectron then loses this excess kinetic energy by ionizing several hundred additional atoms of the gas. Under the influence of an applied voltage, the mobile electrons migrate toward the central wire anode and the slower-moving cations migrate toward the cylindrical metal cathode. Figure 12-11 shows the effect of applied voltage on the number of electrons that reach the anode of a gasfilled transducer for each entering X-ray photon. The diagram indicates three characteristic voltage regions. At voltages less than VI, the accelerating force on the ion pairs is low, and the rate the positive and negative species separate is insufficient to prevent partial recombination. As a result, the number of electrons reaching the anode is smaller than the number produced initially by the incoming radiation. In the ionization chamber region between VI and V" the number of electrons reaching the anode is reasonably constant and represents the total number formed by a single photon. In the proportional counter region between V3 and V" the number of electrons increases rapidly with applied voltage. This increase is the result of secondary ion-pair production caused by collisions between the accelerated electrons and gas molecules; amplification
The conduction of electricity through a chamber operated in the Geiger region, as well as in the proportional region. is not continuous because the space charge mentioned earlier terminates the flow of electrons to the anode. The net effect is a momentary pulse of current followed by an interval during which the tube does not conduct. Before conduction can again occur, this space charge must be dissipated by migration of the cations to the walls of the chamber. During the dead time, when the tube is nonconducting, response to radiation is impossible; the dead time thus represents a lower limit in the response time of the tube. Typically, the dead time of a Geiger tube is in the range from 50 to 200 I's. Geiger tubes are usually filled with argon; a low concentration of an organic quenching gas, often alcohol or methane, is also present to minimize the production of secondary electrons when the cations strike the chamber wall. The lifetime of a tube is limited to some 108 to 109 counts, when the quencher becomes depleted. With a Geiger tube, radiation intensity is determined by counting the pulses of current. The device is applicable to all types of nuclear and X-radiation. However, it lacks the large counting range of other detectors because of its relatively long dead time; this factor limits its use in X-ray spectrometers. Although quantitative applications of Geiger tube transducers have decreased, transducers of this type are still frequently used in portable instruments.
I I I
I : V5 I I I I I
I
I
-+---l----
:
Proportional co U nte r region
I
I I
V, ~
V,
Ioniza~ion 1 V,
chamber region
FIGURE 12-11 Gas amplification for various types of gas-filled detectors.
(gas amplification) of the ion current occurs under these conditions. In the Geiger range Vs to V6, amplification of the electrical pulse is enormous but is limited by the positive space charge created as the faster-moving electrons migrate away from the slower positive ions. Because of this effect, the number of electrons reaching the anode is independent of the type and energy of incoming radiation and is governed instead by the geometry and gas pressure of the tube. Figure 12-11 also illustrates that a larger number of electrons is produced by the more energetic 0.6 A radiation than the longer-wavelength 5 A X-rays. Thus, the size of the pulse (the pulse height) is greater for high-frequency X-rays than for low-frequency X-rays.
Proportional
The Geiger Tube
+ -1 k\' FIGURE
12-10 Cross section of a gas-filled detector.
Counters
The yroportional counter is a gas-filled transducer that is opet-ated in the V3 to V, voltage region in Figure 12-11. In this region, the pulse produced by a photon is amplified by a factor of 500 to 10,000, but tbe number of positive ions produced is small enough so that the dead time is only about II'S. In general, the pulses from a proportional counter tube must be amplified before being counted. The number of electrons per pulse, which is proportional to the puL>eheight, produced in the proportional region depends directly on the energy, and thus the frequency, of the incoming radiation. A proportional counter can be made sensitive to a restricted range of X-ray frequencies with a pulse-height analyzer, which counts a pulse only if its amplitude falls within selectable limits. A pulse-height analyzer in effect permits electronic sorting of radiation; its function is analogous to that of a monochromator.
The Geiger tube is a gas-filled transducer operated in the voltage region between V, and V6 in Figure 12-11; in this region, gas amplification is greater than 10"Each photon produces an avalanche of electrons and cations; the resulting currents are thus large and relatively easy to detect and measure.
_4 •••
j.
Proportional counters have been widely used as detectors in X-ray spectrometers. Ionization
Chambers
Ionization chambers are operated in the voltage range from V, to V, in Figure 12-11. In this region, the currents are small (lO-lJ to 10-16 A typically) and relatively independent of applied voltage. Ionization chambers are not useful for X-ray spectrometry because of their lack of sensitivity. They are, however, applied in radiochemical measurements, which are discussed in Chapter 32. Scintillation
Counters
The luminescence produced when radiation strikes a phosphor is one of the oldest methods of detecting radioactivity and X-rays, and it is still used widely for certain types of measurements. In its earliest application, the technique involved the manual counting of flashes that resulted when individual photons or radiochemical particles struck a zinc sulfide screen. The tedium of counting individual flashes by eye led Geiger to develop gas-filled transducers, which were not only more convenient and reliable but more responsive to radiation. The advent of the photomultiplier tube (Section 7E-2) and better phosphors, however, has given new life to the technique, and scintillation counting has again become one of the important methods for radiation detection. The most widely used modern scintillation detector consists of a transparent crystal of sodium iodide that has been activated by the introduction of 0.2 % thallium iodide. Often, the crystal is shaped as a cylinder that is 3 to 4 in. in each dimension; one of the plane surfaces then faces the cathode of a photomultiplier tube. As the incoming radiation passes through the crystal, its energy is first lost to the scintillator; this energy is subsequently released in the form of photons of fluorescence radiation. Several thousand photons with a wavelength of about 400 nm are produced by each primary particle or photon over a period of about 0.25 I'S, which is the dead time. The dead time of a scintillation counter is thus significantly smaller than the dead time of a gas-filled detector. The flashes of light produced in the scintillator crystal are transmitted to the photocathode of a photomultiplier tube and are in turn converted to electrical pulses that can be amplified and counted. An important characteristic of scintillators is that the number of photons produced in each flash is proportional to
r----~-----------I I I
AI contact
I
I I I I I I Preamplifier
I
~-:I
FIGURE 12-12 Vertical cross section of a lithium-drifted silicon detector for X-rays and radiation from radioactive sources.
the energy of the incoming radiation. Thus, incorporation of a pulse-height analyzer to monitor the output of a scintillation counter forms thc basis of energydispersive photometers, to be discussed later. In addition to sodium iodide crystals, a number of organic scintillators such as stilbene, anthracene, and terphenyl have been used. In crystalline form, these compounds have decay times of 0.01 and 0.1 fls. Organic liquid scintilla tors have also been developed and are used to advantage because they exhibit less selfabsorption of radiation than do solids. An example of a liquid scintillator is a solution ofp-terphenyl in toluene. Semiconductor
Transducers
Semiconductor transducers have assumed major importance as detectors of X-radiation. These devices are sometimes called lithium-drifted silicon detectors, Si(Li), or lithium-drifted germanium detectors, Ge(Li). Figure 12-12 illustrates one form of a lithium-drifted detector, which is fashioned from a wafer of crystalline silicon. There are three layers in the crystal: a p-type semiconducting layer that faces the X-ray source, a central intrinsic zone, and an n-type layer. The outer surface of the p-type layer is coated with a thin layer of gold for electrical contact; often, it is also covered with a thin beryllium window that is transparent to X-rays. The signal output is taken from an aluminum layer that coats the n-type silicon: this output is fed into a preamplifier with a gain of about 10. The preamplifier is frequently a field-effect transistor that is fabricated as an integral part of the detector.
Li-drifted
5i
n-type
Liquid
N,
cryostat (77 K)
Si
(intrinsic layer)
A lithium-drifted detector is formed by vapordepositing lithium on the surface of a p-doped silicon crystal. When the crystal is heated to 400°C to 500°C, the lithium diffuses into the crystal. Because lithium easily loses electrons, its presence converts the p-type region to an n-type region. While still at an elevated temperature, a dc voltage applied across the crystal causes withdrawal of the electrons from the lithium layer and holes from the p-type layer. Current across the pn junction causes migration, or drifting, of lithium ions into the player and formation of the intrinsic layer, where the lithium ions replace the holes lost by conduction. When the crystal cools, this central layer has a high resistance relative to the other layers because the lithium ions in this medium are less mobile than the holes they displaced. The intrinsic layer of a silicon detector functions in a way that is analogous to argon in the gas-filled transducer. Initially, absorption of a photon results in formation of a highly energetic photoelectron, which then loses its kinetic energy by elevating several thousand electrons in the silicon to the conduction band; a marked increase in conductivity results. When a voltage is applied across the crystal, a current pulse accompanies the absorption of each photon. As in proportional detectors, the size of the pulse is directly proportional to the energy of the absorbed photons. Unlike proportional detectors, however. secondary amplification of the pulsc does not occur. As shown in Figure 12-12, the detector and preamplifier of a lithium-drifted detector must be thermo-
statted at the temperature of liquid nitrogen (77 K) to decrease electronic noise to a tolerable level. The original Si(Li) detectors had to be cooled at all times because at room temperature the lithium atoms would diffuse throughout the silicon, thereby degrading the performance of the detector. Modern Si(Li) detectors need to be cooled only during use. Germanium is used in place of silicon to give Iithiumdrifted detectors particularly useful for dctection of radiation shorter in wavelength than 0.3 A. These detectors must be cooled at all times. Germanium detectors that do not require lithium drifting havc been produced from very pure germanium. These detectors, called intrinsic germanium detectors, need to be cooled only during use. Distribution
of Pulse-Heights
from X-ray Transducers
To understand the properties of energy-dispersive spectrometers, it is important to appreciate that the size of current pulses resulting from absorption of successive X-ray photons of identical energy by the transducer will not be exactly the same. Variations resulting from the ejection of photoelectrons and their subsequent generation of conduction electrons are random processes governed by the laws of probability. Thus, there is a Gaussian distribution of pulse heights around a mean value. The width of this distribution varies from one type of transducer to another, with semiconductor detectors providing significantly nar· rower bands of pulses. It is this property that has made lithium-drifted detectors so important for energydispersive X-ray spectroscopy. 12B-5 Signal Processors The signal from the preamplifier of an X-ray spectrometer is the input to a linear fast-response amplifier whose gain can be varied by a factor up to 10,000. Voltage pulses as large as 10 V result. Pulse-Height
Selectors
Most modern X-ray spectrometers (wavelength dispersive as well as energy dispersive) are equipped with discriminators that reject pulses of less than about O.S V (after amplification). In this wav. transducer and amplifier noise is reduced significantly. Some instruments have pulse-height selectors. or ",indo", discriminators, which are electronic circuits that reject not only pulses ~
Exercise: Learn more about X-ra)' transducers.
with heights below some predetermined minimum level but also those above a preset maximum level; that is. they remove all pulses except those that lie within a limited channel or window of pulse heights.' Dispersive instruments are often equipped with pulse-height selectors to reject noise and to supplement the monochromator in separating the analyte line from higher-order, more energetic radiation that is diffracted at the same crystal setting. Pulse-Height
Analyzers
Pulse-height analyzers consist of one or more pulseheight selectors configured in such a way as to provide energy spectra. A single-channel analyzer typically has a voltage range of about 10 V or more with a window of 0.1 to 0.5 V The window can be manually or automatically adjusted to scan the entire voltage range, thus providing data for an energy-dispersive spectrum. Multichannel analyzers typically contain up to a few thousand separate channels, each of which acts as a single channel that corresponds to a different voltage window. The signal from each channel is then accumulated in a memory location of the analyzer corresponding to the energy of the channel, thus permitting simultaneous counting and recording of an entire spectrum. Scalers and Counters
To obtain convenient counting rates, the output from an X-ray transducer is sometimes scaled - that is, the number of pulses is reduced by dividing by some mul· tiple of ten or two, depending on whether the circuit is a decade or a binary device. A brief description of electronic scalers is found in Section4C-4. Counting of the scaled pulses is carried out with electronic counters such as those described in Sections 4C-2 and 4C-3.
Although it is feasible to excite an X-ray emission spectrum by incorporating the sample into the target area of an X-ray tube, this approach is extremely inconvenient for many types of materials. Instead, excitation is usually accomplished by irradiating the sample wilh a beam of X-rays from an X-ray tube or a radioactive source. In this method, the elements in the sample arc excited by absorption of the primary beam and emit their own characteristic fluorescence X-rays.
This procedure is thus properly called an X-ray fluorescence, Or X-ray emission method. X-ray fluorescence (XRF) is a powerful tool for rapid, quantitative determinations of all but the lightest elements. In addition, XRF is used for the qualitative identification of elements having atomic numbers greater that of oxvgen (>8) and is often used for ;emiquantitative ;r quantitative elemental analyses.' A particular advantage of XRF is that it is nondestructive, in contrast to most other elemental analysis techniques.
Various combinations of thc instrument components discussed in the previous section lead to two primary types of spectrometers: wavelength-dispersive X-ray fluorescence (WDXRF) and energy-dispersive X-ray fluorescence (EDXRF) instrumentslO Wavelength-Dispersive
Instruments
Wavelength-dispersive instruments always contain tube sources because of the large energy losses that occur when an X-ray beam is collimated and dispersed into its component wavelengths. Radioactive sources produce X-ray photons at a rate less than 10-4 that of an X-ray tube; the added attenuation by a monochromator would produce a beam that was difficult or impossible to detect and measure accurately. Wavelength-dispersive instruments are of two types, single channel (or sequential) and multichannel (or simultaneous). The spectrometer shown in Figure 12-9 is a sequential instrument that can be easily used for Xray fluorescence analysis. In this type of instrument, the X-ray tube and sample are arranged as shown in the circular insert at the top of the figure. Single-channel instruments may be manual or automatic. Manual instruments are quite satisfactory for the quantitative determination of a few elements. In this application, the crystal and transducer are set at the proper angles (0 and 20) and counting progresses until sufficient counts have accumulated for precise results. Automatic instruments are much more convenient for qualitative analysis. where an entire spectrum must be scanned. In such a device, the motions of the crystal and detector are synchronized and the detector output is connected to the data-acquisition system. ~See R. Jenkins, X-Ray i'Juorescence Spectrometry, Wiley.
2nd ed., New York'
1999
Most modern single-Channel spectrometers are provided with two X-ray sources; typically. one has a chromium target for long wavelengths and the other a tungsten target for short wavelengths. For A> 2 A. it is necessary to remove air between the source and detector by pumping or by displacement with a continuous flow of helium. In this type of instrument, dispersing crystals must also be easily interchangeahle. Singlechannel instruments cost more than $50,000. Multichannel dispersive instruments are large, expensive (>$150,000) installations that permit the simultaneous detection and determination of as many as twenty-four elements. In these instruments, individual channels consisting of an appropriate crystal and a detector are arranged radially around an X-ray source and sample holder. The crystals for all or most of the channels are usually fixed at an appropriate angle for a given analyte line; in some instruments, one or more of the crystals can be moved to permit a spectral scan. Each transducer in a multichannel instrument has its own amplifier, pulse-height selector, scaler, and counter or integrator. These instruments are equipped with a computer for instrument control, data processing, and display of analytical results. A determination of twenty or more elements can he completed in a few seconds to a few minutes. Multichannel instruments are widely used for the determination of several components in industrial materials such as steel, other alloys, cement, ores, and petroleum products. Both multichannel and singlechannel instruments arc equipped to handle samples in the form of metals, powdered solids, evaporated films, pure liquids, or solutions. When necessary, the materials are placed in a cell with a Mylar or cellophane window. Energy-Dispersive
Electronics X-ray detector Alpha detector Collimator Alpha sourCe Door Contact
ring
APXS Front View x_raYdeteClor Alpha detector . ..
with collimator .
•
..
Alpha source Contact
ring
FIGURE 12-13 Energy-dispersive X-ray fluorescence spectrometer. Excitation by X-rays from (a)an X-ray tube and (b) a radioactive substance (curium-244, a 5.81 MeValpha particle and X-raysource) as shown in the sensor head for the Mars alpha proton X-ray spectrometer. The X-ray detector is a new room-temperature type. (Reprinted with permission from R. Gellert et aI., J. Geophys. Res., 2006, 111, E02S05.)
diffractor, as well as the closeness of the detector to the sample, result in a 100-fold or more increase in energy reaching the detector. These features permit the use of weaker sources such as radioactive materials or low-power X-ray tubes, which arc cheaper and less likely to cause radiation damage to the sample. Generally, energy-dispersive instruments cost about one fourth to one fifth the price of wavelength-dispersive systems. Figure 12-13b shows the sensor head from the Mars rover missions of 2004. The head contains a curium244 source that emits X-rays and 5.81 MeV alpha particles. The X-rays cause fluorescence in Martian rock samples, and the alpha particles stimulate X-ray emission as well. X-ray emission stimulated by bombardment by alpha and other subatomic particles such as protons is called particle induced X-ray emission, or PIXE. The X-ray detector is a new room-temperature type, which in the low temperature of the Martian night (below -40'C) exhibits low noise and high signal-to-noise ratio for excellent resolution and sensitivity. Note the concentric design of the sensor head with six Cm-244 sources arranged around the central detector. The X-ray spectrum of Figure 12-14 was acquired with the sensor head. In a multichannel, energy-dispersive instrument. all of the emitted X-ray lines are measured simultane-
Instruments
As shown in Figure 12-13a, an EDXRF spectrometer consists of a polychromatic source - which may be either an X-ray tuhe or a radioactive materiala sample holder, a semiconductor detector, and the various electronic components required for energy discrimination. 11 An obvious advantage of energy-dispersive systems is the simplicity and lack of moving parts in the excitation and detection components of the spectrometer. Furthermore, the ahsence of collimators and a crystal
lOFor a review of recent X-ray fluorescence instruments. see P. J. Potts. A T. Ellisb. P. Kregsamerc. C Strelic, C. Vanhoofd, M. ""este. and P. Wobrauschekc, 1. Anal. Atomic Spectrometry. 2005, 20, 1124
~
....
... P)
ously. Increased sensitivity and improved signal-tonoise ratio result from the Fellgett advantage (see Section 71-1). The principal disadvantage of energydispersive systems, when compared with crystal spectrometers, is their lower resolutions at wavelengths longer than about 1 A. On the other hand, at shorter wavelengths, energy-dispersive systems exhibit superior resolution. Figure 12-15a is a photo of a basic, commercial, henchtop EDXRF instrument that is used for the routine determination of a broad range of elements from sodium to uranium in samples from many industrial processes. The diagram of Figure 12-15b shows a closeup of the bottom of the sample turntable, which is visible from the top in the photo of Figure 12-15a, and the optical layout of the instrument. Radiation from the X-ray tube passes through an appropriate filter hefore striking the boltom of the rotating sample. The X-ray fluorescence emitted by the sample passes to the silicon detector, which provides the signal for the multichannel counting system. The system is equipped with a rhodium anode X-ray tube, five programmable filters, a helium purge system, a twelve-position sample changer, and a spinner to rotate each sample during the dataacquisition process. Spinning the sample reduces errors due to sample heterogeneity. We describe a quantitative application of this instrument in Section 12C-3.
AI
i
Sol 357 Wish stone RAT2 --data --fl(
1.00
--
all components of theoretical model
-g
~ ~ c.. §
0.10
8
I
X-ray
tube (b)
0.01
0.00 0
Zn KI3
8" Energy, keY
Cn Ka Zn Ka
" 20 o
FIGURE 12-14 X-ray spectrum obtained on Mars together with the deconvolution model components. The main elemental characteristic peaks (Ka lines) are labeled and Kf3lines are unlabeled. (Reprinted with permission from R. Gellert et aI., J. Geophys. Res., 2006,
NiKa
;;
I
I
I
"5 i5
Figure 12-16 is a spectrum obtained with an energydispersive instrument. With such equipment, the abscissa is generally calibrated in channel number or energy in ke V. Each dot represents the number of counts accumulated in one of the several hundred channels. Qualitative information, such as that shown in Figures 12-16, can be converted to semiquantitative data by careful measurement of peak heights. To obtain a rough estimate of concentration, the following relationship is used:
where P, is the relative line intensity measured in terms of number of counts for a fixed period, and W, is the weight fraction of the desired element in Ihe sample. The factor P, is the relative intensity of the line that would be observed under identical counting conditions if W, were unity. The value of P, is determined with a sample of the pure element or a standard sample of known composition. The use of Equation 12-7, as outlined in the previous paragraph, carries with it the assumption that the
<Xl
0.14
.S
0.12
,.,
0.10
'§
~ 0.08 c
.5
0.06
111, E02S05.)
12C-2 Qualitative and Semiquantitative Analysis
0.16
~ ~
~ ~ 0.04 ,:§ emission from the species of interest is unaffected by the presence of other elements in the sample. We shall see that this assumption may not be justified. As a result, concentration estimates may be in error by a factor of 2 or more. On the other hand, this uncertainty is significantly smaller than that associated with a semiquantitative analysis by optical emission where orderof-magnitude errors are not uncommon.
Modern X-ray fluorescence instruments are capable of producing quantitative analyses of complex materials with precision greater than or equal to that of the classical wet chemical methods or other instrumental methods. I' For the accuracy of such analyses to approach this level, however, requires either the availability of calibration standards that closely approach the samples in ovcrall chemical and physical composition or suitable methods for dealing with matrix effects. i.'See R E. Van Griek~n and A. A. Markov.icz, cds., Handbook of X-ray Spectrometry. 2nd ed" New '{\lrk: 1I.'larcel Dekker. 2002: R. Jenkins, R. W. Gould. and D Gedcke. Quantitative X-Ray SpeCTrometry, 2nd ed., New York:
Maret'!
Dekka.
1995.
o
0.02
5.2 5.6 6.0 6.4 6.8 7.2 7.6 8.0 8.4 8.8 9.2 9.6 Energy, keV (c)
0
15
30
45
60
75
Concentration,
90
105 120 135 150
Fe ppm
(d)
(a) MiniPal4 benchtop X-ray fluorescence spectrometer showing removable turntable for up to twelve samples. (b) Diagram showing the X-ray source, filter wheel, detector, and sample turntable from the bottom. (c)X-ray fluorescence spectrum of a rice sample. The shaded areas under the curves are proportional to the amount of each element in the sample. (d) Calibration curve obtained from nine rice samples. Integrated areas from spectra similar to the one in (c) are plotted against the certified concentrations of iron in the samples. (Reprinted with permission from V.Sethi, M. Mizuhira,and Y.Xiao, G./.T. Laboratory Journal, 2005.6,22 Copyright 2005 by GITVerlag GmbH & Co.; photo courtesy of PANalyticalB.V.) FIGURE 12-15
Matrix Effects
It is important to realize that the X-rays produced in the fluorescence process are generated not only from atoms at the surface of a sample but also from atoms well below the surface. Thus, a part of both the incident radiation and the resulting fluorescence traverse a significant thickness of sample within which absorption and scattering can occur. The extent either beam is attenuated depends on the mass absorption coefficient of the medium, which in lurn is determined by the absorption coefficients of all of the clements in the sample. There-
fore, although the net intensity of a line reaching the detector in an X-ray fluorescence measurement depends on the concentration of the element producing the line, the concentration and mass absorption coefficients of the matrix elements affect it as well. Absorption effects by the matrix may cause results calculated by Equation 12-7 to be either high or low.lf, for example, the matrix contains a significant amount of an element that absorbs either the incident or the emitted beam more strongly than the element being determined, then W, will be low, because P; was evaluated
4.95 V (Kal
4.66
Cr (Ka)
Si IKa)
590 Mn
2.02 p
IKal
iKa) + Cr (K~I
4.03
2'3S1'12, Rh.70 ••
(Ka)
• •
Ie
• •
.'.
Diffraction peak (anode) ,.\ ;.
3.48
;0.
~
~n/ ~.!:./~.'
: ~::V\ •:~-.t::.:
l
6.40
Fe
(KaJ
5.41
Fe escape
1.74
nitrogen: starch: lithium carbonate: alumina: and boric acid ;r borate glass. By adding a diluent in excess, matrix effects become essentially constant for the diluted standards and samples, and adequate compensation is achieved. This procedure has proved particularly useful for mineral analyses, where both samples and standards are dissolved in molten borax; after cooling, the fused mass is excited in the usual way.
I
•
;'
748 N
:
(~a)
,
iV
~::',
•
• • '
1
..
805 Cu (Ka)
••~. Excitation Tube
anode:
conditions Rh
Filter:
Anode
voltage:
10 kV
Anode
current:
50 A
None
FIGURE 12-16 Spectrum of an iron sample obtained with an energy-dispersive instrument with a Rh anode X-raytube source. The numbers above the peaks are energies in keV. (Reprinted with permission from J. A. Cooper, Amer. Lab., 1976,8 (11), 44. Copyright 1976 by International Scientific Communications, Inc.) with a standard in which absorption was smaller. On the other hand, if the matrix elements of the sample absorb less than those in the standard, high values for Wx result. A second matrix effect, called the enhancement effect, can also yield results that are greater than expected. This behavior occurs when the sample contains an element whose characteristic emission spectrum is excited by the incident beam, and this spectrum in turn causes a secondary excitation of the analytical line. Several techniques have been developed to compensate for absorption and enhancement effects in X-ray fluorescence analyses.
to convert emission data to concentrations. The degree of compensation achieved in this way depends on the closeness of the match between samples and standards. Use of Internal Standards In this procedure, an element is introduced in known and fixed concentration into both the calibration standards and the samples; the added element must be absent in the original sample. The ratio of the intensities between the element being determined and the internal standard is the analytical variable. The assumption here is that absorption and enhancement effects are the same for the two lines and that use of intensity ratios compensates for these effects.
External Standard Calibration The relationship between the analytical line intensity and the concentration must be determined empirically with a set of standards that closely approximate the samples in overall composition. We then assume that absorption and enhancement effects arc identical for samples and standards, and the empirical data are used
Dilution of Samples and Standards Both sample and standards are diluted with a substance that absorbs X-rays only weakly, that is, a substance containing elements with low atomic numbers. Examples of such diluents include water; organic solvents only containing carbon, hydrogen, oxygen, and
Methods and Data Analysis for Multiple Elements When it is possible to establish that total sample X-ray absorption does not vary appreciably over an expected range of analyte concentrations and when enhancement cffects are absent, we generally find a linear relationship between XRF line intensity and element concentration13 When such conditions occur, it is often possible to use type standardization techniques. In these techniques, standards are prepared and characterized or, morc often, purchased from the National Institute of Standards and Technology (NIST) or other sources. These standards are then used to calibrate spectrometers and establish the working curves for analysis. Hundreds of such standards are available for matching samples with particular types of standards. When the nature and composition of the sample is not well known, it is necessary to use influence correction methods, of which there are three primary types: fundamental, derived, and regression. In the fundamental approach, the intensity of fluorescence can be calculated for each element in a standard sample from variables such as the source spectrum, the fundamental e.>juations for absorption and fluorescence, matrix effects: the crystal reflectivity (in a WDXRF instrumene), instrument aperture, the detector efficiency, and so forth. The XRF spectrum of the standard is measured, and in an iterative process the instrument variables are refined and combined with the fundamcntal variables to obtain a calibration function for the analysis. Then the spectrum for an unknown sam pic is measured, and the iterative process is repeated using initial estimates of the concentrations of the analytes. Iteration continues until the calculated spectrum matches the unknown spectrum according to appropriate statistical criteria. This method gives good results with accuracies on the order of 1%~ 4 % but is generally considered to be less accurate than derived
or regression methods." So-called swndardless analysis is accomplished using variations on fundamental calibration methods. Instruments are carefully characterized, and instrument and fundamental parameters are stored in the computer. Spectra are then calculated and matched with samples by iterative methods to estimate concentrations of analytes. Derived methods simplify calculations of the fundamental method by lumping detailed fundamental calculations into generalized parameters to account for instrument functions, but the calculation of fluorescence intensities from analyte concentration is the same as in fundamental methods. Derived methods often show some improvement in accuracy and precision over fundamental methods. Regression methods rely on models of the form Wi = Bi
+
KJ,[
I
+
tl
m,jWij]
where Bi is the background, K, is a sensitivity coefficient, Ii is the intensity due to clement i, mij is the binary influence coefficient that describes the matrix effect of element j on analyte i, and w,j is the average composition of the sample in i and j. To calibrate an instrument, spectra are acquired for standards and regression analysis is performed to determine Ki, Bi, and mij for each binary combination of elements in the standards. These parameters are then used in a regression analysis of spectral data from unknown samples to determine the unknown concentrations W;. A broad range of models and algorithms for regression analysis in XRF are available, and many commercial instruments use combinations and variations on tbese algorithms in their software suites." Accuracies and precisions attained using these methods are typically 1% or better under optimal conditions. Regression methods were used to analyze the data of Figure 12-14 from the Mars rover to determine by EDXRF the concentrations of many elements in rocks and soil. In the early days of XRF, influence correction methods were difficult and time-consuming because sufficient computational power to accomplish them was available only on large. expensive mainframe computers. With the advent of powerful. low-cost, dedicated computers. sophisticated data analysis is now
141 L de Vrks and B. A. R. Vrebo,>. in R. E. Van Grieken and A. A. !\.-larkowicz, cds., Handbook of X·ral Specrromctn'. 2nd ed .. New York Marcel Dekker. 2002. p. 37H. ;\Ibid .. pp ..141- ..WS
routine, and all commercial instruments have mature software suites for instrument operation, calibration, data reduction, and analysis.
With proper correction for matrix effects, X-ray fluorescence spectrometry is one of the most powerful tools available for the rapid quantitative determination of all but the lightest elements in complex samples. For example, Rose, Bornhorst, and Sivonen 16 have demonstrated that twenty-two elements can be determined in powdered rock samples. with a commercial EDXRF spectrometer in about 2 hours (I hour instrument time), including grinding and pellet preparation. Relative standard deviations for the method are better than I % for major elements and better than 5% for trace elements. Accuracy and detection limits as determined by comparison to results from international standard rock samples were comparable or better than other published procedures. For an excellent overview of XRF analysis of geological materials, see the paper by Anzelmo and Lindsay. 17 X-ray methods arc also applied widely for quality control in the manufacture of metals and alloys, Because of the speed of the analysis in these applications, it is possible to correct the composition of the alloy during its manufacture. X-ray fluorescence methods are easily adapted to liquid samples. Thus, as mentioned earlier, methods have been devised for the direct quantitative determination of lead and bromine in aviation fuel samples. Similarly, calcium, barium, and zinc have been determined in lubricating oils by exciting fluorescence in the liquid hydrocarbon samplcs. The method is also convenient for the direct determination of pigments in paint samples. X-ray fluorescence methods are being widely applied to the analysis of atmospheric pollutants. For example, one procedure for detecting and determining contaminants involves drawing an air sample through a stack consisting of a micropore filter for particulates and three filter paper disks impregnated with orthotoIidine, silver nitrate, and sodium hydroxide, respectively. The reagents retain chlorine. sulfides, and sulfur dioxide in that order. The filters containing trapped
analytes then serve as samples for X-ray fluorescence analysis. As an example of the routine application of EDXRF for determining the elemental composition of foodstuffs, consider the data plots of Figure 12-15c and 12-15d.18 In this analysis, iron, copper, and zinc were determined in rice using the spectrometer shown in Figure 12-15a. The spectrometer was calibrated using nine standard samples of rice. The standards were ground into fine powders, pressed into pellets, and loaded into the sample turntable. Each sample was irradiated with X-rays (Rh anode) through an aluminum filter for 5 minutes, and data were acquired to produce spectra such as the one shown in Figure 12-15c. The instrument computer then analyzed the data and calculated the areas under the various peaks in the spectrum as shown by the shaded areas in the figure, and calibration curves similar to Figure 12-15d were produced for each of the analytes. Determination of the analytes in another well-characterized' sample yielded concentrations of 73.49 ppm, 7.46 ppm, and 38.95 ppm for iron, copper, and zinc, respectively. Relative accuracies for the three elements were 0.9% (Fe), 5% (Cu), and 0.3% (Zn) as determined by comparison with values determined by optical spectroscopic methods. . Another indication of the versatility of X-ray fluorescence is its use for the quantitative determination of elements heavier than sodium in rocks and soil encountered near the landing site of the Mars Pathfinder mission.19 The Pathfinder's microrobot Sojourner was equipped with a sensor head that could be placed flat against a material to be analyzed. The head contained curium-244, which emitted a particles and X-rays that bombarded the sample surface as in Figure 12-l3b. The X-ray emission from the sample struck the transducer of an energy-dispersive spectrometer in which the radiant power was recorded as a function of energy, was transmitted from Mars to Earth, and ultimately was analyzed on Earth. Lighter clements were determined by backscattering or proton emission. With these three methods of detection, all of the elements in the periodic table but hydrogen can be determined at concentration levels of a few tenths of a percent. In 2004 two new rovers, Spirit and Opportunity, landed on Mars with X-ray fluorescence spectrometers aboard.") As we write this, the rovers have
lilW. I. Rose, T. 1. Bornhorst, and S. 1. Sivon.:n. t-m.\' Spearometrv. 1986, 15, :55 J. E. Anzelmo and J. R Lindsay,J. Chern. Educ .. 1987.6.J. A181 and A200.
V. Sethi, M. t\'lizuhira. and Y. Xiao, G.I. T. Ll.J.buratory Journal, 2005, 6. 22. IQ"Mars Pathfinder," 1997. http://mars.jpl.nasa.govIMPF' (25 July 1997). ""'Spirit and Opportunity," 200...J, hltpJ/mpf\\.ww.jpl.nasa.gu\'/missions present /2003.html (13 Oct 2(05)
Some Quantitative
Applications
of X-ray Fluorescence
I~
1-
I
spent nearly 2 years moving about their respective landing sites, and the spectrometers continue to send data to Earth revealing the elemental composition of Mars rocks and soil. The spectrum shown in Figure 12-14 was transmitted from one of the rovers to a ground station where the data were analyzed using a regression algorithm, and concentrations of the various elements in the sample were extracted from the data. Details of the intricate calibration procedure appear in the paper by Gellert et al.21 Advantages
and Disadvantages
of X-ray Fluorescence
Methods
X-ray fluorescence offers a number of impressive advantages. The spectra are relatively simple, so spectralline interference is minimal. Generally, the X-ray method is nondestructive and can be used for the analysis of paintings, archaeological specimens, jewelry, coins, and other valuable objects without harm to the sample. Furthermore, analyses can be performed on samples ranging from a barely visible speck to a massive object. Other advantages include the speed and convenience of the procedure, which permit multielement analyses to be completed in a few minutes. Finally, the accuracy and precision of X-ray fluorescence methods often equal or exceed those of other methods.22 X-ray fluorescence methods are generally not as sensitive as the optical methods discussed earlier. In the most favorable cases, concentrations of a few parts per million or less can be measured. More often, however, the concentration range of the method is from about 0.01% to 100%. X-ray fluorescence methods for the lighter elements arc inconvenient; difficulties in detJ:ction and measurement become progressively worse as atomic numbers become smaller than 23 (vanadium), in part because a competing process, called Auger emission (see Section 2IC-2), reduces the fluorescence intensity (see Figure 21-7). Today's commercial instruments have a lower atomic number limit of 5 (boron) or 6 (carbon). Another disadvantage of the X-ray emission procedure is the high cost of instruments, which ranges from less than $10,000 for an 21 R. (,e1krt, R. Rieder, 1. BrUckner, B. C. Clark, G. Dreibu$, G. KlingclhOfer, G. Lugmair, D. W. Ming, H. Wanke, A. Yen, J. Zipfel, and S. W Squyres. 1. Geophys. Res., 2(4)6, J 11. E02S05 22For a comparison of X-ray fluorescence and inductively coupled plasma for the analysis of environmental samples, see T. H. Nguyen, 1. Boman, and t\t Lecrmakers, X-Ray Spectrometry, 1998,27,265.
r::il
lQJ
Tutorial: Learn more about applications of X-ray fluorescence.
energy-dispersive system with a radioactive source to well over $500,000 for automated and computerized wavelength-dispersive systems.
In contrast to optical spectroscopy, where absorption methods are most important, X-ray absorptionapplications are limited when compared with X-ray emission and fluorescence procedures. Although absorption measurements can be made relatively free of matrix effects, the required techniques are somewhat cumbersome and time-consuming when compared with fluorescence methods. Thus, most applications are confined to samples in which matrix effects are minimal. Absorption methods are analogous to optical absorption procedures in which the attenuation of a band or line of X-radiation is the analytical variable. Wavelength selection is accomplished with a monochromator such as that shown in Figure 12-9 or by a filter technique similar to that illustrated in Figure 12-8. Alternatively, the monochromatic radiation from a radioactive source may be used. Because of the width of X-ray absorption peaks, direct absorption methods arc generally useful only when a single element with a high atomic number is to be determined in a matrix consisting of only lighter elements. Examples of applications of this type are the determination of lead in gasoline and the determination of sulfur or the halogens in hydrocarbons. 120-1 X-ray Diffraction Methods Since its discovery in 1912 by von Laue, X-ray diffraction has provided a wealth of important information to science and industry. For example, much of what is known about the arrangement and the spacing of atoms in crystalline materials has been determined directly from diffraction studies. In addition, such studies have led to a much clearer understanding of the physical properties of metals, polymeric materials, and other solids. X-ray diffraction is one of the most important methods for determining the structures of such complex natural products as steroids, vitamins, and antibiotics. The details of these applications are beyond the scope of this book. X-ray diffraction also provides a convenient and practical means for the qualitative identification of crystalline compounds. The X-ray powder diffraction method is the only analytical method that is capable of
providing qualitative and quantitative information about the compounds present in a solid sample. For example. the powder method can determine the percentage KBr and NaCl in a solid mixture of these two compounds. Other analytical methods reveal only the percentage K-. Na-, Br-, and Cl- in the sample." Because each crystalline substance has a unique X-ray diffraction pattern, X-ray powder methods are well suited for qualitative identification. Thus, if an exact match can be found between the pattern of an unknown and an authentic sample, identification is assured.
120-2 Identification of Crystalline Compounds Sample Preparation
For analytical diffraction studies, the crystalline sample is ground to a fine homogeneous powder. In such a form, the enormous number of small crystallites are oriented in every possible direction; thus, when an X-ray beam passes through the matcrial, a significant number of the particles are oriented in such ways as to fulfill the Bragg condition for reflection from every possible interplanar spacing. Samples are usually placed in a sample holder that uses a depression or cavity to mount the sample. These mounts are commonly made of aluminum, bronze, Bakelite, glass, or Lucite. Cavity mounts are most commonly side loaded or back loaded. A frostcd glass surface, ceramic, or caJdboard is placed over the front, and the sample is carefully added via the open side or back. Top-loading mounts are also available as are special mounts known as zero background mounts. Alternatively, a specimen may be mixed with a suitable noncrystalline binder and molded into an appropriate shape. Automatic
diffraction pattern is then recorded by automatic scanning in the same wav as for an emission or absorption spectrum. Instruments of this type offer the advantage of high precision for intensity measurements and automated data reduction and report generation. Photographic
Recording
The classical photographic method for recording powder diffraction patterns is still used, particularly when the amount of sample is small. The most common instrument forthis purpose is the Debye-Scherrerpowder camera, which is shown schematically in Figure 12-17a. Here, the beam from an X -ray tube is filtered to produce a nearly monochromatic beam (often the copper or molybdenum Ka line), which is collimated by passage through a narrow tube. Figure 12-8 shows how a filter can be used to produce a relatively monochromatic beam_ Note that the Kf3 line and most of the continuum from a Mo target are removed by a zirconium filter with a thickness of about 0.01 em. The pure Ka line is then available for diffractometry. Several other target-filter combinations have been developed to isolate one of the intense lines of the targct material. The undiffracted radiation T then passes out of the camera via a narrow exit tube as shown in Figure 12-17a. The camera itself is cylindrical and equipped to hold a strip of film around its inside wall. The inside diameter of the cylinder usually is 5.73 or 11.46 em, so that each lineal millimeter of film is equivalent to 1.0' or 0.5' in 8, respectively. The sample is held in the center of the beam by an adjustable mount. Figure 12-17b shows the appearance of the exposed and developed film; each set of lines (0" 0" and so forth) represents diffraction from one set of crystal planes. The Bragg angle 8 for each line is easily evaluated from the geometry of the camera.
Diffractometers
Diffraction patterns are generally obtained with automated instruments similar in design to that shown in Figure 12-9. In this instrument, the source is an X-ray tube with suitable filters. The powdered sample, however, replaces the single crystal on its mount. In some instances. the sample holder may be rotated to increase the randomness of the orientation of the crystals. The
J.1FOf a more detailed Jisformation regarding the substances and materials,inbluding name, formula (if appropriate), compositio'n, color, line strengths, melting point, mineral classification, density, and a host of other characteristics of the materials as well as bibliographic information. A variety of presentation modes are available so that graphs and other important images may be viewed and printed." If the sample contains two or more crystalline compounds, identification becomes more complex. Here, various combinations of the more intense lines are used until a match can be found. Computer searching and matching of data greatly facilitates this task. One very important application is the determination of the percentage crystallinity of materials. In the analysis of polymeric and fibrous materials, determin-
ing the crystalline-to-amorphous ratio has long been of importance, and X-ray powder methods have unique advantages in these determinations. In the pharmaceutical area, the degree of crystallinity can influence the long-term stability of a formulation as well as its bioactivity. X-ray diffraction methods are being increasingly applied to pharmaceuticals. Crystalline materials produce well-defined diffraction peaks whose widths are related to the crystalline "quality." High-quality materials produce sharp peaks, and poor-quality materials give rise to more diffuse diffraction peaks. Amorphous phases come in different forms depending on how they were formed. A glassy phase produces a diffraction signal that is the radial distribution of nearest neighbor interactions. An amorphous phase derived from a crystalline phase usually corresponds to a poor-quality, or paracrystalline, material. Both glassy and para crystalline specimens produce a low-frequency halo, which can appear as a broad background. One approach to determining the crystalline-toamorphous ratio is to use conventional quantitative analysis methods. Non-overlapped X-ray diffraction peaks arc chosen for the phase to be analyzed. Either peak height or peak area is used for quantitative analysis. Standards of known concentration are then used to prepare a calibration curve. In the Vainshtein approach, the amorphous phase is used as a normalizing factor for the integrated
intensities of the crystalline peaks." This eliminates the effects of sample preparation and instrumcnt drift. Analysis is based on Vainshteins law. which states that the diffracted intensity from a material is independent of its state of order within identical regions of reciprocal space. To apply the law. a single standard with a known percentage of crystallinity is used to establish the normalization ratio between the integrated crystalline peaks and the amorphous "background." The same measurements are then made on thc specimen of unknown crystallinity. The percentage crystallinity of the unknown is thcn found from (CIA)" ] %C" = %C"d [ (C/A)"d where %C" and %C"d are the percentage crystallinities of the unknown and standard respectively, and CIA
!jB_ K. Vainshtein (1~21-1996) \lias a prominent Russian X-ray crystallographer. His monograph Diffraccion of X-rays by Chain MoLecules (Amsterdam: Elsevier. 1966) played an important role in the development of structural studies of polymers.
is the ratio of the integrated intensity of the crystalline phase C to the amorphous background A. Yet another approach is to use Fourier transform methods to split the power spectrum into low- and high-frequency regions. The amorphous phase is associated with the low-frcquency region, and the crystalline phase is associated with the high-frequency region. After filtering the undesired region, the inverse transform gives the amorphous intensity and the crystalline intensity. Standards are used to dctcrmine the width and frcquencies of the filters.
*12-7 Aluminum is to be used as windows for a cell for X-ray absorption measurements with the Ag Ka line. The mass absorption coefficient for aluminum at this wavelength is 2.74; its density is 2.70 g/cm '. What maximum thickness of aluminum foil could be used to fabricate the windows if no more than 3.5% of the radia tion is to be absorbed by them ry *12-8 A solution of I, in ethanol had a density of 0.794 g/cm '. A 1.50-cm layer was found to transmit 27.3% of the radiation from a Mo Ka source. Mass absorption coefficients for I. C, H, and 0 are 39.2,0.70.0.00, and 1.50, respectively. (a) Calculate the percentage of I, present, neglecting absorption by the alcohol. (b) Correct the results in part (a) for the presence of alcohol. *12-9 Calculate the goniometer setting, in terms of 20. required to observe the Ka, lines for Fe (1.76 A), Se (0.992 A), and Ag (0.497 A) when the diffracting crystal is (a) topaz, (b) LiF, (c) NaCI.
An important method for the determination of the elemental composition of surfaces is based on the electron microprobe. In this technique, X-ray emission from the elements on the surface of a sample is stimulated by a narrowly focused beam of electrons. The resulting X-ray emission is detected and analyzed with either a wavelength or an energy-dispersive spectrometer. This method is discussed in detail in Section 21F-1.
12-10 Calculate the goniometer setting, in terms of 20, required to observe the LI3, Iincs for Br at 8.126 A when the diffracting crystal is (a) ethylenediamine d-tartrate. (b) ammonium dihydrogen phosphate. *12-11 Calculate the minimum tube voltage required to excite the following lines. The numbers in parentheses are the wavelengths in A for the corresponding absorption edges. (a) K lines for Ca (3.064) (b) La lines for As (9.370) (c) Ll3lines for U (0.592) (d) K lines for Mg (0.496)
*Answers are provided at the end of the book for problems marked with an asterisk. ~
Manganese was determined in samples of geological interest via X-ray fluorescence using barium as an internal standard. The fluorescence intensity of isolated lines for each element gave the following data:
Problems with this icon are best solved using spreadsheets.
*12-1
What is the short-wavelength limit of the continuum produced by an X-ray tube having a silver target and operated at 90 kV?
*12-2
What minimum tube voltage would be required to excite the KI3and LI3series of lines for (a) U, (h) K, (c) Rh, (d) W? The Ka, lines for Ca, Zn, Zr, and Sn have wavelengths of 3.36,1.44,0.79, and 0.49 A, respectively. Calculate an approximate wavelength for the Ka lines of (a) V, (h) Ni, (c) Se, (d) Br, (e) Cd, (f) Sh. The La lines for Ca. Zn, Zr, and Sn have wavelengths of 36.3, 11.9.6.07, and 3.60 A, respectively. Estimate the wavelengths for the La lines for the elements listed in Prohlem 12-3.
*12-5
*12-6
The mass ahsorption coefficient for Ni, measured with the Cu Ka line, is 49.2 cm2/g. Calculate the thickness of a nickel foil that was found to transmit 47.8% of the incident power of a beam of Cu Ka radiation. The density of Ni is 8.90 g/cm '. For Mo Ka radiation (0.711 A), the mass absorption coefficients for K, L H. and 16.7.39.2.0.0, and 1.50 cm '/g, respectively. (a) Calculate the mass ahsorption coefficient for a solution prepared by mixing 11.00 g of Kl with 89.00 g of water. (h) The density of the solution described in (a) is 1.086 g/cm3 What fraction of the radiation from a Mo Ka source would be transmitted hy a 0.60-cm layer of the solution')
o arc
Wt.%Mn
Ba
Mn
0.00 0.10 020 0.30 0.40
156 160 159 160 151
80 1116 129 154 167
What is the weight percentage manganese in a sample that had a Mn-to-Ba count ratio of 0.735') ~
Challenge Problem
12-13 As discussed in Section 12C-3, the APXS, or alpha proton X-ray spectrometer, has been an important experiment aboard all of the Mars exploration rovers. Journal articles provide details of the APXS experiments on the most recent missions in 2004 and compare the instrumentation and measurement strategies with those on board the Pathfinder mission of 199726 ,~S. W. Squyres et aI., 1. Genphys. Res .. 2003. 108. S06::!;R. Rieder et al.. 1. Ge{)ph.~·5.Res .. 2003. J08. 8066: 1. Bruckner et aL, 1. (;eophys. Res .. 2003, lOS, 809·l; R. Gellert et aL Science, 200·t 305, 829: H. Y. McSween et al., Science. 2004, 305. 8--12;S. W Squyres et a\., Science, 2004. 306, 1709; L A. Soderblom et aL Science, 2004, 306. 1723: G. Khngelhofer ct aL, Scienef:'. 200·1. 306.1740; R. Rieder et al.. Sciena. 2004. 306.1746; A. Banin, Science, 2005. 309. 888.
(a) Consult the cited articles, and describc the construction and operation of the deteclor head on the Spiric and Oppnrcu/lity ro\·ers. Illustrate your answer with basic diagrams of Ihe instrument components, and describe the function of each. (b) What determines the selectivity and sensitivity of the APXS system') (c) What elements cannot be determined by APXSo Why notO (d) Characterize the general elemental composition of all of the Martian landing sites. What are the similarities and differences among the sites. What cxplanation do these workers and others givc for the similarities? (e) How Were the APXS measurements limited bv the time in the Martian day when the experiments were completed" Expl~in the cause of these Iimita-tions. How and why were the APXS experiments terminated? (f) What effect did temperature have on the results of the X-ray mode of the APXS experiments? How does this effect relate to your discussion in (e)? (g) The APXS experiments were used to compare the surface composition with the composition of the interiors. How was this accomplished? What differences were discovered? What explanation was given for the differences? (h) Halogen fractionation was apparent in the Martian rock samples. What explanation was given for this phenomenon? (i) Characterize the overall precision and accuracy of the APXS experiments. The APXS team states that "accuracy is mainly determined by precision." Explain what is meant by this statement. Under what circumstances is it true? (j) Explain in some detail the calibration procedure for the APXS experiments. What calibration standards were used on Mars, and where were they located? How Were individual element peaks extracted from the X-ray spectra? (k) Figure 12-18 shows a plot of corrected calibration data for Fe from the APXS experiments. Note that there are uncertainties in both the x and y data. The 22 20 18 V;
C
~ g ;
§
~
2 ;
~ x ~ " '"'
~
16 14 12 10
6
0..
4
l()
12
14
16
l~
:20
'l,
~4
26
28
)0
Weight percentag~ FIGURE 12-18 APXS calibration curve for Fe corrected for attenuation coefficient. (From R. Rieder et aI., J. Geophys. Res., 2003. 108,8066, with permission.)
data from the plot are tabulated in the table below. Carry out a normallcastsquares analysis of the data using Excel. Determine the slope, intercept, correlation coefficient, and the standard deviation about regression. Peak Area
(T
Mass %
(T
2.36
0.28
2.12
0.13
7.04
0.54
5.75
0.13
6.68 8.01
0.54 0.39
5.85
0.13
8.42
0.44
7.14 7.45
0.13
0.10
7.87 13.20
0.10
15.58 20.24
0.18 0.21
1.18
20.71
0.23
1.26
20.55
0.18
9.04
0.44
14.74
0.74
17.93 21.27
0.90 1.05
23.22 25.02
0.10
(I) Carry out a weighted least-squares analysis of the data using a procedure similar to the one described in Problem 10-14 that allows for uncertainties in both the x and y variables. Compare your results to those obtained in (k).
w~¥
Instrumental Analysis in Action
:""~,~~::;>:
_~-,..~'"'t'~~
t-.fercury is an extremely
important
element in the environ-
concentrations
of mercury are determined
by the life span
ment, in foods, and in industrial processes. The health
of the fish and its feeding habits. The highest concentrations
scares concerning
are found in large fish such as swordfish and sharks.
mercury have been many since the best-
known case, the Minamata Minamata
Bay disaster in Japan in 1956.
is a small industrial town on the coast of the
Shiranui Sea. The major industrial Chisso Corporation,
firm in Minamata,
the
dumped some 37 tons of mercury-
containing compounds
into Minamata
1968. As a result, thousands
Bay from 1932 to
of local residents, whose nor-
Because of its importance reliable determinations determination
mal diet included /ish from the bay, developed symproms
the environment
of methylmercury
measurements
poisoning. The disease became known as
in the environment,
accurate,
of mercury are crucial. Although
of the various forms that mercury takes in is of interest, current regulations
focus on
of total mercury, which is in itself challeng-
Minamata disease. Since then, there have been many warn-
ing. The challenge arises because in complex environmental
ings ahout eating /ish and shellfish known to contain high
samples mercury is present in very small amounts. The EPA
levels of mercury. The most recent recommendations
has established
United States Environmental
Protection
and the Food and Drug Administration child-bearing
of the
Agency (EPA) warn women of
age and young children not to eat shark,
water ecosystems and 25 ppt as the limit for saltwater. The National Toxics rule of the EPA
2
recommends
quently, concentrations
for total dissolved mercury (inorganic
ounces per week of fish that contain lower levels of mercury,
seawater. Some ocean surface waters have been found to
such as shrimp, canned lUna, salmon, pollock, and cat/ish.
have concentrations
apply to fish from certain
FIGURE IA2-1 Cold-vapor atomic fluorescence system for ultratrace determinations of mercury.
that the safe
level for mercury is as low as 1.3 parts per trillion (ppt). Fre-
advise women and young children to eat no more than 12
More stringent recommendations
separator
a level of 12 ppt as the upper limit for fresh-
swordfish, king mackerel, or tilefish. These agencies also
lakes, rivers, and coastal areas.
Gas-liquid
lower than this criterion
are found
plus organic forms) in
lower than 0.05 ppt, and intermediate
water layers can have levels as high as 2 ppt. These low concentrations
can be near or lower than the limits of detection
for many analytical techniques. higher concentrations
In freshwater
have been observed.
systems, much In some Califor-
nia lakes, for example, levels of 0.5 to 100 ppt have been deMercury is, of course, a naturally occurring element. How-
termined.
ever, industrial poHution is a major source of environmental
can be quite a challenge for analytical chemists.
In any case, detection
of these ultra trace levels
persulfate solution, which oxidizes all the mercury forms
liquid reagents from the mercury vapor, which is transferred
to Hg(lI). Stannous chloride (SnCI,) is then used to reduce
to the observation
the Hg(ll) to elemental
intensity mercury vapor lamp excites atomic fluorescence.
observation
mercury, which is swept into the
cell of the atomic absorption
cell by a stream of inert gas. A high-
The EPA method 245.7 uses a system similar to Fig-
spectrometer
by a stream of inert gas. Method 245.1 of the EPA can
ure 1A2-1 for mercury detection.'
achieve sub-parts-per-billion
systems, the digestion-oxidation
sensitivity but gives nonlinear
responses. EPA method 7474 uses a microwave digestion
The digestion is with a mixture of HCI, Br-, and BrO] -.
procedure
The method can achieve a detection
and has a range from about 1 ppb to several
and-trap
method and cold-vapor atomic fluorescence.
Mercury is preconcentrated
coal-burning
amalgamation.
power plants, refineries, runoff from factories, Beca.lJsc regulatory requirements
and industrial waste. Mercury also enters the environment exhausts, sewage treat-
The concentrations
of interest in satisfying regulations
in
are becoming more strin-
gent, -it is desirable to have a more sensitive method for
ment plants, medical and dental facilities, and water runoff
the United States and the United Kingdom are in the parts-
mercury. Atomic fluorescence
from mercury- and gold-mining
per-trillion
tion 9E) can achieve the required detection
operations.
The Clean Air
range and lower. However, conventional
analyti~
spectrometry
cal methods such as flame atomic absorption,
levels of air pollution, including mercury. Likewise, the EPA
coupled plasma atomic emission, and inductively coupled
instrument
has set water-quality
plasma mass spectrometry
on atomic fluorescence spectrometry.
criteria for levels of mercury in both
cury into methylmercury,
which is readily absorbed by in-
sects and other aquatic organisms. The mercury-containing compounds
a variety of sample types ranging from seawarcr to sewage.
companies now market mercury analyzers hased Concurrent
\\lith de-
Measurements
of mercury at the ultratrace
levels demanded
However, a good deal of care must be taken to assure high
or less of the sample is transferred).'
generation' techniques based on liquid-gas-separation
limits because the use of nebulizers
Cold-vapor sometimes
atomic absorption
to transfer
(see Section 9A-3) can
achieve sub-parts-per-billion
In the most sensitive EPA cold-vapor
detection
limits.
atomic absorption
method, the sample is digested with a permanganate-
rapidly move up the food chain as small fish
eat the small organisms and big fish eat the small fish. The
(AFS; see Seclimits when com-
for mercur\, monitoring has been the development
Mercury from the air or from water sources accumulates in streams and lakes. Bacteria in the water convert the mer-
system and claims a working range
from "
where dn is the number of particles and a is a proportionality constant, which can be called the capture cross section. Combining Equations 13-4 and 13-5 and integrating over the interval between 0 and n, we obtain dp, Px
=
!"adn 0 S
When these integrals are evaluated, we find that
log J>" = ---'!"P 2.3035 where n is the total number of particles within the block shown in Figure 13-2. The cross-sectional area S can be expressed as the ratio of the volume of the block V in cubic centimeters to its length I> in centimeters. Thus, 5 = ""cm' I>
x
1000
Po
= ebc = A
13B-1 Application of Beer's Law to Mixtures Beer's law also applies to a medium containing more than one kind of absorbing substance. Provided that the species do not interact, the total absorbance for a multicomponent system is given by Atotal = At
-In!.. = an Po 5 After converting to base 10 logarithms and inverting the fraction to change the sign, we obtain
2.303
Finally, the constants in this equation can be colleeted into a single term e to give logp
Pn
= 6.02 X 10"abc
g P
Recall, now, that d5 is the sum of the capture areas for particles within the section; it must therefore be proportional to the number of particles, or
-r
lO00em'/l 10" mol x V em'
+ Az + ... + An + ... + enl>c
= e[l>c + e2bc
(13-9)
where the subscripts refer to absorbing components 1,2, ... , n. 13B-2 Limitations to Beer's Law Few exceptions are found to the generalization that absorbance is linearly related to path length. On the other hand, deviations from the direct proportionality between the measured absorbance and concentration frequently occur when I> is constant. Some of these deviations, called real deviatiolls, are fundamental and represent real limitations of the law. Others are a result of how the absorbance measurements are made (instrumental deviations) or a result of chemical changes that occur when the concentration changes (chemical deviations).
anI>
2.303V Note that IlIV is the number of particles per cubic centimeter, which has the units of concentration. We can then convert IlIV to moles per liter because the number of moles is given by number mol ~
n p;>HielcS -------. 6.02 X 1021 p.ar-fictl!S1 mol
Real Limitations
to Beer's Law
Beer's law describes the absorption behavior of media containing relatively low analyte concentrations; in this sense, it is a limiting law. At high concentrations (usually >0.01 M), the extent of solute-solvent interactions. solute-solute interactions, or hydrogcn bonding can
r::"iI ~
Exercise: Learn more about absorption spectrophotometry.
affect the analyte environment and its absorptivity. For example. at high concentrations, the average distances between the molecules or ions responsihle for absorption are diminished to the point where each particle affects the charge distribution of its neighbors. Thcse solute-solute interactions can alter the ability of the analyte species to absorb a given wavelength of radiation. Because the extent of interaction depends on concentration, deviations from the linear relationship hetween absorbance and concentration occur. A similar effect is sometimes encountered in media containing low ahsorber concentrations but high concentrations of other species, particularly electrolytes. The proximity of ions to the absorber alters the molar absorptivity of the latter by electrostatic interactions; the effect is lessened by dilution. Although the effect of molecular interactions is ordinarily not significant at concentrations below 0.0 I M, some exceptions oceur among certain large organic ions or molecules. For example, the molar ahsorptivity at 436 nm for the cation of methylene blue in aqueous solutions is reported to increase by 88% as the dye concentration is increased from 1O·5to 10-2 M; even below 10-6 M, strict adherence to Beer's law is not observed. Deviations from Beer's law also arise because absorptivity depends on the refractive index of the medium.' Thus, if concentration changes cause significant alterations in the refractive index n of a solution, departures from Beer's law are observed. A eorrection for this effect can be made by substituting the quantity enl(n 2 + 2)2 for e in Equation 13-8. In general, this correction is never very large and is rarely significant at conc!ntrations less than 0.01 M. Apparent Chemical Deviations
Apparent deviations from Beer's law arise when an analyte dissociates, associates, or reacts with a solvent to produce a product with a different ahsorption spectrum than the analyte. A common example of this behavior is found with aqueous solutions of acid-base indicators. For example, the color change associated with a typical indicator Hln arises from shifts in the equilibrium
Example 13-1 demonstrates how the shift in this equilibrium with dilution results in deviation from Beer's law.
Solutions containing various concentrations of the acidic indicator Hln with K, = 1.42 X 10-5 were prepared in 0.1 M HCI and 0.1 M NaOH. In both media, plots of absorbance at either 430 nm or 570 nm versus the total indicator concentration are nonlinear. However, in both media, Beer's law is obeyed at 430 nm and 570 nm for the individual species HIn and In-. Hence, if we knew the equilibrium concentrations of H In and In -, we eould compensate for the dissociation of Hln. Usually, though, the individual concentrations are unknown and only the total concentration cta,,! = [Hln] + IIn-] is known. We now calculate the absorbance for a solution with CIO
~ ~
is
0.0
(see Equaby
without
greater
represents
detectors
"
the average
is derived
range
photon-type
minimum
measured
'J
and thus
Rearrangement
be
becoming
not give very reliable
=0
J
fluctuations
root of current
f
=
The average
of events
value.
tion 5-5). The
the cathode
broader
Note also that a large range
:j:
§
per unit time is proportional
flux. The frequency
proportional
in the
a junction,
Herc,
a cathode).
the current The
whenever
tube.
a series
from
of
It has its origin
of electrons
of electrons
the precision
which occurs
of a photomultiplier
tric current number
limits
can
error
This increased
tances often
5B-2),
such as the movement
for an instrument.
an experimentally
quality (Scction
centration
the much
uncertainty.
noise-limited
k2 V T2 + T
This type of uncertainty
to the anode
sensitivity
data obtained
=
Case 1/: ST
shot noise
Note
concentration
1
of absorbances spectrophotometers
:':0.56
also
rises
of 0.3% Tis typical of many moder-
arc to be expected
(emission
concentration
than
lies between
are often encoun-
= k1 into Equation
of a particular
in photomet-
of low photocurrents
extremes
SI
0.5. Note
error
x
of the pho-
instruments
such conditions
ST
lower
Curve
of about
concentration
instruments,
sample
is essentially
of noise
of concentration
value for
the precision
noise
conditions
near the wavelength
termined
these
in the
arc observed
sources
the lamp intensity
is low. For example,
tained
absorbances about 1.0.
this type
noise
5B-2) that
when there
and amplifier
with
at an absorbance
the relative
ately priced
the limiting
from Johnson
(Section
ric and spectrophotometric where
is reached that
the
compared important
with
spectrophotometers these,
deviation
the result
instruments
With
standard
ure 13-7 shows a plot of the data. Note that a minimum
can
of the magnitude
of radiation
current
an absolute
An uncertainty
near-infrared
Case
when
"-(sJc)
bFrom Equation 13-13 withsr =k1
with Equa-
of :'::0.003, or :'::0.3% T, was assumed.
the absolute
analog
13-13
of T. The third
is independent
13-4 shows data obtained
d
the
instruments
resolution.
Infrared also exhibit
rYl !QJ
readouts
tion
precision
of Table
0.20
and
of T even though
on the magnitude
instrumental column
or photome-
some digital
readout
ul-
in T is the same from 0% T to 100% T. A similar
limited
tered
in less expensive
and visible spectrophotometers
ited resolution.
tainty
often
a
Case III Noise
rr* transitions generally range between 1000 and is.OOOL mol 1 cm -I Typical absorption spectra are shown in Figure 1.\-2. Saturated organic compounds containing such heteroatoms as oxygen, nitrogen, sulfur. or halogens have non bonding electrons that can be excited by radiation in the range of 170 to 250 nm. Table 14-2 lists a
100,0000 80,000 60,000 -l0000 20000
f3
o
~arOh:ne
[;0
TABLE 14-2 Absorption by Organic Compounds Containing Heteroatoms with Nonbonding Electrons
~ ••••••.•_-
350 400 450 500 550 600 650
-l00
CH,oH
500
(CH,hO CH,Cl CH,' (CH,hS CH,NH2 (CH,hN
210230250270290310330350 Wavelength.
FIGURE
14-2
om
Absorption spectra for typical organic
compounds.
depend on the Iigands bonded to the metal ions. The energy differences between these d-orbitals (and thus the position of the corresponding absorption maximum) depend on the position of the element in the periodic table, its oxidation state, and the nature of the ligand bonded to it, Absorption spectra of ions of the lanthanide' and actinide transitions series differ substantially ffOLDthose shown in Figure 14-3. The electrons responsible for absorption by these elements (4fand Sf, respectively) are shielded from external influences by electrons that occupy orbitals with larger principal quantum numbers. As a result, the bands tend to be narrow and relatively
l[~l
few examples of such compounds. Some of these compounds, such as alcohols and ethers, are common solvents, so their absorption in this region prevents measuring absorption of analytes dissolved in these compounds at wavelengths shorter than 180 to 200 nm. Occasionally, absorption in this region is used for determining halogen and sulfur-bearing compounds.
400
600
700
10'000[8000 6000 4000 2000 ;: 0 0. 400
o ~ A number of inorganic anions exhibit ultraviolet absorption bands that are a result of exciting nonbonding electrons. Examples include nitrate (313 nm), carbonate (217 nm), nitrite (360 and 280 nm), azido (230 nm), and trithiocarbonate (500 nm) ions. In general, the ions and complexes of elemenls in the first two transition series absorb broad bands of visible radiation in at least one of their oxidation states and are, as a result, colored (see, for example, Figure 14-3). Here. absorption involves transitions between filled and unfilled d-orbitals with energies that
500
Zl I~J
'It o
!
-lOO
-l00
500
600
V\"avekngth. FIGURE
14-3
700
mil
Absorption spectra of aqueous solutions
of transition metal ions.
:0:: ,""I -l00
500
Wavelength,
600
700
nm
FIGURE 14-4 Absorption spectra of aqueous solutions of rare earth ions.
unaffected by the species bonded by the outer electrons (see Figure 14-4).
For quantitative purposes, charge-transfer absorption is particularly important because molar absorptivities are unusually large (£ > 10,0(0), which leads to high sensitivity. Many inorganic and organic complexes exhibit this type of absorption and are therefore called charge-transfer complexes. A charge-transfer complex consists of an electrondonor group bonded to an electron acceptor. When this product absorbs radiation, an electron from the donor is transferred to an orbital that is largely associated with the acceptor. The excited state is thus the product of a kind of internal oxidation-reduction process. This behavior differs from that of an organic chromophore in which the excited electron is in a molecular orbital shared by two or more atoms. Familiar examples of charge-transfer complexes include the phenolic complex of iron(IlI). the 1,10-
[l]
Simulation:
Learn more about absorption spectra.
phenanthroline complex of iron(II), the iodide complex of molecular iodine, and the hexacyanoferrate(II)hexacyanoferrate(III) complex responsible for the color of Prussian blue. The red color of the iron(l1l)thiocyanate complex is a further example of chargetransfer absorption. Absorption of a photon results in the transfer of an electron from the thiocyanate ion to an orbital that is largely associated with the iron(lll) ion. The product is an cxcited species involving predominantly iron(II) and the thiocyanate radical SeN. As with other types of electronic excitation, the electron in this complex ordinarily returns to its original state after a brief period, Occasionally, however, an excited complex may dissociate and produce photochemical oxidation-reduction products. Three spectra of charge-transfer complexes are shown in Figure 14-5. In most charge-transfer complexes involving a metal ion, the metal serves as the electron acceptor. Exceptions are the 1,10-phenanthroline complexes of iron(II) and copper(l), where the ligand is the acceptor and the metal ion the donor. A few other examples of this type of complex are known, Organic compounds form many interesting chargetransfer complexes, An example is quinhydrone (a 1: 1 complex of quinone and hydroquinone), which exhibits strong absorption in the visible region. Other examples include iodine complexes with amines, aromatics, and sulfides. 5000 4000 3000 2000 1000
Fe(SCN)2+
o
400 450 500 550 600 650 700
~ 12,000 ~ 108~~~ ~ 6000 ~ 4000 ~ 2000 '0 0 ::;: -l00 450 500 550 600 650 700
~H~.
~StarChlj-
•
10,000 5000
o
-l00 -l50 500 550 600 650 700 \Vavelength.
nm
FIGURE 14-5 Absorption spectra of aqueous chargetransfer complexes.
14C
QUAliTATIVE APPliCATIONS OF ULTRAVIOLET-VISIBLE ABSORPTION SPECTROSCOPY
Spectrophotometric measurements with ultraviolct radiation are useful for detecting chromophoric groups, such as those shown in Table 14-1.' Because large parts of even the most complex organic molecules are transparent to radiation longer than 180 nm, the appearance of one or more peaks in the region from 200 to 400 nm is clear indication of the presence of unsaturated groups or of atoms such as sulfur or halogens. Often, the identity of the absorbing groups can be determined by comparing the spectrum of an analyte with those of simple molecules containing various chromophoric groups" Usually, however, ultraviolet spectra do not have enough fine structure to permit an analyte to be identified unambiguously. Thus, ultraviolet qualitative data must be supplemented with other physical or chemical evidence such as infrared, nuclear magnetic resonance, and mass spectra as well as solubility and melting: and boiling-point information.
Ultraviolet spectra for qualitative analysis are usually measured using dilute solutions of the analyte. For volatile compounds, however, gas-phase spectra are often more useful than liquid-phase or solution spectra (for example, compare Figure 14-1a and b). Gas-phase spectra can often be obtained by allowing a drop or two of the pure liquid to evaporate and equilibrate with the atmosphere in a stoppered cuvette. In choosing a solvent, consideration must be given not only to its transparency, but also to its possible effects on the absorbing system. Quite generally, polar solvents such as water, alcohols, csters, and ketones tend to obliterate spectral fine structure arising from vibrational effects. Spectra similar to gas-phase spectra (see Figure 14-6) are more likely to be observed in
3For a detailed discussion of ultraviolet absorption spectroscopy in the identification of organic functional groups, see R. M. Silverstein, G. C Bassler, and T. C. Morrill, Specrromerric Idefl(~ficalion uf Organic Compounds, 5th ed., Chap. 6, !"iew York: Wiley, 1991. ~I-L H. Perkampus. [lV-VIS AlIas of Organic Compnlll!ds. 2nd ed .. Hoboken. NJ: WHey-VCH.I992. In addition. in the past. several organizations have published catalogs of spectra that may still be useful, including American Petroleum Institute, Ultraviolet Spectral Data, AP.l. Research Project 44. Pittsburgh: Carnegie Institute of Techno log v: Sadtler Handbook of Ultra~'iolet Spectra, Philadelphia: Sadtler Research-Laboratories: American Society for Testing ~'iaterials. Committee E-D. Philaddphia.
~ 0.4 1.4
;; -E 0.3 o
~ -< 0.2
" c
~ 1.2 ~
:;(
0.1
1.6
FIGURE 14-7 Spectra for reduced cytochrome c at four
spectral bandwidths. (1) 20 nm, (2) 10 nm, (3) 5 nm, and (4) 1 nm. (Courtesy of Varian, Inc., Palo Alto, CA.)
FIGURE 14-6 Effect of solvent on the absorption
spectrum of acetaldehyde. nonpolar solvents such as hydrocarbons. In actctttion, the positions of absorption maxima arc influenced by the nature of the solvent. As a rule, the same solvent must be used when comparing absorption spectra for identification purposes. Table 14-3 lists some common solvents and the approximate wavelength below which they cannot be used because of absorption. These wavelengths, called the cutoff wavelengths, depend strongly on the purity of the solvent.' Common solvents for ultraviolet spec-
trophotometry include water, 95% ethanol, cyclohexane, and lA-dioxane. For the visible region, any colorless solvent is suitable.
The effect of variation in slit width, and hence effective bandwidth, was shown previously for gas-phase spectra in Figure 13-8. The effect on solution spectra is illustrated for reduced cytochrome c in Figure 14-7. Clearly, peak heights and separation are distorted at wider bandwidths. Because of this, spectra for qualitative applications should be measured with minimum slit widths.
Even though it may not provide the unambiguous identification of an organic compound, an absorption spectrum in the visible and the ultraviolet regions is nevertheless useful for detecting the presence of certain functional groups that act as chromophores. For example, a weak absorption band in the region of 280 to 290 nm, which is displaced toward shorter wavelengths with increased solvent polarity, strongly indicates the presence of a carbonyl group. Such a shift is tcrmed a hypsochromic, or bLlle,shift. A weak absorption band at about 260 nm with indications of vibrational finc structure constitutes evidence for thc existcnce of an aromatic ring. Confirmation of the presence of an aromatic amine or a phenolic structure may be obtained by comparing the effects of pH on the spectra of solutions containing the sample with those shown in Table 14-4 for phenol and aniline. The ultraviolet spectra of aromatic hydrocarbons are characterized by three sets of bands that originate from 'IT --+ 'IT' transitions. For example, benzene has a strong absorption peak at 184 nm (em" = 60,000): a weaker band, called the E, band, at 204 nm (com" ~ 7900); and a still weaker peak, termed the B band, at256 (emax = 200). The long-wavelength bands of benzene vapor, 1,2,4,5-tetrazine (see Figure 14-la), and many other aromatics contain a series of sharp peaks duc to the superposition of vibrational transitions on the basic electronic transitions. As shown in Figure 14-1, solvents tend to reduce (or sometimes eliminate) this fine structure as do certain types of substitution.
'i Most major suppliers of reagent chemicals ill the United States offer spectrochemical grades of solvents. Spectral-grade solvents have been treated to remove absorbing impurities and meet or exceed the requirements set forth in Reagent Chemicals, 9th cd., Washington, DC: American Chemical Society, 2000. Supplements and updates are available at http://pubs.acs .org/reagentslindex.html
TABLE14-3 Solvents for the Ultraviolet and Visible Regions Lower Wavelength Solvent
Limit,nm
Water Ethanol
180 220 200 200 260
Hexane
Cyclohexane Carbon tetrachloride
Solvent Diethyl ether Acetone Dioxane
Cellosolve
Lower Wavelength Limil,nm 210 330 320 320
B Band
E, Band Compound Benzene
Toluene m-Xylene Chlorobenzene Phenol Phenolate ion Aniline Anilinium ion
Thiophenol Naphthalene Styrene
A..-x, om
C6H6 C6H,CH, C6H,(CH,), C.H,Cl C.HsOH c"H,OC.HsNH2 C.H,NH; C.H,SH CIOHs C.H,CH=CH2
emax
204 207
7900 7000
210 211 235 230 203 236 286 244
7600 6200 9400 8600 7500 10.000 9300 12,000
Amal,nm
256 261 263 265 270 287 280 254 269 312 282
Emax
200 300 300 240 1450 2600 1430 160 700 289 -\50
All three of the characteristic bands for benzene are strongly affected by ring substitution: the effects on the two longer-wavelength bands are of particular interest because they can be studied with ordinary spectrophotometric equipment. Table 14-4 illustrates the effects of some common ring substituents. By definition, an auxochrome is a functional group that does not itself absorb in the ultraviolet region but has the effect of shifting chromophore peaks to longer wavelengths as well as increasing their intensities. Such a shift to longer wavelengths is called a bathochromic, or red, shift. Note in Table 14-4 that -OH and - NH, have an auxochromic effect on the benzene ch~omOphore, particularly with respect to the B band. AUXDchromic substituents have at least one pair of n ele~tro~s capable of interacting with the 7T electrons of the ring. This interaction apparently has the effect of - stabilizing the 7T* state, thereby lowering its energy, and increasing the wavelength of .the corresponding band. Note that the auxochromic effect is more pronounced for the phenolate anion than for phenol itself, probably because the anion has an extra pair of unshared electrons to contribute to the interaction. With aniline, on the other hand, the nOnbonding electrons are lost by formation of the anilinium cation, and the auxochromic effect disappears.
140
QUANTITATIVE ANALYSIS BY ABSORPTION MEASUREMENTS
Absorption spectroscopy based on ultraviolet and visible radiation is one of the most useful tools available to the scientist for quantitative analysis6 Important characteristics of spectrophotometric and photometric methods include (1) wide applicability to both organic and inorganic systems, (2) typical detection limits of lO-4 to lO-5 M (in some cases, certain modifications can lead to lower limits of detection).' (3) moderate to high selectivity, (4) good accuracy (typically, relative uncertainties are 1% to 3%, although with special precautions. errors can be reduced to a few tenths of a percent), and (5) ease and convenience of data acquisition. "For a wealth of detailed. practical information on spectrophotometriC" practices, see Techniques in Visible and (jltra~'iolet Spearomerry. \'01. I. Sumdards in Absorption Spectroscopy, C. Burgess and A. Knowles. eds .. London: Chapman & Hall, 1981; 1. R. Edisbury. Practical If/nls Oil Absorption Spearomelr.r. New York: Plenum Press, 1968. 'See. for example, T. D. Harris. Anal. Chern .. 1982,54, 7.HA,
140-1
Scope
The applications of quantitative, ultraviolet-visible absorption methods not only are numerous but also touch on everv field that requires quantitative chemical information.' The reader can obtain a notion of the scope of spectrophotometry by consulting the series of review articles that were published in Analytical Chemistry' as well as monographs on the subject.9 Applications
to Absorbing Species
Tables 14-1, 14-2, and 14-4 list many common organic chromophoric groups. Spectrophotometric determination of any organic compound containing one or more of these groups is potentially feasible. Many examples of this type of determination are found in the literature. A number of inorganic species also absorb UVvisible radiation and are thus susceptible to direct determination. We have noted that many ions of the transition metals are colored in solution and can .thus be determined by spectrophotometric measurttment. In addition, a numbcr of other species show charactcristic absorption bands, including nitrite, nitrate, and chromate ions, the oxides of nitrogen, the elemental halogens, and ozone. Applications
to Nonabsorbing
Species
Numerous reagents react selectively with nonabsorbing species to yield products that absorb strongly in the ultraviolet or visible regions. The successful application of such reagents to quantitativc analysis usually requires that the color-forming reaction be forced to near completion. If the amount of product is limited by the analyte, the absorbance of the product is proportional to the analyte concentration. Color-forming reagents are frequently employed as well for the determination of absorbing species, such as transitionmetal ions. The molar absorptivity of the product is frequently orders of magnitude greater than that of the species before reaction. A host of complexing agents are used to determine inorganic species. Typical inorganic reagents include thiocyanate ion for iron, cobalt, and molyhdenum; ~L. G. Hargis.]. A. Howell. and R E. Sutlon. Altai. Chern. (Rc\lcwl.1996. 68.169: 1-:\. Howell and R. E. Sutton, Anal. Chern .. (Re\'i.:w).1998. 7{j. 107 9H. Onishi, Pho[omeIric Dnerminatlon of Traces of :\-fetaLI. Part IIA. Part lIB. -Ilh ed .. :-';ew York: \Viky. 1986. 1989: Colorimetric Determination of Nonmetals. 2nd ed .. D. F. Boltz. ed., New Ymk: Intcrscicnce. 197.s: E. B Sandell and H. Onishi. Photometric DeterminatiOfl of Tral"eS of .\krtlis. ..loth ed .. New York: Wiley. 1978: F D. Snell. PholUmerric and Fluor(Jm
hvdrogen peroxide for titanium, vanadium, and chromium; and iodide ion for bismuth, palladIUm, and tellurium. Of even more importance are organicchelating agents that form stable, colored complexes WIth cations. Common examples include dlethyldlthlOcarbamate for the determination of copper. diphenylthiocarbazone for lead, I,lO-phenanthrolene for iron, and dimethylglyoxime for nickel. In the application of the last reaction to the photometric determinatIOn of nickel, an aqueous solution of the cation is extracted with a solution of the chelating agent in an immiscible organic liquid. The absorbance of thc resulting bright red organic laycr serves as a measure of the concentration of the metal.
enees that can result from scratches, etching, and wcar. It is equally important to use proper cell-cleaning and drying techniques. Erickson and Surles 10 recommend the following cleaning sequence for the outSide Windows of cells. Prior to measurement, the cell surfaces should be cleaned with a lens paper soaked in spectrograde methanol. While wiping, it is best to hold the paper with a hemostat. The methanol is then allowed to evaporate, leaving the cell surfaces free of contamtnants. Erickson and Surles showed that thiS method was superior to the usual procedure of wiping the cell surfaces with a dry lens paper, which can leave ltnt and a film on the surface.
140-2
Absorbance and Concentration
Determining Procedural
Details
A first step in any photometric or spectrophotometric analysis is the developmcnt of conditions that yield a reproducible relationship (preferably linear) between absorbance and analyte concentration. Selection of Wavelength
For highest sensitivity, spcctrophotometric absorbance measuremcnts are ordinarily made at a wavelength corresponding to an absorption maximum because the change in absorbance per unit of concentratIOn ISgreatest at this point. In addition, the absorbance tS nearly constant with wavelength at an absorption maximum, which leads to close adherence to Becr's law (sce Figure 13-5). Finally, small uncertainties that arise from failing to reproduce precisely the wavelength setting of the instrument have less influence at an absorptIOn maximum. Variables That Influence Absorbance
Common variables that influence the absorption spectrum of a substance include the naturc of the solvent, the pH of the solution, the temperature, high electroIvte concentrations, and the presence of interfering s~ubstances. The dIects of these variables must be known and conditions for the analysis must be chosen such that the absorbance will not be materially influenced by small. uncontrolled variations in their magnitudes. Cleaning and Handling of Cells
Accurate spectrophotometric analysis requires the use of good-quality, matched cells. These should be regularlv calibrated against one another to detect dlffer-
the Relationship
between
The method of external standards (see Section 10-2) is most often used to establish the absorbance versus concentration relationship. After deciding on the conditions for the analysis, the calibration curve is prepared from a series of standard solutions that bracket the concentration range expected for the samples. Seldom, if ever, is it safe to assume adherence to Beer's law and use only a single standard to determine the molar absorptivity. It is never a good idea to base the results of an analysis on a literature value for the molar absorptivity. . Ideally, calibration standards should approximate the composition of the samples to bc analyzed not only with rcspect to the analyte concentration but als~ WIth regard to the concentrations of the other spectes In the sample matrix. This can minimize thc effects of vanous components of the sample on the measured absorbance. For example, the absorbance of many colored complexes of metal ions is decreased to a varying degree in the presence of sulfate and phosphate Ions because these anions can form colorlcss complexes with metal ions. The desired reaction is often less complete as a consequence, and lowered absorbances are the result. The matrix effect of sulfate and phosphate can often be counteracted by introducing into the standards amounts of the two species that approximate the amounts found in the samples. Unfortunately. matrix matching is often impossible or quite difficult when complex materials such as soils, minerals, and tissues are being analyzcd. When this is the case. the standardaddition method is often helpful in counteracttng
matrix effects that affect the slope of the calibration curve. However, the standard-addition method does not compensate for extraneous absorbing species unless they are present at the same concentration in the blank solution. The Standard-Addition
Method
The standard-addition method can take several forms.l1 The one most often chosen for photometric or spectrophotometric analyses, and the onc that was discussed in some detail in Section 10-3, involves adding one or more increments of a standard solution to sample aliquots. Each solution is then diluted to a fixed volume before measuring its ahsorbance. Example 14-1 illustrates a spreadsheet approach to the multiple-additions method for the photometric determination of nitrite.
Nitrite is commonly determined by a spectrophotometric procedure using the Griess reaction. The sample containing nitrite is reacted with sulfanilimide and N(I-naphthyl)ethylenediamine to form a colored species that absorbs radiation at 550 nm. Five-milliliter aliquots of the sample were pi petted into five 50.00-mL volumetric flasks. Then, 0.00, 2.00, 4.00, 6.00, and 8.00 mL of a standard solution containing 10.00 flM nitrite were pipetted into each flask, and the color-forming reagents added. After dilution to volume, the absorbance for each of the five solutions was measured at 550 nm. Thc absorbances were 0.139, 0.299, 0.486, 0.689, and 0.865, respectively. Devise a spreadsheet to calculate the nitrite concentration in the original sample and its standard deviation.
The spreadsheet is shown in Figure 14-8. Note that the final result indicates the concentration of nitrite in the original sample is 2.8 :+: 0.3 flM. The standard deviation is found from the regression line 12 bv using an extrapolated x value of ~ 1.385 mL and a v ~'alue;f 0.000 as illustrated in Example 1-1 of Chapt~r 1.
I i
In the interest of saving time or sample, it is possible to perform a standard-addition analysis using only two increments of sample. Here, a single addition of V; mL of standard would he added to one of the two samples. This approach is based on Equation 14-1 (see Section 10-3).
See M. Rader, I Chern. Educ.. 1980. 5~. 70.3.
leFor more information on sprcadsh~e( ilpproach~s {u standard additIon methods. see S. R. Crouch and F J Holler. ApplicillWIZS of .\licrosoW:' Excel in Ana(\,'licill Chemistn Chaps. 4 and l~. BdmlmL c.-\ Brooks Cole.200.t.
A,c\.Vs C,
The single-addition ample 14-2.
=
(A, ~-AI)V' method
is illustrated
in Ex-
A 2.00-mL urine specimen was treated with reagent to generate a color with phosphate, following which the sample was diluted to 100 mL. To a second 2.00-mL sample was added exactly 5.00 mL of a phosphate solution containing 0.0300 mg phosphate/mL, which was treated in the same way as the original sample. The absorbance of the first solution was 0.428, and th;t of the second was 0.538. Calculate the concentration of phosphate in milligrams per millimeter of the specimen.
01W1
.'
I
c=-.Mool ~--. -2 00
0.00
2.00
Solution
= (0.428)(O~OJOO mg PO/"/mL)(5.00
C
,
mL)
(0.538 - 0.428)(2.00 mL sample) = 0.292 mg PO.'- I mL sample
Analysis of Mixtures of Absorbing
Substances
The total absorbance of a solution at any given wavelength is equal to the sum of the absorbances of the individual components in the solution (Equation 13-9). This relationship makes it possible in principle to determine the concentrations of the individual components of a mixture even if their spectra overlap completelv. For example, Figure 14-9 shows the spectrum of a solution containing a mixture of species M and species N as well as absorption spectra for the individual components. It is apparent that there is no wavelength where the absorbance is due to just one of these components. To analyze the mixture, molar absorptivities for M and Narc tlrst determined at wavelengths A, and A2 with sufficient concentrations of the two standard solutions to be sure that Beer's law is obeved over an absorbance range that encompasses the ab;orbance of the sample. Note that the wavelengths selected are
ones at which the molar absorptivities of the two components differ significantly. Thus, at A" the molar absorptivity of component M is much larger than that for component N. The reverse is true for A2. To complete the analysis, the absorbance of the mixture is determined at the same two wavelengths. From the known molar absorptivities and path length, the following equations hold: AI
(14-2) (14-3)
where the subscript 1 indicates measurement at wavelength AI' and the subscript 2 indicates measurement at wavelength A,. With the known values of e and b, Equations 14-2 and 14-3 represent two equations in two unknowns (c" and eN) that can be solved. The relationships are valid only if Beer's law holds at both wavelengths and the two components behave independently of one another. The greatest accuracy is obtained by choosing wavelengths at which the differences in molar ahsorptivities are large.
f7l lQ.j
lluorial: Learn more about calibration and analy~ sis of mixtures.
Mixtures containing more than two absorbing species can be analyzed. in principle at least, if a further absorbance measurement is made for each added component. The uncertainties in the resulting data become
.........•.
/-;
..••.
;/
/
'
"
" •••__
,
~+N
\
FIGURE 14-9 Absorption spectrum of a two-component mixture (M + N) with spectra of the individualcomponents. Vertical dashed lines indicate optimal wavelengths for determination of the two components.
greater, however, as the number of measurements increases. Some array-detector spectrophotometers are capable of reducing these uncertainties by overdetermining the system. That is, these instruments use many more data points than unknowns and effectivelv match the entire spectrum of the unknown as closely' as possible by least-squares techniques using the methods of matrix algebra. The spectra for standard solutions of each component are required for the analysis. Computer data-processing methods based on factor analysis or principal components analysis have been developed to determine the number of components and their concentrations or absorptivities in mixturesl3 These methods are usually applied to data obtained from array-detector-based spectrometers. 140-3 Derivative and Dual-Wavelength Spectrophotometry In derivative spectrophotometry, spectra are obtained by plotting the first- or a higher-order derivative of absorbance with respect to wavelength as a function of wavelength.'" Often, these plots reveal spectral detail that is lost in an ordinary spectrum. In addition, concentration measurements of an analyte in the presence of an interference or of two or more analytes in a mixlUre can sometimes be made more easily or more accurately using derivative methods. Unfortunately, the advantages of derivative spectra are at least partially offset by the degradation in signal-to-noise ratio that accompanies obtaining derivatives. In some parts of the ultraviolet and visible regions, however, signal-tonoise ratio is not a limiting factor. Even if signal-tonoise ratio is degraded by differentiation, smoothing methods can be applied to help improve precision. Several different methods have been used to obtain derivative spectra. For modern computer-controlled digital spectrophotometers, the differentiation can be performed numerically using procedures such as derivative least-squares polynomial smoothing, which is discussed in Section 5C-2. With older analog instruments, derivatives of spectral data could be obtained electronically with a suitable operational amplifier circuit (see
li
L R Malinowski. Factor Analysis in Chemistry, 3rd ed .. Chap_ 9, New
York:
Wiley,
2002
"For additional informal Ion see G. Talsky. Dcrh'l1lit,f.' 5pec!ropho(omelry LOII'und HIgh Order, New York: VCH. IlN-t: T C O'Ha\'t~r. Anal. Chern., 1979.51. <JIA: F. Sanchez Rojas. C Bosch Ojeda. and 1. M. Cana Pavon, "Lllilfltu. 1988.35.753: C. Bosch Ojeda. F Sanchez Rojas, and J ,\I. Cano PawlD, Talanw, 1995, 42,1195
14E
Section 3E-4). Another technique uses mechanical oscillation of a refractor plate to sweep a wavelength interval of a few nanometers repetitively across the exit slit of a monochromator while the spectrum is scanned, a technique known as wavelength modulation. Alternatively, the spectrum can be scanned using two wavelengths offset by a few nanometers, which is called dua/wavelength speetrophotometry. Applications
I'Spreadsheet applicatIOns involving derivative tcchniqu P + E
(14-5)
I
k,
I
I
In this so-called Michaelis-Menten mechanism, the enzyme E reacts reversibly with the substrate S to form an enzyme-substrate complex ES. This complex then decomposes irreversibly to form the products and the regenerated enzyme. The rate of this reaction often follows the rate law k,[EJo[S]
d[PJ dt
L __+ k 2 + [S] _'
I Initial rate. dlPj
Time
te
Change in concentration of analyte [A]and product [P]as a function of time. Untiltime t,the analyte and product concentrations are continuously changing. This is the kinetic regime. Inthe equilibrium region, after I" the analyte arid product concentrations are static. 14-14
o
to teo when analyte and product concentrations are changing continuously. Kinetic methods can be more selective than equilibrium methods if reagents and conditions are chosen to maximize differcnces in the rates at which the analyte and potential interferents react. In equilibriumbased methods, selectivity is realized by maximizing differences in equilibrium constants.
diP! dt
Km + [S]
Kinetic methods can employ several different types of reactions. Catalyzed reactions are among the most popular. With these, a catalyst is determined by its influence on the reaction rate or one of the reactants is determined. For example, iodide is a catalyst in the reaction of Ce(IV) with As(III). Trace quantities of 1can be determined by measuring the rate of this reaction as a function of the 1- concentration. Normally, the method of external standards is used to prepare a calibration curve of rate versus iodide concentration. More than forty inorganic cations and more than fifteen anions have been determined based on their catalytic effect. Organic catalvsts have also been determined bv kinetic methods. T'he most important applications of catalyzed reactions to organic analyses involve the use of enzymes as catalysts. The behavior of a large number
[l]
Simulation:
Hence, measurements of the rate can be used to obtain the enzyme activity (concentration), [Elo. ~ Substrates can also be determined by kinetic methods. Under conditions where [S] BiY-
where tu is the thiourea molecule (NHz),CS. Predict the shape of a photometric titration curve based on this process, given that the Bi(III) or thiourea complex is the only species in the system that absorbs light at 465 nm, the wavelength
+$6$34'85) -
+ H,Y'-
from its thiourea complex:
M. M. Oldham. Anal. Chern., 1971, 43, 262).
o 0.147 0.271 0.375
calculate the species composition as a function of initial concentrations. Several modern versions. including some that operate in the Windows environment. are availahle.
Calculate the concentration
of the Pd( II) solution, given that the ligand-to-cation
ratio in the colored product is 2: I *14-7 A 3.65-g petroleum specimen was decomposed by wet ashing and subsequently diluted to 500 mL in a volumetric flask. Cobalt was determined hy treating 25.00-mL aliquots of this diluted solution as follows:
are provided at the end of the hook for problems marked with an asterisk
Prohlems with this icon are hest solved using spreadsheets.
. 20.00
*14-1 A 25.0-mL aliquot of an aqueous quinine solution was diluted to 50.0 mL and found to have an absorhance of 0.656 at 3-lS nm when measured in a 2.50-cm cell.
20.00
0.276 O~91
Assume that the Co(II)-ligand chelate obeys Beer's law, and calculate the percentage of cohalt in the original sample. *14·8 A simultaneous detcrmination for cohalt and nickel can he hased on absorption by their respective 8-hydroxyquinolinol complexes. Molar absorptivities corresponding to their absorption maxima arc as follows:
ond 25.00-mL aliquot of the acid, which contained a small amount of the indicator under consideration, the absorbance was found to be 0.333 at 485 nm and 0.655 at 625 nm (I.OO-cmcells). Calculate the pH of the solution and K, for the weak acid. (e) What would be the absorhance o[ a solution at 485 and 625 nm (1.50-cm cells) that was 2.00 x 10-' M in the indicator and was buffered to a pH of 6.000" A standard solution was put through appropriate dilutions to give the concentrations of iron shown helow. The iron(I1)-1,IO,phenanthroline complex was then formed in 25.0·mL aliquots of these solutions, following whieh each was diluted to 50.0 mL. The following absorbances (1.00-cm cells) were recorded at510 nm:
428.Y 10.2
Calculate the molar concentration of nickel and cohalt in each of the following solutions using the following data:
Fe(lI) Concentration in Original Solutions, ppm 0.160
4.00 10.0
0.3YO
16.0
0.630
0.426
0.026
24.0
0.792
0.081
32.0
0.Y50 1.260
40.0
1.580
*14·9 When measured with a 1.00-cm cell, a 7.50 X 105 M solution of species A ~xhibited absorhances of 0.155 and 0.755 at 475 and 700 nm, respectively. A 4.25 x 10 ) M solution of species B gave absorbanees of 0.702 and 0.091 under the same circumstances. Calculate the concentrations of A and B in solutions that yielded the following absorbance data in a 2.50-em cell: (a) 0.439 at 475 nm and 1.025 at 700 nm; (b) 0.662 at 475 nm and 0.815 at 700 nm. *14-10 The acid-base indicator Hln undergoes the following reaction in dilute aqueous solution:
The following absorbance data were ohtained for a 5.00 X IW' M solution of HIn in 0.1 M NaOH and 0.1 M HCI. Measurements were made at wavelengths of 485 nm and 625 nm with 1.00·cm cells. 0.1 MNaOH
Am
0.1 MHCI
A.S) = 0.487
=
0.075
A62; = 0.904
A62j
=
0.181
[n the NaOH solution, essentially all of the indicator is present as In ; in the acidic solution, it is essentiallv all in the form of HIn. (a) Calculate molar absorpti~ities for In - and HIn at 485 and 625 nm. (h) Calculate the acid dissociation constant for the indicator if a pH 5.00 buffer containing a small amount of the indicator exhibits an absorbance of 0.567 at .+85nm and 0.395 at 625 nm (1.00-cm cells). (c) What is the pH of a solution containing a small amount of the indicator that exhihits an absorbance of 0.492 at 485 nm and 0.2'+5 at 635 nm (l.OO-cm cells)'! (d) A 25.00-mL aliquot of a solution of purified weak organic acid HX required exactly 2.+.20m L of a standard solution of a strong hase to reach a phenolphthalein end point. When exactly 12.10 mL of the hase was added to a sec-
(a) Plot a calibration eurve from these data. (b) Use the method of least squares to find an equation relating absorbance and the concentration of iron(II). (c) Calculate the standard deviation of the slope and intercept. 14.U The method developed in Problem 14-11 was used for the routine detcrmination of iron in 25.0-mL aliquots of groundwater. Express the concentration (as ppm Fe) in samples that yielded the accompanying absorbance data (1.00-cm cell). Calculate the relative standard deviation of the result. Repeat the calculation assuming the absorbance data are means of three measurements. (a) 0.143 (c) 0.068 (e) 1.512 (b) 0.675 (d) 1.009 (f) 0.546 Copper(II) forms a 1: 1 complcx with the organic complexing agent R in acidic medium. The formation of the complex can be monitored by spectrophotometry at 480 nm. Use the following data collected under pseudo-first-order conditions to construct a calibration curve of rate versus concentration of R. Find the concentration of copper(Il) in an unknown whose rate under the same conditions was 6.2 x 1O-'As-1
3.6 5.4
X X
10' 10-'
7.Y X 10-3 1.03 x 10 '
*14-14 Aluminum forms a I: I complex with 2-hydroxy-l·naphthaldehyde p-methoxyhenzovlhvdraxonal. which absorbs UV radiation at 285 nm. Under pseudo-firstorder ~o~ditions, a plot of the initial rate of the reaction (absorbance units per
second) versus the concentration scribed by the equation rate
Reagent Vulumes, mL
of aluminum (in J.lM)yields a straight line de1.74c" - 0.225
Find the concentration of aluminum in a solution that exhibits a rate of 0.76 absorbance units per second under the same experimental conditions. *14-15 The enzyme monoamine oxidase catalyzes the oxidation of amines to aldehydes. For tryptamine, Km for the enzyme is 4.0 x to-' M and "m" = k,[EJo = 1.6 x 10-' J.lM/min at pH 8. Find the concentration of a solution of tryptamine that reacts at a rate of 0.18 J.lm/min in the presence of monoamine oxidase under the above conditions. Assume that [tryptamine] 1T* system that rapidly converts to the triplet state and prevents fluorescence. Fusion of benzene rings to a hcterocyclic nucleus, however, results in an increase in the molar absorptivity of the absorption band. The lifetime of an excited state is shorter in such structures, and fluorescence is observed for compounds such as quinoline, isoquinoline, and indole. H
I
CO Substitution on the benzene ring causes shifts in the wavelength of absorption maxima and corresponding changes in the fluorescence emission. In addition, substitution frequently alIects the quantum efficiency_ Some of these effects are illustrated by the data for benzene derivatives in Table IS-I. The influence of halogen substitution is striking: the decrease in fluorescence with increasing molar mass of the halogen is an example of the heavy-atom effect (page 404), which increases the probability for intersystem crossing to the triplet state. Predissociation IS thought to play an important role in iodobenzene and in nitro derivatives as well, because these compounds
Wavelengtb of Compound
Formula
Benzene
C,li" C,H,CH3 c"H,C3H, CoHsF C,H,Cl C,H,Br C,HsI C,H,OH C,HsOC,H,OCH, C,HsNH2 c"HsNH3 ' C,H,COOH C,H,CN C,H,N02
Toluene Prapylbenzenc Fluorabenzene Chlorabenzene Bromobenzene
Iodobenzene Phenol Phenolate ion Anisole
Aniline Anilinium lon Benzoic acid Benzonitrile Nitrobenzene
have easily ruptured bonds that can absorb the excitation energy following internal conversion. Substitution of a carboxylic acid or carbonyl group on an aromatic ring generally inhibits fluorescence. In these compounds, the energy of the n -> 7T* transition is less than in the 7T -> 7T* transition, and as discussed previously, the fluorescence yield from the n -> 7T* systems is ordinarily low. Effect of Structural
Fluorescenc~ om
Relative IntensitI of fluorescence
270-310
10
270-320
17
270-320
17
270-320
10
275-345
7
290-380
5
285-365
18
0 310-400
10
285-345
20
310-405
20 0
310-390
3
280-360
20 O·
metal ion. For example, the fluorescence intensity of 8-hydroxyquinoline is much less than that of its zinc complex:
Rigidity
It is found empirically that fluorescence is particularly favored in molecules with rigid structures. Forexample, the quantum efficiencies for fluorene and biphenyl are nearly 1.0 and 0.2, respectively, under similar conditions of measurement. The difference in behavior is largely a result of the increased rigidity furnished by the bridging methylene group in fluorene. Many similar examples can be cited.
Lack of rigidity in a molecule probably causes an enhanced internal conversion rate (k,c in Equation 15-1) and a consequent increase in the likelihood for radiationless deactivation. One part of a nonrigid molecule can undergo low-frequency vibrations with respect to its other parts: such motions undoubtedly account for some energy loss. Temperature and Solvent Effects
The influence of rigidity has also been invoked to account for the increase in fluorescence of certain organic chciating agents when thev arc complcxed with a
The quantum efficiency of fluorescence in most molecules decreases with increasing temperature because the increased frequency of collisions at elevated temperatures improves the probability for deactivation by external conversion. A decrease in solvent viscosity also increases the likelihood of external conversion and leads to the same result.
The fluorescence of a molecule is decreased by solvents containing heavy atoms or other solutes with such atoms in their structure: carbon tetrabromidc and ethyl iodide are examples. The effect is similar to that which occurs when heavy atoms are substituted into fluorescing compounds: orbital spin interactions result in an increase in the rate of triplet formation and a corresponding decrease in fluorescence. Compounds containing heavy atoms are frequently incorporated into solvents when enhanced phosphorescence is desired. Effect of pH on Fluorescence
The fluorescence of an aromatic compound with acidic or basic ring substituents is usually pH dependent. Both the wavelength and the emission intensity arc likely to be different for the protonated and unprotonated forms of the compound. The data for phenol and aniline shown in Table 15-1 illustrate this effect. The changes in emission of compounds of this type arise from the differing number of resonance species that are associated with the acidic and basic forms of the molecules. For example, aniline has several resonance forms but anilinium has only one. That is, H H
'" {
H
H
V/
H
H
V/
HHIH
'" /
6-6-6 6 The additional resonance forms lead to a more stable first excited state; fluorescence in the ultraviolet region is the consequence. The fluorescence of certain compounds as a function of pH has been used for the detection of end points in acid-base titrations. For example, fluorescence of the phenolic form of l-naphthol-4-sulfonic acid is not detectable by the eye because it occurs in the ultraviolet region. When the compound is converted to the phenolate ion by the addition of base, however, the emission band shifts to visible wavelengths, where it can readily be seen. It is significant that this change occurs at a different pH than would be predicted from the acid dissociation constant for the compound. The explanation of this discrepancv is that the acid dissociation constant for the excited molecule differs from that for the same species in its ground state. Changes in acid or base dis-
r71 lQ.J
.Simulation:
Learn more about luminescence
spectroscopy.
sociation constants with excitation are common and are occasionally as large as four or five orders of magnitude. These observations suggest that analytical procedures based on fluorescence frequently require close control of pH. The presence of dissolved oxygen often reduces the intensity of fluorescence in a solution. This effect mav be the result of a photochemically induced oxidatio~ of the fluorescing species. More commonly, however, the quenching takes place as a consequence of the paramagnetic properties of molecular oxygen, which promotes intersystem crossing and conversion of excited molecules to the triplet state. Other paramagnetic species also tend to quench fluorescence. Effect of Concentration Fluorescence
on
Intensity
The power of fluorescence emission F is proportional to the radiant power of the excitation beam that is absorbed by the system. That is,
where Po is the power of the beam incident on the solution, P is its power after traversing a length b of the medium,
0 _~
'
-i -It= = =::~ ~~:~--~-~
tJi;L - ~ ~ ~ E
Sample D
Reference aperture
Sample photomultiplier tuhe
disk Xenon
compartment to reduce the amount of scattered radiation reaching the detector. Baffles are often introduced into the compartment for this purpose. Even more than in absorbance measurements, it is important to avoid fingerprints on cells because skin oils often fluoresce, Low-volume micro cells are available for situations in which sample volumes are limited. Several companies make flow cells for fluorescence detection in chromatography and in continuous flow analysis. Samplehandling accessories include micro-plate readers, microscope attachments, and fiber-optic probes. Lowvolume cells are often used for room-temperature phosphorescence and for chemiluminescence. Special cells and sample handling are needed for low-temperature phosphorescence measurements. Although the right-angle geometry shown in Figure 15-8 is most common. two other cell configurations are uscd. Front-surface geometry allows measurements on solutions with high absorbances or on opaque solids. The 180°, or in-line. geometry is rarely used because the weak luminescence signal must be isolated from the intense excitation beam by the emission wavelength selector. Data Manipulation
Modern computer-based luminescence instruments have many different data-manipulation schemes available in software, Common data-manipulation and display options include blank signal subtraction, production of corrected excitation and emission spectra. calculation and display of difference and derivative
spectra, peak dctection and processing, deconvolution, production of three-dimensional total hlminescence plots, fitting of calibration data, calclJl~tion of statistical parameters, and smoothing of spectra by various methods. Specialized software is available for kinetics, for high-performance liquid chromatography (HPLC) detection, for analysis of mixtures, and for time-resolved measurements.
Fluorometers
Filter fluorometers provide a relatively simple, lowcost way of performing quantitative fluorescence analyses. As noted earlier, eithcr absorption or interference tilters are used to limit thc wavelengths of thc excitation and emitted radiation. Generally, fluorometers are compact, rugged, and easy to use. Figure 15-10 is a schematic of a typical tilter fluorometer that uses a mercury lamp for fluorescence excitation and a pair of photomultiplier tubes as transducers. The source beam is split near the source into a reference beam and a sam pic beam. The reference beam is attenuated by the aperture disk so that its intcnsity is roughly the same as the fluorescence intensity. Both beams pass through the primary filtcr, with the reference beam then bcing reflected to the reference photomultiplier tube. The sample beam is focused on the sample by a pair of lenses and causes fluorescence emission. The emitted radiation passes through a second filter and
r::;l lQ.J
Tutorial: Learn more about fluorescence instrumentation.
lamp
then is focused on the second photomultiplier tube. The electrical outputs from the two transducers are then processed to compute the ratio of the sample to reference intensities, which serves as the analytical variable. The instrument just described is representative of the dozen or more fluorometers available commercially. Some of these are simpler single-beam instruments. Some are portable instruments for field work. The cost of such fluorometers ranges from several hundred dollars to more than $10,000. Spectrofluorometers
Several instrument manufacturers offer spectrofluorometers capable of providing both excitation and emission spectra. The optical design of one of these, which employs two grating monochromators, is shown in Figure IS-II. Radiation from the excitation monochromator is split. part passing to a reference photomultiplier and part to the sample. The resulting fluorescence radiation, after dispersion by the emission monochromator, is detected by a second photomultiplier. An instrument such as that shown in Figure 15-11 provides perfectly satisfactory spectra for quantitative
analysis. The emission spectra obtained will not, however, necessarily compare well with spectra from other instruments because the output depends not only on the intensity of fluorescence but also on the characteristics of the lamp, transducer, and monochromators. All of these instrument characteristics vary with wavelength and differ from instrument to instrument. A number of methods have been developed for obtaining a corrected spectrum, which is the true fluorescence spectrum freed from instrumental effects (see next section). Spectrofluorometers
Based on Array Detectors
A number of spectrofluorometers based on diodearray and charge-transfer devices have been described that permit fluorescence spectra to be obtained in fractions of a second" Several commercial instruments arc now available with CeD detectorss
~S~e, for example, R. S. Pomeroy in Charge Tramfer Devices in Spectroscopy, 1. V. Sweedler, K. L. Ratzlaff and t-.1. B. Denton. cds._ New York VCH, 199..t pp. 281-3l4; P. .\1. Epperson, R. D. Jalkian, and M. B. Denton. 4nal. Chon" 1989,61,282. 'For example. see instrumems made by Ocean Optics, Inc. Dunedin Florida. and Spa Division. Jobin Yvan. Edison. New la,ey.
l<XJ 11m). Because
characterized
vibrational
tions and rotations
level is quite small and corresponds 100 cm-'
are several
discrete
leaving
region.
quan-
of the har-
to describe
up next.
FIGURE 16-2 Types of molecular vibrations. Note that + indicates motion from the page toward the reader and - indicates motion away from the reader. and for
between
of a series
is highly restricted
samples,
disappear,
consists
there
for each
rotation
differences
to the mid-IR
lines, because
The
cannot
Transitions
energy
levels arc also quantized.
the energy
of a gas usually
in such tional
Transitions
correspond
spectrum
For a simple Rotational
16A-2 Mechanical
The
film. Note the scale change on the
Vibrational
ergy of
of mass results in
0> N" or CI,. As a result, such compounds IR radiation.
fre-
in the amplitude
fluctuations
650
to the theory
lield.
in dipole
or rotation
vibrational
of
of the radiation
their centers
moment
a
and
with the elec-
a natural
a change
~OO
Vibration
Vibrational-Rotational
vibrates, occurs,
If the frequency
Similarly,
around
tion with the radiation vibration
molecule
absorption
1000
J
of a thin polystyrene
the two centers
can interact
matches
em
1200
consider harmonic
discussed.
can be approximated
moment
with radiation.
exactly
of the
chloride
in its dipole
a field is established the radiation
between
spectrum
I~OO
1600
we first
are needed
interactions
in the char-
by a simple
Modilications
30
Wavenumber.
metric
that
represented which
a ~O(}O
quency
follows,
model.
two
of vibrations
is a change
treatment
oscillator,
than
involve bonds to a single ceninvolved.
monic
1(,-2 may
morc
or coupling
of the vibrations vihrations
oscillator ~O
10
regular
interaction
schematically
in Figure
containing
tral atom. The result of coupling
,
sorb
In addition.
are shown
tvpes shown
in a molecule
90
70
~
These
in Figure 16-2. All of the vibration
15.0
OSCillator. (b) Curve 1, harmonic
a disof force
F is proportional That is,
to the displacement
(Hooke's law).
where k is the force constant. which depends on the stiffness of the spring. The negative sign indicates that F is a restoring force. This means that the direction of the force is opposite the direction of the displacement. Thus, the force tends to restore the mass to its original position. Potential Energy of a Harmonic
Oscillator
The potential energy E of the mass and spring can be arbitrarily assigned a value of zero when the mass is in its rest, or equilibrium, position. As the spring is compressed or stretched, however, the potential energy of this system increases by an amount equal to the work required to displace the mass. If, for example, the mass is moved from some position y to y + dy, the work and hence the change in potential energy dE is equal to the force F times the distance dy. Thus, dE
=
-Fdy
Molecular
d'v m dr', = -ky
A solution to this equation must be a periodic function such that its second derivative is equal to the original function times - k/m. A suitable cosine relationship meets this requirement. Thus, the instantaneous displacement of the mass at time r can be written as
where " •• is the natural vibrational frequency and A is the maximum amplitude of the motion. The second derivative of Equation 16-6 is
d'y --"
dt"
V,;,Acos21TVmt
-41T2
=
Substitution of Equations tion 16-5 gives
l6-6 and 16-7 into Equa-
dE = ky dy
i'dE o
=
a and
= j"'ydy 0
E = !ky' 2 The potcntial-energy curve for a simple harmonic oscillation, derived from Equation 16-4, is a parabola, as depicted in Figure l6-3a. Notice that the potential energy is a maximum when the spring is stretched or compressed to its maximum amplitude A, and it decreases to zero at the equilibrium position. Vibrational Frequency
where "m is the natural frequency of the mechanical oscillator. Although it depends on the force constant of the spring and the mass of the attached body, the natural frequency is independent of the energy imparted to the system; changes in energy merely result in a change in the amplitude A of the vibration. The equation just developed may be modified to describe the behavior of a system consisting of two masses ml and m, connected by a spring. Here, it is only necessary to substitute the reduced mass I' for the single mass m where
The motion of the mass as a function of time r can be deduced from classical mechanics as follows. Newton's second law states that
m1n12
1'=----Inl
Thus. the vibrational given by where m is the mass and a is its acceleration. But acceleration is the second derivative of distance with respect to time. Thus,
1 Vm
=
n1~
frequency for such a svs[em is
!k
l;-\/;
+
'[(nil + m,)
I
=
21T
\.
fJljJ112
because v in Equations 16-11 and 16-12 can assume only whole numbers; that is,
h
j.E=hv
=-
••
rk
i-
27r \ I'
At room temperature, the majority of molecules are in the ground state v = 0; thus, from Equation 16-12, 1
Eo
"2h"
=
••
16A-3 Quantum Treatment of Vibrations The equations of ordinary mechanics that we have used thus far do not completely describe the behavior of particles of atomic dimensions. For example, the quantized nature of molecular vibrational energies, and of other atomic and molecular energies as well, does not appear in these equations. We may, however, invoke the 'concept of the simple harmonic oscillator to develop the wave equations of quantum mechanics. Solutions of these equations for potential energies have the form
E=(V+l)!!-2
Combining Equations 16-3 and 16-2 yields
Integrating between the equilibrium positiony y gives
Vibrations
The approximation is ordinarily made that the behavior of a molecular vibration is analogous to the mechanical model just described. Thus, the frequency of the molecular vibration is calculated from Equation 16-10 after substituting the masses of the two atoms for ml and m,. The quantity k is the force constant of the chemical bond, which is a measure of its stiffness.
27r\);
(£
(v
+ ~ )h"",
(16-12)
where v'" is the vibrational frequency of the classical model.' We now assume that transitions in vibrational energv levels can be brought about by absorption of radi;iion. provided the energy of the radiation exactly matches the difference in energy levels j.E between the vibrational quantum stales and provided also the vibration causes a change in dipole moment. This difference is identical between any pair of adjacent levels. 'Lnfortunatdv. the generally accepted ~"ymbol tor the vibrational quantum numher r'is similar in appearance [0 the Greek nu. Il. which symboliZeS frequeno.:y. Thus. conslant care must he exercised to avoid confusing, the two 1Il equations -.;uch as Equation 16-12
•• - !h" 2 •• ) = h"••
The frequency of radiation v that will bring about this change is identical to the classical vibrational frequency of the bond "",. That is, E radiation
where h is Planck's constant, and v is the vibrational quanttlm number, which can take only positive integer values (including zero). Thus, in contrast to ordinary mechanics where vibrators can assume any potential energy, quantum mechanical vibrators can take on onlv certain discrete energies. it is interesting to note that the factor Vk/J1./2rr appears in both the classical and the quantum equations; by substituting Equation 16-10 into 16-11, we find
F. =
("i2h"
-
y
I..).
-
v=v
II
'E' = h,' m =!!21T \j f..L
- h •. -
••
=~
0-
2rr \I I'
If we wish to express the radiation in wave numbers, we substitute Equation 6-3 and rearrange:
v
1'-';
=
-,12rrc 'IJ I'
=
5.3x
" ,-,;
1O-'"\!-' I'
where v is the wavenumber of an absorption maximum (cm - I), k is the force constant for the bond in newtons per meter (N/m), c is the velocity of light (cm sol), and I' is the reduced mass (kg) defined by Equation 16-93 IR measurements in conjunction with Equation 16-14 or 16-15 permit the evaluation of the force constants for various types of chemical bonds. Generally, k has been found to lie in the range between 3 X la' and 8 X 10' N/m for most single bonds, with 5 x 10' serving as a reasonable average value. Double and triple bonds are found by this same means to have force constants of about two and three times this value (1 X 103 and l.5 X 103 N/m, respectively). With these
average experimental values, Equation 16-15 can be used to estimate the wavenumber of the fundamental absorption band, or the absorption due to the transition from the ground state to the first excited state, for a variety of bond types. The following example demonstrates such a calculation.
is, the selection rule states that ilv = :$100,000), and required frequent mechanical adjustments. For these reasons, their use was limited to special applications where their unique characteristics (speed, high resolution, sensitivity, and unparalleled wavelength precision and accuracy) were essential. FT instru-
5For detailed discu~ions of Fourier transform IR spectroscopy, see S. Davis, M. Abrams. J. Brault, Fourier Trallsforll! Spectrometry, San Diego' Academic Press, 20t.H: B. C. Smith. FundameJltllls of Fourier Transform Infrared SpeCIr05copy. Boca Raton. FL: eRe Press. 1996; P. R Gnfiiths and J. A. dd-Iaselh. Fourier Trans/ormln(rared Spectroscopy. :\cw York:
Three types of instruments for IR absorption mea~ surements are commonly available: (1) dispersive spectrophotometers with a grating monochromator; (2) Fourier transform spectrometas employing an
Wile\'. 1986 "'For"a description of tht: Hadamard transform and Hadamard tran.sform spectroscopy. see D. K. Graff. I Cht'm. Educ.. 1995, 72, 30-L Fourier, Hadamard, and Hilbert Tramjorms ill Chemistn'. A. G.I\Iarshall, cd .. Ne\\ York: Plenum Press. 19S2.
ments have now been reduced to benchtop size and have become reliable and easy to maintain. Further~ more, the price of simpler models has been reduced to the point where they are competitive with all but the simplest dispersive instruments (-$15.000 and more). For these reasons, FT instruments have largely displaced dispersive instruments in the laboratory.Components
of FT Instruments
The majority of commercially available FTIR instru~ ments are based on the Michelson interferometer, al~ though other types of optical systems are also encoun~ teredo We shall consider the Michelson design only, which is illustrated in Figure 7~43.8 Drive Mechanism, Requirements for satisfactory in~ terferograms (and thus satisfactory spectra) are that the moving mirror have constant speed and a position exactly known at any instant. The planarity of the mir~ ror must also remain constant during its entire sweep of 10 em or more. In the far-IR region, where wavelengths range from 50to 1000 ~m (200 to 1Oem-I),displacementofthe mir~ ror bv a fraction of a wavelength, and accurate mea~ sure~ent of its position, can be accomplished by means of a motor-driven micrometer screw. A more precise and sophisticated mechanism is required for the mid~ and near-IR regions, however. Here, the mirror mount is generally floated on an air bearing held within close~ fitting stainless steel sleeves (see Figure 16~4). The mount is driven by a linear drive motor and an electromagnetic coil similar to the voice coil in a loudspeaker; an increasing current in the coil drives the mirror at constant velocity. After reaching its terminus, the mirror is returned rapidly to the starting point for the next sweep by a rapid reversal of the current. The length of travel varies from 1 to about 20 cm; the scan rates range from 0.01 to 10 cm Is. Two additional features of the mirror system are necessary for successful operation. The first is a means of sampling the interferogram at precisely spaced re~ tardation intervals. The second is a method for determining exactly the zero retardation point to permit signal averaging. If this point is not known preciselv.
"For a r.:view of commercial FTIR spectromd~rs, see 1. P. Smith JnJ Y_Hinson-Smith, Anal. Chon .. 2003. 75, 37:\ ~The \.tichdso/l intafaometer was designed and built in UNl by .-\ . .-\ Michelson. He wa, awarded the 190"7Nobel Prizplltter
detector
/
Mirror, Cen[ef
'\JIll
hole
for laser beam
FIGURE 16-8 Single-beam FTIRspectrometer. In one arm of the interferometer, the IR source
radiation travels through the beamsplitter to the fixed mirror, back to the beamsplitter, and through the sample to the IR transducer. In the other arm, the IR source radiation travels to the beam splitter, is reflected to the movable mirror, and travels back through the beam splitter to the sample and to the transducer. When the two beams meet again at the beamsplitter, they can interfere with each other if the phase difference (path difference) is appropriate. A plot of the signal versus mirror displacement is the interferogram. The interferogram contains information about all the frequencies present. The spectrum, intensity versus wavenumber, is the FT of the interferogram. It can be calculated with a computer from the signal versus mirror displacement. An empty sample compartment allows the reference spectrum to be calculated. Next, the sample is placed in the sample compartment and the sample spectrum is obtained. The absorbance is then calculated at each wavenumber from the ratio of the sample intensity to the reference intensity. lution of 4 cm' 1. This performance can be obtained with a scan time as brief as 1second. More expensive instruments with interchangeable beamsplitters, sources, and transducers offer expanded frequency ranges and higher resolutions. For example, one instrument is reported to produce spectra from the far-IR (10 em-lor 1000 ~m) through the visible region to 50,000 em -1, or 200 nm. Resolutions for commercial instruments vary from 8 to less than 0.01 cm -1 Several minutes are required to obtain a complete spectrum at the highest resolution.' Advantages
of FT Spectrometers
Over most of the mid-IR spectral range, FT instruments have signal-to-noise ratios that are better than those of a good-quality dispersive instrument. usually by more than an order of magnitude. The enhanced
signal-to-noise ratio can, of course, be traded for rapid scanning, with good spectra being attainable in a few seconds in most cases. Interferometric instruments arc also characterized by high resolutions «0.1 cm 1) and highly accurate and reproducible frequency determinations. The latter property is particularly helpful when spectra are to be subtracted for background correction. A thcoretical
advantage of FT instruments is that their optics provide a much larger energy throughput (one to two orders of magnitude) than do dispersive instruments, which are limited in throughput by the need for narrow slit widths. The potential gain here, however, may be partially offset by the lower sensitivity of the fast-response detector required for the interferometric measurements. Finally, it should he noted that
the interferometer is free from the problem of stray radiation because each IR frequency is. in effecl, chopped at a different frequency. The areas of chemistry where the extra performance of interferometric instruments has been particularly useful include (l) very high-resolution work that is encountered with gaseous mixtures having complex spectra resulting from the superposition of vibrational and rotational bands; (2) the study of samples with high absorbances; (3) the study of substances with weak ahsorption bands (for example. the study of compounds that are chemisorbed on catalyst surfaces); (4) investigations
requiring
fast scanning
such as kinetic
studies
or detection of chromatographic eftluents; (5) collecting IR data from vcrv small samples; (0) obtaining reflection spectra; and (7) IR emission studies.
Wavenumber.
4000
cm-1
,
2000
5UOO
1500
1300
1100
1000
800
900
700
650
100 90
" Doubk~beam
mode
80 1J'
~. Sample compartment
~ .~
1- - - - - - - - -I I
d [I
(/~;J
§
I
.[..
J..... .
·
,
·.·.:.:·~
:::/::::..)~
f-
70 60
Single-beam
50
mode
40 30
H2O
CO2
20 H2O
10
CO2
0 4
// .••
I I
~ /'~'
//1:
"',
Wavelength.
"
12
13
14
15
16
_
Double-beam FTIRspectrometer. The beam emerging from the interferometer strikes mirror M" which in one position directs the beam through the reference cell and in the other position directs it through the sample cell. MirrorM" which is synchronized to M" alternately directs the reference beam and the sample beam to the transducer. FIGURE
II
16-10 Single- and double-beam spectra of atmospheric water vapor and CO,. In the lower. single-beam trace. the absorption of atmospheric gases is apparent. The top. doublebeam spectrum shows that the reference beam compensates very well for this absorption and allows for a stable 100% T baseline to be obtained. (From J. D. Ingle Jr. and S. R. Crouch. Spectrochemical Analysis, p. 409, Upper Saddle River, NJ: Prentice-Hall, 1988. With permission.)
:1 1-
10 ,um
FIGURE
I I I I
:1
9
6
" .....
16-9
168-2 Dispersive Instruments Although most instruments produced today are FT systems, many dispersive spectrophotometers are still found in laboratories. Dispersive IR spectrophotometers are generally double-beam, recording instruments, which use reflection gratings for dispersing radiation. As was pointed out in Section 130-2, the double-beam design is less demanding with respect to the performance of sources and detectors - an important characteristic because of the relatively low intensity of IR sources, the low sensitivity of IR transducers, and the consequent need for large signal amplifications (see Section 16C). An additional reason for the general use of doublcbeam instruments in the lR region is shown in Figure 16-10. The lower curve reveals that atmospheric water and carbon dioxide absorb radiation in some important spectral regions and can cause serious interference problems. Thc upper curve shows that the
reference beam compensates nearly perfectly for absorption by both compounds. A stable 100% T baseline results. Generally, dispersive IR spectrophotometcrs incorporatc a low-frequency chopper (five to thirty cycles per sccond) that permits thc detector to discriminate betwccn the signal from the source and signals from extraneous radiation, such as fR emission from various bodics surrounding the transducer. Low chopping rates are demanded by the slow response times of the IR transducers used in most dispersive instrumcnts. In general, the optical designs of dispersive instruments do not differ greatly from the double-beam UV -visible spectrophotometers discussed in the previous chapter except that the sample and reference compartments are always located between the sourcc and the monochromator in IR instruments. This arrangement is possible because IR radiation, in contrast to UV-visible, is not suiliciently energetic to cause photochcmical decomposition of thc sample. Placing the sample and
reference before the monochromator, however, has the advantage that most scattered radiation and IR emission, generated within the cell compartment, is effectively removed by the monochromator and thus does nol reach the transducer.
Attenuat<Jr
Reference
.'h
Figure 16-11 shows schematically the arrangement of components in a typical IR spectrophotometer. Like many inexpensive dispersive IR instruments, it is an optical null type, in which the radiant power of the reference beam is reduced, or attenuated, to match
~7Jmntor
Soun.:c
>-.J
\
,t_--EJ---1
_~J__~_-,____ Chopper
I
•
16-11 Schematic diagram of a double-beam, dispersive IR spectrophotometer. The heavy black tines indicate mechanical linkages, and the light lines indicate electrical connections. The radiation path is designated by dashed lines. FIGURE
15 I-'m). For example. heavy-metal iodides generally absorb radiation in the region below l00cm-l, and the bromides and chlorides have bands at higher frequencies. Absorption frequencies for metal-organic bonds ordinarily depend on both the metal atom and the organic portion of the species. Far-IR studies of inorganic solids have also provided useful information about lattice energies of crystals and transition energies of semiconducting materials. Molecules composed only of light atoms absorb far-IR radiation if they have skeletal bending modes that involve more than two atoms other than hydrogen. Important examples are substituted benzene derivatives, which generally show several absorption bands. The spectra are frequently quite specific and useful for identifying a particular compound. There are also characteristic group frequencies in the far-IR region. Pure rotational absorption by gases is observed in the far-IR region, provided the moleculcs have permanent dipole moments. Examples include H,O. 0" HCL and AsH). Absorption by water is troublesome: elimination of its interference requires evacuation or at least purging of the spectrometer. Prior to the advent of Fourier transform spectrometers, experimental difficulties made it difficult to obtain good far-IR spectra. The sources available in this region are quite low in intensities. Order-sorting filters
are needed with grating instruments in this region to minimize radiation diffracted from higher grating orders. These reduced the already low throughputs of dispersive spectrometers. It is no surprise that Fourier transform spectrometry was first applied in this spectral region. The high throughput of interferometers and the relatively low mechanical tolerances required made it fairly simple to obtain FTIR spectra in the farIR region with good signal-to-noise ratios.
When they are heated, molecules that absorb IR radiation are also capable of emitting characteristic IR wavelengths. The principal deterrent to the analytical application of this phenomenon has been the poor signal-to-noise characteristics of the IR emission signal. particularly when the sample is at a temperature only slightly higher than its surroundings. With)nterferometry, however, interesting and useful applications have appeared in the literature. An early example of the application of IR emission spectroscopy is found in a paper that describes the use of a Fourier transform spectrometer for the identification of microgram quantities of pesticides.21 Samples were prepared by dissolving them in a suitable solvent followed by evaporation on a NaCI or KBr plate. The plate was then heated electrically near the spectrometer entrance. Pesticides such as DOT, malathion. and dieldrin were identified in amounts as low as 1 to 10 I-'g. Equally interesting has been the use of interferometry for the remote detection of components emitted from industrial smoke stacks. In one of thcse applications. an interferometer was mounted on an 8-inch reflecting telescope." With the telescope focused on the plume from an industrial plant. CO, and SO, werc readily detected at a distance of several hundred feet. The Mars Global Surveyor launched from Cape Canaveral in November 1996. It reached Mars orbit in 1997. One of fivc instruments on board was an IR emission spectrometer, called a thermal emission spectrometer. The spacecraft completed its mapping mission in 20Dl. providing measurements of the Martian surface and atmosphcre. The Mars rover Spirit has a
» 0.95
~ U3 0.9
17-18 Spectra from Mars rover Spirit showing an unidentified mineral containing bound water in its crystal structure. Minerals such as zeolites and gypsum are possible candidates. Mini-TES = mini thermal-emission spectrometer. (Courtesy of NASA/JPLlArizona State University.)
FIGURE
mini thermal-emission spectrometer on board capable of indicating the composition of nearby soils and rocks. Figure 17-18 shows an IR emission spectrum taken in early 2004 that showed evidence of an unidentified water-containing mineral, Thermal emission spectra have also indicated the presence of carbonates and other hydrated minerals. These may have been produced by long-standing bodies of water.
IR microspectrometry is used for obtaining absorption or reflection spectra of species in samples having physical dimensions in the range of 10 to 500 1-'01." IR microscopes, which were first introduced bv several instrument manufacturers in the 1980s, gen~rally consist of two microscopes. one an ordinary optical microscope and the other an IR device with reflection optics that reduce the size of the IR beam to about that of the sample. The optical microscope is used to visuallv locate the sample particle or spot to be studied with the IR beam. The IR source is an ordinary Fourier transform spectrometer and not a grating instrument because of the much greater sensitivity of FTiR instruments. The detector is usually a liquid-nitrogen-cooled mercury telluride-cadmium telluride photoconductive device that is more sensitive than other types of IR detectors. The use of IR microscopy is still fairly new but appears to be a technique that will find increasing applications in the future. Some of its current applications include identification of polymer contaminants, imperfections in polymer films, and individual layers of laminated polymer sheets; identification of tiny samples of fibers, paint, and explosives in criminalistics; characterization of single fibers in the textile industry; and identification of contaminants on electronic components. ee Practical Guide to Infrared Microspectroscopy, H. J. Humecki. ed., New York: Marcel Dekker, 1995~J. Katon. Tnfrared Microspectroscopy in Modern Techniques in Molecular Spectroscopy, F. Mirabella, ed., New York: Wiley, 1998.
23S
* Answers are provided at the end of the book for problems marked with an asterisk. ~
Problems with this icon are best solved using spreadsheets.
17-1 Cyclohexanone exhibits its strongest IR absorption band at 5.86I-'m, and at this wavelength there is a linear relationship between absorbance and concentration. (a) Identify the part of the molecule responsible for the absorbance at this wavclength. (b) Suggest a solvent that would be suitable for a quantitative analysis of cyclohexanone at this wavelength. (c) A solution of cyclohexanone (4.0 mg/mL) in the solvent selected in part (b) exhibits a blank-corrected absorbance of 0.800 in a cell with a path length of 0.025 mm. What is the detection limit for this compound under these conditions if the noise associated with the spectrum of the solvent is 0.001 absorbance units'!
*17-2 The spectrum in Figure 17-19 was obtained for a liquid with the empirical formula of C,H60. Identify the compound. 17-3 The spectrum in Figure 17-20 is that of a high-hailing-point liquid having the empirical formula C,HIOO. Identify the compound as closely as possihle. *17-4 The spectrum in Figure 17-21 is for an acrid-smelling liquid that boils at 50°C and has a molecular weight of about 56. What is the compound') What impurity is clearly present" *17-5 The spectrum in Figure 17-22 is that of a nitrogen-containing hails at 9TC. What is the compound"
substance that
~,.
.-
!-'-.. -
r'c-
~
=
17-7 Discuss the origins of photoacoustic IR spectra. What are the usual types of samples for photoacoustic measurements'? 17·8 Why do IR spectra seldom show regions at which the transmittance
c-
!_.t-
*17-11 Estimate the thickness of the polystyrene film that yielded the spectrum shown in Figure 16-1.
'"'"
''"" a:
==
,
,.-
"'k~
=:+
,,i\..I-I-,
"1-
t~=f
~
T
i-
f
f L=
r-'
...T)---
...
.~
---
1-
--
_._,
-_.'
- -
==\:.
t
, .LMfT'1\.
....
---
----
,J.(E
f--
.•.
r
i
~
i
i2
-
_1
i
0
i2
1-; i
1:+
t'
iC" t-
.,
i
8}, .--
-
''1 ....
~
-;
§ ri' .c E
;
'"
o ~ ~~ ~ § 0:'= (J
;'l
E(fJ :J
'"
~~ 0.0
I
~
0 0
t T
0 or,
:it
0'
;!
~
::0
,---
::-:1
c
~
0 N
i~r:-l't r
1 '
q; ;, '"
! 'i
7"
L::
N=o
~
,··Hi
..-
== ~~ ,
0
---
cr:i:t=. r--
~
E~
'"
.£1::J
-§::?' ~o-
::: "~
.",
-.,..
...
r:===
c__
.\
!
(J
E
(fJO
le-f
\IW
=
106
60
~o
"
~
50
60 mle
FIGURE 20-1 Mass spectrum of ethyl benzene.
describe several of the current applications of molecular mass spectrometry.'
Figure 20-1 illustrates how mass spectral data are usually presented. The analyte was ethyl benzene, which has a nominal molecular mass of 106 daltons (Da). To obtain this spectrum, ethyl benzene vapor was bombarded with a stream of electrons that led to the loss of an electron by the analyte and formation of the molecular ion M' as shown by the reaction
The charged species C"HsCH,CHj- is the molecular ion. As indicated by the dot, the molecular ion is a radical ion that has the same molecular mass as the molecule. The collision hetween energetic electrons and analyte molecules usually imparts enough energy to the molecules to leave them in an excited state. Relaxation then often occurs by fragmentation of part of the molecular ions to produce ions of lower masses. For exFor dct
~ ~
60 40
20 ~_ / C,H'6
atomic beam
Energetic beam of ions High temperature
mass spectrum from a soft ionization source often consists of the molecular ion peak and only a few, if any, other peaks. Figure 20-2 illustrates the difference in spectra obtained from a hard ionization source.and a soft ionization source. , Both hard- and soft-source spectra are useful for analysis. The many peaks in a hard-source spectrum provide useful information about the kinds of functional groups and thus structural information about analytes. Soft-source spectra are useful because they supply accurate information about the molecular mass of the analyte molecule or molecules.
+-~I-----l--------r-
0 40
60
120
140
100 -
80
"=
Base peak CHJ(CH,J,CH,'
u
~
-0
§
60
">
40
-;;
~ ~
20
70
0
Historically, ions for mass analysis were produced by electron impact. In this process, the sample is brought to a temperature high enough to produce a molecular vapor, which is then ionized by bombarding the resulting molecules with a beam of energetic electrons. Despite certain disadvantages, this technique is still of major importance and is the one on which many libraries of mass spectral data are based. Figure 20-3 is a schematic of a basic electron-impact ion source. Electrons are emitted from a heated tungsten or rhenium filament and accelerated by applying approximately 70 V between the filament and the anode. As shown in the figure, the paths of the electrons and molecules are at right angles and intersect near the center of the source, where collision and ionization occur. The primary product is singly charged positive ions formed when the energetic electrons approach molecules closelv enough to cause
60
FIGURE 20-2 Mass spectrum of 1-decanol from (a)a hard ionization source (electron impact) and (b) a soft ionization source (chemical ionization).
An electron-impact ion source. (Adapted from R. M. Silverstein and F.X. Webster, Spectrometric FIGURE 20-3
Identification of Organic Compounds,
6th ed., p. 4, New York:Wiley, 1998. Reprinted with permission of John Wiley & Sons, Inc.)
them to lose electrons by electrostatic repulsion. Electron-impact ionization is not very efticient. and only about one molecule in a million undergoes the primary reaction
ThUS, if all ions acquire the same amount of kinetic energy. those ions with largest mass must have the smallest velocity.
L
(a) Calculate the kinetic energy that a singly charged ion (z = 1) will acquire if it is accelerated through a potential of 103 V in an electron-impact source. (b) Does the kinetic energy of the ion depend on its mass? (c) Does the velocity of the ion depend on its masso Solution
where e is the electronic coulombs). Thus, for z ~ 1
charge
(1.6 x 10-19
(b) The kinetic energy that an ion acquires in the source is independent of its mass and depends only on its charge and the accelerating potential. (c) The translational component of the kinetic energy of an ion is a function of the ion mass m and its vclocity v as given by the equation
ABCD + e- -. ABCD·· + 2e-
To form a significant number of gaseous ions at a reproducible rate, electrons from the filamcnt in the source must be accelerated by a voltage of greater than about 50 V. The low mass and high kinetic energy of the resulting electrons cause little increase in the translational energy of impacted molecules. Instead. the molecules are left in highly excited vibrational and rotational states. Subsequent relaxation then usually takes place by extensive fragmentation, giving a large number of positive ions of various masses that are less than (and occasionally, because of collisions, greater than) that of the molecular ion. These lower-mass ions are called daughter ions. Table 20-2 shows some typical fragmentation reactions that follow electron.impact formation of a parent ion from a hypothetical'/Uolecule ABeD. In Example 20-2, the kinetic energy of electrons accelerated through a potential difference of 70 V is calculated.
EXAMPLE 20-2
(a) Calculate the energy (in llmol) that electrons acquire as a result of being accelerated through a potential of 70 V. (b) How does this encrgy compare to that of a typical chemical bond?
(a) The kinetic energy KE of an individual electron is equal to the product of the charge on the electron e times the potential V through which it has been accelerated. Multiplying the kinetic energy of a single electron by Avogadro's number. N, gives the energy per mole: KE
=
eVN
= (1.60
X
= (I.l2
X
= 6.7
t:
Spectra
Solution
(a) The kinetic energy (KE) added to the ion is due to the accelerating potential V and is given by the equation
Fragmentation
ABCD·' -. A' Electron-Impact
Here. M represents the analyte molecule, and M'+ is its molecular ion. The positive ions produced by electron impact arc attracted through the slit in the first accelerating plate by a small potential difference (typically 5 V) that is applied between this plate and the repellers shown in Figure 20-3. With magnetic sector instruments, high voltages (103 to 10' V) are applied to the accelerator plates, which give the ions their final velocities before they enter the mass analyzer. Commercial electron-impact sources are more complex than that shown in Figure 20-3 and may use additional electrostatic or magnetic fields to manipulate the electron or ion beam. A typical kinetic energy produced in an electron-impact source is calculated in Example 20-1.
Molecular ion formation
10-19 C/e-)(70 V)N 10-17 CVle )(6.02 X 1023e-/mol)
X 1061lmol
or
6.7 X !OJ kllmol
(b) Typical bond energies fall in the 200- to 600-kl1mol range. Therefore, an electron that has been accelerated through 70 V generally has considerably more energy than that required to break a chemical bond.
A. CD.
---c~~.:~~:
Rearrangement followed by fragmentation
ABCD·' -. ADBC
Collision followed by fragmentation
ABeD·' + ABCD ....•(ABCD);'....•BCD· + ABCDA'
The complex mass spectra that result from electronimpact ionization are useful for compound identification. On the other hand, with certain types of molecules, fragmentation is so complete that no molecular ion persists. Without a molecular ion, important information for determining the molecular mass of the analyte is lost. Figure 20-4 shows typical electron-impact spectra for two simple organic molecules: methylene chloride and I-pentano!. Note that in each of the spectra. the base peak corresponds to a fragment of the molecule. which has a mass significantly less than the molecular mass of the original compound. For methylene chloride, the base peak occurs at a mass-to-charge ratio mlz of 49, which corresponds to the loss of one CI atom. For I-pentanol, the base peak is found at an mlz of 44, which is that of the daughter CH2CHOH+. More often than not, the base peaks in electron-impact spectra correspond to fragments such as these rather than the molecular ion. The molecular ion peak occurs at a mass corresponding to the molecular mass of the analyte. Thus. molecular ion peaks appear at mlz = 84 for methylene chloride and at mlz = 88 for I-pentanol. The molecular ion peak is, of course. very important in structural determinations, because its m/z value provides the molecular mass of the unknown. Unfortunately, it is not always possible to identify the molecular ion peak. Indeed, electron-impact ionization of certain molecules yields no molecular ion peak at all (see Figure 20-2a). Isotope Peaks
It is interesting to note in the spectra shown in Figures 20-1 and 20-4 that peaks occur at mass-to-charge ~
AS"
+ BCD· + BCD.c-.BC'+D + AB + -------" B + A' 4A + B+ D+C + CD'---CC + D'
Tutorial: Learn more about sources for MS.
ratios greater than that of the molecular ion. These peaks are attributable to ions having the same chemical formula, but different isotopic compositions. For example, for methylene chloride, the more important isotopic species are 12CIH/'CI, (ctl = 84), uCIH/'CI2 Ctl = 85), 12C1H,J5C1"C1 (elt = 86), lJCIH,35CIJ7Cl (.M = 87), and 12C1H/'Cl, (At = 88), where Jtl is molecular mass. Peaks for each of these species can be seen in Figure 20-4a. The size of the various peaks depends on the relative natural abundance of the isotopes. Table 20-3 lists the most common isotopes for atoms that occur widely in organic compounds. Note that fluorine, phosphorus, iodine, and sodium occur only as single isotopes. The small peak for ethyl benzene at mlz 107 in Figure 20-1 is due to the presence of 13Cin the molecules. The intensities of peaks due to incorporation of two or more lJC atoms in ethyl benzene can be predicted with good precision but are normally so small as to be undetectable because of the low probability of there being more than one 13Catom in a small molecule. As will be shown in Section 200-1, isotope peaks sometimes provide a useful means for determining the formula for a compound. Collision Product Peaks
Ion-molecule collisions. such as that shown by the last equation in Table 20-2, can produce peaks at higher mass numbers than that of the molecular ion. At ordinary sample pressures, however. the only important reaction of this type is one in which the collision transfers a hydrogen atom to the ion to give a protonated molecular ion. The result is an enhanced (M + 1)' peak. This transfer is a second-order reaction, and the amount of product depends strongly on the reactant concentration. Consequentlv, the height of an (M + 1) +
~ ~
80
§ -;:
60
peak due to this reaction increases much morc rapidly with increases in sample pressure than do the heights of other peaks. This phenomenon usually makes it possible to detect this atom-transfer rcaction.
49
100
Base peak
84
,CH,CI'
CH,CI, MW = 84
"
~1+
CH,CI/
:;
u >
Advantages
'"
20 -
II
I,
0 0
I
I
\0
20
40
30
I
50
70
60
80
I
I
90
\00
110
mlz
(a)
100
M - (HoG and CH,=CH,)
~ ~ ~
Base peak
(CII,=OH')
M - (H,o and CIl,)
=
.0
'0
50
M - (H,O)
~ ~~ 0 0
10
20
40
30
50
60
70
80
90
100
Sources
Electron-impact sources are convenient to use and produce high ion currents, thus giving good sensitivities. The extensive fragmentation and resulting large number of peaks is also an advantage because it often makes unamhiguous identification of analytes possible. Extensive fragmentation can also be a disadvantage, however, when it results in the disappearance of the molecular ion peak so that the molecular mass of analytes cannot be easily established. Another limitation of the electron-impact source is the need to volatilize the sample, which may result in thermal degradation of some analytes before ionization can occur. The effects of thermal decomposition can sometimes be minimized by carrying out the volatilization from a heated prohe located close to the entrance slit of the spectrometer. At the lower pressure of the source area, volatilization occurs at a lower temperature. Furthermore, less time is allowed for thermal decomposition to take place. As mentioned earlier, electron-impact sources are applicable only to analytes having molecular masses smaller than about 10' Da.
40
-,;=
and Disadvantages
of Electron-Impact
110
mlz
shown in Figure 20-3 by adding vacuum pump capacity and by reducing the width of the slit to the mass analyzer. These measures allow a reagent pressure of about I torr to be maintained in the ionization area while maintaining the pressure in the analyzer below 10-' torr. With these changes, a gaseous reagent is introduced into the ionization region in an amount such that the concentration ratio of reagent to sample is 10' to 10'. Because of this large concentration difference, the electron beam reacts nearly exclusively with reagent molcculcs. One of the most common reagents is methane, which reacts with high-energy electrons to give scveral ions such as CH, ' , CHJ " and CH, +. The first two predominate and represent about 90% of the reaction products. These ions react rapidly with additional methane molecules as follows: CH, - + CH,
-->
CHs'
CH3 + + CH,
-->
C,Hs'
+ CH3 + H,
Generally, collisions between the analyte molecule MH and CHs; or C2Hs' are highly reactive and involve proton or hydride transfer. For example,
+ MH --> MH,' + CH4 + MH --> MH,' + C2H4 C,H5 + + MH --> M+ + C,H6 CHs'
proton transfer
C,H5'
proton transfer hydride transfer
(b)
20B-2 Chemical Ionization Sources and Spectra
FIGURE 20-4 Electron-impact mass spectra of (a) methylene chloride and (b) 1-pentanol.
Abundance of Other Isotopes Relative to 100 Parts of the Most Ahundant"
Most Abundant Isotope
Element' Hydrogen Carbon Nitrogen Oxygen
'H
"c "N 160
'H BC
0,0]5
ISN
0.37
"0 0 33S
0.04 0.20
1.08
18
Us
Sulfur
0.80 4.40
"s Chlorine
350 79Br 2.~Si
Bromine Silicon
'Fluorine
(1"F'I,
phosphoru~
(.;lpl.
sodium ('\~a).
and indio.:
~The numerical entries indicate the average numhcr uf atoms there will he an average of 1.08 I 'C alom5.
lie
isulOPlC
37CI
32.5
81Br
98.0 5.1 3.4
29Si JOSi I) have
IW
additional
natlHally
occurring
alums present f\Jr ..:ach lOUatoms
(}f
Isot()PC~
lhe most abundant
i~\ltup "
Matrix-Assisted
'"
Matrix-assisted
of magnitude
electron-impact
used
is rel-
~o
maximum
sources;
currents
ionization
the ionizing
ods are not applicable stable
samples.
methods
have
heen
developed
(see Tahle
mass spectra
icate biochemical masses followed
20-1). These
to be obtained
than methods
energy
spectra
formation arc greatly
'"
chamber
methods
have del-
dispense
with
in I'arious
of gaseuus simplified
forms
volatilization analyte
mole-
is introduced
in such a way as to cause ions. As a consequ~nce. and often
consist
of ani I
to several
for glufrom
groups,
plate.
The plate
to the
.,
~O
I
scribed.'
80
lascr
The MALDI
radiation.
The
usual
can
in molecular
mass
thousand
oa,
simultaneously
one German
and the is avail-
steel probe
is then placed
of the
is focused has
or placed
in a vacuum
onto the sample.
vacuum-chamher
matrix
be
information
in a solid or liquid matrix
MALoI matrix
mass
a low concentration
dispersed
and a laser beam
that
instrumentation
technique,
atmospheric-pressure ,.
peak
(MALol)
nearly
on the end of a stainless
In addition
de-
the protonated
hundred
was first described
is uniformly
deposited
un-
100,000 Da.
into the solid or liquid sample Jircct
-;;
having molecular
bv ionizat ion of the gaseous
Instead.
that
Such meth-
for thermally
ranging
In the MALoI
on a metal
this
spectrum
method
biopolymers
in 1988 by two research
" ~o
with
thermal
is complete.
of only
other Japanese." Commercial able for MALO!.'
>
ionization
consists
molecular
The method
"~
for dealing
species and species
of greater
Desorption
of desorption
polar
analyte
or thermally
With by pass-
than the spectrum
accurate
(b)
are on the
so far require samples.
to nonvolatile
A number
tvpe of sample enabled
discussed
act on gaseous
ionization
is an ionization
from a few thousand
"" ~
methods
5
to obtain
about
80
c
agents
takes
Laser Desorption-Ionization
mI-
less than that of
of 10-11 A.
the wire. As a result.
laser desorption-ionization
spectrometry
is its sensitivity,
which is at least an order
and
again
to heat the emitter
It is even simpler
with
is reinserted
to this electrode.
20-6c is a field desorption
acid.
-;;
peak at mlz = 148.
FIGURE 20-5 Photomicrograph of a carbon microneedle emitter. (Courtesy of R. P. Lattimer, BF Goodrich Research and Development Center.)
Figure
that can he re-
ionization
may occur before
to that In this
molecular ion peak at mlz = 148 and an isotope at mlz = 149.
60
~
(M + 1)'
arc
and coated
the probe
a high voltage
field ionization
d
§
After
compartment,
through
similar
is employed.'
on a probe
it is necessary
ing a current gradation
emitter
compartment
of the sample.
into the sample
at lower
spectrum
distinguished
is mounted
place by applying
"""
ion. In ions
is not well understood.
sources
from the sample
a solution
1]0
ob-
of how
a multitipped
in field ionization
moved
elec-
acid
147 is not detectable.
(mlz
peak
hy the molecular
cules.
case. the electrode
I
fragmentation
molecular
mechanism
fragmentation
In
energy
spectrum,
without
used
by the microtips
ionization
In the electron-impact
exact
M'
via a quan-
for glutamic
the
Field Desorption Methods
1;9 I
is concentrated
lillie
formed
tamic
ionization.
The
CO()H
1M .. H,O + It)'
Figure
order
r-
.
1M - H,Oj':
occurs.
water
-CH
ion or the protonated
cases
In field desorption,
is allowed
or rotational
and
.
NH.
the micro-
occurs
mechanism
vibrational
'O()H-CII-CH,
mi-
as a slit. The
around
are extracted
Lillle
most
0.5 to 2 mm
system
area
electric
from the analyte
the molecular
20-5.
are mounted
tips, and ionization
mechanical
is imparted
of carbon
of Figure
into the high-field
tips of the anode.
(10 to 20 kV)
consisting
of less than
under
from
or
of ben-
of the wire as can
which often also serves
sample
to diffuse
trons
field (10' V/em). Such fields
hundreds
cmillers
from the cathode,
dendrites,
field. The result of this treat-
from the surface
Field ionization
of the anode.
of a large electric
carhon
hy the pyrolysis
he secn in the photomicrograph
tum
In field ionization sources,
grown
of mam'
projecting
at the emiller
influence
microscopic
been
in a high electric
crotips
hy cleavage
or (M - 1) - peaks
or abstraction
of the reagent
spec-
diameter)
MALDI,
also
must strongly and analyle
been
de-
absorb
the
are then
de-
mI,
FIGURE 20-6 Mass spectra of glutamic acid electron-impact ionization, (b) field ionization, desorption. (From H. D. Beckey, A. Heindrich, Winkler, Int. J. Mass Spec. Ion Phys., 1970,3. With permission.)
with (a) and (c) field and H. U. App. ] 1
4Sec L. PrakaL Fjeld Desorption Mass 5pectronll:tr)'. New '{ark: i\larcd Dekker, !l}9(); R P. Lattimer and H. R. Schullen, Ana!. Chem., 1989,61, 1201A. jFor additional infnrmation, see C Dass, Principii's and Practice IIf Biological AltHS Spectrometry. New York: Wiley, ,2001; J. R. Chapman, ,\1a.H Spt!clrumeU} uf Proteins and Pepl/des, Totowa. ;..iJ: Humans. 20()(j ~S$400,000). Commercial models are available with superconducting magnets with fields varying from 1.2 to 12 T. The high-field models are quite useful in biological applications, including protcomics.
(b)
Time-domain (a) and (b) frequency- or mass-domain spectrum for 1,1,1,2-tetrachloroethane. (Reprinted with permission from E. B. Ledford Jr. et al., Anal. Chern., 1980, 52, 463. Copyright 1980 American Chemical Society.) FIGURE
20-20
20C·5 Tandem Mass Spectrometry Tandem mass spectrometry, sometimes called mass spectrometry-mass spectrometry (MS/MS), is a method that allows the mass spectrum of preselected and fragmented ions to be obtained.I7 The basic idea is illustrated in Figure 20-21. Here, an ionization source, I; For additional informatIOn, see K. L. Busch, G, L. Glish. and S. A tt.lcLuckey, .\fass Spear-ornet,-y 'Afass Spectrometry: Techniques and AppliTandem .Wass Specrromerry. ~ew York: \·CH. 198B: Tandem \lass Spectrometn. F. W. McLafferty. cd .. New York: Wiley. 1983.
catIOns of
FIGURE
20-21
spectrometer.
Block diagram of a tandem mass
~
149
Ion source
279
~
;:1
167
Quadrupole
I
first-stage
Ionization
ti
>
I
I
I
= ti =
Quadrupole
ColhslOn
mass separatlon
focusing
2
Quadrupole
3
Electron multiplier
-~
Detection
I second-stage mass separation
I
mlz279
FIGURE 20-22 Product-ion spectra for dibutylphthalate and sulfamethazine obtained after the protonated precursor ion peaks at 279 Da were isolated by the first mass analyzer of an MS/MS instrument. (Reprinted from K. L. Busch and G. C. DiDonato, Amer. Lab., 1986, 18 (8), 17. Copyright 1986 by International Scientific Communications, Inc.)
often a soft ionization source, produces ions and some fragments. These are then the input to the first mass analyzer, which selects a particular ion called the precursor ion and sends it to the interaction cell. In the interaction cell, the precursor ion can decompose spontaneously. react with a collision gas, or interact with an intense laser beam to produce fragments, called product ions. These ions are then mass analyzed by the second mass analyzer and detected by the ion detector. Types of Tandem Mass Spectra
Several different types of spectra can be obtained from the MS/MS experiment. First, the product-ion spectrum can be obtained by scanning mass analyzer 2, while mass analyzer I is held constant, acting as a mass selector to select one precursor ion. Figure 20-22 shows product-ion spectra for dibutylphthalate and sulfamethazine. Both compounds produce molecular ions with mlz values of 279. However, the product-ion spectra of the two compounds are very different. A precursor ion spectrum can be obtained, in addition to product-ion spectra, by scanning the first mass analyzer while holding the second mass analyzer constant to detect a given product ion. In a mixture of compounds, those that give the same products are readily identified by precursor ion spectra. Closely related compounds often give several of the same product ions, so that this method of operation provides a measure of identity and concentration of the members of a class of closely related compounds. Consider, for example, a mixture of ABCD. BCDA. IJKL, and IJMN in the sample. To identify species containing the IJ group, thc second analyzer is set to the mass corresponding to
~II HNj o
CH,
H,N~S-N-{
,i
11
o
N CH]
-f .5 ti
>
~
vc.:
124 156186
92
213
ml?.
the Ir ion and the molecular ions ABCD" BCDA +, IJKL +, and IJMN+ are sequentially selected by the first analyzer. Ion signals in the detector would be observed only when IJKL + and IJMN+ are selected by the first analyzer, indicating the presence of the IJ group. By scanning both analyzers simultaneously with an offset in mass between them, a neutral loss spectrum can be obtained. This gives the identity of those precursor ions that undergo the same loss such as the loss of a H20 or CO neutral. Finally, by scanning mass analyzer 1 and obtaining the product-ion spectrum for each selected precursor ion, a complete threedimensional MSIMS spectrum can be obtained. Dissociative
Interactions
in the Interaction
Cell
Several types of interactions can be used to produce fragmentation in the interaction cell. In some cases, the ions selected by mass analyzer 1 in Figure 20-21 are themselves metastable and decompose into fragments after a certain time. In general, however, the kinetics of the decomposition process can greatly limit the applicability and sensitivity of the process. In such cases, fragmentation can be induced by adding a collision gas to the interaction cell so that interaction with precursor ions occurs, leading to decomposition into product ions. In this case, the cell is called a collision cell, and the interactions arc termed collisionally activated dissociation (CAD) or alternatively collision-induced dissociation (CID). Another type of interaction is surface-induced dissociation (SID), in which precursor ions interact with a surface to induce dissociation. Ions have been reflected off cell walls or trapping plates to increase their internal
Ionizer '" FIGURE 20-23
Analyzer Turbomolccular
pumps
/
Schematic of a triple quadrupole mass spectrometer. (Courtesy of Thermo-
Finnigan Corp.)
energy and promote dissociation. Chemically modified surfaces such as thin films have also been employed. Another dissociation technique that has been applied to large multiply charged ions is electron-capture dissociation (ECD), in which precursor ions capture a low-energy electron to produce an intermediate that rapidly dissociates. In some cases, a background gas is added to aid in the dissociation process. Photo-induced dissociation (PID) is another process to stimulate decomposition of precursor ions. In nearly all cases, an intense laser beam is used in the interaction cell to promote the dissociation. A difficulty with PID is that the ion beam and photon beam must overlap in the interaction region for a time long enough for absorption and bond rupture to occur. In some cases ion-trap cells have been used to allow for long periods of overlap. Instrumentation
for Tandem Mass Spectrometry
Tandem mass spectrometry has been implemented in a number of ways.'8 These can be classified as tandem in space and tandem in time.lq IK For a description of commercial tandem mass spectrometers, sce D. Noble. Anal. Chern., 1995,67.265:\. HSec 1. W. Hager. Anal. Bioonal. Chern .. 2004. 378. R..t5:S. A. McLuckey and 1. \1- Wells. Chem, Rn'" 2001. 10/, 571.
Tandem-in-Space Spectrometers. In tandem-in-space instruments, two independent mass analyzers are used in two different regions in space. The triple quadrupole mass spectrometer is the most common of these instruments. In commercial triple quadrupole instruments, such as the instrument illustrated in Figure 20-23, the sample is introduced into a soft ionization source, such as a CI or FAB source. The ions are then accelerated into quadrupole 1 (0), which is an ordinary quadrupole mass filter. The selected fast-moving ions pass into quadrupole 2 (q), which is a collision chamber where dissociation of the ions sciected by quadrupole I occurs. This quadrupole is operated in a radio-frequencyonly mode in which no dc voltage is applied across the rods. This mode basically traps the precursor and product ions in a relatively high concentration of collision gas so that CAD can occur. Ouadrupole 3 (0) then allows mass analysis of the product ions formed in the collision cell. The configuration is known as the OqO configuration. Sector instruments and hybrid quadrupole-sector instruments have also heen used in a tandem manner. The first tandem mass spectrometers were sector instruments that combined an electric sector spectrometer with a magnetic sector spectrometer. either in forward geometry (electric sector followed by magnetic
sector, or EB) or in reverse geometry (magnetic sector followed bv electric sector, or BE). The reverse geometry is so~etimes called a mass-analyzed ion kinetic energy spectrometer (MIKES). Such instruments were not very efficient, but they allowed the principles of tandem mass spectrometry to be demonstrated. Hybrid instruments include the BEqQ spectrometer (magnetic sector, B; electric sector, E; RF-only quadrupole, q; quadrupole mass analyzer, Q) and the BTOF (magnetic sector, B; TOF analyzer, TOF) spectrometer. The QqTOF spectrometer is similar to the triple quadrupole (QqQ) instrument except that the final quadrupole mass analyzer is replaced with a TOF analyzer. In another variant, the Qq section can be replaced by a quadrupole ion trap to yield an ion-trapTOF instrument. A final type of tandem-in-space spectrometer is the TOF-TOF spectrometer, in which a TOF instrument followed by a timed ion selector separates the precursor ions. A collision cell then induces fragmentation, and the product ions are mass analyzed in the final TOF stage.20 Mass resolution of several thousand was reported. Tandem-in- Time Spectrometers. Tandem-in-time instruments form the ions in a certain spatial region and then at a later time expel the unwanted ions and leave the selected ions to be dissociated and mass analyzed in the same spatial region. This process can be repeated many times over to perform not only MS/MS experiments, but also MS/MS/MS and MS" experiments. Fourier transform ICR and quadrupole ion-trap instruments are well suited for performing MS" experiments. In principle, tandem-in-time spectrometers can perform MS/MS experiments much more simply than tandem-in-space instruments because of the difficulty in providing different ion focal positions in the latter. Although tandem-in-time spectrometers can readily provide product-ion scans, other scans, such as precursor ion scans and neutral loss scans, are much more difficult to perform than they are with tandem in space instruments. 20C-6 Computerized
Mass Spectrometers
Computers are an integral part of modern mass spectrometers. A characteristic of a mass spectrum is the wealth of structural data that it provides. For example, a molecule with a molecular mass of 500 may be fragmented by an EI source into 100 or more different
ions, each of which leads to a discrete spectral peak. For a structural determination, the heights and massto-charge ratios of each peak must be determined, stored, and ultimately displayed. Because the amount of information is so large, it is essential that acquisition and processing be rapid; computers are ideally suited for these tasks. Moreover, for mass spectral data to be useful, several instrumental variables must be closely controlled or monitored during data collection. Computers are much more efficient than a human operator in exercising such controls. Figure 20-24 is a block diagram of the computerized control and data-acquisition system of a triple quadrupole mass spectrometer. This figure shows two features encountered in any modern instrument. The first is a computer that serves as the main instrument controller. The operator communicates via a keyboard with the spectrometer by selecting operating parameters and conditions via easy-to-use interactive software. The computer also controls the programs responsible for data manipulations and output. The second 'f~ature common to almost all instruments is a set of microprocessors (often as many as six) that are responsible for specific aspects of instrument control and the transmission of information between the computer and spectrometer. The interface between a mass spectrometer and a computer usually has provisions for digitizing the amplified ion-current signal plus several other signals that are used for control of instrumental variables. Examples of the latter are source temperature, accelerating voltage, scan rate, and magnetic field strength or quadrupole voltages. The digitized ion-current signal ordinarily requires considerable processing before it is ready for display. First, the peaks must be normalized, a process by which the height of each peak relative to some reference peak is calculated. Most often the base peak, which is the largest peak in a spectrum, serves as the reference and is arbitrarily assigned a peak height of 100 (sometimes 1000). The mlz value for each peak must also be determined. This assignment is frequently based on the time of the peak's appearance and the scan rate. Data are acquired as intensity versus time during a carefullv controlled scan of the magnetic or electric fields. Co~version from time to mlz requires careful periodic calibration; for this purpose, perftuorotri-n-butylamine (PFTBA) or perftuorokerosene is often used as a standard. For high-resolution work, the standard ma\" be admitted with the sample. The computer is programmed to then recognize and use the peak.s of the
Sample introduction
GC LC SFC Solid probe Special
inlets
FIGURE 20-24 Instrument control and data processing for a triple quadrupole mass spectrometer.
standard as references for mass assignments. For lowresolution instruments, the calibration must generally be obtained separately from the sample, because of the likelihood of peak overlaps. With most systems the computer stores all spectra and related information on a disk. In routine applications, bar graphs of the normalized spectra can be sent directly to a printer or display. However, in many cases, the user will employ data-reduction software to extract specific information prior to producing a printed copy of a spectrum. Figure 20-25 is an example of the printout from a computerized mass spectrometer. The first and next-to-Iast columns in the table list mlz values in increasing order. The second and last columns contain the corresponding ion currents normalized to the largest peak found at mass 156. The current for this ion is assigned the number of 100. and all other peaks are expressed relative to this one. Thus, the height of the peak at mass 141 is 53% of the base peak.
As is true with infrared and nuclear magnetic resonance spectroscopy, large libraries of mass spectra (> 150,000 entries) are available in computer-compatible formats." Most commercial mass spectrometer computer systems have the ability to rapidly search all or part of such files for spectra that match or closely match the spectrum of an analyte.
200
APPLICATIONS OF MOLECULAR MASS SPECTROMETRY
The applications of molecular mass spectrometry are so numerous and widespread that describing them adequately in a brief space is not possible. Table 20-5 lists
:: For example, sa F \V. ~kLaffcrty. n"ile,\" Regisrn of .Has5 Spectri.ll Dara. 7th cd .. ~cw Y~)rk: Wile!. 2000 It lS also 3\"ailable combmed with XIST ."'lassSpectral Libran. on CD· RO.\1
Molecular Masses from Mass Spectra Rei. In\. 9 14 5 4 5 5
m/z 41 43 55 69 71 98
ReI. Int. 53 4 6 100 21 5
m/z 141 142 155 156 157 197
For compounds
that can be ionized
ion or a protonated by one of the methods trometer
described
is an unsurpassed
of molecular quires
r or
To determine
,.,
etry,
=~ 60 ~ ,. ~ 40
known.
6. Identification
The
be realized
mass by mass spectrom-
of the molecular is therefore
larly with electron-impact
;:1
When
ion peak is absent
always sources.
additional
field, and desorption
in thin-layer and paper chromatograms
of amino acid sequences in sample of polypeptides
and identification
of species separated
of drugs of abuse and metabolites
by chromatography
7. !vlonitoring gases in patient's breath during surgery 8. Testing for the presence of drugs in blood in race horses and in Olympic athletes 9. Daling archaeological
must
advisable.
particu-
to impurity spectra
ionization
11. Determination
ion peak
be
specimens
of pesticide residues in food
12. tvIonitoring volatile organic species in water supplies
peaks.
by chemical.
arc particularlv
TABLE 20-6 Isotopic Abundance Masses for Various Combinations
Percentages and Molecular of C, H, 0. and N
useful.
Molecular Formulas from
Molecular 0
50
100
200
150
250
FIGURE 20-25 A computer display of mass-spectral data. The compound was isolated from a blood serum extract by chromatography. The spectrum showed it to be the barbiturate pentobarbital. some of these applications capabilities
to provide
of mass spectrometry.
describe
a few of the most widely
of these
applications.
peak
can be identified
This
application.
few thousandths
used and important
peak
cision of a pure compound
eral kinds of data that are useful The first is the molecular the second
is its molecular
of fragmentation
patterns
revealed
by the mass spec-
functional
by comparing compounds
and
In addition.
absence
of a compound
for its identifieation2,
formula.
information
tual identity
sev-
mass of the compound.
trum often provides of various
provides
about groups. can often
its mass spectrum until a close match
study
the presence Finally,
or
the ac-
be established
with those
of known
is realized.
on the order
"'I.
Silvcrsh:lo, F. X. Wdlster, and D. Kicmk .. ')P~'Clro'1lI;lri( Identl/i.CI1(Wfl of Org(1!Hc Compotuzds, 7th ed., ~ew York: Wil.:y, 2004; F. W McLatt •.~rt~ and F Turccek. Inraprel,ltum ,lton S{lt!l'tra. ·Hh cJ .. Mill Valle!. CA. Lniv300,000 spectra) is marketed by John Wiley and Sons.'6 A unique feature of this compilation is that it is available on CD-ROM and can be searched on a personal computer. Small libraries usually contain a few hundred to a few thousand spectra for application to a limited area, such as pesticide residues, drugs, or forensics. Small libraries are often part of the equipment packages offered by instrument manufacturers, and it is almost always possible for the instrument user to generate a library or to add to an existing library. Mass spectra for some 15,000 compounds are available from the National Institute of Standards and Technology (NIST) on the Internet." For large numbers of spectra, such as are obtained when a mass spectrometer is coupled with a chromatograph for identifying components of a mixture, the instrument's computer system can be used to perform a library search on all. or any subset, of the mass spectra '< F W. t>.lcLafferly and D A. Stiwflcr. The ~rllf'\i.vBS Regi~lr} of MIi.nSpeara[ Data, 7 \'ols .. New York: Wile\'. 19!$9 "~F. \\i. t\1cLaffcrty. U'iiey Regisu:" vj Ma5S Specrral Datil. 7th ed., New York: Wiley. 2000. It IS also available combined with :\'IST Mass Specrral Lihmry. on CD-ROt>.1
.. http::';'v..ebhook.mst.goY,'.
associated with a particular sample. The results are reported to the user, and if desired. the reference spectra can be displayed on a monitor or printed for visual comparison. 200-2
Analysis
Mass Spectral
of Mixtures
by Hyphenated
Methods
Although ordinary mass spectrometry is a powerful tool for thc identification of pure compounds. its usefulness for analysis of all but the simplest mixtures is limited because of the immense number of fragments of differing mlz values produced. It is often impossible to interpret the resulting complex speetrum. For this reason, chemists have developed methods in which mass spectrometers are coupled with various efficient separation devices in so-called hyphenated methods. Chromatography-Mass
Spectrometry
Gas chromatography-mass spectrometry (GC/MS) has become one of the most powerful tools available for the analysis of complex organic and biochemical mixtures. In this application. spectra are collected for compounds as they exit from a chromatographic column. These spectra are then stored in a computer for subsequent processing. Mass spectrometry has also been coupled with liquid chromatography (LC/MS) for the analysis of samples that contain nonvolatile constituents. A major problem that had to be overcome in the development of both of these hyphenated methods is that the sample in the chromatographic column is highly diluted by the gas or liquid carrying it through the column. Thus, methods had to be developed for removing the diluent before introducing the sample into the mass spectrometer. Instruments and applications of GC/MS and LC/MS are described in Sections 27B-4 and 28C-6, respectively. Capillary Electrophoresis-Mass
Spectrometry
The first report on coupling capillary electrophoresis with mass spectrometry was published in 1987.oxSince then. it has become obvious that this hyphenated method will become a powerful and important tool in the analysis of large biopolymers. such as proteins, polypeptides, and DNA species. In most of the applications reported to date, the capillary effluent is passed
.:~1. A,. Oli\ares, N. T Nguyen. N. T. '(onkcr, and R. D. Smith. Anal. Chern., 1987,51),1230. See also R. D. Smith. 1. A. Olivares, N. T Nguyen. and H. R Hudseth, Anal. Chern .. 1988.60,436
directly into an electrospray ionization device. and the products then enter a quadrupole mass filter for analysis. Continuous ftow FAB has also been used for ionization in some applications. Capillary electrophoresis-mass spectrometry is discussed in more detail in Section 30B-4
petrochemicals, polychlorinated biphenyls, prostaglandins. diesel exhausts. and odors in air. One of the most promising areas of applications is that of proteamics, the study of proteins produced by a cell or by a species."
Applications
20E
of Tandem Mass Spectrometry
Dramatic progress in the analysis of complex organic and biological mixtures began when the mass spectrometer was first combined with gas chromatography and subsequently with liquid chromatography. Tandem mass spectrometry offers some of the same advantages as GC/MS and LC/MS but is significantly faster. Separations on a chromatographic column are achieved in a time scale of a few minutes to hours, but equally satisfactory separations in tandem mass spectrometers are complete in milliseconds. In addition. the chromatographic techniques require dilution of the sample with large excesses of a mobile phase and subsequent removal of the mobile phase, which llreatly enhances the probability of introduction of interferences. Consequently, tandem mass spectrometry is potentially more sensitive than either of the hyphenated chromatographic techniques because the chemical noise associated with its use is generally smaller. A current disadvantage of tandem mass spectrometry with respect to the other two chromatographic procedures is the greater cost of the required equipment; this gap appears to be narrowing as tandem mass spectrometers gain wider use. For some complex mixtures the combination of GC or LC and MS does not provide enough resolution. In recent years, it has become feasible to couple chromatographic methods with tandem mass spectrometers to form GC I MS I MS and LC I MS I MS systems.29 There have also been reports of LC/MS" instruments.'o To date, tandem mass spectrometry has been applied to the qualitative and quantitative determination of the components of a wide variety of complex materials encountered in nature and industry. Some examples include the identification and determination of drug metabolites, insect pheromones, alkaloids in plants, trace contaminants in air. polymer sequences. :"For recent JL:\'dopments in LC~fSil\.IS. See R. Thomas, Specrroscopy. 2001, 16, 28 ·'tlSee. for example. 1. C A. WUllloud, S. R. GratL B. M. Gamble, and K. A. Wolnik. Analysr. 2004.129.150; E. W. Taylor. W lia. M. Bush, and G. O. O\)llinger, Anal. Chern .. 2002. 74. 3232: L. Ho\\.ells and M. 1. Sauer. Ana(nl, 200L /26.155.
QUANTITATIVE APPLICATIONS OF MASS SPECTROMETRY
Applications of mass spectrometry for quantitative analyses fall into two categories. The first involves the quantitative determination of molecular species or types of molecular species in organic, biological, and occasionally inorganic samples. The second involves the determination of the concentration of elements in inorganic and, less commonly, organic and biological samples. In the first type of analysis, all of the ionization sources listed in Table 20-1 are used. Mass spectroscopic elemental analyses, which are discussed. in detail in Chapter 11, are currently based largely on inductively coupled plasma sources, although glow discharge, radio-frequency spark, laser, thermal, and secondary ion sources have also found use. 20E-1 Quantitative of Molecular
Determination
Species
Mass spectrometry has been widely applied to the quantitative determination of one or more components of complex organic (and sometimes inorganic) systems such as those encountered in the petroleum and pharmaceutical industries and in studies of environmental problems. Currently. such analyses are usually performed by passing the sample through a chromatographic or capillary electrophoretic column and into the spectrometer. With the spectrometer set at a suitable mlz value, the ion current is then recorded as a function of time. This technique is termed selected ion monitoring. In some instances, currents at three or four mlz values are monitored in a cyclic manner by rapid switching from one peak to another. The plot of the data consists of a series of peaks, with each appearing at a time that is characteristic of one of the several components of the sample that yields ions of the chosen value or values for mlz. Generally. the areas under the peaks are directly proportional to the component concentrations and are used for determinations. In this type of
procedure, the mass spectrometer simply serves as a sophisticated selective detector for quantitative chromatographic or electrophoretic analyses. Further details on quantitative gas and liquid chromatography are given in Sections 27B-4 and 28C-6. The use of a mass spectrometer as a detector in capillary electrophoresis is described in Section 30B-4. In the second type of quantitative mass spectrometry for molecular species, analyte concentrations are obtained directly from the heights of the mass spectral peaks. For simple mixtures, it is sometimes possible to find peaks at unique mlz values for each component. Under these circumstances. calibration curves of peak heights versus concentration can be prepared and used for analysis of unknowns. More accurate results can ordinarily be realized, however, by incorporating a fixed amount of an internal standard substance in both samples and calibration standards. The ratio of the peak intensity of the analyte species to that of the internal standard is then plotted as a function of analyte concentration. The internal standard tends to reduce uncertainties arising in sample preparation and introduction. These uncertainties are often a major source of indeterminate error with the small samples needed for mass spectrometry. Internal standards are also used in GC/MS and LC/MS. For these techniques, the ratio of peak areas serves as the analytical variable. A convenient type of internal standard is a stable, isotopically labeled analog of the analyte. Usually, labeling involves preparation of samples of the analytc in which one or more atoms of deuterium, carbon-13, or nitrogen-iS have been incorporated. It is then assumed that during the analysis the labeled molecules behave in the same way as do the unlabeled ones. The mass spectrometer easily distinguishes between the two. Another type of internal standard is a homolog of the analyte that yields a reasonably intense ion peak for a fragment that is chemically similar to the analyte fragment being measured. With low-resolution instruments, it is seldom possible to locate peaks that are unique to each component of a mixture. In this situation. it is still possible to complete an analysis by collecting intensity data at a number of mlz values that equal or exceed the number of sample components. Simultaneous equations are then developed that relate the intensity of each mlz value to the contribution made hy each component to
Ul IQj
Tutorial: Learn more about quantitative applications of MS.
this intensity. the
desired
chemometric principal
equations
analysis
provides
In environmental
Alternatively,
such as partial
least squarcs
ing use of TOF, or
are used.
of quantitative
mass spectral
just described
2% and 10% relative. considerably
the mixture ponents,
analyzed
For gaseous
usually
ranges accuracy
on the complexity
and the nature
hydrocarbon
ing five to ten components, mole percent
measure-
The analytical
depending
being
transform
mixtures
absolute
of
of its com-
ionization
tion
and
errors
contain-
of 0.2 to 0,8
are typical.
methods
quantitative
nated
diphenyl
disinfection,
ethers,
methyl-r-butyl are
ether,
etry tended
compounds
of interest
In forensic are widely
dustrial
materials
quantitative many diverse
areas,
industrial
samples,
materials.
is widely
such
powerful
applications,
application,
the
products
complex
for polymer sample
characterization.
is first
heating
of a direct
can
inlet system.
sentially
a single fragment:
natural
rubber,
styrene
from polyethylene,
molecular
the
for analyon the
from
isoprene
polystyrene,
can provide
from
which depend
in
temperature.
Studies
information
regard-
bonds,
as well as the ap-
mass distribution.
l=See P. tv!. Peacock and C ;-..:.McEwen, AWl!. Chern .. 2004, 7(" J.t17~ H. Pasch and W. Schrcpp .. lUl.D/- [0,..- ,Has.\" Speetmmern' of SynrhclI( Polymers. lkrlin: Spring,er-\'crlag. ~()(J3
events,
In the tandem
clinical
mass spectrometry
plication,36
GC/MS
The
urinary
20·Z
How do the spectra for electron-impact, sources differ from one another"
ZO-3
Describe the difference desorption sources.
and GC I MS
ZO-4
The following figure is a simplified impact source.
and materials
metabolic
disorders.
becoming
the standard
for metabolic
Many trometry been
LC/MS
ever, intact
proteins
been
directly
try."
Electrospray
field Fourier useful
as trypsin.
between
to
gaseous
__
What are the advantages
of each'!
and chemical
ionization
field ionization
diagram
sources
of a commercially
and field
available
electron-
transform
(a)
MS
of mass
must be applied
(b) What will happen ized at point P?
between
the filament
and target
so that elec-
at the point marked
SS (sample
source)
to a molecule
that diffuses
the filament
and is ion-
instrument
was operated
toward
will
spec-
has always
*20-5
(a)
with
Recently,
how-
fragments
have
sector
103 V, a field of 0.126 T was required
What
range
tween
16 and 250, for singly charged
of field strengths
What
range
of accelerating
range between held constant?
with high to
Mass
a magnetic
x
*20-6
a major role in the field of
be required
+
voltage
on the detector.
to scan the mass range
ions, if the accelerating
Calculate
voltages
the accelerating
*ZO· 7 The ion-accelerating
ZO-8
would
be required
16 and 250, for singly charged
voltage
charged ions of mass 7,500 through described in Example 20-·t
proteomics.
\)5. D. Richardson, Annl. Chen!. 2004, 7n, 3337 '~w.D. Smith. Anill. Chl'm .. 2002. 7-1. 462.-\ I'See J. Yinon. Forensit' Applications of Muss Spedrometry. Boca Raton. FL eRe Press. 1995 "'See D. H. Chace. Ch01/. Rev.. 2001. IOJ. ~-l5 "K. C Kooky. Chll. B/ochem .. 2003. 36 . .171. ;'G. E. Reid and S. A. ~teLuckcy. 1. .\fa5S Spec(ron! ,2002 . .17. 6fi:;
would
with an accelerating
to focus the CH,
voltage
be-
is held
constant? (b)
spectromeappears
When 3.00
particularly
determinations.
What voltage
trons interacting with molecules have 70 c V of kinetic energy"
determina-
MS/MS
Accelerating
now
immunological
mass
~ __
plates and slit
babies
and tandem
in conjunction
in such
is now playing
are
from digestions
by tandem
ionization
differ"
field ionization,
of having
newborn
identification,
and large protein
analyzed
sources
FIlament]
and toxicology.
derived
such
used
MS methods
applications
in protein
enzymes
suspected
Mass spectrometry
of peptides
proteolytic
spectrometry
ap-
is widely
in quantitative
biological
important
he particularly
increasing
drug monitoring
other
in the analysis
arc finding
some traditional
are appearing.
and desorption
Mass spec-
and
for screening
methods
tions involving
using spreadsheets.
horses
LC/N1$.,
Tandem
are replacing
with an asterisk.
eviden-
GC/MS,
The
marked
tools in the forensic
of patients
disease.'7
for problems
body fluids
in testing
and fibers."
technique
profiles
with this icon are best solved
How do gaseous
microorgan-
and in examining
laboratory,
Problems
20-1
security.'"
for drugs,
at the end of the hook
spectrometric
explosives
athletes
~
laboratory.
magnetic
ethylene
from Kel-F. Other
products,
of the various
In this and
yield es-
and kind on the pyrolysis
ing the stabilities
are
be performed
and CF,=CFCI
effects
sub-
Some polymers
for example,
yield two or more
of temperature
pyrolyzed,
into GC/MS
are admitted
sis. Alternatively,
polymeric with GC/MS
combined
of
surfactants,
mass spectrometry
such as paints
and fluorometric
MS are very
mass
are now indispensable
methods
of size exclusion
with MALDI
methods
mass spec-
of choice. 32Hyphenated
for characterizing
also quite popular
proximate
to
polymeric
MALDI
as the combination
Pyrolysis
amount
en-
used for the characteri-
has been the method
techniques
polymers
polymers,
and increasingly
of high-molecular-mass
and liquid chromatography
probe
to
byproducts
in setting fires, in analyzing
materials
widely
is also used to determine
in homeland
science,
at equine
trometers
analyze
In recent
trometry
volatile
years,
applied
materials.
and analysis
stances.
has been
including
and forensic
tiary
and on in-
In recent
spectrometry
Mass spectrometry zation
of mass spectromproducts
characterization:
mass
vironmental biological
applications
using
are provided
polybromi-
and various
used in detecting
used by arsonists
to focus on petroleum
out
* Answers
Detec-
of such
algal toxins,
arsenic,
Fourier
to desorp-
as MALDp3
pharmaceuticals,
Mass spectrometry
for drugs
The early quantitative
such
increas-
and
in addition
pesticides,
now carried
methods.
has been
ion-trap,
as perfluoroorganics,
and hair, in testing Applications
there
determination
contaminants
water isms
analysis. quadrupole,
mass spectrometers
tion
diverse
by the procedure
between varies
then
information.
and Accuracy
precision
ments
these
methods
component
Precision The
Solving quantitative
voltage
that would
be required
an instrument
in a particular
to direct
that is identical
quadrupole cyclohexane
15.0 em length of the rod assembly" in the:: direction is zero.
Assume
that the initial
On page 288 a qualitative
described
xz
plane
(positive
discussion dc potential
plane)
is
singly to the one
mass spectrometer
5.00 V How long will it take a singly charged
in the
to scan the mass
ions, if the field strength
ion to travel
how a positive
of a quadrupole
velocitv
is the
of the ion
ion would
behave
mass filter. Con-
of
struct a similar argument for the behavior of positive ions in the yz plane (negative dc potential plane). 20-9 Why do double-focusing mass spectrometers give narrower peaks and higher resolutions than single-focusing instruments'! 20-10 Discuss the differences between quadrupole Fourier transform ICR mass spectrometers.
ion-trap mass spectrometers
20-19 Figure 20-27 shows the mass spectrum of the same compound from an e1ectronimpact ionization source and an ionization source.
!OO
and
*20-11 Calculate the resolution required to resolve peaks for (a) CH,N (ell = 28.0187) and N; (At = 28.0061). (b) C,H"' p( = 28.0313) and CO' (ell = 27.9949). (c) CjH,N1' (JH = 85.0641) and C,H90+ (At = 85.0653). (d) androst-4-en-3,17,-dione (M') at mlz = 286.1930 and an impurity at 286.1240. ~
Challenge Problem
SO
""~ C
-0
"
>
;;
~
20-12 What mass differcnces can just be resolved at m values of 100, 500, 1500,3000, and 5000 if the mass spectrometer has a resolution of (a) 500. (h) WOO. (c) 3000. (d) 5000?
20-15 Measuring the approximate mass of an ion without using a standard can he accomplished via the following variant of the peak-matching technique described in Prohlcm 20-14. The peak-matching technique is used to alternately cause the pion and the (P + I) + ions to reach the detector. It is assumed that the difference in mass hetween p+ and (P + I) - is due to a single 'JC replacing a 12Catom. (a) If the accelerating voltage for (P + 1)+ is laheled V, and that for P' is V" derive a relationship that relates the ratio V,W, to the mass of P'. (h) If V,W, = 0.987753, calculate the mass of the P+ ion. 20-16 Discuss the major differences between a tandem-in-space mass spectrometer and a tandem-in-time mass spectrometer. Include the advantages and disadvantages of each type. 20-17 Identifv the ions responsible for the peaks in the mass spectrum shown in Figure 20-20b. 20-18 Identifv the ions responsihle for the four peaks having greater mass-to-charge ratios than the M - peak in Figure 20-4a.
40 20
0 0
*20-13 Calculate the ratio of the (M + 2)' to M' and the (M + 4)+ to M peak heights for (a) ClllH,Br" (b) C,H7CIBr, (c) C6H"C1,. 20-14 In a magnetic sector (single-focusing) mass spectrometer, it might be reasonahle under some circumstances to monitor one mlz value, to then monitor a second mlz. and to repeat this pattern in a cyclic manner. Rapidly switching between two accelerating voltages while keeping all other conditions constant is called peak matching. (a) Derive a general expression that relates the ratio of the accelerating voltages to the ratio of the corresponding mlz values. (b) Use this equation to calculate mlz of an unknown peak if mlz of the ion used as a standard, CF1', is 69.00 and the ratio of VU"knuwn/V;"nd'Cd is 0.965035. (c) Based on your answer in part (b), and the assumption that the unknown is an organic compound that has a mass of 143, draw some conclusions about your answer in part (b), and about the compound.
60
~
IIKl SO
"~ § 60 'j
-fl
"
> .~
40
"iJ
x
20
0 0
FIGURE 20-27 Electron-impact spectrum (a) and chemical ionization spectrum (b) of the same biologically important compound. (From H. M. Fales, H. A. Lloyd, and G. A. W. Milne, J. Amer, Chem. Soc., 1970,92,1590-1597. American Chemical Society.)
(a) Which mass spectrum would be hest for determining the molecular mass of the compound? Why? (b) Which mass spectrum would he best for determining the chemical structure') Whvo (c) Th; electron-impact source was a pulsed source used with a Tal' mass analvzer. If the flight tube were 1.0 m long and the accelerating voltage were 3000 V. what \~ould the flight time be for the ion at m/z = 58', (d) For two ions of m/z values m,/z and m,/z. derive an equation for the difference in flight times .lIF as a function of the two masses. the charges. and the accelerating voltage. (e) For the same Tal' analyzer as in part (c). calculate the difference in flight times between ions of mlz = 59 and m/z = 58.
(f) To get more structural information, the compound of Figurc 20-27 was subjected to tandem mass spectrometrv. Which ionization source, electronimpact or chemical. would be most suitable for this purpose? Why" (g) Using the ionization source chosen in part (f), describe the types of mass spectra that could he obtained from an MS/MS experiment by: (I) holding the first mass analyzer constant and scanning the second analyzer. (2) scanning both analyzers with a small mlz offset between them. (3) scanning the first analyzer while holding the second analyzer constant. (4) scanning the second mass analyzer for every mass selected by the first analyzer.
21A
urface haracterization
INTRODUCTION TO THE STUDY OF SURFACES
Before considering how surfaces are characterized, wc first need to define what constitutes the surface of a solid that is in contact with a gaseous or liquid second phase.
y .$pe~tro~copy nd:Microscopy
In your answer, use features of the mass spectrum of Figure 20-27 to illustrate your description.
';0-:'
he~urface ola solid in contact with a liq-
'f'
.uid or gaseq~
I
sf.Witially frtJm the interior of the solid both
phase usually differs sub-
,'in chemical composition and physical properties. .'(;haracter4:ation
e
of t/lese surface properties
f vital irrqjrrtance
ill
~eteroge,,:~ous catalysis, sensordevelopment "?pplicati0tlf,
is often
a number of fields, including
and semiconductor
"pgy. Such characterization
and
thin-film technol-
We will consider a surface to be the boundary layer between a solid and a vacuum, a gas, or a liquid. Generally, we think of a surface as a part of the solid that differs in composition from the average composition of thc bulk of the solid. By this definition, the surface comprises not only the top layer of atoms or molecules of a solid but also a transition layer with a nonuniform composition that varies continuously from that of the outer layer to that of the bulk. Thus, a surface may be several or even several tens of atomic layers deep. Ordinarily, however, the difference in composition of the surface layer does not significantly affect the measured overall average composition of the bulk because the surface layer is generally only a tiny fraction of the total solid. From a practical standpoint, it appears best to adopt as an operational definition of a surface that volume of thc solid that is sampled by a specific measurement technique. This definition recognizes that if we use several surface techniques, we may in fact be sampling different surfaces and may obtain different, alheit useful, results.
also aids in under-
standing corrosion and adhesion mechanisms, activity of metal surfaces, embrittlement (Lnd behavior and functions
properties,
of biological mem-
branes. This chapter deals with the investigation of solid suifaces by spectroscopic
and microscopic
methods. Although the emphasis is on solid surfaces, some of the techniques are also applicable to other interfaces, such as liquid-liquid
and
liquid-gas interfaces.
r3l
Throughout this chapter, this logo indicates an opportunity for online self-study at www .thomsonedo.com/chemistry/skoog, linking you to interactive tutorials, simulations, and exercises. ~
During the last century, a wide variety of methods have heen developed for characterizing surfaces. The classical methods, which are still important, provide much useful information about the physical nature of surfaces but less ahout their chemical nature. These methods involve obtaining optical and electron microscopic images of surfaces as wcll as measurements of adsorption isotherms. surface areas, surface roughness, pore sizes, and reflectivity. Beginning in the 1950s, spectroscopic surface methods began to appear that provided information about the chemical nature of surfaces. This chapter is divided into several major parts. After an introduction to surface methods in Section 21B. we then discuss electron spectroscopic techniques, ion spectroscopic techniques. and photon spectroscopic tcchniques to identify the chemical species making up
the surface of solids and to determine their concentrations. Sections 21F and 21G describe modern microscopic methods for imaging surfaces and determining their morphology and their physical features.
Primary Beam
Detected Beam
Information
X-ray photons
Electrons
Chemical composition Chemical structure
Electrons
Chemical composition
Electron energy-lossspectroscopy (EELS)
Electrons or X-ray photons Electrons
Electrons
Electron microprobe (EM) Secondary-ion mass spectrometry (SIMS)
Electrons Ions
X-ray photons Ions
Ion-scattering spectroscopy (ISS) and Rutherford backscattering
Ions
Ions
Chemical structure Adsorbate binding Chemical composition Chemical composition Chemical structure Chemical composition
Laser-microprobe
Photons
Ions
Method and Acronym X-ray photoelectron spectroscopy (XPS). or electron spectroscopy
218
analysis (ESCA) Auger electron spectroscopy (AES)
SPECTROSCOPIC SURFACE METHODS
Generally, the chemical composition of the surface of a solid differs, often significantly, from the interior or bulk of the solid. Thus far in this text, we have focused on analytical methods that provide information about bulk composition of solids only. In certain areas of science and engineering, however, the chemical composition of a surface layer of a solid is much more important than is the bulk composition of the material. Spectroscopic surface methods provide both qualitative and quantitative chemical information about the composition of a surface layer of a solid that is a few tenths of nanometers (a few angstroms) to a few nanometers (tens of angstroms) thick. In this section we describe some of the most widely used of these spectroscopic techniques' 21 B-1 Spectroscopic
Surface
Experiments
Figure 21-1 illustrates the general way spectroscopic examinations of surfaces are performed. Here, the solid sample is irradiated with a primary beam made up of photons, electrons, ions, or neutral molecules. Impact of this beam on a surface results in formation of a secondary beam also consisting of photons, electrons, molecules, or ions from the solid surface. The secondary beam is detected by the spectrometer. Note that the type of particle making up the primary beam is not necessarily the same as that making up the secondary beam. The secondary beam. which results from scattering, sputtering, or emission, is then studied by a variety of spectroscopic methods. The most effective surface mcthods are those in which the primary beam. the secondary beam, or both is made up of either electrons, ions, or molecules and not photons because this limitation assures that the measurements are restricted to the surface of a sample and not to its bulk. For example, the maximum penetration depth of a beam of J-ke V electrons or ions is For a d~scription of surface spectroscopic techniques, see Surface Ana{ylis - The Principal Techniques, 1. C Vickerman. ed .. Chichester, CK: Wiley. 1997: Specrmscopy of Surfaces, R. G. H. Clark and R. E. Hester. cds., 'ew York: \\'ile\. 19RB.
for chemical
FIGURE 21-1 General scheme for surface spectroscopy. Beams may be photons. electrons. ions. or neutral molecules.
approximately 2.5 nm (25 A), whereas the penetration depth of a photon beam of the same energy is about 1000 nm (l0' A). Thus, for many methods that involve two beams of photons, such as X-ray fluorescence (see Chapter 12). infrared reflection spectroscopy (see Chapter 17), ellipsometry, or resonance Raman spectroscopy (see Chapter 18), precautions must be taken to limit the measurements to a surface layer. The techniques involving primary and detected (secondary) beams of photons discussed in this section are surface plasmon resonance, nonlinear optical spectroscopy, and ellipsometry. There are several ways to classify surface techniques. Many of these are based on the nature of the primary and detected beams. Table 21-1 lists the most widely used spectroscopic techniques. These will be discussed further in this section. 21B-2
Sampling
Surfaces
Regardless of the type of spectroscopic surface method being used, three types of sampling methods are employed. The first involves focusing the primary beam on a single small area of the sample and observing the secondary beam. Often, the spot is chosen visually with an optical microscope. The second method involves mapping the surface, in which a region of the surface is scanned by moving the primary beam across the surface in a raster pattern of measured increments and observing changes in the secondary beam that result. The mapping may be linear or two dimensional. The third technique is known as depth profiling. Here, a beam of ions from an ion gun etches a hole in the surface by sputtering. During this process a finer primary beam produces a secondary beam from the center of the hole. which provides the analytical data on the surface composition as a function of depth.
mass
spectrometry (LMMS) Surface plasmon resonance (SPR)
Atomic structure
Photons
Photons
Sum frequency generation (SFG)
Photons
Photons
Ellipsometry
Photons
Photons
Most of the surface spectroscopic techniques require a "vacuum" environment. High vacuum conditions ensure that the particles used have long mean free paths to interact with the surface of interest. The vacuum environment also keeps the surface free from adsorbed gases during the surface analysis experiment. The exceptions to the high vacuum requirement are the photon-photon techniques given in the last three rows of Table 21-1. These allow examination of surfaces under conditions more akin to those used in applications such as catalysis. sensing, and corrosion studies. A problem frequently encountered in surface analyses is contamination of the surface by adsorption of components of the atmosphere, such as oxygen, water, or carbon dioxide. Even in a vacuum, this type of contamination occurs in a rclatively short time. For example, at a pressure of Hj' h torr (1 torr = 133 Pal, a monolayer of gas molecules will cover a clean surface in just 3 s. At 10-; torr. coverage occurs in about 1 h. At 10-10 torr. 10 h is required.' Because of adsorption
III
Chemical composition
Chemical structure
Tutorial: Learn more ahout surface methods.
Composition
and concentration
of thin films Interface structure. adsorbate binding Thin-film thickness
problems, provisions must often be made to clean the sample surface, usually in the chamber used for irradiating the sample. Cleaning may involve baking the sample at a high temperature; sputtering the sample with a beam of inert gas ions from an electron gun; mechanical scraping or polishing of the sample surface with an abrasive; ultrasonic washing of the sample in various solvents; and bathing the sample in a reducing atmosphere to remove oxides. In addition to atmospheric contamination, the primary beam itself can alter the surface as a measurement progresses. Damage caused by the primary beam depends on the momentum of the primary beam particles. Thus, of the beams listed in Table 21-1, ions are the most damaging and photons the least.
The lirst three methods listed in Table 21-1 arc based on detection of emitted electrons produced by incident beams. Here. the signal from the analvte is encoded in a beam of electrons rather than photons. The spectrometric measurements then consist of the determination of the power of this beam as a function of the energy hv or frequency v of the electrons. This type of spectroscopy is termed electron spectroscopy.
Although the basic principles of electron spectroscopy were well understood a century ago, the widespread application of this technique to chemical problems did not occur until relatively recently. Studies in the field were inhibited by the lack of technology necessary for performing high-resolution spectral measurements of electrons having energies varying from a few tenths to several thousand electron volts. By the late 19605, this technology had developed, and commercial electron spectrometers began to appear in the marketplace. With their appearance, an explosive growth in the number of publications dcvoted to electron spectroscopy occurred.' There are three types of electron spectroscopy for the study of surfaces. The most common type, which is based on irradiation of the sample surface with monochromatic X-radiation, is called X-ray photoelectron spectroscopy (XPS). It is also termed electron spectroscopy for chemical analysis. Much of the material in this chapter is devoted to XPS. The primary beam for photoelectron spectroscopy can also consist of ultraviolet photons, in which case the technique is called ultraviolet photoelectron spectroscopy (UPS). Here, a monochromatic beam of ultraviolet radiation causes ejection of electrons from the analyte. This type of electron spectroscopy is not as common as the other two, and we shall not discuss it further. The second type of electron spectroscopy is called Auger (pronounced oh-ZHAY) electron spectroscopy (AES). Most commonly, Auger spectra are excited by a beam of electrons, although X-rays are also used. Auger spectroscopy is discussed in Section 21C-2. The third type of electron spectroscopy is electron energy-loss spectroscopy (EELS), in which a low-energy beam of electrons strikes the surface and excites vibrations. The resultant energy loss is then detected and related to the vibrations excited. We briefly describe EELS in Section 21C-3. Electron spectroscopy is a powerful tool for the identification of all the elements in the periodic table with the exception of hydrogen and helium. More important, the method permits determination of the oxidation state of an element and the type of species to which it is bonded. Finally, the technique provides useful information about the electronic structure of molecules. For additional information, see 1. F. \Vatts and 1. \Volstenholme, An Introduction to Surface Ana(vsLs by XPS and AES, Chichester. CK: Wiley, 2003; D Briggs and M. P. Scah, Practical Surface Analysis h,\ Auger and X·ray Photoelectron Spectroscop-",,'. 2nd ed .. Chichester. UK: \Viky, 1990.
3
Electron spectroscopy has been successfully applied to gases and solids and more recently to solutions and liquids. Because of the poor penetrating power of electrons, however, these methods provide information about solids that is restricted largely to a surface layer a few atomic layers thick (2 to 5 nm). Usually, the composition of such surface layers is significantly different from the average composition of the entire sample. Indeed, the most important and valuable current applications of electron spectroscopy are to the qualitative analysis of the surfaces of solids, such as metals, alloys, semiconductors, and heterogeneous catalysts. Quantitative analysis by electron spectroscopy finds somewhat limited applications.
FIGURE 21-2 X-ray photoelectron spectrum of tetrapropylammoniumdifluoridethiophosphate. The peaks are labeled according to the element and orbital from which the emitted electrons originate.
21C-1 X-ray Photoelectron Spectroscopy It is important to emphasize the fundamental difference between electron spectroscopy (both XPS and AES) and the other types of spectroscopy we have thus far encountered. In electron spectroscopy, thl'l ~netic energy of emitted electrons is recorded. The spectrum thus consists of a plot of the number of emitted electrons, or the power of the electron beam, as a function of the energy (or the frequency or wavelength) of the emitted electrons (see Figure 21-2). Principles
of XPS
The use of XPS was pioneered by the Swedish physicist K. Siegbahn, who subsequently received the 1981 Nobel Prize in Physics for his work.· Siegbahn chose to call the technique electron spectroscopy for chemical analysis (ESCA) because, in contrast to the other two electron spectroscopies, XPS provides information about not only the atomic composition of a sample but also the structure and oxidation state of the compounds being examined. Figure 21-3 is a schematic representation of the physical process involved in XPS. Here, the three lower lines labeled Eb, Eb, and E;; represent energies of the inner-shell K and L electrons of an atom. The upper three lines represent some of the energy levels of the outer shell, or valence, electrons. As shown in the illustration, one of the photons of a monochromatic X-ray beam of known energy hv displaces an electron ~For a brief description of the hislory of XPS, see K. Siegbahn, Science, 1981, 217, 111: D. Nt Hercules, 1. Chern. Educ., 2004, 81, 1751. For monographs, see S. Hufner, Photoelectron Spectroscopy: Principles and Applications, Berlin: Springer-Verlag, 1995; T. L. Barr, Modern ESCA: The Principles and Practice of X-Ray Photoelectron Spectroscopy. Boca Raton, FL: eRe Press, 199..t.
500 Binding
400 energy
e - from a K orbital of energy Eb• The process can be represented as
where A can be an atom, a molecule, or an ion and AU is an electronically excited ion with a positive charge one greater than that of A.
Eb
Schematic representation of the ESCA process. The incident beam consists of monoenergetic X-rays. The emitted beam is made up of electrons. FIGURE
21-3
The kinetic energy of the emitted electron Ek is measured in an electron spectrometer. The binding energy of the electron Eb can then be calculated by means of the equation
In this equation, IV is the IVork function of the spectrometer, a factor that corrects for the electrostatic environment in which the electron is formed and measured. Various methods are available to determine the value of IV. The binding energy of an electron is characteristic of the atom and orbital that emit the electron. Figure 21-2 shows a low-resolution, or survey, XPS spectrum consisting of a plot of electron-counting rate as a function of binding energy Eb. The analyte consisted of an organic compound made up of six elements. With the exception of hydrogen, well-separated peaks for each of the elements can be observed. In addition, a peak for oxygen is present, suggesting that some surface oxidation of the compound had occurred. Note that, as expected, the binding energies for Is electrons increase with atomic number because of the increased positive charge of the nucleus. Note also that more than one peak for a given element can be observed: thus peaks for both 2s and 2p electrons for sulfur and phosphorus can be seen. The large background count arises
because associated with each charactcristic peak is a tail of ejected electrons that ha\·c lost part of their energy by inelastic collisions within the solid sample. These electrons have lcss kinetic energy than their nonscattered counterparts and will thus appear at lower kinetic encrgies or higher binding energies (Equation 21-2). It is evident from Figure 21-2 that XPS provides a means of qualitative identification of the elements present on the surface of solids. Instrumentation
Instruments for electron spectroscopy are offered by several instrument manufacturers. Thesc products differ considerably in types of components. configurations. and costs. Some are designed for a single type of application, such as XPS, and others can be adapted to AES and UPS by purchase of suitable accessories. All are expensive ($300,000 to >$106). Electron spectrometers are made up of components whose functions are analogous to those encountered in optical spectroscopic instruments. These components include (1) a source; (2) a sample holder; (3) an analyzer, which has the same function as a monochromator; (4) a detector; and (5) a signal processor and readout. Figure 21-4 shows a typical arrangement of these components. Electron spectrometers generally require elaborate vacuum systems to reduce the pressure in all of the components to as low as 10-8 to 10-10 torrS Sources. The simplest X-ray sources for XPS spectrometers are X-ray tubes equipped with magnesium or aluminum targets and suitable filters. The Ka lines for these two elements have considerably narrower bandwidths (0.8 to 0.9 eV) than those encountered with higher atomic number targets; narrow bands arc desirable because they lead to enhanced resolution. Nonmonochromatic sources typically illuminate a spot a few centimeters in diameter. Relatively sophisticated XPS instruments, such as that shown in Figure 21-4. employ a crystal monochromator (Section 12B-3) to provide an X-ray beam having a bandwidth of about 0.3 e V. Monochromators eliminate bremsstrahlung background, thus improving signal-to-noise ratios. They also allow much smaller spots on a surface to be examined (spot sizes ~50 11m). 'Specifications for several representative commercial instruments are given in D. Nuble. AM/. Chern. 1995, 67, 675A. For a perspc:ctive on commercial XPS instrumenlalion. set: M ... \_ Kelly. 1. Chern. Fduc 20(}4, 81.1716
Thc increased availability of synchrotron radiation in recent years has given XPS experimenters another useful source. The synchrotron produces hroadband radiation that is highly collimated and polarized. Such sources when used with a monochromator can provide a source of X-rays that is tunahle for photoelectron experiments. Sample Holders. Solid samples are mounted in a fixed position as close as possible to the photon or clectron source and the entrance slit of the spectrometer (see Figure 21-4). To avoid attenuation of the electron beam, the sample compartment must be evacuated to a pressure of 10-5 torr or less. Often, however, much better vacuums (10-9 to 10-10 torr) are required to avoid contamination of the sample surface by substances such as oxygen or water that react with or are adsorbed on the surface. Gas samples are leaked into the sample area through a slit of such a size as to provide a pressure of perhaps 10-2 torr. Higher pressures lead to Jx"Cssive attcnuation of the electron beam, which is due to inelastic collisions: on the other hand, if the sample pressure is too low, weakened signals are obtained. Analyzers. The analyzer consists of the collection lens or lenses and the electron energy analyzer, which disperses the emitted electrons according to their kinetic energy. The lens system usually allows a wide collection angle (-30') for high efficiency. In some angleresolved experiments, an aperture reduces the angles collected. Such experiments are used in depth-proliling studies. Typically, photoelectron experiments are carried out in constant analyzer energy mode, in which electrons are accelerated or retarded by the lens system to sOme user-defined energy as they pass through the analyzer (the pass energy, E in Figure 21-4). Often, pass energies of 5-25 eV will give high-resolution spectra, and 100-200 eV pass energies are used for survey scans. The signal intensity decreases as the pass energy decreases. Most energy analyzers are of the type illustrated in Figure 21-4, in which the electron beam is deflected by the electrostatic field of a hemispherical capacitor. The electrons thus travel in a curved path from the lens to the multichannel transducer. The radius of curvature depends on the kinetic energy of the electrons and the magnitude of the electrostatic field. An entire spcc-
FIGURE 21-4 Principle of a modern ESCA instrument
using a monochromatic X-ray source and a hemispherical field spectrometer.
trum is obtained by varying the field so as to focus electrons of various kinetic energies on the transducer. Transducers. Most modern electron spectrometers are based on solid-state, channel electron multipliers, which consist of tubes of glass that have been doped with lead or vanadium. When a potential difference of several kilovolts is applied across these materials, a cascade or pulse of 106 to 108 electrons is produced for each incident electron. The pulses are then counted electronically (see Section 4C). Several manufacturers are now offering two-dimensional multichannel electron detectors that are analogous in construction and application to the multichannel photon detectors described in Section 7E-3. Here, all of the resolution elements of an electron spectrum are monitored simultaneously and the data stored in a computer for suhsequent display. The advantages of such a system are similar to those realized with multichannel photon detectors. Data Systems. Modern XPS instruments have nearly all components under computer control. Thus. electron guns, ion guns, valves, lens voltages, sample position, and analyzer parameters are all selected by the computer. Current software on XPS instruments al-
lows many data-analysis options, including peak finding, peak identification, and peak intensity measurement. Many packages also include chemometric data analysis such as multivariate statistical processing and pattern recognition. Applications
of XPS
XPS provides qualitative and quantitative information about the elemental composition of matter, particularly of solid surfaces. It also often provides useful structural information.6 Qualitative Analysis. Figure 21-2 shows a low-resolution, wide-scan XPS spectrum, called a survey spectrum, which serves as the basis for the determination of the elemental composition of samples. With a magnesium or aluminum Ka source, all elements except hydrogen and helium emit core electrons having characteristic binding energies. Typically, a survey spectrum encompasses a kinetic energy range of 250 to 1500 eV. which corresponds to binding energies of about 0 to ~For reviews of applicatIons of XPS (and AES as w'ell). see J. F Walts and 1. Wolstenholme, An lmroductiofl to Sur/ace Analysis by XPS and AES, Chichester. UK: Wiley. 2003: N, H. Turner and 1. A. Schreifels, Anal Chern" 2000, 72. 9YR: 1998. 70, 129K 1996 68. 309R. See also D. M Hercules, I Chf'/1t.bluc-. 200,t.sf, 1751
F I
Elementb
H I
H I
F-y-\~-o(~-T\H -2
Nitrogen (Is) Sulfur (15) Chlorine (2p) Copper (Is) Iodine (45) Europium (3d)
0 II
-1
0
*0' -2.0
+1 +4.5'
+2
+3 +5.1
*0
+5
+3.8 +0.7
+6
F \ \
+7
I
+8.0
I /
+5.8
+4.5
*0 *0
+4
/
+7.1
+9.5
+5.3
+6.5
I\H
H;
\
/
\ \ \
+4.4
*0 '0
+9.6
• All shifts afc in electron votts measured relative to the oxidation states indicated by (*). (Reprinted AnaL Chern., 1970,42, 28A. Copyright 1970 American Chemical Society.)
with permission from D. M. Hercuks.
GType of electrons given in parentheses. C
Arbitrary zero for measurement,
end nitrogen in NaN;.
dMiddle nitrogen in NaN,.
1250 eY. Every element in the periodic table has one or more energy levels that will result in the appearance of peaks in this region. [n most instances, the peaks are well resolved and lead to unambiguous identification provided the element is present in concentrations greater than about 0.1 %. Occasionally, peak overlap is encountered such as 0(15) with Sb(3d) or AI(2s, 2p) with Cu(3s, 3p). Usually, problems due to spectral overlap can be resolved by investigating other spectral regions for additional peaks. Often, peaks resulting from Auger electrons are found in XPS spectra (see, for example, the peak at about 610 eV in Figure 21-2). Auger lines are readily identified by comparing spectra produced by two X-ray sources (usually magnesium and aluminum Ka). Auger lines remain unchanged on the kinetic energy scale but photoelectron peaks are displaced. The reason for the behavior of Auger electrons will become apparent in the next section. Chemical Shifts and Oxidation States, When one of the peaks of a survey spectrum is examined under conditions of higher energy resolution. the position of the maximum depends to a small degree on the chemical environment of the atom responsible for the peak. That is, variations in the number of valence electrons, and the type of bonds they form, influence the binding energies of core electrons. The effect of the number of valence electrons and thus the oxidation state is demonstrated by the data for several elements shown in Table 21-2. Note that in each case. binding energies increase as the oxidation state becomes more positive. This chemical shift can be explained by assuming that the attraction of the nucleus for a core electron is di-
minished by the presence of outer electrons. When one of these electrons is removed, the effective charge sensed for the core electron is increased, and an increase in binding energy results. , One of the most important applications of ~PS has been the identification of oxidation states of elements in inorganic compounds. Chemical Shifts and Structure. Figure 21-5 illustrates the effect of structure on the position of peaks for an element. Each peak corresponds to the 15 electron of the carbon atom indicated by dashes above it in the structural formula. Here, the shift in binding energies can be rationalized by taking into account the influence of the various functional groups on the effective nuclear charge experienced by the Is core electron. For example, of all of the attached groups, fluorine atoms have the greatest ability to withdraw electron density from the carbon atom. The effective nuclear charge felt by the carbon Is electron is therefore a maximum, as is the binding energy. Figure 21-6 indicates the position of peaks for sulfur in its several oxidation states and in various types of organic compounds. The data in the top row clearly demonstrate the effect of oxidation state. Note also in the last four rows of the chart that XPS discriminates between two sulfur atoms contained in a single ion or molecule. Thus, two peaks are observed for thiosulfate ion (S,o,"). suggesting different oxidation states for the two sulfur atoms. XPS spectra provide not only qualitative information about types of atoms present in a compound but also the relative number of each type. Thus, the nitro-
FIGURE21-5 Carbon 1s X-ray photoelectron spectrum for ethyl trlfluoroacetate. (From K. Siegbahn et aI., ESCA: Atomic, Molecular, and Solid-State Studies by Means of Electron Spectroscopy, p. 21, Upsala: Almquist and
Wiksells, 1967. With permission.)
162 I
I S'I SO RSH(2)H RSR(3)H
I SOj'- SO}'H (3) HRS ...• O(3) RSO,R'H(9) RSOj-H
520/I--i RSiSO)RI----1 (3)
I
I Precision of I---l RS(SO,)R (4) measurement
Quanlitative Applications. Once, XPS was not considered to be a very useful quantitative technique. However, there has been increasing use of XPS for determining the chemical composition of the surface region of solids.7 If the solid is homogeneous to a depth of several electron mean free paths, we can express the number of photoelectrons detected each second I as
/--I RSO; is)
ArSR(3)H RSSR (3) H I
gen Is spectrum for sodium azide (Na+Nj') is made up of two peaks having relative areas in the ratio of 2: 1 corresponding to the two cnd nitrogens and the center nitrogen, respectively. It is worthwhile pointing out again that the photoelectrons produced in XPS are incapable of passing through more than perhaps 1 to 5 nm of a solid. Thus, the most important applications of electron spectroscopy, like X-ray microprobe spectroscopy, are for the accumulation of information about surfaces. Examples of some of its uses include identification of active sites and poisons on catalytic surfaces, determination .of surface contaminants on semiconductors, analysis of the composition of human skin, and study of oxide surface layers on metals and alloys. It is also evident that the method has a substantial potential in the elucidation of chemical structure (see Figures 21-5 and 21-6). Information from XPS spectra is comparable to that from nuclear magnetic resonance (NMR) or [R spectroscopy. The ability of XPS to distinguish among oxidation states of an clement is noteworthy. Note that the information obtained by XPS must also be present in the absorption edge of an X-ray absorption spectrum for a compound. Most X-ray spectrometers, however, do not have sufficient resolution to permit ready extraction of this structural information.
I
RSS03-
I
I
I
162
164
166
FIGURE21-6 Correlation chart for sulfur 2s electron binding energies. The numbers in parentheses indicate the number of compounds examined. (Reprinted with permission from D. M. Hercules, Anal. Chem., 1970, 42, 35A. Copyright 1970, American Chemical Society.)
where n is the number density of atoms (atoms cm -3) of the sample, 1> is the flux of the incident X-ray beam (photons cm" S'l), a is the photoelectric cross section for the transition (cm'/atom), e is the angular efficiency factor for the instrument, '7 is the efficiency of producing photoelectrons (photoelectrons/photon), A is the area of the sample from which photoelectrons are detected (em '), T is the efficiency of detection of
~For a review of 4uantitati\'e applications of XPS and AES, see K. W. :\ebesnv, B. L !\faschhoff, and 1'\. R. Armstrong, Anal. Chern .. 1989,61. 469.-\. For a discussion of the reliability of XPS, see C 1. Powell. 1. Chern. EdtlC".. 2004, 8/. 1734.
the photoelectrons, and I is the mean free path of the photoelectrons in the sample (cm). For a given transition, the last six terms arc constant, and we can write the atomic sensitivity factor S as
For a given spectrometer, a set of relative values of S can be developed for the elements of interest. Note that the ratio liS is directly proportional to the concentration n on the surface. The quantity I is usually taken as the peak area, although peak heights are also used. Often, for quantitative work, internal standards are used. Relative precisions of about 5 % are typical. For the analysis of solids and liquids, it is necessary to assume that the surface composition of the sample is the same as its bulk composition. for many applications this assumption can lead to significant errors. Detection of an element by XPS requires that it be present at a level of at least 0.1 %. Quantitative analysis can usually he performed if 5% of the element is present. 21 C-2
Auger Electron
Spectroscopy
In contrast to XPS, AES' is based on a two-step process in which the first step involves formation of an electronically excited ion A-* by exposing the analyte to a beam of electrons or sometimes X-rays. With X-rays, the process shown in Equation 21-1 occurs. For an electron beam, the excitation process can be written
where e, represents an incident electron from the source, e; - represents the same electron aftcr it has interacted with A and has thus lost some of its energy, and eA represents an electron ejected from one of the inner orbitals of A. As shown in Figure 21-7a and h, relaxation of the excited ion A ~* can occur in two ways:
Here, e A corresponds to an Auger c-Iectron and represents a fluorescence photon. and J \\'Obl<e"ohullll107 V/cm) that electrons are produced by a quantum mechanical tunneling process 10 in which no thermal energy is required to free the electrons from the potential barrier that normally prevents their emission. Field emission sources provide a beam of electrons that have a crossover diameter of only 10 nm compared with 10 flm for LaB. rods and 50 flm for tungsten hairpins. The disadvantages of this type of source are its fragility and the fact that it also requires a better vacuum than does an ordinary filament source. Electron guns produce a beam of electrons with energies of 1 to 10 keY, which can be focused on the surface of a sample for Auger electron studies. One of the special advantages of Auger spectroscopy is its capability for very high spatial-resolution scanning of solid surfaces. Normally, electron beams with diameters ranging from 5 to 500 flm are used for this purpose. 'OJ In quantum mechanics, there is a finite probahility that a particle can pass through a potential ~nergy barrier and appear in a region forbidden by classical mechanics. This process is called tunneling. It can be an important process for light particles, such as protons and electrons.
of AES
Qualitative Analysis of Solid Surfaces. Typically, an Auger spectrum is obtained by bombarding a small area (5 to 500 flm diameter) of the surface with a beam of electrons from a gun. A derivative electron spectrum, sueh as that shown in Figure 21-8, is then obtained with an analyzer. An advantage of Auger spectroscopy for surface studies is that the low-energy Auger electrons (20 to 1000 e V) are able to penetrate only a few atomic layers, 0.3 to 2 nm (3 to 20 A) of solid. Thus, whereas the electrons from the electron guns penetrate to a considerably greater depth below the sample surface, only those Auger electrons from the first four or five atomic layers escape to reach the analyzer. Consequently, an Auger spectrum is likely to reflect the true surface composition of solids. , • The two Auger spectra in Figure 21-8 are for samples of a 70% Cu to 30% Ni alloy, which is often used for structures where saltwater corrosion resistance is required. Corrosion resistance of this alloy is markedly enhanced by preliminary anodic oxidation in a strong solution of chloride. Figure 21-8A is the spectrum of an alloy surface that has been passi vated in this way. Spectrum B is for another sample of the alloy in which the anodic oxidation potential was not great enough to cause significant passivation. The two spectra clearly reveal the chemical differences between the two samples that account for the greater corrosion resistance of the former. First, the copper-to-nickel ratio in the surface layer of the nonpassivated sample is approximately that for the bulk, whereas in the passivated material the nickel peaks completely overshadow the copper peak. Furthermore, the oxygen-to-nickel ratio in the passivated sample approaches that for pure anodized nickel, which also has a high corrosion resistance. Thus, the resistance toward corrosion of the alloy appears to result from the creation of a surface that is largely nickel oxide. The advantage of the alloy over pure nickel is its significantly lower cost.
FIGURE21-10 Schematic representation of the simultaneous use of ion sputter etching and Auger spectroscopy for determining depth profiles. (Courtesy of Physical Electronics, USA, Chanhassen, MN.)
ter is the more common. Figure 21-10 shows schematically how the process is carried out with a highly focused Auger microprobe with a beam diameter of about 5 flm. The microprobe and etching beams are operated simultaneously, with the intensity of one or more of the resulting Auger peaks being recorded as a function of time. Because the etching rate is related to time, a depth profile of elemental composition is obtained. Such information is of vital importance in a variety of studies such as corrosion chemistry, catalyst behavior, and properties of semiconductor junctions.
Line Scanning. Line scans are used to characterize the surface composition of solids as a function of distance along a straight line of 100 flm or more. For this purpose, an Auger microprobe is used that produces a beam that can be moved across a surface in a reproducihle way. Figure 21-12 shows Auger line scans along the surface of a semiconductor device. In the upper ligure, the relative peak amplitude of an oxygen peak is recorded as a function of distance along a line; the lower figure is the same scan produced when the analyzer was set to a peak for gold.
u
~
<J:
i
C
3
./
::j
.-.- •••••••••••
U
_._.
• __
.--1.......
/
~ 1.0
• __
• __
:-~.~.~.-
Qg
• .----'
o •• --------
__ .
•
• __
• .--
\ .4
.----' .----'
()
Depth Profiling of Surfaces. Depth profiling involves the determination of the elemental composition of a surface as it is being etched awav (sputtered) by a beam of argon ions. Either XPS or Auger spectroscopy can be used for elemental detection, although the lat-
FIGURE21-11 Auger sputtering profiles for the copper-nickel alloys shown in Figure 21-8: A, passivated sample; B, nonpassivated sample; C, chemically etched sample representing the bulk material. (Adapted from G. E. McGuire et aI., J. Electrochem. Soc., 1978,125,1802. Reprinted by permission of the pUblisher,the Electrochemical Society, Inc.)
Section 21G). However, dedicated instruments and instruments combined with other electron spectroscopy techniques (XPS. AES) are available commercially. Typically. the resolution of EELS instruments is > 10 cm", which is low compared to [R and Raman instruments but quite suitable for identifying and characterizing surface species.
The techniques named in rows 5 -7 of Table 21-1 detect a secondary beam of ions and are classified as ion spectroscopic techniques. These include secondaryion mass specrrometry, ion-scattering spectroscopy, Rutherford backscattering spectroscopy, and lasermicroprobe mass spectromerry. 210-1 Secondary-Ion Mass Spectrometry
Linear distance FIGURE 21-12 Auger line scans for oxygen (top) and
gold (bottom) obtained for the surface of a semiconductor device. (Courtesy of Physical Electronics, USA, Chanhassen, MN.) 21C·3 Electron Energy-Loss Spectrometry [n EELS,II a low-energy (1 to 10 e V) bcam of electrons is focused on the surface of a sample and the scattered electrons are analyzcd according to scattcring cnergy and scattering angle. Some of the scattered electrons will suffer losses in energy because of vibrational excitation of surface moleculcs. With high-resolution EELS, a vibrational spectrum can be obtained by counting the number of electrons with a given energy loss relative to the elastically scattered electrons and reporting this count as a function of energy. Such spectra have been used to identify functional groups in the first laver of a surface including adsorbates and provide infor~ation on chemical bonding. such as oxidation states and coordination numbers. [n manv cases EELS spcctra are ootained in conjunction ~ith electron microscopy experiments (see JISee R. F Egerton, Electron Energy Loss Specrroscop.\· in the Electrun New York: Plenum Press, 19H6
.••• flcruscope,
Secondary-ion mass spectrometry (SIMS) is the most highly developed of the mass spectrometri~ surface methods, with several manufacturers offering instruments for this technique. SIMS has proven useful for determining both the atomic and the molecular composition of solid surfaces. L2 There are basically three variations of the SIMS experiment. Static SIMS is used for elemental analysis of sub-monolaycrs on surfaces. Although SIMS is basically a destructive technique, static conditions maintain the surface integrity during the time scale of the experiment. Dynamic SIMS is used to obtain compositional information as a function of depth below the surface. 1ne dynamic SIMS experiment takes advantage of the destructive nature of SIMS to obtain information on various layers of materials. Imaging SIMS, also called scanning SIMS. is used to provide spatial images of surfaces. There are two types of SIMS instruments: secondary-ion mass analyzers are used for static and dynamic SIMS. and microprobe analyzers are used for imaging SIMS. Both are based on bombarding the surface of the sample with a beam of 5- to 20-keY ions. Usually. Ar+ le1. C. Vickerman and A. 1. Swift. in Surface Analysis - The Principal Techniques, 1. C. Vickerman, ed .. Chichester. UK: Wiley, 1997, Chap. 5; R. G. Wilson. F. A. Stevie. and C. \V. Maga, Secondary Ion Mass Spectrometry' A PraClical Handbook fur Depth Profiling and Bulk Impurity AfUllysis, !'\ew York: Wiley, 1989; A. Bcl\oinghoven, F. G. Rudenauer, and H. W Werner. Secondan' Ivn '\[US5 Spectromerr:I-'-" Basic Concepts, Instrumental Aspects, and Appiicalions and Trends. :"Iew York: Wiley, 1987; Secondar~: Ion \fan Spectmmt'fr.\ Theon Tutorial, Evans Analytical Group, http:// wv,v.'.eaglabs.com ien -L'S Ireferenccs -'tutorial Isimstheo,·caistheo.html.
ions are used. although Cs', N, -. or 0, + are also common. The ion oeam is formed in an ion gun in which the gaseous atoms or molecules are ionized by an elcctronimpact source. The positive ions are then accelerated by applying a high dc voltage. The impact of these primary ions causes the surface layer of atoms of the sample to be stripped (sputtered) off. largely as neutral atoms. A small fraction. however, forms as positive (or negative) secondary ions that are drawn into a spectrometer for mass analysis. [n static SIMS, the sputtering is so slow that consumption of the sample is essentially negligible. [n secondary-ion mass analyzers, which serve for general surface analysis and for dcpth profiling. the primary ion-beam diameter ranges from 0.3 to 5 mm. Double-focusing, single-focusing. time-of-flight. and quadrupole spectrometers are used for mass determination. Typical transducers for SIMS are electron multipliers, Faraday cups. and imaging detectors. These spectrometers yield qualitative and quantitative information about all of the isotopes (hydrogen through uranium) prescnt on a surface. Relative sensitivity factors vary considerably from ion to ion. Detection limits for most trace elements varv from 1 X lO" atoms/em] to 1 X 1016 atoms/cm3 By ~onitoring peaks for one or a few isotopes, as a function of time, concentration profiles can be ootained with a depth resolution of 5 nm to 10 nm (50 to 100 A). Ion microprobe analyzers are more sophisticated (and more expensive) instruments based on a beam of primary ions focused to a diameter of 200 nm to 1 flm. This beam can be moved across a surface (rastercd) for about 300 flm in ooth the x and y directions. A microscope is provided to permit visual adjustment of the beam position. Mass analysis is performed with a douole-focusing spcctrometer. [n somc instruments. the primary ion beam passes through an additional low-resolution mass spectrometer so that only a single type of primary ion oomoards the sample. The ion microprobe version of SIMS permits detailed studies of solid surfaces. 210-2 lon-Scattering and Rutherlord Backscattering Spectroscopy [on-scattering spectroscopv backscattering spectroscopy niques in that a primary ion surface.'-\ [n ooth techniques.
(155) and Rutherford (RBS) are similar techoeam is used to probe a the energy distributIon
FIGURE 21-13 Rutherford backscattering apparatus. An
ion beam from an accelerator is focused on the sample. Backscattered ions are detected with a solid-state particle detector.
of ions backscattered from the sample is measured. Ions striking a solid surface can give risc to a variety of collisional processes as well as electronic excitations. Analysis of the encrgy spectra of the scattered ions can give information aoout the atomic masses, their concentrations, and their geometric arrangement on the surface. The major difference betwcen the two techniques lies in the energies of the incoming ion beam. In [SS. also callcd low-energy ion scattering, the primary ion energies are in the range of 0.5-5 keY. Noole gas ions, such as He'. Ar', and Ne +, and alkali ions, such as Li T. Na' . or K+. arc used. An electron-impact ion source is most often used with an electrostatic or time-of-night analyzer. In the [SS technique. information is ootained from the topmost atomic laycr or. in some cases. from one or two layers directly below. [n Rutherford oackscattering. the primary ion beam ranges in energy from 100 keY for H' to several Me Y for Hc-, He'+ (alpha particles). and heavier ions. Sources of energetic ions are often of the Van de Graaff generator type. As shown in Figure 21-13. RBS instruments often use solid-state particle detectors and multichannel analyzers for cnerg\' resolution. Magnetic and electrostatic analvzers are also cmplo\'ed for highresolution studies. Information in RBS arises from a
thickness of about 100 nm, although with spccial techniques surface analysis is also possible, With RBS, it is possible to determine atomic masses and elemental concentrations as a function of depth below the surface, Because of its sensitivity to the top layer of the surface, ISS has provcn very useful in providing surface compositional analysis of materials such as catalysts and alloys, ISS can also providc structurallOformatlon on metal, semiconductor, metal oxidc, and adsorbatc surfaces, The major limitations of ISS are associ at cd with difficulties in providing quantitative results, because of neutralization rcactions and other interactions, Collisional processes and inelastic energy losses also make absolute mass determinations difficult In compositional analysis, ISS is complementary to AES although not as generally applicable. . RBS can provide absolute quantitative analySIS of elemental composition with an accuracy of about 5')10. It can provide depth-profile information from surface layers and thin films to a thickness of about I pm. In some cases, however, the high-energy beam can damage the surface. This is particularly a problem with insulating materials, such as polymers, alkah hahdes, and oxides. The Mars Pathfinder mission in 1997 contained an alpha proton X-ray spcctrometer (APXS). In its RBS mode, the spectrometer bombarded samples with alpha particles and determined elemental composition via energy analysis of the backscattered particles. In addition to RBS, the APXS instrument was designed to carry out proton emission and particleinduced X-ray emission (P[XE) experiments. Soil and rock compositions were measured and compared to those from the carlier Viking mission.
ing current research attention. [n addition, the laser microprobe has been used to vaporize samples prior to introduction into inductively-coupled plasmas for either emission or nlass spectral analysis. U Laser-microprobe mass spectrometry has an unusually high sensitivity (down to 10-'0 g), is applicable to both inorganic and organic (including biological) samples, has a spatial resolution of about I J.lm.and produces data at a rapid rate. Some typical applications of laser-microprobe mass spectrometry mclude determination of Na/K concentration ratios in frog nerve fiber, determination of the calcium distribution in retinas, classification of asbestos and coal mine dusts, determination of fluorine distributions in dental hard tissue, analysis of amino acids, and study of polymer surfaces."
21E
SURFACE PHOTON SPECTROSCOPIC METHODS
In this section we discuss methods in which photons provide both the primary beam and the detected beam. The techniques discussed are listed in Table 21-1; namely, surface plasmon resonance, sum frequency generation, and ellipsometry. The electron and ion speetroscopic surface techniques described previously all suffer from one disadvantage: they require an ultrahigh vacuum environment and provide no access to buried interfaces. The photon spectroscopic methods described here can all deal with surfaces in contact with liquids and, in some cases, surfaces that are buried under transparent layers. 21E-1 Surface
210-3
Laser-Microprobe
Mass Spectrometry
Laser-microprobe mass spectrometers are used for the study of solid surfaces. Ablation of the surlace IS accomplished with a high-power, pulsed laser, usually a Nd-YAG laser. After frequency quadrupling, the NdYAG laser can produce 266-nm radiation focused to a spot as small as 0.5 pm. The power density of the radiation within this spot can be as high as 10 lO to 10 II W/cm2 On ahlation of the surface a small fraction of the atoms are ionized. The ions produced are accelerated and then analyzed, usually by timc-of-flight mass spectrometry. 1n some cases laser microprobes have been combined with quadrupole ion traps and with Fourier transform mass spectrometers. Lasermicroprobe tandem mass spectrometry is also receiy-
Plasmon
Resonance
Surface plasmon waves are surface electromagnetic waves that propagate in the xy plane of a metal film when the free electrons interact with photons. An easy way to obtain the resonance condition is to arrange for total internal refleetion at an interface, as shown 10 Figure 21-14. Here, a monochromatic light beam from a laser propagates in a medium of higher refraetlve 10dex, such as glass. If the radiation strikes an interface to a medium of lower refractive index such as air or water, total internal reflection can occur if the angle of I~Sa,forexample. R. E. Russo, X. Mau, and S. S. Mall. Allai. Ch.:m.. 2002. 74, 70A; B. Hattendorf. C. Latkoczy, and D. Gunther. AnaL Chern .. 2003,
~;F~:~'~therdetails. see L. Van Vacek (hem .. 1990,336. 7·D. 755.
and R. Gijbels, Fresenius J Anal
FIGURE 21-14 Surface plasmon resonance. Laser radiation is coupled into the glass substrate coated with a thin metal film by a half-cylindrical prism. Iftotal internal reflection occurs, an evanescent wave is generated in the medium of lower refractive index. This wave can excite surface plasmon waves. When the angle is suitable for surface plasmon resonance, a sharp decrease in the reflected intensity is observed at the detector.
incidence is greater than the critical angle. The radiation is focused and coupled into the interface by a prism coupler or a diffraction grating. With total internal reflection, an evanescent ware (see Section 17B-3) is generated in the medium of lower refractive index that decays exponentially with distanee from the interface. As we have seen in Chapter 17, the evanescent wave can be absorbed in the less dense medium and the beam attenuated by attenuated total reflection. If the internally reflecting interface is coated with a conducting material, such as a thin metal film, the p-polarized component of the evanescent wave may penetrate the metallic layer and excite surface plasmon waves. If the metal is nonmagnetic, such as a gold !ilm, the surface plasmon wave is also p-polarized, which cre'ltes an enhanced evanescent wave. Because of the penetration of the electric field into the lowerrefractive-index medium, the interaction is quite sensitive to the refractive index at the metal Iilm surface. When the angle is suitable for surface plasmon resonance, a sharp decrease in the reflected intensity is observed, as can be seen in Figure 21-14. The resonance condition can be related to the refractive index of the metal film and can be used to measure this quantity and other properties of the surface. The most interesting aspect of surface plasmon resonance (SPR) is its sensitivity to materials adsorbed onto the metal film and the interactions of these materials, particularly biomolecules16 A linear relationship
is often found between the resonant energy and the concentration of biologically relevant materials such as sugars. DNA molecules. and proteins. Because of this sensitivity, SPR has become an important technique for biosensors. Here. biomolecular interactions, such as antibody-antigen binding or enzyme-substrate binding, occur at the sensor surface. Such interactions alter the refractiye index and change the SPR angle needed to achieve resonance. The SPR angle, 0SPR, can be monitored as a function of time to give information on the kinetics of binding reactions at the surface. Commercial instrumentation for SPR is available17 Many other potential applications of surface plasmon waves have been envisioned, including miniaturized devices, such as filters, polarizers, and light sources. The field has been termed molecular plasnlonics. tS
21 E-2 Sum-Frequency
Generation
Sum-frequenc\' generation (SFG) is a nonlinear optical technique based on the interaction of two photons at a surface19 The result of the wave-mixing interaction is the production of a single photon whose frequency is the sum of the incident frequencies. If the two incident photons are of the same frequency, the technique is called second-harmonic generation because the exiting photon has a frequency twice that of the incident photons. Because this is a weak second-order process, intense lasers must be used. SFG can be applied to solid-liquid, solid-gas, Iiquidgas, or liquid-liquid interfaces. The process becomes most efficient when either the incident frequency or the outgoing frequency correspond to an allowed electronic or vibrational transition. Usually, one of the sources is a tunable laser to allow the incident frequency to be varied. One of the most useful of the possible sumfrequency techniques is vibrational sum-frequeney spectroscopy in which one of the incident beams is in the infrared spectral region and the other is in the visible region.'" Figure 21-15 shows two configurations that can be used. In Figure 21-15a, the arrangement for studying the interface between two immiscible liquids I-See R. \lukh\lpadhyay -tfJlll. Chem.. 2005,77, "It:lA hR. P. Van DuvncPPY. ~cc not:: 27, For r::vicws on ;It',lllIC l'.If":': mlcf\hCilP) F 1. (;ic~'lhl. Rn .\lod E'hl''' .. ltH)J. ~5. 9--t\); H.! ak:\fl,l, 1. R Kt:n~dh.:-), Wong..l C O'Bri::n. :mJ ~l D. PllTter Chem Re\'. 1999. QQ, ~,S--t):D R. L)u~it'rand B .--\.Parkinson, Anar Chl'm,. 1995. 6- :'Y'.--\ For bio[OgIC,ll ;lprlications, See' A[UII'IC Forcc\'ficroll''''!,L B/dmedi,,',I! \[,-rhrdImilar in form lo Equation 22-11 are described as nernstian relationships: electrodes and sensors whose bcha\:ior can be described bv the Nernst equation are said to exhibit ncrnstian beha\ior, and RPTlF (2.303 RT/nFwhen base iO logarithms are used) is often called the nartSlin" factor
Both hydrogen ions and chloride ions tend to diffuse across this boundary from the more concentrated to the more dilute solution, and the driving force for this movement is proportional to the concentration difference. The diffusion rates of various ions under the influence of a fixed force vary considerably (that is, the mobilities are different). In this example, hydrogen ions are about a factor of 5 more mobile than chloride ions. As a result, hydrogen ions tend to diffuse faster than the chloride ions, and this difference in diffusion ratc produces a separation of charge (see Figure 22-4). The more dilute side (the right side in the figure) of the boundary becomes positively charged becausc hydrogen ions diffuse more rapidly. The concentrated side, therefore, acquires a negative charge from the excess of slower-moving chloridc ions. The charge separation that occurs tends to counteract the differences in mobilities of the two ions, and as a result, equilibrium is soon achieved. The junction potential difference resulting from this charge separation may amount to 30 mV or more. In a simple system such as that shown in Figure 22-4, the magnitude of the junction potential can be calculated from the mobilities of the two ions involved. However, it is seldom that a cell of analytical importance has a sufficiently simple composition to permit such a computation.s Experiment shows that the magnitude of the junction potential can be greatly reduced by introduction of a concentrated electrolyte solution (a salt bridge) between the two solutions. The effectiveness of a salt bridge improves not only as the concentration of the salt increases but also as the difference between the mohilities of the positive and negative ions of the salt approaches zero. A saturated potassium chloride solution is particularly effective from hoth standpoints. Its For methods for approximatlOg junction potentials. ~ee k J Bard and L R Faulkner. £lectrochemical\fethods, 2nd ed .. PP 09-71. :"cw '"ork Wiley. 2001
j
...-Ej
---.--
FIGURE 22·4 Schematic representation of a liquid junction showing the source of the junction potential E,. The length of the arrows corresponds to the relative mobility of the two ions.
concentration is greater than 4 M at room temperature, and equally important, the mobilities of potassium and chloride ions differ by only 4%. When chloride ion interferes with a particular experiment, a concentrated solution of potassium nitrate can be substituted. With such bridges, the net junction potential is typically a few millivolts or less, which is negligible in most analytical measurements.
It is useful to think of the cell reaction of an electrochemical cell as being made up of two half-cell reactions, each of which has a characteristic electrode potential associated with it. As will be shown later, these electrode potentials measure the driving force for the two half-reactions when, by convention, they are both written as reductions. Thus, the two half-cell or electrode reactions for the cell
2AgCI(s) + 2e-~2Ag(s) 2H+ + 2e- ~
-t-
2C1-
H,(g)
To obtain the spontaneous cell reaction, the second half-reaction is subtracted from the tirst to give
If the electrode potentials E"ge", and Efr H, are known for the two half-reactions. we ma~ then tind
the cell potential E~t1 by subtracting the electrode potential for the second reaction from the first. That is, Ecell
=
EAgCIJAg
-
EW'tL
A more general statement of the last relationship is
where E,;ght is the potential of the half-cell written on the right in the diagram of the cell or in the shorthand representation, and E'elt is the electrode potential for the half-reaction written on the left. We discuss this convention further in Section 22C-5.
The potential of an electrochemical cell is the difference between the potential of one of the electrodes and the potential of the other. and it is therefore important to have a clear idea of what is meant by the potential of an electrode. This potential is a measure of an electrode's electron energy. For a metallic conductor immersed in a solution of an electrolyte, all excess charge resides on its surface, and it is possible to adjust the charge density on this surface by adjusting the output of an external power supply attached to the conductor. As this external source forces electrons onto the surface of an electrode, the electrons become more crowded, and their energy increases because of coulombic repulsion. The potential of the electrode thus becomes more negative. If the external circuitry withdraws enough electrons from the electrode, the surface will have a positive charge, and the electrode becomes more positive. Itis also possible to vary the electron energy, and thus the potential, of a metallic electrode by varying the composition of the solution that surrounds it. For example, there is a potential at a platinum electrode immersed in a solution containing hexacyanoferrate(lI) and hexacyanoferrate(III) as result of the equilibrium Fe(CN)h1
+ e-;=="
Fc(CN)h"
If the concentration of Fe( CN)6" - is made much larger than that of Fe(CN)6" hcxacyanoferrate(II) has a tendency to donate electrons to the metal. thus creating a negative charge at the surface of the metal. Under this condition, the potential of the electrode is negative. On the other hand, if Fe(CN),,' is present in large excess, there is a tendency for electrons to be removed from the electrode, causing surface layer ions to ~
I2J
Simulation: Learn more about electrochemical cell potentials.
form in the solution and leaving a positive charge on the surface of the electrode. The platinum electrode then exhibits a positive potential. We must emphasize that no method can determine the absohue value of the potential of a single electrode, because all voltage-measuring devices determine only differences in potential. One conductor from such a device is connected to the electrode under study. To measure a potential difference, however, the second conductor must make contact with the electrolyte solution of the half-cell under study. This second contact inevitably creates a solid-solution interface and hence acts as a second half-cell in which a chemical reaction must also take place if charge is to flow. A potential is associated with this second reaction. Thus, we cannot measure the absolute value for the desired half-cell potential. Instead, we can measure only the difference bctween the potential o(interest and the half-cell potential for the contact betwcen the voltagc-measuring device and the solution. Our inability to measure absolute potential~ fllr halfcell processes is not a serious problem because relative half-cell potentials, measured versus a common reference electrode, are just as useful. These relative potentials can be combined to give real cell potentials. In addition, they can be used to caleulate equilibrium constants of oxidation-reduction processes. To develop a useful list of relative half-cell or electrode potentials, we must have a carefully defined reference electrode that is adopted by the entire chemical community. The standard hydrogen electrode, or the normal hydrogen electrodc, is such a half-cell.
Hydrogen gas electrodes were widely used in early electrochemical studies not only as reference electrodes but also as indicator electrodes for determining pH. The composition of this type of electrode can be represented as Pt,H,(patm)jH+(aw
=
x)
The terms in parcntheses suggest that the potential at the platinum surface depends on the hydrogen ion activity of thc solution and on the partial pressure of the hydrogen used to saturate the solution. The half-cell shown on the left in Figure 22-5 shows the components of a typical hydrogen electrode. The conductor is made of platinum foil that has been platinized. Platinum electrodes are platinized by coating their surfaces with a finely divided layer of platinum by
1033:
IJI
Com
+
FIGURE 22-5 Measurement of the electrode potential for an M electrode. Ifthe M'+ ion activity in the right-hand compartment is 1.00, the cell potential is the standard electrode potential of the half-reaction M2+(aq)+ 2e-
rapid chemical or elcctrochemical reduction of HzPtCI6• The finely divided platinum on the surface of the electrode does not reflect light as does polished platinum, so the electrode appears black, Because of its appearance, the deposited platinum is called platinum black. Platinum black has a very large surface area to ensure that the reaction
is rapid at the electrode surface. As was pointed out earlier, the stream of hydrogen simply keeps the solution adjacent to the electrode saturated with the gas. The hydrogen electrode may act as the positive or the negative electrode, depending on the half-cell with which it is coupled with the salt bridge shown in Figurc 22-5. When the cell is short circuited, hydrogen is oxidized to hydrogen ions when the electrode is an anode; the reverse reaction takes place when the electrode is a cathode. Under proper conditions, then, the hydrogen electrode is electrochemically reversible. When the cell is connected as shown in Figurc 22-5, there is essentially no current in the cell because of the very high impcdance of the meter. Under short circuit, the meter is replaced with a wire or low-resistance load as shown in Figure 22-1b, and the reaction proceeds. The potential of a hydrogen electrode depends on the temperature, the hydrogen ion activity in the solu-
;=='
M(s).
tion, and the pressure of the hydrogen at the surface of the electrode. Values for these experimental variables must be defined carefully for the half-cell to serve as a reference, Specifications for the standard hydrogen electrode (SHE) call for a hydrogen ion activity of unity and a partial pressure for hydrogen of exactly one atmosphere. By convention, the potential of this electrode is assigned the value of exactly zero volt at all temperatures.
Although the SHE has great fundamental importancc, the difficulty in preparing the electrode surface and controlling thc activities of the reactants make it so impractical that it is rarely used for routine measurements. Instead, reference electrodes simple to prepare, more rugged, and easier to use are nearly always substituted for the hydrogen gas electrode. One of the most common of these is the silver -silver chloride electrode. This electrode can be prepared by applying an oxidizing voltage to a silver wire immersed in a dilute solution of hydrochloric acid. A thin coating of silver chloride forms that adheres tightly to the wire. The wire is then immersed in a saturated solution of potassium chloride. A salt bridge connects the potassium chloride solution to the dectrode system being studied. The potential of
this electrode is about +0.22 V with respect to the SHE. The electrode half-reaction is
A second widely used reference electrode is the saturated calomel electrode (SCE), which consists of a pool of mercury in contact with a solution that is saturated with mercury(I) chloride (calomel) as well as potassium chloride. Platinum wire dipping in the mercury provides electrical contact to the other conductor, and a salt bridge to the second electrolyte completes the circuit. The potential of this reference is about 0.24 V positive. The electrode reaction is Hg2Clb)
+ 2e- ~
2Cl- + 2Hg(l)
Section 23A gives more detailed descriptions of the silver-silver chloride and the calomel reference electrode systems. Both reference electrodes can be purchased from suppliers of electrochemical equipment.
An electrode potential is defined as the potential of a cell in which the electrode under investigation is the right-hand electrode and the SHE is the left-hand electrode.6 We must emphasize that, in spite of its name, an electrode potential is in fact the potential of an electrochemical cell that contains a carefully defined reference electrode on the left. Electrode potentials could more properly be called relative electrode potentials, but they seldom are. Note that this cell potential may be positive or negative depending on the electron energy of the electrode under study. Thus, when this energy is greater than that of the SHE, the electrode potential is negative; when the electron energy of the electrode in question is less than that of the SHE, the electrode potential is positive. The cell in Figure 22-5 illustrates the definition of the electrode potential for the half-reaction M2+ + 2e- ~
M(s)
In this figure, the half-cell on the right consists of a strip of the metal M in contact with a solution of M2+. The half-cell on the left is a SHE. By definition, the potential E observed on the voltmeter is the electrode potential for the M2+/M couple. In this general example. we assume that the junction potentials across the salt
bridge are zero. If we further assume that the aetivity of M'- in the solution is exactly 1.00, the potential is called the standard electrode potential for the system and is given the symbol EO That is, the standard electrode potential for a half-reaction is the electrode potential when the reactants and products are all at unit activity. If M in the figure is copper, and if the copper ion activity in the solution is 1.00, the compartment on the right is positive, and the observed potential is +0.337 V as shown in the figure. The spontaneous cell reaction, which would occur if the voltmeter were replaced by a wire, is Cu"
+ H2(g)~Cu(s)
+ 2H'
Because the hydrogen electrode is on the left, the measured potential is, by definition, the electrode potential for the Cu-Cu 2+ half-cell. Note that the copper electrode is positive with respect to the hydrogen electrode; thus, we write
If M in Figure 22-5 is cadmium instead of copper, and the solution has a cadmium ion activity of 1.00, the potential is observed to be -00403 V. In this case, the cadmium electrode is negative, and the cell potential has a negative sign. The spontaneous cell reaction would be Cd(s) + 2H+ ~
Cd'+ + Hz(g)
A zinc electrode in a solution of zinc ion at unity activity exhibits a potential of -0.763 V when coupled with the SHE. The zinc electrode is the negative electrode in the galvanic cell, and its electrode potential is also negative. The standard electrode potentials for the four halfcells just described can be arranged in the order Cu ,+ + 2e' ~
Cu(s)
2H' + 2e- ~
H,(g)
Cd"
+2e-~Cd(s)
Zn'+ + 2e- ~
Zn(s)
Ell
= +0.337 V
EO = 0.000 V EO=
-0.403 V
EO
-0.763 V
=
The magnitudes of these standard electrode potentials show the relative strengths of the four ionic species as electron acceptors (oxidizing agents). In other words, we may arrange the ions in order of their decreasing strengths as oxidizing agents, Cu" > H' > Cd'- > Zn '+, or alternatively, the elements in order of
their increasing strengths H, < Cd < Zn.
as reducing agents, Cu
(O.0200 M) II Ag +(0.0200 M)IAg If we always follow this convention, the value of Eall is a measure of the tendency of the cell reaction to occur spontaneously in the direction written from left to right. That is, the direction of the overall process has Cu metal being oxidized to Cu 2+ in the left-hand compartment and Ag+ being reduced to Ag metal in the right-hand compartment. In other words, the reaction for the process occurring in the cell is considered to be Cu(s) + 2Ag+ ~ Implications
Cu'+ + 2Ag(s)
of the IUPAC Convention
Several implications of the sign convention may not be obvious. First, if the measured value of Eall is positive, the right-hand electrode is positive with respect to the left-hand electrode, and the free energy change for the reaction as written is negative according to .lG = -nFE'dl (Equation 22-8). Hence, the reaction in the direction being considered will occur spontaneously if the cell is short -circuited or connected to some device to perform work (e.g., light a lamp, power a radio, start a car). On the other hand, if E"11 is negative, the righthand electrode is negative with respect to the left-hand electrode, the free energy change is positive, and the reaction in the direction considered (oxidation on the left, reduction on the right) is not the spontaneous cell reaction. For our previous copper-silver cell, E''''I = +0.412 and the oxidation of Cu and reduction of
v:
Ag+ occur spontaneously when the cell is connected to a device and allowed to do so. The IUPAC convention is consistent with the signs that the electrodes actually exhibit in a galvanic cell. That is, in the Cu-Ag cell, the Cu electrode is electron rich (negative) because of the tendency of Cu to be oxidized to Cu 2+, and the Ag electrode is electron deficient (positive) because of the tendency for Ag + to be reduced to Ag. As the galvanic cell discharges spontaneously, the silver electrode is the cathode, and the copper electrode is the anode. Note that for the same cell written in the opposite direction
the measured cell potential would be E,ell = -00412 V, and the reaction considered is
This reaction is not the spontaneous cell reaction because Eoell is negative and !1G is thus positive. It does not matter to the cell which electrode is written in the schematic on the right and which is written on the left. The spontaneous cell reaction is always
By convention, we just measure the cell in a standard manner and consider the cell reaction in a standard direction. Finally, we must emphasize that no matter how we write the cell schematic or arrange the cell in the laboratory, if we connect a wire or a low-resistance circuit to the cell, the spontaneous cell reaction will occur. The only way to achieve the reverse reaction is to connect an external voltage source and force the electrolytic reaction2Ag(s) + Cu2+~2Ag+ + Cu(s) to occur. Half-Cell
Potentials
The potential of a cell such as that shown in Figure 22-5 is the diffcrence between two half-cell or single-electrode potentials, one associated with the half-reaction at the right-hand electrode (E,ight), the other associated with the half-reaction at the left-hand electrode (E1"1)' According to the IUPAC sign convention, as long as the liquid-junction potential is negligible or there is no liquid junction, we may write the cell potential E'dl as E'dl = E'i'hl - F'eft as given hy Equation 22-12. Although we ~annot determine absolute potentials of electrodes such as these, we can easily determine relative electrode potentials as discussed in Section 22C-4.
Any sign convention must be based on half-cell processes written in a single way - that is, entirely as oxidations or as reductions, According to the IUPAC convention, the term electrode potential (or more exactly, relative electrode potential) is reserved exclusively for half-reactions written as reductions. There is no objection to using the term oxidation potential to indicate an electrode process written in the opposite sense, but an oxidation potential should never be called an electrode potential.
22C-6 Effect of Activity on Electrode Potential Let us consider the half-reaction pP + qQ + ... + ne- ~
rR + sS
where the capital letters represent formulas of reacting species (whether charged or uncharged), e- represents the electron, and the lowercase italic letters indicate the number of moles of each species (including electrons) participating in the half-cell reaction. By invoking the same arguments that we used in the case of the silversilver chloride-SHE cell in Section 22B-l, we obtain E = EO _ RT In (aR)~'(as)f'" nF (ap)f·(aQ)?··· At room temperature (298 K), the collection of constants in front of the logarithm has units of joules per coulomb or volt. Therefore, RT
8.316Jmol-1K-1
x 298K
n X 96487Cmol-1
nF
2.568
X
10-2 J C-I n
2.568
X
10-2 V
n
When we convert from natural (In) to base ten logarithms (log) by multiplying by 2.303, the previous equation can be written as E
=
0.0592 EO - --Iog( n
(aR)" (as)' ... )P ( )q .. ap'
aQ
For conveniencc, we have also deleted the i subscripts, which were inserted earlier as a reminder that the bracketed terms represented nonequilibrium concentrations. Hereafter, the subscripts will not be used; you should, however, keep in mind that the quotients that appear in this type of equation are not equilibrium constants, despite their similarity in appearance. Equation 22-13 is a general statement of the Nernst equation, which can be applied to both half-cell reactions and cell reactions.
22C-7 The Standard Electrode Potential, EO Equation 22-13 reveals that the constant EO is equal to the half-cell potential when the logarithmic term is zero. This condition occurs whenever the activity quotient is equal to unity, such as, for example, when the activities of all reactants and products are unity. Thus, the standard potential is often defined as the electrode potential of a half-cell reaction (versus SHE) when all reactants and products have unit activity. The standard electrode potential is an important physical constant that gives a quantitative description of the relative driving force for a half-cell reaction. Keep in mind the following four facts regarding this constant. (1) The electrode potential is temperature dependent; if it is to have significance, the temperature at which it is determined must be specified. (2) The standard electrode potential is a relative quantity in the sense that it is really the potential of an electrochemical cell in which the left electrode is a carefully specified reference electrode - the SHE - whose poten~ial is assigned a value of zero. (3) The sign of a standard potential is identical with that of the conductor in the righthand electrode in a galvanic cell, with the left electrode being the SHE. (4) The standard potential is a measure of the driving force for a half-reaction. As such, it is independent of the notation used to express the half-cell process. Thus, although the potential for the process Ag+ + e- ~
Ag(s)
EO = +0.799 V
depends on the concentration of silver ions, it is the same regardless of whethcr we write the half-reaction as the preceding or as 100 Ag+ + 100 e- ~
100 Ag(s)
EO = +0.799 V
The Nernst equation must be consistent with the halfreaction as it is written. For the reaction written for one mole of silver, the Nernst equation is E
=
0.0592 0.799 - --log-I
I aAg'
and for 100 moles of silver, =
0.799
=
1
-100 log (a~g' )100
= 0.799 -
0.799 -
0.0592 [ J.OOlog- I ] -100 aA< 0.0592 --log1
EO at 2S'C, V CI,(g) + 2e- ~
+1.359
2CI,
O,(g) + 4H+ + 4e- ~ Br,(aq) + 2e- ~
2H,O
+1.087
2Br,
Br,(l) + 2e- ~ Ag+ +e-~Ag(s) Fe3++e-~Fe2+
+1.065
2Br,
+0.799 +0.771
13-+2e-~31Cu2-
+0.536
+ 2e- ~
Hg2C1,(s)
Cu(s)
+ 2e-
~
+ 2CI, + CI2 Ag(s) + 2S,032-
H,(g)
+ 2e- ~
+0.268 +0.222 +0.010 0.000
+ I,
Agl(s) + e-~Ag(s) PbS04(s)
+0.337
+ 2e-~2Hg(l)
AgCl(s) + e- ~Ag(s) Ag(S,03),'- + e- ~ 2H+
+1.229
Pb(s) + SO/-
-0.151 -0.350
Cd'+ + 2e- ~Cd(s)
-0.403
Zn2+ + 2e- ~
-0.763
Zn(s)
hypothetical electrode to which experimentally determined potentials can be referred only by suitable computation. The reason that the electrode, as defined, cannot be prepared is that we are unable to prepare a solution with a hydrogen ion activity of exactly unity. Neither the Oebye-HUckel theory (see Appendix 2) nor any other theory of electrolyte solutions permits the determination of the activity coefficient of hydrogen ions in solutions with ionic strength approaching unity, as required by the definition of the SHE. Thus, the concentration of HCI or another acid required to give a hydrogen ion activity of unity cannot be calculated accurately. In spite of this limitation, data for more dilute solutions of acid, for which activity coefficients can be determined, can be used to compute hypothetical potentials at unit activity. The example that follows illustrates how standard potentials can be ohtained in this way.
22C-8 Measuring Electrode Potentials
0.0592
E
hydrogen electrode or other reference electrode as reference. It is possihle. however, to calculate EO values from equilihrium studies of oxidation-reduction systems and from thermochemical data relating to such reactions. Many of the values found in the literature were calculated in this way.' For illustrative purposes, a few standard electrode potentials are given in Table 22-1; a more comprehensive table is found in Appendix 3. The species in the upper-left-hand part of the equations in Tahle 22-1 are most easily reduced, as indicated by the large positive EO values; they arc therefore the most effective oxidizing agents. Proceeding down the left-hand side of the table, each succeeding species is a less effective acceptor of electrons than the one above it, as indicated by its increasingly negative standard potential. The half-cell reactions at the bottom of the table have little tendency to take place as reductions as written. On the other hand, they do tend to proceed in the opposite sense, as oxidations. The most effective reducing agents, then, are species that appear in the lower-righthand side of the equations in the tahle. Compilations of standard potentials provide information regarding the extent and direction of electrontransfer reactions between the tabulated species. Table 22-1 suggests, for example, that zinc is more easily oxidized than cadmium, and we conclude that when a piece of zinc is immersed in a solution of cadmium ions, metallic cadmium will deposit on the surface of the zinc, which will dissolve and produce zinc ions as long as there is an appreciable concentration of cadmium ions in the solution. On the other hand, cadmium has no tendency to reduce zinc ions, so a piece of cadmium immersed in a solution of zinc ions will remain unaffected. Table 22-1 also shows that iron(III) is a better oxidizing agent than triiodide ion. Therefore, in a solution containing an equilibrium mixture of iron(III), iodide, iron(II), and triiodide ions, we predict that iron(II) and triiodide will predominate.
I aAg-
Standard electrode potentials have been tabulated for manv half-reactions. Manv have been determined directly' from voltage measu~ements of cells with a
Although the SHE is the universal reference standard, we must emphasize once again that the electrode, as described, is almost never used in the laboratory; it is a 'ComprchcOSl\, see Y. Umczawa. eRe Handbook uf Ion Se/coin' Elecrrodt's 'ie/eeci_ill" CoefficienL~, Boca Raton, FL CRe Press. \I}(XJ 1\
The departures from linearity at the extremes in Figure 23-7 should be constant reminders that pH values below () and above 12 must be viewed with a very critical eye. Theoretical descriptions of even the simplest solutions in these pH regions are complex, and physical interpretation of the results is dimcult.12 Measurements on real samples in these pH regions should be regarded as qualitative or semiquantitative at best.
The alkaline error in early glass electrodes led to investigations concerning the effect of glass composition on the magnitude of this error. One consequence has been the development of glasses for which the alkaline error is negligible below about pH 12. Other studies have discovered glass compositions that permit the determination of cations other than hydrogen. This application requires that the hydrogen ion activity a, in Equation 23-15 be negligible relative to kH.Bb,; under these circumstances, the potential is independent of pH and is a function of pB instead. Incorporation of AI,03 or B,03 in the glass has the desired effect. Glass electrodes for the direct potentiometric measurement of singly charged species such as Na +, K +, NH/, Rb +, Cs +, Li', and Ag+ have been developed. Some of these glasses arc reasonably selective for certain singly charged cations. Glass electrodes for Na+, Li+, NH4 +, and total concentration of univalent cations are available from commercial sources.
The most important type of crystalline membranes is manu[actured from an ionic compound or a homogeneous mixture of ionic compounds. [n some instances the membrane is cut from a single crystal; in others, disks are formed from the finely ground crystalline solid by high pressures or by casting from a melt. Typical membranes have a diameter of about 10 mm and a thickness of 1 or 2 mm. To form an electrode, a membrane is sealed to the end of a tube made from a chemically inert plastic such as Teflon or polyvinyl chloride (PVC). Conductivity
of Crystalline Membranes
Most ionic crystals are insulators and do not have sufficient electrical conductivity at room temperature to be used as membrane electrodes. Those that are con-
ductive are characterized hy having a small singly charged ion that is mobile in the solid phase. Examples are fluoride ion in certain rare earth fluorides, silver ion in silver halides and sulfides, and copper(I) ion in copper(I) sulfide. The Fluoride Electrode
Lanthanum fluoride, LaF], is a nearly ideal substance for the preparation of a crystalline memhrane electrode for the determination of fluoride ion. Although this compound is a natural conductor, its conductivity can be enhanced by doping with europium fluoride, EuF,. Membranes arc prepared by cutting disks from a single crystal of the doped compound. The mechanism of the development of a fluoridesensitive potential across a lanthanum fluoride membrane is quite analogous to that described for glass, pH-sensitive membranes. That is, at the two interfaces, ionization creates a charge on the memhrane surface as shown by the equation LaF] ;=== LaF,+ + F1 Ca", >1 Sr2+, >0.5 Sr2', 1 X 10-2 Zn" Hg" and Ag' (poisons electrode at >10-7 M), Fe" (at >0.1[Cd2'], Pb" (at >[Cd2+], Cu2'(possible) 10-5 Pb2+. 4 X 10-' Hg2' H' 6 X 10-' Sr"· 2 X 10-2 Fe2+·4 X 10-' Cu'" 5 X 10-2 2'; 0.2 NH,; 0.2 N~'; 0.3 Tris'; 0.3 Li'; 0.4 K'; 0:7 Ba"; 1.0Zn"';
Ni
1.0 Mg2'
Maximum allowableratio of interferent to [cq: OH- 80, Br- 3 X 10-', [- 5 X 10-7,52- 10-6, CN- 2 X 10-7, NH, 0.12, 5,0,'- 0.01 5 X 1O-7C[O,-; 5 X 10-6 r;5 X 10-5 ClO, -; 5 X 10-' CN-; 10'" Br-; 10-' N02-; 5 X 10-' NO,-; 3 X 10-' HCO,-, 5 X 10-2 CI-; 8 X 10-2 H,PO,-, HPO,'-, pol-; 0.2 OAc-; 0.6 P-; 1.050,'10-7 CIO,-; 5 X 10-61-; 5 X 10-' ClO, -; 10-4 CN-; 7 X 10-' Br-; 10-' HS-; 10-2 HCO,-, 2 X 10-2 CO,'-; 3 X 1O-'CI-; 5 X 10-2 H2PO,-, HPO,'-; pol-; 0.2 OAc-; 0.6 P-; 1.0SO,'7 X 10-1 salicylate,2 X 10-' r, 10-1 Br-, 3 X 10-1 ClO, -,2 X 10-[ acetate, 2 X 10-1 HCO,-,2 X 10-1 NO,-,2 X 10-1 SO,'-, 1 X 10-1 CI-, 1 X 10-[ 00.-,
1.4 X 10-6 to 3.6 X 10-6
1 X 10-1 F-
K' Water hardness (Ca2+ + Mg2+)
10° to 1 X 10-6 10-' to 6 X 10-6
All electrodes are the plastic-membrane
•
2 X 10-" r;2 X 10-2 CIO,-; 4 X 10-2 CN-, Br-; 5 X 10-' NO, -, NO, -; 2 HC~,-, CO,'-; CI-, H2PO,-. HPO,'-, pol-, OAc-, F-, 50,'3 X 10-4 Cst; 6 X 10-' NH.', TI'; 10-2 H'; 1.0 Ag', Tris'; 2.0 Li', Na' 3 X 10-5 Cu2', Zn2'; 10'" Ni2'; 4 X 10-' Sr'; 6 X 10-' Fe"; 6 x 10-' Ba2+; 3 X 10-2 Na'; 0.1 K'
type.
'From product catalog, Boston, MA: Thermo Orion, 2006. With permission of Thermo Electron Corp., Waltham. MA. (From product instruction
manuals, Boston, MA: Thermo Orion. 2003. With permission of Thermo Electron Corp .. Waltham. MA.
channel. As shown in Figure 23-11. instead of the usual metallic contact, the gate of the [SFET is covered with an insulating layer of silicon nitride (SiJN4). The analyte solution, containing hydrogen ions in this example, is in contact with this insulating layer and with a reference electrode. The surface of the gate insulator functions very much like the surface of a glass electrode. Protons from the hydrogen ions in the test solution are adsorbed on available microscopic sites on the silicon nitride. Any change in the hydronium ion concentration of the solution results in a change in the concentration of adsorbed protons. The changc in concentration of adsorbed protons then gives rise to a changing electrochemical potential between the gate and source, which in turn changes the conductivity of the channel of the [SFET. The conductivity of the channel can be monitored electronically to provide a signal that is proportional to the logarithm of the concentration of H' in the solution. Note that the entire [SFET except the gate in-
sulator is coated with a polymeric encapsulant to insulate all electrical connections from the analyte solution.
The ion-sensitive surface of the ISFET is naturally sensitive to pH changes, but the device may be rendered sensitive to other species by coating the silicon nitride gate insulator with a polymer containing molecules that tend to form complexes with species other than hydronium ion. Furthermore, several ISFETs may be fabricated on the same substrate so that multiple measurements may be made simultaneously. All of the [SFETs may detect the same species to enhance accuracy and reliability, or each [SFET may be coated with a different polymer so that measurements of several different species may be made. ISFETs offer a number of significant advantages over mcmbrane electrodes, including ruggedness, small
23F-1 Gas-Sensing Probes
size, inertness toward harsh environments. rapid response. and low electrical impedance. [n contrast to membrane electrodes, ISFETs do not reqUire hydration before use and can be stored indefimtely m ~he dry state. Despite these many advantages, no ISFETspecific-ion electrode appeared on the market untllthe early 19905, more than 20 years after their Illvenlion. The reason for this delay is that manufacturers were unable to develop the technology of encapsulatlllg the devices to create a product that did not exh[blt dnft and instability. The only significant disadvantage of ISFETs other than drift appears to be that they reqUire a more or less traditional reference electrode. This reqUIrement places a lower limit on the size of the ISFET probe. Work continues on the development of a differential pair of ISFETs, one selective for the analyte Ion and the other not. The second reference [SFET IScalled a REFET, and a differential amplifier is used to measure the voltage difference between the ISFET and the REFET, which is proportional to pX.[S Many [SFETbased devices have appeared on the market over the past decade for the determination of pH, and research has continued on the development of deVices that are selective for other analytes. Well over 150 [SFET patents have been filed over the last three decades, and more than twenty companies manufacture [SFETs 10 various forms. The promise of a tiny, rugged sensor that can he used in a broad range of harsh and unusual env[ronments is being achieved as the reference electrode problem is being sol ved." l~
P. Bergveld,
I~lbid_,
Sens ActuatorS. B. 2O(H, 88. 9.
pp. 18·11}
During the past three decades. several gas-sensing electrochemical devices have become available from commercial sources. In the manufacturer literature, these devices are often called gas-sensing "electrodes." Figure 23-12 shows that these devices are not, III fact, electrodes but instead are electrochemical cells made up of a specific-ion electrode and a reference electrode immersed in an internal solution retamed by a thm gas-permeable membrane. Thus, gas-sensing probes [S a more suitable name for these gas sensors. . Gas-sensing probes are remarkably selective and sensitive devices for determining dissolved gases or
NaHCOJ NaCI internal solution
Internal solution of glass electrode
Thin film of internal solution
FIGURE 23-12 Schematic of a gas-sensing probe for carbon dioxide.
TABLE 23-5
ions that can be converted to dissolved gases by pH adjustment.
CO,(g) ~
int¢Tnal jolution
CO,(aq) + 2H,O ~
Membrane Probe Design
Gas-Permeable
Membranes
Equilibrium iu Internal Solution
HCO, - + H]O'
InternJI
Figure 23-12 is a schematic showing details of a gassensing probe for carbon dioxide. The heart of the probe is a thin, porous membrane, which is easily replaceable. This membrane separates the analyte solution from an internal solution containina sodium bicarbonate and sodium chloride. A pH-se~sitive glass electrode having a fiat membrane is held in position so that a very thin film of the internal solution is sandwiched between it and the gas-permeable membrane. A silver-silver chloride reference electrode is also located in the internal solution. It is the pH of the film of liquid adjacent to the glass electrode that provides a measure of the carbon dioxide content of the analyte solution on the other side of the membrane.
then
interllal sulution
50[uti HCN + 2CJI,,06 + benzaldehyde glucose + 0, ---> gluconic acid + H,O, Penicillin ---> Penicilloicacid
From E. Bakker and f\.t. E. Meyerhoff, in Encyclopedia of £leCITochemutry,
eN-solid-state H+-glass or polymer H+-glass or polymer
A.1. Bard., Ed., \01. 9, Bloe1ecrrochemISITy, G. S. Wilson, Ed., New
York: Wiley, 2002, p. 305, with permission
211,0
2NH3 + 2H36~
Glutamate decarboxylase I3-Glucosidase Glucose oxidase
Creatinine ---> N-methylhydantoin + NH3 NH,-gas sensor L (D) AA ---> RCOCOOH + NH; + H20, NH,-gas sensor L-Glutamine ---> glutamic acid + NH3 NH,-gas sensor Adenosine ----* inosine + NH3 NH,-gas sensor L-Glutamate ---> GABA + CO,
NH. + glass or polymer NH r gas sensor H' -glass or polymer NH, +-glass or polymer
(23-23)
The electrode in Figure 23-13a is a glass electrode that responds to the ammonium ion formed by the reaction shown in the upper part of Equation 23-23. The electrode in Figure 23-13b is an ammonia gas probe that responds to the molecular ammonia in equilibrium with the ammonium ion. Unfortunately, both electrodes have limitations. The glass electrode responds to all monovalent cations, and its selectivity coefficients for NH4 + over Na+ and K' are such that interference occurs in most biological media (such as blood). The ammonia gas probe has a different problem - the pH of the probe is incompatible with the enzymc. The cnzyme requires a pH of about 7 for maximum catalytic activity, but the sensor's maximum response occurs at a pH that is greater than 8 to 9 (where essentially all of the NH, + has been converted to NH3). Thus, the sensitivity of the electrode is limited. Both limitations are ovcrcome by use of a fixedbed enzyme system where the sample at a pH of about 7 is pumped over the enzyme. The resulting solution is then made alkaline and thc liberated ammonia determined with an ammonia gas probe. Automated instruments (see Chapter 33) based on this technique have been on the market for several years. Factors that affect the detection limits of enzymebased biosensors include the inherent detection limits of the ion-selective electrode coupled with the enzyme layer, the kinetics of the enzyme reaction, and the mass-
transfer rate of substrate into the layer.24 Despite a large bod y of research on these devices and, as shown m Table 23-6, the several potentially useful enzyme-based membranes, there have been only a few commerCial potentiometric enzyme electrodes, due at least in part to limitations such as those cited previously. The enzymatic determination of urea nitrogen in clinical applications discussed in the following paragraphs is an exceptional example of this type of sensor. A number of commercial sources offer enzymatic electrodes based on voltammetric measurements on various enzyme systems. These electrodes are discussed in Chapter 25. Applications
in Clinical Analysis
An example of the application of a potentiometric enzyme-based biosensor in clinical analySIS ISan automated monitor designed specifically to analyze blood samples at the bedside of patients. The i-STAT Portable Clinical Analyzer, shown in Figure 23-14a, IS a handheld device capable of determining a broad range of clinically important analytcs such as potas~~E. Bakker and M. E. Meyerhoff, in Encyclopedw of Eleclro~hemi~lr}' A.1. Bard, ed .. Vol. 9, Bioelectrochemi~ln', G, S. \Vllson, cd .. Nev. 'turk Wiley, 2002. p. 3fH, P. W. Carr and L. D. Bl)WCrS, ImmobIlI~ed Enzymey. in Analytical and Clirlica{ Chemistry __Fundamentals and AppftcatlOns. Nc\\ York: \Viley, 1980.
sium, sodium, chloride, pH, pCO" pO" urea nitrogen, and glucose. In addition, the computer-based analyzer calculates bicarbonate, total carbon dIOXide, base excess 0, saturation, and hemoglobin in whole blood. Rel~tiv~ standard deviations on the order of 0.5% to 4% are obtained with these devices. Studies have shown that results are sufficiently reliable and cost effective to substitute for similar measurements made m a traditional, remote clinicallaboratory.25 'c Most of the analytes (pCO" Na+, K+, Ca- , urea nitrogen, and pH) are determined by potentiometric measurements using microfabricated membranebased ion-selective electrode technology. The urea nitrogen sensor consists of a polymer layer contaming urease overlying an ammonium ion-selective electrode. The chemistry of the BUN determmatlOn ISdescribed in the previous section. The hematocnt IS measured by electrolytic conductivity detection, and pO, is determined with a Clark voltammetnc sensor (see Section 25C-4). Other results are calculated from these data. The central component of the mom tor IS the single-use disposable electrochemical i:STAT sensor array depicted in Figure 23-14b. The mdlvldual sensor electrodes are located on silicon chips along a narrow flow channel, as shown in the figure. The
~ _
Polyimide Ion-selective
_HEMA _AgCl _Ag C]Au _Cr CJ Kapton _SolidKCl
membra
R,;.~~~;;~~~i~~'~l;~ ".
--------1IDiii/~;~,;,~u:;
&
>
FIGURE23-15 A microfabricated potentiometric sensor for in vivo determination of analytes. The sensor was fabricated on a flexible plastic substrate using thick-filmtechniques. There are nine ion-selective electrodes (ISEs)on one side of the filmand corresponding reference electrodes on the opposite side. (From E. Lindner and R. P. Buck, Anal. Chem., 2000, 72, 336A, with permission. Copyright 2000 American Chemical SoCiety.)
(b)
~~T~RE 23-14 (a) Photograph of i-STAT1 portable clinical analyzer. (b) Exploded view of I :r sensor array cartridge. (Abbott Point of Care Inc.)
integrated biosensors are manufactured by a patented mIcrofabncation process.'" .Each new sensor array is automatically calibrated pnor to the measurement step. A blood sample withdrawn from the patient is deposited into the sample entry well, and the cartridge is inserted into the i-STAT analyzer. The cali brant pouch, which contains a standard buffered solution of the analytes, is punctured by the i-STAT analyzer and is compressed to force the calibrant through the flow channel across the surface of the sensor array. When the calibration step is complete, the analyzer compresses the air bladder, which lorces the blood sample through the flow channel to ex-
pel the calibrant solution to waste and to bring the blood (20 fIL to 100 fIL) into contact with the sensor array. Electrochemical measurements are then made, and the results are calculated and presented on the liquid crystal display of the analyzer. The results are stored in the memory of the analyzer and may be transmitted to the hospital laboratory data management system for permanent storage and retrieval (see Section 4H-2). Cartndges are available that are configured for different combinations of more than twentv different analytes and measurements that can be ~made with this system. Instruments similar to the i-STAT bedside monitor have heen available for some time [or in vitro potentlOmetnc determination of various analytes in biomedIcal and biological systems. In recent years, there
has been much interest in the development of miniature potentiometric sensors for in vivo studies as well. Figure 23-15 shows a small array (4 x 12 mm) of nine potentiometric electrodes fabricated on a thin Kapton® polyimide filmY Nine separate electrodes (along with corresponding reference electrodes on the opposite side of the array) are fabricated by thick-film techniques similar to those used for printed circuit boards. A chromium adhesion layer and a gold layer are vapor deposited on the polymer to provide electrical connection to the sensor areas. The array is next coated with photoresist and exposed to UV light through a mask that defines the electrode areas. The photoresist is developed to expose the electrode pads. Silver is then deposited electrochemically followed by silver chloride to form the internal reference electrode for each sensor. A mixture of hydroxyethyl methacrylate (HEMA) and an electrolyte is added to provide a salt bridge between the internal reference electrode and the ionselective memhrane. Finally, the ion-selective membrane is applied ovcr the internal reference electrode along with a protective layer of polyimide. The sensor array has been used successfully to monitor H ~, K Na +, Ca " , and other analytes in heart muscle.
Other disposable electrochemical cells based on ion-selective electrodes, which are designed for the routine determination of various ions in clinical samples, have been available for some time. These systems are described briefly in Section 33D-3. Light Addressable Potentiometric
Sensor
An intriguing and useful application of semiconductor devices and potentiometric measurement principles is the light addressablc potentiometric sensor (LAPS)." This device is fabricated from a thin, flat plate of p- or n-type silicon with a 1000-A-thick coating of silicon oxynitride on one side of the plate. If a bias voltage is applied between a reference electrode immersed in a solution in contact with the insulating oxynitride layer and the silicon substrate, the semiconductor is depleted of majority carriers (see Section 2C-l). When light from a modulated source strikes the plate from either side, a corresponding photocurrent is produced. By measuring the photocurrent as a function of bias voltage, the surface potential of the device can be determined. Because the oxynitride layer is pH sensitive. the surface potential provides a measure of pH with a nernstian response over several decades. '~D_ A. Haf~man, 1.JO.l11'\2.
1- W. Parce, and H. M. McConnelL
Science. 1988.
· The versatility of the device is enhanced by attachIng to the underside of the silicon substrate an arrav of lIght-emIttIng diodes. By modulating the diodes in'sequence: dIfferent regions of the surface of the device can be Interrogated for pH changes. Furthermore, by applyIng membranes containing various ionophores o-r enzymes to the oxynitride layer, each LED can monitor a different analyte. When this device is used to monItor the response of living cells to various biochemIcal stImuli, it is referred to as a microphysiomeler. For a more complete description of the LAPS and Its blOanalytical applications, see the Instrumental Analysis in Action feature following Chapter 25.
where I is the current in this circuit consisting of the cell and the measurIng de"ice . The current is then given by 0.800:v'._~ __ (20 + 100) X 10' l! --6.67
I = ~_
X
10-' A
The potential drop across the measuring device (whIch IS the potential indicated by the device E ) is IR". Thus, ., -." EM
= (6.67
x 10 'A)(IOO
X
10" 0) = 0667 V
and 'I 0.667 V - O.80()V re error = ---0.800\;--~ . X 100% -'0.133 V
INSTRUMENTS FOR MEASURING CELL POTENTIALS
= OBOO-V- X 100%
An important consideration in the design of an instrument for measuring' cell potentials is that its resistance be large with respect tot he cell. If it is not, the I R drop !lI the cell producesslgmficant error (see Section 2A -3). We demonstrate thISeffect in the example that follows.
":e can easily show that to reduce the loading error to I Yo, the resistance of the yoltagc measuring device must be about 100 times greater than tbe cell resistance; for a rclative error of 0.1%, the res'isrance must be WOOtimes greater. Because the electrical resistan~e of cells containing ion-selective electrodes may be 100 Mfl or more, voltage measuring devices to be 'used WIth these electrodes generally have internal resistances of at least 1012 n. It is important to appreciate that an error in measured voltage, such as that shown in Example 23-1 (-0.133 V), would have an enormous effect on the accuraey.of a concentration measurement based on that potentIaL Thus, as shown in Section 23H-2, a 0.001 V uncertainty in potential leads to a relative error of about 4% in the determination of the hydrogen ion concentratIOn of a solution by potential measurement WIth a glass electrode. An error of the size found in Example 23-1 would result in a concentration uncertamty of two orders of magnitude or more. Direct-reading digital voltmeters with high internal reSIstances are used almost exclusively for pH and pIon measurements. We descrihe these devices in the next section.
23G
The true potential of a glass-calomel electrode system IS0.800 V; ItS!lite mal resistance is 20 MO. What would be the relative error in the measured potential if the measunng device has a resistance of 100 Mfl? Solution The following schematic diagram shows that the measurement circuit can be considered as a voltage source E, and two resIstors in series: the source resistance R and the internal resistance of the measuring device R,,'
23G-1 Direct-Reading
From Ohm's law, we may write E, = IR, + IR"
-17%
Instruments
Numerous direct-reading pH meters are available comme.rcially. Generally. these are solid-state devices With a fIeld-effect transistor or a voltage follower as the first amplilier stage to provide the necessary high input resIstance. FIgure 23-16 is a schematic of a simple. batten-operated pH meter that can be huilt for about
Frn", reference
eteelrode
~
FIGURE 23-16 A pH meter based on a quad Junction-FETinput operational amplifier integrated circuit. Resistors R ,-R, and potentiometers P,-P, are 50 kll. The circuit may be
powered by batteries as shown or an appropriate power supply. See the original paper for descriptions of the circuit operation and the calibration procedure. (Adapted from D. L. Harris and D. C. Harris, J. Chern. Educ., 1992, 69, 563. With permIssion.) $10, exclusive of the pH prohe and digital multimeter, which is used as the readout.'9 The output of the probe is connected to a high-resistance voltage follower A (see Sections 3B-2 and 3C-2), which has an input resistance of to 12 fl. Operational amplifiers Band C provide gain (slope, or temperature control) and offset (calibration) for the circuit readout. The inverting amplifIer C (see Section 3B-3) inverts the sense of the signal so that an increase in pH produces a positive increase in the output voltage of the circuit. The circuit is calibrated with buffers to display a range of output voltages extending from 100 to 1400 mY, corresponding to a pH range of 1 to 14. The three junction-FET operational amplifiers are located in a single quad integrated circuit package such as the LF347 (made hy National Semiconductor).
The range of pion meters available from instrument manufacturers is simply astonishing.''' We can classify four groups of meters based on price and readability. '''D. L !farris ~JTl~naks(he tni.h~:Standardization of pH Measurements, NIST Special Publication 260-53. Gaithersburg, MD: U.S. Department of Commerce, 1988. http://ts.nist.gov/ts/htdocsf230/232/SP_PUBUCA'110NS/documents/SP260-53.pdf. Updated valul::s from most recent NIST SRM certificateS. m
= molality (mol solute/kg H20).
aAII uncertainties
H - H (Eu - Es) P u - P s0.0592
are ::'::0.005pH except for solutions of KHC:!04' 2H2C'lO~, which have uncertainty
of ::!::0.01pH.
bThe buffer capacity is the number of moles of a monoprotic strong acid or base that causes 1.0 L to change pH by 1.0 "Change in pH that occurs when one volume of buffer is diluted with one volume of H20.
Equation 23-32 has been adopted throughout the world as the operational definition ofpH.37 Workers at NIST and elsewhere have used cells without liquid junctions to study primary-standard buffers extensively. Some of the properties of these buffers are presented in Table 23-7 and discussed in detail elsewhere.·18 For general use, the buffers can be prepared from relatively inexpensive laboratory
of pH
The utility of pH as a measure of the acidity or alkalinity of aqueous media, the wide availability of commercial glass electrodes, and the proliferatio'n of inexpensive solid-state pH meters have made the potentiometric measurement of pH one of the most common analytical techniques in all of science. It is thus extremely important that pH be defined in a manner that is easily duplicated at various times and vari-
TABLE
Pnlt'lltiollidric
pH, -
I f;~;- Es)F -- --~-1.9&l x lo-~
d38°C.
reagents. For careful work, certified buffers can be purchased from NlST.39
The potential of a suitable indicator electrode is convenient for determining the equivalence point for a titration (a potentiometric titration).'o A potentiometric titration provides different information than does a direct potentiometric measurement. For example, the T
whc~e Tis th.:: temperature 01 lhl.- sample and [he standard butler and pHs IS the pH of the standard at temperature T '~.R G. Bates, [)nermllwf/on of plr 2nd cd., Chap_ ~, N('w Yurk \\'llcy, !Y73
)~Sec hups:t;srmors.nisLgovldctaiLcfm. kevword pH wFor a monograph on this method. see E. P. Sergeant. Pmenriomccry and Potenti.ometric Titratlons, New York: Wiky. 198..1..reprint: Melbourne:, FL Krieger, 1991.
direct measurement of 0.100 M acetic and 0.100 M hydrochloric acid solutions with a pH-sensitive electrode yield widely different pH values because acetic acid is only partially dissociated. On the other hand, potentiometric tit rations of equal volumes of the two acids require the same amount of standard base for neutralization. The potentiometric end point is widely applicable and provides inherently more accurate data than the corresponding method with indicators. It is particularly useful for titration of colored or turbid solutions and for detecting the presence of unsuspected species in a solution. Unfortunately. it is more time-consuming than
r:::;l
b2J
~imu!atjon: Learn more about potentiometric fltrahons.
FIGURE 23-19 High-performance automated titrator. Accommodates up to six buret drives, has userprogrammable software, permits high sample throughput with an automatic sample turntable (not shown). The unit can be adapted for several different types of t;trations. (Copyright 2006 Mettler-Toledo,Inc.)
Simulation: Learn more about derivative titrations.
* Answers ~
an indicator titration unless an automatic titrator is used. We will not discuss details of the potentiometric titration techniques here because most elementarv analytical texts treat this subject thoroughly." . Automated titrators are available from a number of manufacturers. One such instrument appears in the photo of Figure 23-19. These devices are equipped with a titrant reservoir, a titrant delivery device such as a syringe pump, and an arrangement of tubes and valves to deliver measured volumes of titrant at an appropriate rate. The titrator acquires data from a pH probe or other sensor to monitor the progress of the titration. The end point of the titration is determined either by a built-in program based on first- and secondderivative techniques" or by another method specified or programmed by the user. Many of these devices are capable of calculating analyte concentrations from standard-concentration data entered by the user, and experimental results are printed, stored, or transmitted via a serial or other appropriate interface to a laboratory information management system,(see Section 4H-2). Automatic titrators are especially useful in industrial or clinical laboratories where large numbers of samples must be routinely analyzed. ~lForcx:aOlplc,sce D. A. Skoog. D. M. West, F 1. Holler, and S. R. Crouch, Fundamentals of Analytical Chemistry, 8th ed., Chap. 21, Belmont, CA: Brooks/Colc.2004. ~·'S. R. Crouch and F. J. Hotler, Applications of Microsoft@ Excel in Analytical Chemistry, Belmont, CA: Brooks/Cole, 2004, pp. 134-42.
are provided at the end of the book for problems marked with an asterisk.
Problems with this icon are best solved using spreadsheets.
23-7 What is the source of (a) the asymmetry potential in a membrane electrode? (b) the boundary potential in a membrane electrodeo (c) a junction potential in a glass-reference electrode systemO . (d) the potential of a crystalline memhrane electrode used to determllle the concentration of F-? 23-8 List several sources of uncertainty in pH measurements with a glass-reference electrode system. 23.9 What is an ionophore? What is the purpose of ionophores in membrane elcctrodeso 23-10 List the advantages and disadvantages of a potentiometric titration with visual indicators.
titration relative to a
23-11 What is the operational definition of pH and how is it usedo 23-U What are the advantages of microfabricated ion-selective electrodes? Describe typical applications of this type of sensor. *23-13 Calculate the theoretical potential of the following cells. ([n each case assume that activities are approximately equal to molar concentrations and that the tempcrature is 25"C.) (a) SCEllFe 3+(0.0250 M),Fc2+(0.0l50 M)lpt (b) SCEIIZn'+(0.00228 M)IZn (c) Saturated Ag-AgCI referenceIITi3+(0.0250 M),Ti'+(0.0450 M)!Pt (d) Saturated Ag-AgCl referencell13- (0.00667 M)T(O.00433 M)lpt *23-14 (a) Calculate the standard potential for the reaction CuBr(s) + e-;=='
Cu(s) + Br,
For CuBr, K,p = 5.2 X 10-9 . . . Give a schematic representation of a cell With a copper IIldlcator electrode and a reference SCE that could he used for the determination of Br,. Derive an equation that relates the measured potential of the cell in (b) to pBr (assume that the junction potential is zero):. . Calculate the pBr of a bromide-containing solution that IS saturated WIth CuBr and contained in the cell described in (b) if the resulting potential IS -0.095 V *23-15 (a) Calculate the standard potential for the reaction
23-1 What is meant by nernstian behavior of an indicator electrode? 23-2 What is the source of the alkaline error in pH measurement with a glass electrode'> 23-3 Compare the average temperature coefficients in the range of 15"C to 35'C for the five reference electrodes listed in Table 23-1. 23·4 What occurs when the pH-sensiti\'e tip of a newly manufactured glass electrode is immersed in water? 23-5 Differentiate between an electrode of the first kind and an electrode of the second kind.
Ag,AsO,(s)
+ 3e;=='
3Ag(s)
+ AsO,J-
For Ag,AsO" K,p = 1.2 X \0-22 . .. (b) Give a schematic representation of a cell with a Silver mdlcator electrode and an SCE as reference that could be used for determining AsO,J(c) Derive an equation that relates the measured potential of the cell in (b) to pAsO, (assume that the junction potential is zero). (d) Calculate the pAsO, of a solution that is saturated with AgJAsO, and contained in the cell described in (b) if the resulting potential is 0.247 V *23-16 The following cell was used for the determination
of pCrO,:
SCE!!CrO,'- (xM ),Ag,CrO ,(sat' d) I Ag Calculate pCrO, if the cell potential is -(U86 V.
*23-17 The following cell was used to determine the pSO, of a solution: SCEII SO 4 2 - (x M),Hg,SO.( sat' d) IHg Calculate the pSO, if the potential was -0.537 V. *23-18 The formation constant for the mercury(lI)
+ 2e- ~
Hg(OAch(aq)
*23-25 The following cell was found to have a potential of 0.2897 V:
acetate complex is
Hg(l) + 20Ac
*23-19 The standard electrode potential for the reduction of the Cu(lI) complex of EDTA is given by CuY'-
+ 2e- ~
Cu(s) + y4-
EO
=
0.13 V
Calculate the formation constant for the reaction Cu"
+ y'- ~
AgIAgCl(sat'd)IIH+(a
=
CuY'-
x)lglass electrode
has a potential of -0.2094 V when the solution in the right-hand cOqlpartme!1t is a buffer of pH 4.006. The following potentials are obtained when the buffer is replaced with unknowns: (a) -0.2806 V and (b) -0.2132 V. Calculate the pH and the hydrogen ion activity of each unknown. (c) Assuming an uncertainty of 0.001 V in the junction potential, what is the range of hydrogen ion activities within which the true value might be expected to lie? *23-21 The following cell was found to have a potential of 0.124 V: AgIAgCI(sat'd)IICu'+(3.25
X
(c) Generate a first- and second-derivative curve for these data." Does the volume at which the second-derivative curve crosses zero correspond to thc theoretical equivalence point" Why or why not"
103 M)lmembrane
electrode for Cu"
When the solution of known copper activity was replaced with an unknown solution, the potential was found to be 0.086 V. What was the pCu of this unknown solution? Neglect the junction potential. *23-22 The following cell was found to have a potential of -1.007 V: SCEIIX-(0.0200 M),CdX,(sat'd)ICd Calculate the solubility product of CdX" neglecting the junction potential.
SCEIIMg"(a
= 3.32 X 10'
M)lmembrane
electrode for Mg"
(a) When the solution of known magnesium activity was replaced with an unknown solution, the potential was found to be 0.2041 V What was the pMg of this unknown solution? (b) Assuming an uncertainty of :!:0.002 V in the junction potential, what is the range of Mg'+ activities within which the true value might be expected'? (c) What is the relative error in [Mg"l associated with the uncertainty in E," *23-26 A 0.400-g sample of toothpaste was boiled with a 50-mL solution containing a citrate buffer and NaCI to extract the fluoride ion. After cooling. the solution was diluted to exactly 100 mL. The potential of an ion-selective electrode with a Ag-AgCI(sat'd) reference electrode in a 25.0-mL aliquot of the sample was found to be -0.1823 V. Addition of 5.0mL of a solution containing 0.00107 mg F-/mL caused the potential to change to -0.2446 V. Calculate the mass percentage of F- in the sample.
IiJ Challenge
Problem
23-27 Ceresa, Pretsch, and Bakker44 investigated three ion-selective electrodes for determining calcium concentrations. All three electrodes used the same membrane. but differed in the composition of the inner solution. Electrode 1 was a conventional ion-selective electrode with an inner solution of 1.00 X 10-3 M CaCl, and 0.10 M NaCl. Electrode 2 (low activity of Ca '+) had an inner solution containing the same analytical concentration of CaCI" but with 5.0 X 10-' M EDTA adjusted to a pH of 9.0 with 6.0 X 10-2 M NaOH. Electrode 3 (high Ca2+ activity) had an inner solution of 1.00 M Ca(N03),. (a) Determine the Ca'+ concentration in the inner solution of Electrode 2. (b) Determine the ionic strength of the solution in Electrode 2. (c) Use the Debye-HOekel equation and determine the activity of Ca ,+ in Electrode 2. Use 0.6 nm for the ax value for Ca (see Appendix 2). (d) Electrode 1 was used in a cell with a calomel reference electrode to measure standard calcium solutions with activities ranging from 0.001 M to 1.00 X 10-9 M. The following data were obtained.
,+
*23-23 The following cell was found to have a potential of -0.492 V: AgIAgCI(sat'd)IIHA(0.200
M),NaA(0.300 M)IH,(l.CXl atm),Pt
Calculate the dissociation constant of HA, neglecting the junction potential. 23-24 A 40.00-mL aliquot of 0.0500 M HNO, is diluted to 75.0 mL and titrated with 0.0800 M Ce'+. Assume the hydrogen ion concentration is at 1.00 M throughout the titration. (Use 1.44 V for the formal potential of the cerium system.) (a) Calculate thc potential of the indicator electrode with respect to a AgAgCl(sat'd) reference electrode after the addition of 5.00, 10.00. 1500. 20.00,25.00,40.00,45.00,49.00,49.50,49.60.49.70. 49.80. 49.90. 49.95, 49.99. 50.00.5001. 50.05. 50.10, 50.20. 50.30, 50.40. 50.50, 51.00, 55.00, 60.00, 75.00, and 90.00 mL of cerium(IV). (b) Construct a titration curve for these data.
1.0 x 10
3
1.0 x 10-' 1.0 X 10.5 1.0 x 10-' 1.0 x 10-1.0
X
10-5
10 x 10-'
'is R. Crnuch and F 1. Holler. Applications of .Hicrosoft~ Excel in Analvlical Chemisln Broub :C 20H-
+ H,(g)
In these experiments, the cathode must be isolated from the solution, or the reagent must be generated externally to prevent interference from the hydroxide ions produced at that electrode. Precipitation
For a summary of applications, see 1. A. Dean. Analytical C!!emistry Handbook, Section 14, pp. 14.127-14.133, New York: McGraw*HiII,1995. lJ
Electrolyte solution from reservoir I Anode reaction H20 _ tOz
t
+ 2H+ + 2e-
I
and Complex-Formation
HgNH]y2- + NH," + 2e ~
FIGURE 24-10 A cell for external generation of acid
and base.
Titrations
A variety of coulometric tit rations involving anodically generated silver ions have been developed (see Table 24-1). A cell, such as that shown in Figure 24-9, can be used with a generator elcetrode constructed from a length of heavy silver wire. End points are detected potentiometrically or with chemical indicators. Similar analyses, based on the generation of mercury(I) ion at a mercury anode, have been described. An interesting coulometric titration makes use of a solution of the amine mercury(lI) complex of ethylenediaminetetraacetic acid (H4 Y)14 The camp Iexing agent is released to the solution as a result of the following reaction at a mercury cathode: Hg(l) + 2NH] + HyJ(24-6)
Summary of Coulometric Titrations InvolvingOxidation-Reduction Reactions
TABLE 24-1 Summary of Coulometric Titrations Involving Neutralization, Precipitation, and Complex-Formation Reactions
TABLE 24-2
Substance Determined
Species Determined
Acids Bases Cl-, Br-, 1-
Mercaptans (RSH) Cl-, Br-, 1Zn2+
Ca2+, Cu2+, Zn2+, Pb2+
2H,O + 2e- ~20H+ H, H,o ~ 2H+ + ~O, + 2eAg~Ag++eAg~Ag+ +e2 Hg~Hg," + 2eFe(CN),'- + e- ~ Fe(CN):See Equation 24-6
OH-+H+~H,O H+ +OH-~H,O Ag+ + X- ~ AgX(s) Ag' + RSH ~ AgSR(s) + H' Hg,'+ + 2X- ~ Hg,X,(s) 3Zn2+ + 2K+ + 2Fe(CN),'- ~ K,Zn,[Fe(CN)61,(S) Hy3- + Ca" ~ CaY'- + H+, etc.
2Cl-~Cl,+2e2r ~I, + 2eCe3+ ~ Ce4+ + e-
Cl, I,
Ce" Mn3+
Mnh~Mn3+
Ti3+
Because the mercury chelate is more stable than the corresponding complexes with caleium, zinc, lead, or copper, complexation of these ions will not occur until the electrode process frees the ligand. Coulometric
Titration of Chloride
commercial coulometric titrator called a chloridometer is shown in Figure 24-11. Other popular methods to determine chloride are ion-selective electrodes (see Section 230), photometric titrations (see Section 14E), and isotope dilution mass spectrometry.
in Biological Fluids
The accepted reference method for determining chloride in blood serum, plasma, urine, sweat, and other body fluids is the coulometric titration procedure." In this technique, silver ions are generated coulometrically. The silver ions then react with chloride ions to form insoluble silver chloride. The end point is usually detected by amperometry (see Section 25C-4) when a sudden increase in current occurs on the generation of a slight excess of Ag+. In principle, the absolute amount of Ag + needed to react quantitatively with Clean be obtained from application of Faraday's law. In practice, calibration is used. First, the time I, required to titrate a chloride standard solution with a known number of moles of chloride using a constant current I is measured. The same constant current is next used in the titration of the unknown solution, and the time III is measured. The number of moles of chloride in the unknown is then obtained as follows:
Oxidation-Reduction
Titrations
Table 24-2 indicates the variety of reagents that can be generated coulometrically and the analyses to which they have been applied. Electrogenerated bromine is
+e"
Ag'~Ag'++eFe3+ + e- ~ Fe2+ Ti02+ + 2H+ + e- ~Ti3+ + H20 Cu2' + 3CI- + e - ~ CuCI,'UO,'+ + 4H' + 2e- ~ U'+ + 2H,O
Ag'+ Fe2+
CuCI,'V'+
particularly useful among the oxidizing agents and forms the basis for a host of methods. Of interest also are some ofthc unusual reagents not ordinarily used in volumetric analysis because of the instability of their solutions. These reagents include dipositive silver ion, tripositive manganese, and the chloride complex of unipositive copper. An interesting recent application of coulometric titrations is the determination of total antioxidant capacity in human serum'" Many antioxidants appear in serum: low-molecular-mass compounds such as tocopherols, ascorbate, {:l-carotene, glutathione, uric acid, and bilirubin and proteins such as albumin, transferrin, caeruloplasmin, ferritin, superoxide dismutase, catalase, and glutathione peroxidase. By far the greatest contributor to total antioxidant capacity is serum albumin. Coulometric titration of serum samples with electrogenerated bromine gives a value of antioxidant capacity, which may be an important clinical variable in assessing the status of patients undergoing hemodialysis. This method for determining antioxidant capacity is straightforward and quite precise (2:0.04% RSO).
Comparison of Coufometric
If the volumes of the standard solution and the unknown solution are the same, concentrations can be substituted for number of moles in this equation. A
'sc. A. Burtis and E. R. Ashwood, Tier:. FundamemaL5 of Clinical Chemistry, 5th ed., p. 500, Philadelphia: Saunders. 2001; L. A. Kaplan and A. J. Pesce. Clinical Chemistry: Theory, AnalysL5, iJnd Correlation. p 1060, St. Louis, .\10: C. V. Mosby, 1984
and Volumetric Titrations
commercial digital chloridometer. This coulometric titrator is designed to determine chloride ion in such clinical samples as serum, urine, and sweat. It is used in the diagnosis of cystic fibrosis. The chloridometer is also used in food and environmental laboratories. (Courtesy of Labconco Corp., Kansas City,MO.) FIGURE 24-11
A
There are several interesting analogies between coulometric and volumetric titration methods. Both require a detectable end point and are subject to a titration
I~G. K. Ziya{dinova, If. C Budnikov, \'. I. Pogorel'tzev, and T S. Ganee\" Tu/unra,
2006.
68, SOO
As(IIl), Sb(Ill), U(IV), Ti(I), 1-, SCW, NH" N,H" NH,OH, phenol, aniline, mustard gas, mercaptans, 8-hydroxyquinoline,oleins As(IIl), 1-, styrene, fatty acids As(IIl), Sb(IIl), S,O,'-, H,S, ascorbic acid Fe(lI), Ti(IIl), V(IV), As(IIl), r, Fe(CN)6'H,~O" Fe(lI), As(IIl) Ce(IIl), V(IV), H,~O" As(lll) Cr(VI), Mn(VlI), V(V), Ce(IV) Fe(IIl), V(V), Ce(IV), U(VI) V(V), Cr(VI), 10,Cr(VI), Ce(IV)
error as a consequence. Furthermore, in both techniques, the amount of analyte is determined through evaluation of its combining capacity - in the one case, for a standard solution and, in the other, for electrons. Also, similar demands are made of the reactions; that is, they must be rapid, essentially complete, and free of side reactions. Finally, there is a close analogy between the various components of the apparatus shown in Figure 24-7 and the apparatus and solutions employed in a conventional volumetric analysis. The constantcurrent source of known magnitude has the same function as the standard solution in a volumetric method. The timer and switch correspond closely to the buret, the switch performing the same function as a stopcock. During the early phases of a coulometric titration, the switch is kept closed for extended periods. As the end point is approached, however, small additions of "reagent" are achieved by closing the switch for shorter and shorter intervals. This process is analogous to the operation of a buret. Coulometric tit rations have some important advantages in comparison with the classical volumetric process. The most important of these advantages is the elimination of problems associated with the preparation, standardization, and storage of standard solutions. This advantage is particularly important with labile reagents such as chlorine, bromine, or titanium(lII) ion. Because of their instability, these species are inconvenient as volumetric reagents. Their use in coulometric analysis is straightforward, however, because they undergo reaction with the analyte immediately after being generated.
Where small quantities of reagent are required, a coulometric titration offers a considerable advantage. By proper choice of current, microquantities of a substance can be introduced with ease and accuracy. The equivalent volumetric process requircs dispensing small volumes of very dilute solutions, which is always difficult. A single constant current source can be used to generate precipitation, complex formation, oxidationreduction, or neutralization reagents. Furthermore, the coulometric method adapts easily to automatic titrations, because current can be controlled quite easily. Coulometric titrations are subject to five potential sources of error: (1) variation in the current during electrolysis, (2) departure of the process from 100% current efficiency, (3) error in the current measurement, (4) error in the measurement of time, and (5) titration error due to the difference between the equivalence point and the end point. The last of these difficulties is common to volumetric methods as well. For situations in which the indicator error is the limiting factor, the' two methods are likely to have comparable reliability.
With simple instrumentation, currents constant to 0.2% relative are easily achieved, and with somewhat more sophisticated apparatus, current may be controlled to 0.01 %. In general, then, errors due to current fluctuations are seldom significant. Although it is difficult to generalize when discussing the magnitude of uncertainty associated with the electrode process, current efficiencies of 99.5% to better than 99.9% are often reported in the literature. Currents can be measured to :to. 1% relative quite easily. To summarize, then, the current-time measurements required for a coulometric titration are inherently as accurate as or more accurate than the comparable volume-molarity measurements of a classical volumetric analysis, particularly where small quantities of reagent are involved. Often, however, the accuracy of a titration is not limited by these measurements but by the sensitivity of the end point; in this respect, the two procedures are equivalent.
Suppose that a cell was formed by immersing a silver anode in an analyte solution that was 0.0250 M Cl-, Br-, and 1- ions and connectmg the halt-cell to a saturated calomel cathode via a salt hridge. . (a) Which halide would form first and at what potential? Is the cell galvamc or electrolytic" --5 (b) Could I and Br be separated quantitatively') (Take 1.00 x IO M as the criterion for quantitative removal of an ion.) If a separation IS feaSIble, what range of cell potential could be used" (c) Repeat part (h) for 1- and Cl-. (d) Repeat part (b) for Br' and Cl -. What cathode potential (versus SCE) would he required to lower the total Hg(II) concentration of the following solutions to 1.00 X 10 6 M (assume reaction product in each case is elemental Hg): (a) an aqueous ~olution of Hg2+? _ . (b) a solution with an eqUlhbnum SCN concentration Hg2+ + 2SCN- ~
Kf
Hg(SCNh(aq)
(c) a solution with an equilihrium Br- concentration HgBrl
+ 2e- ~
Hg(l) + 4Br-
_ ') of 0.1)0 M. =
1.8
X
10'
of 0.150 M') E"
=
0.223 V
Calculate the time required for a constant currcnt of 0.750 A to deposit 0.270 g of (a) Co(ll) as the element on a cathode and (h) as ColO, on an anode. Assume 100% current efficiency for both cases. Calculate the time required for a constant current of 0.905 A to deposit 0.300 g of (a) TI(IIl) as the element on a cathode, (b) TI(I) as the TI,OJ on an anode, and (c) TI(I) as the element on a cathodc.
* Answers ~ *24-1
are provided at the end of the book for problems marked with an asterisk.
Prohlems with this icon are best solved using spreadsheets. Lead is to be deposited at a cathode from a solution that is 0.100 M in Pb + and 0.200 M in HClO •. Oxygen is evolved ata pressure of 0.800 atm at a 30-cm' platinum anode. The cell has a resistance of 0.950 n. (a) Calculate the thermodynamic potential of the cell. (b) Calculate the IR drop if a current of 0.250 A is to be used. lower the concentration of the metal M, to 2.00 X 10" M in a solution that is l.00 x 10-1 M in the less-reducible metal M2 where (a) M, is univalent and M, is divalent, (b) M, and M1 are both divalent, (c) M, is trivalent and MI is univalent, (d) M2 is divalent and M, is univalent, (e) M, is divalent and MI is trivalent.
24-3 It is desired to separate and determine hismuth, copper, and silver in a solution that is 0.0550 M in BiO+, 0.125 M in Cu2+, 0.0962 M in Ag', and 0.500 M in HCIO~. (a) Using 1.00 x 10-6 M as the criterion for quantitative removal, determine whether separation of the three species is feasible by controlled-potential electrolysis. (b) If any separations are feasible, evaluate the range (versus Ag-AgCI) within which the cathode potential should be controlled for the deposition of each. Halide ions can be deposited at a silver anode, the reaction being
in methanol is
2CCI, + 2H+ + 2e- + 2Hg(l) ----> 2CHCIJ + Hg,Cl,(s) 2
*24-2 Calculate the minimum difference in standard electrode potentials needed to
24-4
At a potential of --1.0 V (versus SCE), carhon tetrachloride rcduced to chloroform at a Hg cathode:
At -1.80 V, the chloroform further reacts to givc methanc: 2CHCl3 + 6H+ + 6e- + 6Hg(l)
---->
2CH~ + 3Hg,Cl,(s)
Several 0.750-g sampies containing CCl" CHCI" and inert organic species were dissolved in methanol and electrolyzed at -1.0 V until the current approached zero. A coulometer indicated the charge required to complete the reaction, as given in the second column of the following tahle. The potential of the cathode was then adjusted to -1.80 V. The additional charge reqUired to complete the reaction at this potential is given in the third column of the table. Calculate the percent CCl~ and CHClJ in each mixture. Sample No.
Charge Required at-1.DV.C
Charge Required at-1.8V,C
11.63
68.60
21.52
~5.33
.1
6.22
4
12.92
4598 55.31
A 6.39-g sample of an ant-control preparation was decomposed by wet ashing with H2S04 and HNOJ. The arsenic in the reSidue was reduced to the trIvalent
state with hydrazine. After the excess reducing agent had been removed, the arsenic(III) was oxidized with electrolytically generated I, in a faintly alkaline medium: HAsO/-
+ I, + 2HCO) -
--> HAsO,z-
+ 21- + 2CO + H20
The titration was complete after a constant current of 127.6 mA had been passed for II min and 54 s. Express the results of this analysis in terms of the percentage As,O) in the original sample. A O.0809-g sample of a purified organic acid was dissolved in an alcohol-water mixture and titrated with coulometrically generated hydroxide ions. With a current of 0.0441 A, 266 s was required to reach a phenolphthalein end point. Calculate the equivalent mass of the acid.
A digital chloridometer was used to determine the mass of sulfide in a wastewater sample. The chloridometer reads out directly III ng Cl . In chlonde de: terminations, the same generator reaction is used, but the tltratton reach~n IS Cl- + Ag' -> AgCl(s). Derive an equation that relates ~he deSired quantity, mass 52- (ng), to the chloridometer readout m mass CI (ng). _ A particular wastewater standard gave a readmg of 1689.6 ng CI . What ,total charge in coulombs was required to generate the Ag' needed to preCIpitate the sulfide in this standard? . . The following results were obtained on 20.00-mL samples contammg known amounts of sulfide.17 Eaeh standard was analyzed in triplicate and t~= mass of chloride recorded. Convert each of the chloride results to mass S (ng). Known Mass 52-, ng
*24-11 Traces of aniline can be determined by reaction with an excess of electrolytically generated Br,: c"HsNH, + 3Br, --> c"H,Br)NH,
+ 3H' + 3Br-
6365
10918.1
4773
8416.9
3580
8366.0 6320.4
10654.9 8416.9
The polarity of the working electrode is then reversed, and the excess bromine is determined by a coulometric titration involving the generation of CU(I):
1989
6528.3 3779.4
796
1682.9
1713.9
Br2 + 2Cu' --> 2Br- + 2Cu2+
699
1127.9
466 373
705.5 506.4
1180.9 736.4
233
278.6
278,6
247.7
-22.1
-19.9
-17.7
Suitable quantities of KBr and copper(II) sulfate were added to a '25.0-mL sample containing aniline. Calculate the mass in micrograms of C6HsNH2 in the sample from the accompanying data: Working Electrode Functioning As
Generation Time (min) with a Constant Current of 1.00 mA
Anode
3.76
Cathode
0.270
Construct a eoulometric titration curve of 100.0 mL of a I M H,S04 solution containing Fe(lI) titrated with Ce(IV) generated from 0.075 M Ce(III). The titration is monitored by potentiometry. The initial amount of Fe(lI) present is 0.05182 mmol. A constant current of 20.0 mA is used. Find the time corresponding to the equivalence point. Then, for about ten values of time before the equivalence point, use the stoichiometry of the reaction to calculate the amount of Fe" produced and the amount of Fe'+ remaining. Use the Nemst equation to find the system potential. Find the equivalence point potential in the usual manner for a redox titration. For about ten times after the equivalence point, calculate the amount of Ce 4+produced from the electrolysis and the amount of Ce 3+ remaining. Plot the curve of system potential versus electrolysis time. ~
Mass CI- Determined, ng 10447.0
Challenge Problem
24-13 Sulfide ion (S'· ) is formed in wastewater by the action of anaerobic bacteria on organic matter. Sulfide can be readily protonated to form volatile, toxic H,S. In addition to the toxicity and noxious odor, sulfide and H,S cause corrosion problems because they can be easily converted to sulfuric acid when conditions change to aerobic. One common method to determine sulfide is by coulometric titration with generated silver ion. At the generator electrode, the reaction is Ag -> Ag' + eO. The titration reaction is S'- + 2Ag' -> Ag,5(s).
0
3763.9
521.9
6638.9 3936.4 1669.7 1174.3 707.7 508.6
Determine the average mass of 5'- (ng), the standard deviation, and the % RSD of each standard. Prepare a plot of the average mass of 5'- determined (ng) versus the actual, mass (ng). Determine the slope, the intercept, the standard error, and the R value. Comment on the fit of the data to a linear modeL . (f) Determine the detection limit (ng) and in parts per mllhon usmg a k factor of2 (see Equation 1-12). _ An unknown wastewater sample gave an average reading of 893.2 ng Cl . What is the mass of sulfide (ng)? If 20.00 mL of the wastewater sample was introduced into the titration vessel, what is the concentration of 5' m parts per million?
Voltammetry
.. \I
oltammetry
comprises a group of electro-
·analytical.methods
in which information
about the a.na(rte is obtained by measur-
ing current as ajunction
of ap~lied potential
conditions that prodlOte polarization
under
of an indica-
tor, or [corking, electrode. When currentproportional to analyte coijcentration potentia~
is monitored at fl:I:ed
the technique is called amperometry.
Generally, to enhance polarization, trodes in voltammetryand
working elec-
arnperometryhave
sur-
face areas of a few square millimeters at the most and, in SOme applications,
a few square micrometers
or less.
01 I2J
Throughout this chapter, this logo indicates an opportunity for online self-study at www .thomsouedu.com/chemistry/skoog, linking you to interactive tutorials, simulations, and exercises. 716
Let us begin by pointing out the basic differences between voltammetry and the two types of electro_ chemical methods that we discussed in earlier chapters. Voltammetry is based on the measurement of the current that develops in an electrochemical cell under conditions where concentration polarization exists. Recall from Section 22E-2 that a polarized electrode is one to which we have applied a voltage in excess of that predicted by the Nernst equation to cause oxidation or reduction to occur. In contrast, potentiometric measurements are made at currents that approach zero and where polarization is absent. Voltammetry differs from coulometry in that, with coulometry, measures are taken to minimize or compensate for the effects of concentration polarization. Furthermore, in voltammetry there is minimal consumption of analyte, whereas in coulometry essentially all of the analyte is converted to another state. Voltammetry is widely used by inorganic, physical, and biological chemists for nonanalytic:il purposes, including fundamental studies of oxidation and reduction processes in various media, adsorption processes on surfaces, and electron-transfer mechanisms at chemically modified electrode surfaces. Historically, the field of voltammetry developed from polarography, which is a particular type of voltammetry that was invented by the Czechoslovakian chemist Jaroslav Heyrovsky in the early 1920s1 Polarography differs from other types of voltammetry in that the working electrode is the unique dropping mercury electrode. At one time, polarography was an important tool used by chemists for the determination of inorganic ions and certain organic species in aqueous solutions. In the late 1950s and the early 19605,however, many of these analytical applications were replaced by various spectroscopic methods, and polarography became a less important method of analysis except for certain special applications, such as the determination of molecular oxygen in solutions. In the mid-1960s, several major modifications of classical voltammetric techniques were developed that enhanced significantly the sensitivity and selectivity of the method. At about this same time, the advent of low-cost operational amplifiers made possible the commercial development of relatively inexpensive instruments that incorporated many of these modifications and made them available to all chemists. The result was a resurgence of interest in
11. Hevrovsh Chern. Ust}', 1922.16.256. Ht:\Tovsh 'A'asawarded the 1959 Nobel Priz~ in Chc~jstry for his discO\"ery a~d development of polarograph~
Type of voltammetry
{2J
Differcntialpulse vo!tammetry
r~\ I
EI.!
I
/
\
\
\
Time-----.FIGURE
25-1
Voltage versus time excitation signals used in voltammetry.
applying polarographic methods to the determination of a host of species, particularly those of pharmaceutical, environmental, and biological interest.' Since the invention of polarography, at least 60,000 research papers have appeared in the literature on the subject. Research activity in this field, which dominated electroanalytical chemistry for more than five decades, peaked with nearly 2,000 published journal articles In 1973. Since that time, interest in polarographIc methods has steadily declined, at a rate nearly twice the rate of growth of the general chemical literature, until In 2005 only about 300 papers on these methods appeared. This decline has been largely a result of concerns about the use oflarge amounts of mercury in the laboratory as well as in the environment, the somewhat cumbersome nature of the apparatus, and the broad availability of faster and more convenient (mainly spectroscopIc) methods. For these reasons, we will discuss polarographv only briefly and, instead, refer you to the many so~rces that are available on the subject.' Although polarography declined in importance, voltammetry and amperometry at working electrodes Broadening Eleecrochemical Horizons: Principles and illustration of \/oltammetric and Related Techniques. New York: Oxford, 2003; (:. M. A. Brett and A. M. Oliveira Brett. In Encyclopedw of Electrochemi~-trv A. J. Bard and M. Stratmann, eds .. Vol. 3. InsrrnmentatlOfI and £It:c~roanalvtical Chemistry, P. Unwin, ed., New York: WIley. 2002, pp. 105 -24> A. 1. Bard and L R. Faulkner, Elecrrochemu:.al ~elhods: 2nd ed. New York: Wile .•..2001. Chap. 7. pp. 261-30-4; Laborator.\ .Technl~Ue5 in t:leclroanalvrical Chemistry, 2nd ed., P. T Kissinger and \\'. R. Hememan. -:ds.. Ne~- York: Dekker. 1996, pp. 4-W -61. ~A. Bond.
other than the dropping mercury electrode have grown at an astonishing pace' Furthermore, voltammetry and amperometry coupled with liquid chromatography have become powerful tools for the analysis of complex mixtures. Modern voltammetry also continues to be an excellent tool in diverse areas of chemistry, biochemistry, materials science and engineering, and the environmental sciences for studYing oXIdatIon, reduction, and adsorption processes.'
25A
EXCITATION SIGNALS IN VOLTAMMETRY
In voltammetry, a variable potential excitation signal is impressed on a working electrode in an electrochemIcal cell. This excitation signal produces a charactenstlc current response, which is the measurable quantity III this method. The waveforms of four of the most common excitation signals used in voltammetry are shown in Figure 25-1. The classical voltammetric excitation JFrom 1973 to 2005. the annual numbc:r of journal articles on \'o~tammetrv and amperometry grew at three times and two and on:-half tlmes, res~ectivelY, the rate of production of articles ~n all of chemistry. 'Some general references on voltammetry IOclu~e ~-\.,1. ~a~'i:;\~ ~~~: faulkner Elecrrochomcal Merhods, 2nd ed., Ne\\ .lork. .' - _ ' S. p, Ko~naves, in Handbook of Instrumental Te~hntq~es for Analyt!cal Chemistry, Frank A. Settle. ed., Upper Saddle RIVC:r.1\1: Pren~lCe-Hal~, 1997 . 711-28' Laboratory Techmques In ElectfOu.nalj tical ChemlSrr}. , pp K.' . d W R Heineman. eds .. "ew York: Dekker. 2nd ed .. P. T. Issmger an . " _ 'Jew York: 1996; Analytual Foltammerry. \-1. R. Smyth and F G. \ o~. eds.,. Elsener, 1992
signal is the linear scan shown in Figure 25-1a, in which the voltage applied to the cell increases linearly (usually over a 2- to 3-V range) as a function of time. The current in the cell is then recorded as a function of time, and thus as a function of the applied voltage. In amperometry, current is recorded at fixed applied voltage. Two pulse excitation signals are shown in Figure 25-1 band c. Currents are measured at various times during the lifetime of these pulses. With the triangular waveform shown in Figure 25-1d, the potential is cycled between two values, first increasing linearly to a maximum and then decreasing linearly with the same slope to its original value. This process may be repeated numerous times as the current is recorded as a function of time. A complete cycle may take 100 or more seconds or be completed in less than 1 second. To the right of each of the waveforms of Figure 25-1 is listed the types of voltammetry that use the various excitation signals. We discuss these techniques in the sections that follow.
Figure 25-2 is a schematic showing the components of a modern operational amplifier potentiostat (see Section 24C-1) for carrying out linear-scan voltammetric measurements. The cell is made up of three electrodes immersed in a solution containing the analyte and also an excess of a nonreactive electrolyte called a supporting electrolyte. One of the three electrodes is the work-
ing electrode, whose potential is varied linearly with time. Its dimensions are kept small to enhance its tendency to become polarized (see Section 22E-2). The second electrode is a reference electrode (commonly a saturated calomel or a silver-silver chloride electrode) whose potential remains constant throughout the experiment. The third electrode is a counter electrode, which is often a coil of platinum wire that simply conducts electricity from the signal source through the solution to the working electrode. The signal source is a linear-scan voltage generator similar to the integration circuit shown in Figure 3-16c. The output from this type of source is described by Equation 3-22. Thus, for a constant dc input potential of Ei, the output potential E" is given by Ei
Eo = ~ RiCe
i' 0
E,t
dt = - RiCe
The output signal from the source is fed into a potentiostatic circuit similar to that shown in Figure 25-2 (see also Figure 24-6c). The electrical resistante.ofthe control circuit containing the reference electrode is so large (> 10" 0) that it draws essentially no current. Thus, the entire current from the source is carried from the counter electrode to the working electrode. Furthermore, the control circuit adjusts this current so that the potential difference between the working electrode and the reference electrode is identical to the output voltage from the linear voltage generator. The resulting current, which is directly proportional to the potential difference between the working electrode-reference
r:::il l.Q.J
Tutorial: Learn more about voltammetric instrumentation
and waveforms.
Linear sweep generator
Dal3 acquisition sysh::m
FIGURE 25-2 An operational amplifier potentiostat. The three-electrode cell has a working electrode (WE).reference electrode (RE),and a counter electrode (CE).
electrode pair, is then converted to a voltage and recorded as a function of time by the data-acquisition system.' It is important to emphasize that the independent variable in this experiment is the potenllal of the working electrode versus the reference electrode and not the potential between the working electrode and the counter electrode. The working electrode is at virtual common potential throughout the course of the experiment (see Section 38-3).
~ 0.75 em
I I j
I I
I
7.5 em
Hg
I I
258-1 Working Electrodes The working electrodes used in voltammetry take a variety of shapes and forms.' Often, they are small flat disks of a conductor that are press filled into a rod of an inert material, such as Teflon or Kel-F, that has embedded in it a wire contact (see Figure 25-3a). The conductor may be a noble metal, such as platinum or gold; a carbon material, such as carbon paste, carbon fiber, pyrolytic graphite, glassy carbon, dia~ond,. or carbon nanotubes; a semiconductor, such as tm or mdlUm oxide; or a metal coated with a film of mercury. As shown in Figure 25-4, the range of potentials that can be used with these electrodes in aqueous solutions varies and depends not only on electrode material but also on thc composition of the solution in which it is immersed. Generally, the positive potential limitations arc caused by the large currents that develop because of oxidation of the water to give molecular oxygen. The negative limits arise from the reduction of water to produce hydrogen. Note that relatively large negative potentials can be tolerated with mercury electrodes because of the high overvoltage of hydrogen on this metal.
6Earty vohammetry was performed with a two-electrode system rather than the three-electrode system shown in Figure 25-2. With a t •••. 'oelectrode syskm, the second electrode is either a large metal. electr~de or a reference electrode large enough to prevent its polarization dunng an experiment. This second electrode combines the functiom of the rcference electrode and the counter electrode in Figure 25-2. 1n the twoelectrode system, we assume that the potential of this second electrode is constant th'rouohout a scan so that the working ekctrode potential is simply the differe~ce be~ween the applied.potentialand the potential of the second electrode. With solutions of high electncal resistance, ho .••.e\cr, this assumption is not valid because the IR drop is significant and increases as the current increases. Distorted voltammograms are the result. ..••• Im{)st aU .•.. oltammetry is now performed with three-electrode systems )Manv of the ~'orking electrodes that we dt:scribe in this chapter have -di· mensi'ons in the millimeter range. There is nnw intense interest in studies ""ith electrodes having dinwnsions in the mi...:romet~r range and smaller We will term ~uch electrodes microelectrodes. Such electrodes have seVeral ad\'antages ewer classical working e1ectrodes_ Vie descrihe some of the uni4ue characteristics ,)f microelectfl)des in Section 25[
I .I
-I ~ 6mm
\ (bl
(a)
(e)
FIGURE 25-3 Some common types of commercial
voltammetric electrodes: (a)a disk electrode; (b) a hanging mercury drop electrode (HMOE);(c) a microelectrode; (d) a sandwich-type flow electrode. (Electrodes (a], [c], and [d]courtesy of Bioanalytical Systems, Inc., West ~afayetle, IN. with permission.)
Mercury working electrodes havc been widely used in voltammetrv for several reasons. One IS the relatively largc n;gative potential range just described.
I M H,SO, ------~I
tochemical, or electrochemical polymerization methods. Immobilized enzyme biosensors, such as the amperometric sensors described in Section 25('-4. are a type of modified electrode. These can be prepared by covalent attachment, adsorption, or gel entrapment. Another mode of attachment for electrode modification is by self-assembled m",wlayers, or SAMs.' In the most common procedure, a long-ehain hydrocarbon with a thiol group at one end and an amine or carboxyl group at the other is applied to a pristine gold or mercury film electrode. The hydrocarbon molecules assemble themselves into a highly ordered array with the thiol group attached to the metal surface and the chosen functional group exposed. The arrays may then be further functionalized by covalent attachment or adsorption of the desired molecular species. Modified electrodes have many applications. A primary interest has been in the area of electrocatalysis. In this application, electrodes capable of reducing oxygen to water have been sought for use in fuel cells and batteries. Another application is in the production of e1ectrochromic devices that change color on oxidation and reduction. Such devices are used in displays or smart windows and mirrors. Electrochemical devices that could serve as molecular electronic devices, such as diodes and transistors, are also under intense study. Finally, the most important analytical use for such electrodes is as analytical sensors selective for a particular species or functional group (see Figure 1-7).
I Pt)
pH 7buffer iPtI 1M NaOH (Ptl 1MH,SO,iHgl --------
FIGURE25-4 Potential ranges for three types of electrodes in various supporting electrolytes. (Adapted from A. J. Bard and L R. Faulkner, Electrochemical Methods, 2nd ed., back cover, New York:Wiley, 2001. Reprinted by permission of John Wiley& Sons, Inc.)
O,or.
...•1 1 M KCI (Hg)
>---------- P from a stirred solution of A. See Figure 25-6 for potentials corresponding to curves X, Y, and Z.
FIGURE
Profiles for Electrodes
in Stirred Solutions
Let us now consider concentration-distance profiles when the reduction described in the previous section is performed at an electrode immerscd in a solution that is stirred vigorously. To understand the effect of stirring, wc must develop a picture of liquid flow patterns in a stirred solution containing a small planar electrode. We can identify two types of flow depending on the average flow velocity, as shown in Figure 25-11. Laminar flow occurs at low flow velocities and has smooth and regular motion as depicted on the left in the figure. Turbulent flow, on the other hand, happens at high velocities and has irregular, fluctuating motion as shown on the right. In a stirred electrochemical cell, we have a region of turbulent flow in the bulk of solution far from the electrode and a rcgion of laminar flow
close to the electrode. These regions are illustrated in Figure 25-12. In the laminar-flow region, the layers of liquid slide by one another in a direction parallel to the electrode surface. Very near the electrode, at a distance D centimeters from the surface, frictional forces give rise to a region where the flo~ velocity is essentially zero. The thin layer of solution"i.n this region is a stagnant layer called the Nernsr diffusion layer. It is only within the stagnant Nernst diffusion layer that the concentrations of reactant and product vary as a function of distance from the electrode surface and that there are concentration gradients. That is, throughout the laminar-flow and turbulent-flow regions, convection maintains the concentration of A at its original value and the concentration of P at a very low level.
Ii Distance
x from electrode,
em
Ii Nernst diffusion
laye~
_
of:~a:~:~: :~I~l:~:ion { j 25-12 Flow patterns and regions of interest near the working electrode in
0( 0(
hydrodynamic voltammetry.
0(
FIGURE
•
J 1
Figure 25-13 shows two sets of concentration profiles for A and P at three potentials shown as X, Y, and Z in Figure 25-6. In Figure 25-13a, the solution is divided into two regions. One makes up the bulk of the solution and consists of both the turbulent- and laminar-flow regions shown in Figure 25-12, where mass transport takes place by mechanical convection brought about by the stirrer. The concentration of A throughout this region is CA, whcreas Cp IS essentially zero. The second region is the Nernst diffUSIOnlayer, which is immediately adjacent to the electrode surface and has a thickness of D centimeters. Typically, 8 ranges from to -, to 10-3 cm, depending on the efficiency of the stirring and the viscosity of the lIqUid. Within the static diffusion layer, mass transport takes
place by diffusion alone, just as was the case with the unstirred solution. With the stirred solutIOn, however, diffusion is limited to a narrow layer of liquid, which even with time cannot extend indefinitely into the solution. As a result, steady, diffusion-controlled currents appear shortly after applying a voltage. . As is shown in Figure 25-13, at potential X, the equIlibrium concentration of A at the electrode surface has been reduced to about 80% of its original value and the equilibrium concentration P has increased by an equivalent amount; that is, c~ = c~ - c~. At potential Y, which is the half-wave potential, the equilibrium concentrations of the two species at the surface arc approximately the same and equal to CAlL Finally. at potential Z and beyond, the surface concentration of A
approaches zero, and that of P approaches the original concentration of A, CA' Thus, at potentials more negative than Z, essentially all A ions entering the surface layer are instantaneously reduced to P. As is shown in Figure 25-13b, at potentials greater than Z the concentration of P in the surface laver remains constant at c~ = C A because of diffusion ~f P back into the stirred region.
This derivation is based on an ovcrsimplified picture of the diffusion layer in that the interface between the moving and stationary layers is viewed as a sharply defined edge where transport by convection ceases and transport by diffusion begins. Nevertheless, this simplified model does provide a reasonable approximation of the relationship between current and the variables that affect the current.
Earpl
The current at any point in the electrolysis we have just discussed is determined by the rate of transport of A from the outer edge of the diffusion layer to the electrode surface. Because the product of the electrolysis P diffuses from the surface and is ultimately swept away by convection, a continuous current is required to maintain the surface concentrations demanded by the Nernst equation. Convection, however, maintains a constant supply of A at the outer edge of the diffusion layer. Thus, a steady-state current results that is determined by the applied potential. This current is a quantitative measure of how fast A is being brought to the surface of the electrode, and this rate is given by dcAldx where x is the distance in centimeters from the electrode surface. For a planar electrode, the current is given by Equation 25-4. Note that dcAldx is the slope of the initial part of the concentration profiles shown in Figure 25-13a, and these slopes can be approximated by (cA - c~)IS. When this approximation is valid, Equation 25-4 reduces to . I
=
nFAD"
~-S~
(c, - c~)
=
k,(c,-
c~)
(25-5)
where the constant kA is equal to nFAD A/S. Equation 25-5 shows that as c1 becomes smaller as a result of a larger negative applied potential the current increases until the surface concentration approaches zero, at which point the current becomes constant and independent of the applied potential. Thus, when c~ ---> 0, the current becomes the limiting current i" and Equation 25-5 reduces to Equation 25-6." . II
liCarcful
nFAD, =
~-S~
c,
=
k,c,
(25-6)
analysis of the unib of the variables in thIS equation leads to
mol e - ) n (' ----I-I. - mo ana)te
F
(
C "J . '(' --. - --:- Afcm-jIJA" _mol e ,
em'"J (mol c.•.. ---- ,nalyte ---~ em},
-
) /ij
for Reversible
Reactions
il --,;;,-
0_ CA -
i
The surface concentration of P can also be expressed in terms of the current by using a relationship similar to Equation 25-5. That is, nFADp
,
i = ---S~(cp
r
- c~)
where the minus sign results from the negative slope of the concentration proftle for P. Note that Dp is now the diffusion coefficient of P. But we have said earlier that throughout the electrolysis the concentration of P approaches zero in the bulk of the solution and, therefore, when Cp = 0, . I
where kp
=
-nfADpc~ = --S---
-nFADp/S.
II
= kpcp
Rearranging gives c~ = ilkp
Substituting Equations 25-7 and 25-10 into Equation 25-3 yields, after rearrangement, E
- EO ,ppl- "A
-
0.0592 -~Iog-kn
kA 'p
0.0592 - -~Iog-.--. n
i II -
- E", I
(25-11) When i = i,/2, the third term on the right side of this equation becomes equal to zero, and, by definition, E,pplis the half-wave potential. That is, _
_ -
(I
EA
-
0.0592 ~--log n
kA - - E"r kp
(25-12)
Substituting this expression into Equation 25-11 gives an expression for the voltammogram in Figure 25-6. That is,
_.!.-
00592 -
----;.; -1 og 1
_ 1
i
species A
Voltage Relationships
for Irreversible
To develop an equation for the sigmoid curve shown in Figure 25-6, we substitute Equation 25-6 into Equation 25-5 and rearrange, which gives
E,ppl - EII2 (em)
Relationships
El!2
Often, the ratio kA1kl' in Equation 25-11 and in Equation 25-12 is nearly unity, so that we may wflte for the
currentCurrent-Voltage
. =
Reactions
Many voltammetrie electrode processes, particularly those associated with organic systems, are lfreverslble, which leads to drawn-out and less well-defined ·waves. To describe these waves quantitatively reqUIres an additionalterm in Equation 25-12 involving the activation energy of the reaction to account for the kmetlcs of the electrode process. Although half-wave potentials for irreversible reactions ordinarily show some dependence on concentration, diffusion currents remaIll linearly related to concentration. Some IrreverSible processes can, therefore, be adapted to quantltatlve analysis if suitable calibration standards are available. Voltammograms
for Mixtures
of Reactants
The reactants of a mixture generally behave independently of one another at a working electrode, Thus, a voltammogram for a mixture is just the sum of the waves for the individual components. Figure 25-14 shows the voltammograms for a pair of two-component mixtures. The half-wave potentials of the two reactants differ by about 0.1 V in curve A and by about 0.2 Y 1lI curve B. Note that a single voltammogram may permit the quantitative determination of two or more speclCs provided there is sufficient difference between succeeding half-wave potentials to permit evaluatIOn of md,vldual diffusion currents. Generally, a difference of 0.1 to 0.2 Y is required if the more easily reducible species undergoes a two-electron reduction; a minimum of about 0.3 V is needed if the ftrst reduction is a one-electron process.
FIGURE 25-14 Voltammograms for two-component
mixtures. Half-wave potentials differ by 0.1 V in curve A, and by 0.2 V in curve B. Fe2~ ~Fe3t-
+ e~
As the potential is made more negative, a decrease in the anodic current occurs; at about -0.02 Y, the current becomes zero because the oxidation of iron(II) ion has ceased. Curve C represents the voltammogram for a solution of iron(III) in the same medium. Here, a cathodiC wave results from reduction of iron(Ill) to iron (II). The half-wave potential is identical with that for the anodic wave, indicating that the oxidation and reduc-
t
----+
Fe2+
~ c
"~
0
u
::I:
l
Anodic and Mixed Anodic-Cathodic +0.4
Voltammograms
Anodic waves as well as cathodic waves arc encountered in \'oltammetry. An example of an anodic wave IS iIlust~ate-d in curve A of Figure 25-15, where the electrode reaction is the oxidation of iron( II) to iron( Ill) in the presence of citrate ion. A limiting current IS observed at about +0.1 Y (versus a saturated calomel electrode [SeED, which is due to the half-reaction
+0.2
0.0 Eappl' V
-0.2 \'s.
-0.4
-0.6
-0.8
SeE
FIGURE 25-15 Voltammetric behavior of iron(t1)and
iron(lIl)in a citrate medium. Curve A: anodic wave for a solution in which CFe" ~ 1 x 10 -4 M. Curve B: anodlccathodic wave for a solution in which CFel- = CFe3- == 0.5 x 10 -, M. Curve C: cathodic wave for a solution in which (Fe)-
=
1 x 10 --4 M.
Inlet
moved by passing an inert gas through the analyte so. lulton for several mmutes (sparging). A stream of the same gas, usually mtrogen, ISpassed over the surface of the solulton during analysis to prevent reabsorption of oxygen. The lower curve in Figure 25-16 is a voltam_ mogram of an oxygen-free solution. 25C-4 Applications Voltammetry
o
-0.4 -0.8
-1.2
Eappl' V vs.
-1.6
-2.0
seE
FIGURE25-16 Voltammogram for the reduction of oxygen in an air-saturated a.l-M KCIsolution. The lower curve IS for a a.l-M KCIsolution in which the oxygen is removed by bubbling nitrogen through the solution. tion of the two iron species are perfectly reversible at the working electrode. Curve B is the voltammogram of an equimolar mixture of lron(II) and iron(III). The portion of the curve below the zero-current line corresponds to the oxidatIOn of the iron(II); this reaction ceases at an applied potential equal to the half-wave potential. The upper portIOn of the curve ISdue to the reduction of iron(III).
of Hydrodynamic
The most important uses of hydrodynamic voltammetry Include (1) detection and determination of chemical species. as they exit from chromatographic columns Or f1ow-InJeclton apparatus; (2) routine determination of oxygen and certain species of biochemical interest. such as gluc?se, lactose, and sucrose; (3) detection of end POlOtS 10 eoulometrie and volumetric titrations; and (4) fundamental studies of electrochemical processes. Voltammetric
Electrical connection to counter electrode block
Electrical connection to working electrode
Detectors in Chromatography
and Flow-Injection
Analysis
Hydrodynamic voltammetry is widely use'd.ior de teelton and determination of oxidizable or reducible compounds or ions that have been separated by liquid
25C-3 Oxygen Waves
Dissolved oxygen is easily reduced at many working elect~odes. Thus, as shown in Figure 25-16, an aqueous solulton saturated with air exhibits two distinct oxygen waves. The first results from the reduction of oxygen to hydrogen peroxide: 02(g) + 2H' + 2e' ~
FIGURE25-17 (continued) (b) Detailof a commercial flow cell assembly. (c) Configurations of working electrode blocks. Arrows show the direction of flow in the cell. ([b]and [c]courtesy of Bioanalytical Systems, Inc., West Lafayelle, IN.) chromatography or that are produced by flow-injection methods. 16 A thin-layer cell such as the one shown schematically in Figure 25-17a is used in these applications. The working electrode in these cells is usually embeddcd in the wall of an insulating block separated
H20,
The second wave corresponds to the further reduction of the hydrogen peroxide: H20,
+ 2H' + 2e- ~2H20
Because both reactions are two-electron reductions the two waves are of equal height. ' Voltammetric measurements offer a convenient and widely used method for determining dissolved oxygen In solutions. However, the presence of oxygen often Interferes with the accurate determination of other species. Thus. oxygen removal is usuallv the first step in amperometrie procedures. Oxygen c~n be re-
16Voitammetric detectors are a particular type of transducer called /imiJtransducers. In this dIScussion and subsequent discussions involving voltammetric transducers. we use the more common tcrm volrammetric de/ector. When a voltammetric transducer is inherently selective for a particular speCies by virtue of control of various experimental variables or ""hen it is co\ereu with a chemically selective layer of polymer or other membranous material. we rder to It as a voltammecric sensor. For a discussion of transducc:rs. detectors. sensors. and their definitions, see
ing-CIIrrmt (a)
FIGURE25·17 (a)A schematic of a voltammetric system for detecting eiectroactive species as they elute from a coiumn. The cell volume is determined by the thickness of the gasket.
Section 1C4.
from a counter electrode by a thin spacer as shown. The volume of such a cell is typically 0.1 to I ilL. A voltage corresponding to the limiting-current region for analytes is applied between the working electrode and a silver-silvcr chloride reference electrode that is located downstream from the detector. We present an exploded view of a commercial flow cell in Figure 25-17b, which shows clearly how the sandwiched cell is assembled and held in place by the quick -release mechanism. A locking collar in the counter electrode block, which is electrically connected to the potentiostat, retains the reference electrode. Five different configurations of working electrode are shown in
Figure
25-l7c.
These
tIon of dctector
configurations
sensitivity
under
pcrmit
optimiza-
a variety
of experi-
acetate
membrane.
which is permeable
type of application of voltammetry (or amperometry) has detection limits as low as 10-' to W-w M. We dis-
cules, such as hydrogen
cuss. voltammetric phy rn more detail
fuses through
the outer
lized enzyme,
where
detection in Section
for liquid 28C-6.
used as labels in immunoassays,
is an immobilized enzyme (see Section 23F-2). glucose oxidase in this example. The inner layer is a cellulose
mental conditions. Working electrode blocks and electrode materials are described in Section 25B-1. This
immersed
chromatogra-
peroxide.
in a glucose-containing
to small mole-
When
this device
solution,
glucose
membrane
the following
been replaced is
dif-
In Section
and Amperometric
23F-2,
potentIometriC molecular There
we described
sensors
free
catalytic
piezoelectric
reaction
much
research
A number mercially
systems
for the determination
rndustrlal,
biomedical,
applications.
These
devices
or detectors
metric
cells and are better that
years
of specific and
are sometimes referred
com-
called
In the
two commercially
avaIlable sensors and one that is under this rapidly expanding field.
development
in
Oxygen
Sensors.
water,
blood,
The determination of aqueous
sewage,
medIcal
of dissolved
from
and environmental
icine. One of the most common
and convenient
cylindrical insulator
insulator.
embedded
lator and electrodes der that contains
a buffered
is sho~n platinumlocatcd
the lower e~d of this
silver anode.
are mounted
meth-
in a centrally
Surrounding
is a ring-shape
med-
is with the Clark by L. C. Clark Jr in
of the Clark oxyg~n sensor
electrode
bio-
and clinical
in Figure 25-18. The cell consists of a cathodic disk working
plants,
to industry,
research,
ods for making such measurements oxygen sensor, which was patented 1956.18 A schematic
chemical
importance
oxy-
such as sea-
The tubular
insu-
inside a second
cylin-
solution
ride. A thin (- 20 11m), replaceable,
of potassium
lO
FIGURE 25-18 The Clark voltammetric Cathodic reaction: 0, + 4H- + 4e ~ reaction: Ag + CI- ~ AgCI(s) + eo.
membrane
of Teflon or polyethylene
end of the tube by an a-ring.
is held in place at The thickness
Mthe electrolyte solution between the cathode membrane is approximately W 11m.
solution
oxyger ~ensor. 2H,6.~odic
struments
diately
."'-L'r.:
sensor
is immersed
of the analyte,
diffuses
through imme-
adjacent
oxygen
in a flowing or
and the
L I:b.kk.:r ,md lU
I~Fur a detailed discussion of the CI;uk oxvgen sen"(lT, see M. L. Hitchman Mcasurrment (If Dissolved Orygm, Chaps. 3-5, New York~ \Vile). 197",
widely
other
to the disk cathode,
to the electrode
and is immediately
where
it diffuses
reduced
to water.
zyme electrodes on measuring Immunosensors.
For
clusively
tween
the membrane
period
and
condition
the electrode
to be reached
(10 to 20 s), the thickness
of the membrane
film must be 20 11m or less. Under
the electrolyte conditions,
surface.
in a reasonable
it is the rate of equilibration
and these
of the transfer
of oxygen across the membrane that steady-state current that is reached.
determines
the
voltammetric example
Sensors. sensors
is a glucose
ical laboratories
A number
are available sensor
for the routine
of three
sensor
that is permeable
lavcr
to glucose
comrl~ex IS
of glu-
in construc-
shnv.'o in Figure
in this caSe is more layers. The outer
is similar
An
used it; clin-
determi~ation
Cose In blood "~crum. This de\'ice membrane
comme~ciallv.
that is widelv
the analyte,
A var-
gles in the figure,
with a second
perox-
of other species
A different
enzyme
In some
on measuring in Section
specificity
electrode,
is. of
electron
oxidation
oxygen
or
Antibodies
specificity
the recognition
clements
Immunosensors
cated hy immobilizing either
through
are proteins
toward
munosensors.")
analytes
most commonly arc
antibodies
adsorption, or other
that
and arc
used in im-
typically
fabri-
on the sensor
surface
covalent
attachment,
poly-
of assay formats
are used with immuno-
One of the most common
tihodies.
one that is immobilized
methods
uses two an-
on the sensor
and is used to capture
the target
analyte,
is labeled
to detect
the captured
(a sandwich allilr). Traditionally,
ous paragraph.
surface
and one that
proteins
radionuclides
analyte were
Ag-AgCl
to quinone
This
was fabricated
In this procedure, The
(D). The resulting
described
array used in the previ-
consists
of an array
being
an independent permits
The array
over
The polymer working
strate.
The
similar
procedure
the
was patterned
Iridium entire
electrode
and depositing
by
was the negative (-100
substrate
was then removed
and counter
refcrence
industry.
that is easily removed
of the electrodes.
deposited
techni-
in the semiconductor
of the polymer
of
multiple
simultaneously.
the glass substrate
pattern
cur-
concentra-
of the biosensor
(photoresist)
of the pattern sputtering.
a two-
on glass using photolithographic
with a polymer
was then
to the
undergoes
arrangement
to be determined
When
is applied
to the original
The biosensor
ques that are common
iridium
the conversion
with each electrode
immunoscnsor.
or
with the enzyme
hydroquinone
25-19b is a photo
electrodes,
into
catalyzes
out the immunoassay
solvent.
methods.
sensors.
and is used
achieved
that react ex-
with the anti-
to hydroquinone.
rent is directly proportional tion of the analyte. Figure
con-
as blue trian-
is tagged
diphosphate
working
en-
adsorption."
with a solution
that has been tagged,
which
lac-
23F-2.
is often
elements
the antibody
of 320 m V versus
cases.
is immobi-
by the stars in the figure (e).
a voltage
sucrose,
analyte
a
an an-
(A). In this example,
by physical
antibody
phosphatase,
of hydroquinone
using
25-19a),
is then rinsed and brought
which is indicated
alkaline
on reso-
strategies.
proteins
it binds preferentially
contact labeled,
detection
which is represented
patients. in-
plasmon
(Figure
is in contact
body (B). The electrode
chemical
include
species.
recognition
with the analyte.
have exceptional
electrodes
nm) using
to leave the on the sub-
was prepared
using a
silver. The reference
25-1 X. The and cunsists
a polvcarbonate
but impe~meable
him
(If blood. The middle
to prolaver
S, Wit'ion and W Nl
+0.4
1
+0.6
'"
0::
+0.8
reversal takes place (in this case, -0.15 and +0.8 V) are called switching potentials. The range of switching potentIals chosen for a given experiment is one in which a diffusion·controlled oxidation or reduction of one or more analytes occurs. The direction of the initial scan may be either negative, as shown, or positive, depending on the composition of the sample (a scan in the direction of more negative potentials is termed a forward scall, and one in the opposite direction is called a reverse scan). Generally, cycle times range from I ms or less to 100 s or more. In this example, the cvcle time is 40 s. Figure 25-24b shows the current response when a solution that is 6 mM in K]Fe(CN)6 and 1 M in KNO, is subjected to the cyclic excitation signal shown in Figures 25-23 and 25·24a. The working electrode was a carefully polished stationary platinum electrode and the reference electrode was an SCE. At the initial potential of +0.8 V, a tiny anodic current is observed, which immediately decreases to zero as the scan is continued. This initial negative current arises from the oxidation of water to give oxygen (at more positive potentials, this current rapidly increases and becomes quite large at about +0.9 V). No current is observed between a potential of +0.7 and +0.4 V because no reducible or oxidizable species is present in this potential range. When the potential becomes less positive than approximately +0.4 V, a cathodic current begins to develop (point B) because of the reduction of the hexacyanoferrate(llI) ion to hexacyanoferrate(ll) ion. The reaction at the cathode is then
A rapid increase in the current occurs in the region of of Fe(CN)6'- becomes smaller and smaller. The current at the peak is made up of two components. One is the initial current surge required to adjust the surface concentration of the reactant to its equilibrium concentration as given by the Nernst equation. The second is the normal ditfusion-controlled current. The first current then decays rapidly (points D to F) as the diffusion layer is extended farther and farther away from the electrode surface (see also Figure 25-lOb). At point F( -0.15 V), the sean direction is switched. The current, however, continues to be cathodic even though the scan is toward more positive potentials because the potentials are still negative enough to cause reduction of Fe(CN)63-. As the potential sweeps in the positive direction, eventu-
Important variables in a cyclic voltammogram are the cathodic peak potential E"", the anodic peak potential Epa- the cathodic peak current ip" and the anodic peak current ip,' The definitions and measurements of these parameters are illustrated in Figure 25-24. For a reversible electrode reaction, anodic and cathodic peak currents are approximately equal in absolute value but opposite in sign. For a reversible electrode reaction at 25°C, the difference in peak potentials, j.Ep' is expected tobe
20 u
b C
~
u
F 10
(h)
-
C Amatore
E. Maisonhaute,
and
)'0. O. Wipf,Anal. '»ISee note 36
2003,
422, 614
AnaL Chern.. Chern., 1996, 68. 187L
2005,
77,303A
In the past, linear-scan voltammetry was used for the quantitative determination of a wide variety of inorganic and organic species, including molecules of biological and biochemical interest. Pulse methods have largely replaced classical voltammetry because of their greater sensitivity, convenience, and selectivity. Generally, quantitative applications are based On calibration curves in which peak heights are plotted as a function of analyte concentration. In some instances the standard-addition method is used in lieu of calibration curves. In either case, it is essential that the composition of standards resemble as closely as possible the composition of the sample, both as to electrolyte concentrations and pH. When this is done, relative precisions and accuracies in the range of I % to 3% can often be achieved. 25G-1 Inorganic Applications Voltammetry is applicable to the analysis of many inorganic substances. Most metallic cations, for example, are reduced at commOn working electrodes. Even the alkali and alkaline-earth metals are reducible, provided the supporting electrolyte does not react at the high potentials required; here, the tetraalkyl ammonium halides are useful electrolytes because of their high reduction potentials. The successful voltammetric determination of cations frequently depends on the supporting electrolyte that is used. To aid in this selection, tabular compilations of half-wave potential data are available.'9 The judicious choice of anion often enhances the selectivity of the method. For example, with potassium chloride as a supporting electrolyte, the waves for iron(III) and copper(lI) interfere with one another- in a fluoride medium, however, the half-wave potential of iron(III) is shifted by about -0.5 V and that for copper(lI) is altered by only a few hundredths of a volt. The presence of fluoride thus results in the appearance of well-separated waves for the two ions. Voltammetry is also applicable to the analysis of such inorganic anions as bromate, iodate, dichromate, vanadate, selenite, and nitrite. In general, voltammograms for these substances are affected by the pH of 3~Fur example, see 1. A. Dean. Analytical Chemistry Handbook, Sec14, pp. l-t6n-14_70. New York: \kGra\.\-HiIL 1995; D. T Sawyer .~- SO,bkowiak. and J L. Roberts. Experimental Electrochemistry fvr ChemlSts. 2nd ed_. pp 11)2-30, New York: Wiley. 1995 lIOn
the solution because the hydrogen ion is a participant in their reduction. As a consequence, strong buffering to some fixed pH is necessary to obtain reproducible data (see next section).
Almost from its inception, voltammetry has been used for the study and determination of organic compounds, with many papers being devoted to this subject. Several organic functional groups are reduced at common working electrodes, thus making possible the determination of a wide variety of organic compounds.'" Oxidizable organic functional groups can be studied voltammetrically with platinum, gold, carbon, or various modified electrodes.
and cause drawn-out, poorly defined waves. Moreover, where the electrode process is altered by pH, as in the case of benzaldehyde, the diffusion current-concentration relationship may also be nonlinear. Thus, in organic voltammetry good buffering is generally vital for the generation of reproducible half-wave potentials and diffusion currents. Solvents for Organic Vo/tammetry
Effect of pH on Voltammograms
Solubility considerations frequently dictate the use of solvents other than pure water for organic voltammetry; aqueous mixtures containing varying amounts of such miscible solvents as glycols, dioxane, acetonitrile, alcohols, Cellosolve, or acetic acid have been used. Anhydrous media such as acetic aeid, formamide, diethylamine, and ethylene glycol have also been investigated. Supporting electrolytes are often lithium or tetraalkyl ammonium salts.
Organic electrode processes often involve hydrogen ions, the typical reaction being represented as
Reactive Functional
R+nH'
+ne-~RHn
where Rand RHn are the oxidized and reduced forms of the organic molecule. Half-wave potentials for organic compounds are therefore pH dependent. Furthermore, changing the pH may produce a change in the reaction product. For example, when benzaldehyde is reduced in a basic solution, a wave is obtained at about -1.4 V, attributable to the formation of benzyl alcohol: C6HsCHO + 2H' + 2e-~C6HjCH,oH If the pH is less than 2, however, a wave occurs at about - 1.0 V that is just half the size of the foregoing one: here, the reaction involves the production of hydrobenzoin: 2C6HjCHO + 2H' + 2e ~C6H5CHOHCHOHC6H5 At intermediate pH values, two waves are observed, indicating the occurrence of both reactions. We must emphasize that an electrode process that consumes or produces hydrogen ions will alter the pH of the solution at the electrode surface, often drastically, unless the solution is well buffered. These changes affect the reduction potential of the reaction ->lJFor a Jdai":d JI,;cussion of urganic ek.:trochemistry. see Lncyclopedia of ElectrQchenllSlry, A. 1. Bard and M, Stratmann, cds .. Vol. 8. Organic E/ecrrocht!misIr\'. H_ J Schatcr. ed_. :-Jew '{ork: Wiley. 2002; Organic Elecrrochemisrn 4th ed_. H_ Lund and 0. Hammeri;:h. cds .. New York Dekker. 2001.
Groups
Organic compounds containing any of the following functional groups often produce one or more voltammetric waves. 1. The carbonyl group, including aldehydes, ketones, and quinones, produce voltammetric waves. In general, aldehydes are reduced at lower potentials than ketones; conjugation of the carbonyl double bond also results in lower half-wave potentials. 2. Certain carboxylic acids are reduced voltammetrically, although simple aliphatic and aromatic monocarboxylic acids are not. Dicarboxylic acids such as fumaric, maleic, or phthalic acid, in which the carboxyl groups are conjugated with one another, give characteristic voltammograms; the same is true of certain keto and aldehydo acids. 3. Most peroxides and epoxides yield voltammetric waves.
4. Nitro, nitroso, amine oxide, and azo groups are generally reduced at working electrodes. 5. Most organic halogen groups produce a voltammetric wave, which results from replacement of the halogen group with an atom of hydrogen. 6. The carbon-carbon double bond is reduced when it is conj ugated with another double bond, an aromatic ring, or an unsaturated group. 7. Hydroquinones and mercaptans produce anodic waves.
In addition. a number of other organic groups cause catalytic hydrogen waves that can be used for analysis.
These include amines, mercaptans, acids, and hetero· cyclic nitrogen compounds. Numerous applications to biological systems have been reported" I 1
Stripping methods encompass a variety of electrochemical procedures having a common, characteristic initial step'2 In all of these procedures, the analyte is first deposited on a working electrode, usually from a stirred solution. After an accurately measured period, the electrolysis is discontinued, the stirring is stopped, and the deposited analyte is determined by one of the voltammetric procedures that have been described in the previous section. During this second step in the analysis, the analyte is redissolved or stripped from the working electrode; hence the name attached to these methods. In anodic stripping methods, the working electrode behaves as a' cathode during the deposition step and as an anode during the stripping step, with the analyte being oxidized back to its original form. In a cathodic stripping method, the working electrode behaves as an anode during the deposition step and as a cathode during stripping. The deposition step amounts to an electrochemical preconcentration of the analyte; that is, the concentration of the analyte in the surface of the working electrode is far greater than it is in the bulk solution. As a result of the preconcentration step, stripping methods yield the lowest deteetion limits of all voltammetric procedures. For example, anodic stripping with pulse voltammetry can reach nanomolar detection limits for environmentally important species, such as Pb2+, Ca 2+, and TI'. Figure 25-34a illustrates the voltage excitation program that is followed in an anodic stripping method for determining cadmium and copper in an aqueous solution of these ions. A linear scan method is often used to complete the analysis. Initially, a constant cathodic potential of about -1 V is applied to the working electrode, which causes both cadmium and copper ions to be reduced and deposited as metals. The electrode is maintained at this potential for several minutes until a significant amount of the two metals has accumulated
Encyclopedia of Electrochemistry, '-\. 1. Bard and M. Stratmann, eds VoL 9, Bioelecrrochemiscry. G. S. Wilson, ed .. New York: Wiley. 200:!. 4JFor detailed discu5sionsof stripping methods. see H. D. Dewald, in ,Wad ern Techniques In Eleclroanalrsis, P. Vanysck, ed., Chap. 4, p. 151. New York: Wiley-Inlerscience, lli96: 1. Wang., Stripping Analnts. Deerfield Beach. FL: VCH. !1}85 41
I
~ c ~
o ::>,
-0.6
1 I
- ---1----I 1
0.0
- -/1- -
(a) Excitation signal
I I I I 1
I I 4-
I
I
_
-Time-..----...I I
: 'eu -- Cu2+ +.2e-
1
Cd-
Cd'+
42e-
e
I
~
\
u
I
Only a fraction of tbc analyte is usually deposited during the electrodeposition step; hence, quantitative results depend not only on control of electrode potential but also on such factors as electrode size, time of deposition, and stirring rate for both the sample and standard solutions used for calibration. Working electrodes for stripping methods have been formed from a variety of materials, including mercury, gold, silver, platinum, and carbon in various forms. The most popular electrode is the HMDE shown in Figure 25-3b. RDEs may also be used in stripping analysis. To carry out the determination of a metal ion by anodic stripping, a fresh hanging drop is formed, stirring is begun, and a potential is applied that is a few tcnths of a volt more negative than the half-wave potential for the ion of interest. Deposition is allowed to occur for a carefully measured period that can vary from a minute or less for 10-1 M solutions to 30 min or longer for 10-'1 M solutions. We should reemphasizc that these times seldom result in complete removal of the ion. The electrolysis period is determined by the sensitivity of the method ultimately used for completion of the analysis.
25H-2 Voltammetric
Completion
simultaneously with the analyte deposition. Because the average diffusion path length from the film to the solution interface is much shorter than that in a drop of mercury, escape of the analyte is hastened; the consequence is narrower and larger voltammetric peaks, which leads to greater sensitivity and hetter resolution of mixtures. On the other hand, the hanging drop electrode appears to give more reproducible results, especially at higher analyte concentrations. Thus, for most applications the hanging drop electrode is used. Figure 25-35 is a differential-pulse anodic stripping voltammogram for five cations in a sample of mineralized honey, which had been spiked with I x 10 5 M Gael]. The voltammogram demonstrates good resolution and adequate sensitivity for many purposes. Many other variations of the stripping technique have been developed. For example, a number of cations have been determined by electrodeposition on a platinum cathode. The quantity of electricity required to remove the deposit is then measured eoulometrically. Here again, the method is particularly advantageous for trace analyses. Cathodic stripping methods for the halides have also been developed. In these methods, the halide ions are first deposited as mercury(I) salts on a mercury anode. Stripping is then performed by a cathodic current.
of the Analysis FIGURE 25-34 (a) Excitation signal for stripping determi-
nation of Cd2+ and Cu2+. (b) Stripping voltammogram. at the electrode. The stirring is then stopped for 30 s or so while the electrode is maintained at -1 V. The potential of the electrode is then decreased linearly to less negative values and the current in the cell is recorded as a function of time, or potential. Figure 25-34b shows the resulting voltammogram. At a potential somewhat more negative than -0.6 V, cadmium starts to be oxidized, causing a sharp increase in the current. As the deposited cadmium is consumed, the current peaks and then decreases to its original level. A second peak for oxidation of the copper is then observed when the potcntial has decreased to approximately -0.1 V. The heights of the two peaks are proportional to the weights of deposited metal. Stripping methods are important in trace work because the preconeentration step permits the determination of minute amounts of an analyte with reasonable accuracy. Thus, the analysis of solutions in the range of 10-' to 10' , M becomes feasible by methods that are both simple and rapid.
------~~
The analyte collected in the working electrode can be determined by any of several voltammetric procedures. For example, in a linear anodic scan procedure, as described at the beginning of this section, stirring is discontinued for 30 s or so after stopping the deposition. The voltage is then decreased at a linear fixed rate from its original cathodic value, and the resulting anodic current is recorded as a function of the applied voltage. This linear scan produces a curve of the type shown in Figure 25-34b. Analyses of this type are generally based on calibration with standard solutions of the cations of interest. With reasonahle care, analytical precisions of about 2% relative can be obtained. Most of the other voltammetric procedures described in the previous section have also been applied in the stripping step. The most widely used of thes.: app.:ars to he an anodic differential-pulse t.:chnique. Often. narrower peaks arc produced by this proc.:durc, which is desirable when mixtures are analyzed. Another method of ohtaining narrower peaks is to use a mercurv film electrode. Here, a thin mercury film is elcctrodeposited on an inert electrode such as glassy carbon. Usuallv. the mercury deposition is carried out
Adsorptive stripping methods are quite similar to the anodic and cathodic stripping methods we have just considered. In this technique, a working electrode is immersed in a stirred solution of the analyte for several minutes. Deposition of the analyte then occurs by physical adsorption on the electrode surface rather than by electrolytic deposition. After sufficient anaIyte has accumulated, the stirring is discontinued and the deposited material determincd hy linear scan or pulsed voltammetric measurements. Quantitative information is acquired by calibration with standard solutions that are treated in the sam.: way as samples. Many organic molecules of clinical and pharmaceutical interest
have a strong
tendency
to be adsorbed
trom aqueous solutions onto a mercury or carbon surface. particularly if the surface is maintained at a voltage where the charge on the electrode is near zero. With good stirring. adsorption is rapid, and only 1 to 5 min is required
to accumulate
sufficient
analyle
for
analysis from 10'- tv! solutions and 10 to 20 min for ~
TW(lrial:
Learn murt.' ahout stripping methods.
251
FIGURE 25-35 Differential-pulse anodic stripping voltammogram in the analysis of a mineralized honey sample spiked with GaCI3 (finalconcentration in the analysis solution: 1 x 10 -5 M). Deposition potential: -1.20 V; deposition time: 1200 s in unstirred solution; pulse height: 50 mV;and anodic potential scan rate: 5 mVs -1. (Adapted from G. Sannaa. M. I. Pilo, P. C. Piu, A.Tapparo, and R. Seeber, Anal. Chim. Acta, 2000,415, 165, with permission.)
c
~
o
2.0
-0.8
-0.6 Applied
10-9 M solutions. Figure 25-36a illustrates the sensitivity of differential-pulse adsorptive stripping voltammetry when it is applied to the determination of ealfthymus DNA in a 0.5 mg/L solution. Figure 25-36b shows the dependence of the signal on deposition time. Many other examples of this type can be found in the recent literature.
-0.4 potential,
-0.2 V
Adsorptive stripping voltammetry has also been applied to the determination of a variety of inorganic cations at very low concentrations. In these applications the cations are generally complexed with surface active complexing agents, such as dimethylglyoxime, catechol, and bipyridine. Detection limits in the range of 10-10 to 10-11 M have been reported.
T
In recent years, many voltammetric studies have been carried out with electrodes that have dimensions smaller by an order of magnitude or more than normal working electrodes. The electrochemical behavior of these tiny electrodes is significantly different from classical electrodes and appears to offer advantages in certain analytical applications." Such electrodes are often called microscopic electrodes, or microelectrodes, to distinguish them from classical electrodes. Figure 25-3c shows one type of commercial microelectrode. The dimensions of these electrodes are typically smaller than about 20 J.lmand may be as small as 30 nm in diameter and 2 J.lmlong (A = 0.2 J.lm'). Experience has led to an operational definition of microelectrodes. A microelectrode is any electrode whose characteristic dimension is, under the given experimental conditions, comparable to or smaller than the diffusion layer thickness, 0. Under these conditions, a steady state or, in the case of cylindrical electrodes, a pseudo-steady state is attained."" 251-1Voltammetric Currents at Microelectrodes In section 25C-2, we discussed the nature of the current that is produced at an ordinary planar electrode in voltammetric experiments. Using a more elaborate treatment, it can be shown 45 that the concentration gradicnt at a spherical electrode following application of a voltage step is
c; = c~( ~
0.6~A ,
1
tional to t112 By substituting this relation into Equation 25-4, we obtain the time-dependent faradaic current at the spherical electrode.
VOLTAMMETRY WITH MICROELECTRODES
!
aa
+ ~) =
c~G
+ ~)
(25-21)
where r is the radius of the sphere, {j = v1il5i is the thickness of the Nerost diffusion layer, and t is the time after the voltage is applied. Note here that 0 is proporFIGURE 25-36 Effectof preconcentration period on the voltammetric (a) stripping response at the pretreated carbon paste electrode. Preconcentration at +0.5 Vfor (A)1, (B)30, (C)60, (D)90, (E)120, and (F) 150 s. Squarewave amplitude, 10 mV;trequency, 40 Hz; 0.5 mg/L calf-thymus DNA.(b) Peak current versus deposition time. (Adapted from J. Wang, X.Cai, C. Jonsson, and M. Balakrishnan, Electroanalysis, 1996,8, 20, with permission.)
h• \0=::~_r j; ~
ee R. M. Wightman, Science, 1988,240,415; Anal. Chern .. 1981, 53, 1325A S. Pons and M. Fleischmann, Anal. Chern .. 1981, 59. l391A: J Heinze. Agnew. Chem.,Inc. Ed .. 1993, 32,1268; R. M. Wightman and D. 0 Wipf, in Electroanalytical Chemistr)'. Volume 15, A. 1. Bard, ed., New York: Dekker, 1989; A. C. Michael and R. M. Wightman, 10 LaboratOf} Techniques in Electroanalytical Chemistr.v. 2nd ed., P. T. Kissinger and W. R. Heinemann. eds., Chap. 12. New York: Dekker. 1996: C (j. Zoski. in Modern Techniques in E/ectroallalysis. P. Vanysek, cd .. Chap. 6. New York: \\.'ilev, 1996. uFor a dis~ussion of microelectrodes, including terminology, characterization. and applications, see K. Stulfk, C Amatore, K Holub, V. Mareeek. and W. Kutner, Pure Appl. Chern., 2000, 72, 1483. http://w\\w.iupac,org publications/pac /2000/7208-'7208pdfs !7208stulik_I-l-83.pdf
43S
.B
.A
50 Deposition
100 time,s
~sSee note
.1-3.
i = nFADC~O
+ ~)
Note that if r p 0, which occurs at short times, the 110 term predominates, and Equation 25-22 reduces to an equation analogous to Equation 25-5. If r "'" 0, which occurs at long times, the l/r term predominates, the electron-transfer process reaches a steady state, and the steady-state current then depends only on the size of the electrode. This means that if the size of the electrode is small compared to the thickness of the Nerost diffusion layer, steady state is achieved very rapidly, and a constant current is produced. Because the current is proportional to the area of the electrode, it also means that microelectrodes produce tiny currents. Expressions similar in form to Equation 25-22 may be formulated for other geometries, and they all have in common the characteristic that the smaller the electrode, the more rapidly steady-state current is achieved. The advantages of microelectrodes may be summarized '6 as follows: 1. Steady state for faradaic processes is attained very rapidly, often in microseconds to milliseconds. Measurements on this time scale permit the study of intermediates in rapid electrochemical reactions. 2. Because charging current is proportional to the area of the electrode A and faradaic current is proportional to Air, the relative contribution of charging to the overall current decreases with the size of the microelectrode. 3. Because charging current is minimal with microelectrodes, the potential may be scanned very rapidly. 4. Because currents are so very small (in the picoampere to nanoampere range), the IR drop decreases dramatically as the size of the microelectrode decreases. 5, When micro electrodes operate under steady-state conditions, the signal-to-noise ratio in the current is much higher than is the case under dynamic conditions. 6. The solution at the surface of a microelectrode used in a flow system is replenished constantly, which minimizes 0 and thus maximizes faradaic current. 7. Measurements with microelectrodes can be made on incredibly small solution volumes, for example, the volume of a biological cell.
8, Tiny currents make it possible to make voltammet_ ric measurements in high-resistance, nonaqueous solvents, such as those used in normal-phase liquid chromatography. As shown in Figure 25-37, microelectrodes take several forms. The most common is a planar electrode formed by sealing a 5-flm-radius carbon fiber or a 0.3to 20-flm gold or platinum wire into a fine capillary tube; the fiber or wires are then cut flush with the ends of the tubes (see Figures 25-3e and 25-37a and b). Cylindrical electrodes are also used in which a small portion of the wire extends from the end of the tube (Figure 25-37f). This geometry has the advantage of larger currents but the disadvantages of being fragile and difficult to clean and polish. Band electrodes (FigUre 25-37d and e) are attractive because they can be fabricated on a nanometer scale in one dimension, and their behavior is determined by this dimen~ion except that the magnitude of their currents increases with length. Electrodes of this type of 20 A ha~C""beenconstructed by sandwiching metal films between glass Or epoxy insulators. Other configurations such as the microdisk array, microsphere, microhemisphere, fiber array, and interdigitated array (Figure 25-37c, g, h, i, and
FIGURE 25-37 Most important geometries of microelectrodes and microelectrode arrays: (a)microdisk, (b) microring: (c) microdisk array (a composite eiectrode); (d) lithographically produced microband array; (e)microband; (I) single fiber (microcylinder);(g) microsphere; (h) microhemisphere; (i) fiber array; (j) interdigitated array. (From K. Stulik, C. Amatore, K. HolUb,V. Mareek, and W. Kutner, Pure Appl. Chem., 2000, 72, 1483, with permission.)
lr
j, respectively) have been used successfully. Mercury microelectrodes are formed by electrodeposition of the metal onto carbon or metal electrodes.
biosensors for determining analytes in minuscule volumes of solution, it is likely that research and development in this fertile area will continue for some time.
251-2 Applications
251-3 The Scanning
of Microelectrodes
In Section 25F-2, we described the use of a carbon fiber electrode to monitor concentration of the neurotransmitter dopamine in rat brains in response to behavioral change. In Figure 25-38, we see the results of the differential-pulse voltammetric determination of dopamine at 100-1000 flM levels." The working electrode in this study was a nanoneedle consisting of a multi wall carbon nanotube attached to the end of a tungsten wire tip. This electrode may be the smallest fabricated up to this time. The entire surface of the probe except the nanoneedle (30 nm in diameter and 3 flm long) was coated with a nonconducting UV-hardening polymer. Both CV and differentialpulse voltammetry were performed with the nanoneedle electrode with good results. The inset in the figure shows a working curve of the peak currents from the voltammograms plotted versus concentration. In light of tremendous interest in nanomaterials and
* Answers ~
Electrochemical
Microscope
Another application of microelectrodes is the scanning electrochemical microscope (SECM), introduced by Bard in 198948 The SECM is closely related to the scanning probe microscopes (SPMs) discussed in Section 21G. The SECM works by measuring the current through a microelectrode (the tip) in a solution containing an electroactive species while the tip is scanned over a substrate surface. The presence of the substrate causes a perturbation of the electrochemical response of the tip, which gives information about the characteristics and nature of the surface. Surfaces studied have included solids, such as glasses, polymers, metals, .and biological substances, and liquids, such as mercury or oils. The SECM, which is now commercially available, has been used to study conducting polymers, dissolution of crystals, nano materials, and biologically interesting surfaces.
are provided at the end of the book for problems marked with an asterisk.
Problems with this icon are best solved using spreadsheets.
1---- f·-
\()OO~M 6(~)pM ~()l,1 ~i
25-1 Distinguish between (a) voltammetry and amperometry, (b) linear-scan voltammetry and pulse voltammetry, (c) differential-pulse voltammetry and squarewave voltammetry, (d) an RDE and a ring-disk electrode, (e) faradaic impedance and double-layer capacitance, (f) a limiting current and a diffusion current, (g) laminar flow and turbulent flow, (h) the standard electrode potential and the half-wave potential for a reversible reaction at a working electrode. (i) normal stripping methods and adsorptive stripping methods.
\1
25-2 Define (a) voltammograms, (b) hydrodynamic voltammetry, (c) Nernst diffusion layer, (d) mercury film electrode, (e) half-wave potential, and (f) voltammetric sensor. 00 Eappl'
0.2 V
'is.. AglAgCI
FIGURE 25-38 Detection of dopamine at a multiwallcarbon nanotube-based nanoneedle electrode. Differential-pulsevoltammograms of dopamine at the nanoneedie eiectrode in various concentrations from 100 to 1000 ~M. Inset is the calibration curve. (From H. Boo et aI., Anal. Chern., 2006, 78, 617. Withpermission. Copyright 2006 American Chemical Society.)
25-3 Why is a high supporting electrolyte concentration cal procedures?
used in most electroanalyti-
25-4 Why is the reference electrode placed near the working electrode in a threeelectrode cell" 25-5 Why is it necessary to buffer solutions in organic voltammetry" 25-6 Why are stripping methods more sensitive than other voltammetric procedures"
25-7 What is the purpose of the electrode position step in stripping analysis? 25-8 List the advantages and disadvantages of the mercury film electrode compared with platinum or carbon electrodes. 25-9 Suggest how Equation 25-13 could be used to detcrmine the number of electrons n involved in a reversible reaction at an electrode. *25·10 Quinone undergoes a reversible reduction at a voltammetric working electrode. The reaction is /H
¢ ¢ .".,.°
°
O"H
(a) Assume that the diffusion coefficient for quinone and hydroquinone are approximately the same and calculate the approximate half-wave potential (versus SCE) for the reduction of hydroquinone at an ROE from a solution buffered to a pH of 7.0. (b) Repeat the calculation in (a) for a solution buffered to a pH of 5.G. *25-11 In experiment 1, a cyclic voltammogram at an HMOE was obtained'fUlm a 0.167-mM solution of Pb2+ at a scan rate of 2.5 Vis. In experiment 2, a second CV is to be obtained from a 4.38-mM solution of Cd 2+ using the same HMOE. What must the scan rate be in expcriment 2 to record the same peak current in both experiments if the diffusion coefficients of Cd" and Pb'+ are 0.72 X 105 cm' s" and 0.98 cm' s", respectively. Assume that the reductions of both cations are reversible at the HMOE. ~
in HN03, produced a net limiting current working electrode at a potential of -0.85 5.00 mL of a 2.25 x 10-3 M standard Cd" duced a current of 4.48 flA. Calculate the
of 1.78 flA at a rotating mercury film V (versus SCE). Following addition of solution, the resulting solution proconcentration of Cd'" in the samplc.
Sulfate ion can be determined by an amperometrie titration procedure using Pb'+ as the titrant. If the potential of a rotating mercury film electrode is adjusted to -1.00 V versus SCE, the current can be used to monitor the Pb concentration during the titration. In a calibration experiment, the limiting current, after correction for background and residual currents, was found to be related to the Pb'" concentration by i, = 10crb'" where i, is the limiting current in mA and Crb" is the Pb 2+ concentration in mM. The titration reaction is
,+
If 25 mL of 0.025 M Na,S04 is titrated with 0.040 M Pb(N03)z, develop the titration curve in spreadsheet format and plot the limiting current versus the volume of titrant. Suppose that a spherical electrode can be fabricated from a single nano onion, C60-C'4D-C'4D-C960-C'500-C,'60-C,940·C3840-C4860, shown here. Nano onions comprise concentric fullerenes of increasingly larger size as indicated in the formula. Assume that the' nano onion has been synthesized with a carbon nanotube tail of sufficient size and strength that it can be electrically connected to a 0.1 flm tungsten needle and that the needle and nanotube tail can be proper! y insulated so that only the surface of the nano onion is exposed.
25-12 The working curve for the determination of dopamine at a nanoneedle electrode by differential-pulse voltammetry (Figure 25-38) was constructed from the following table of data. Concentration Dopamine, mM
Peak Current, nA
0.093 0.194 0.400 0.596 0991
0.66 1.31 2.64 4.51 5.97
(a) Use Excel to perform a least-squares analysis of the data to determine the slope, intercept, and regression statistics, including the standard deviation about regression. (b) Use your results to find the concentration of dopamine in a sample solution that produced a peak current of 3.62 nA. This value is the average of duplicate experiments. (c) Calculate the standard deviation of the unknown concentration and its 95% confidence interval assuming that each of the data in the table was obtained in a single experiment. *25-13 A solution containing Cd'+ was analyzed voltammetrically using the standard addition method. Twenty-five milliliters of the deaerated solution, which was 1 M
(a) Given that the radius of the nano onion is 3.17 nm, find the surface area in cm', neglecting the area of the nanotube attachment. (b) If the diffusion coefficient of analyte A is 8 X 10-'" m'ls, calculatc the concentration gradient and the current for A at a concentration of 1.00 mM at the following times after the application of a voltage at which A is reduced: I X 108s,] X 10"s, 1 X 1O.6s, 1 X 1O-5s,1 X 1O.4s,1 X 10-3s,] X lO"s, 1 X 10" s, 1 s, and 10 s. (c) Find the steady-state current. (d) Find the time required for the electrode to achieve steady-state current following the application of the voltage step. (e) Repeat these calculations for a 3-flm spherical platinum electrode and for a spherical iridium electrode with a surface area of 0.785 mm '. (f) Compare the results for the three electrodes, and discuss any differences that you find. 25-16 (a) What arc the advantages of performing voltammetry with microelectrodes" (b) Is it possible for an electrode to be too small'? Explain your answer.
~
Challenge Problem 25-17
A new method voltammetrv
for determining
2002,74,3575). volume lution
ultrasmall
has been proposed In this mcthod,
to be measured
hy anodic
and I. Fritsch,
a metal is exhaustively
onto an electrode,
V, is related
volume
(nL) volumes
(W. R. Vandaveer
deposited
stripping
Anal. Chern., from the small
from which it is later stripped.
Q required
to the total charge
The so-
to strip the metal by
Traditionally.
to provide fundamental
information
plex systems. Armed with analytical information
and C is the molar (a) (b)
Beginning for v.,.
of moles of electrons
concentration
with Faraday's
temS that might lead to understanding
of the metal ion hefore
the metal deposited
8.00 mM in AgN03• of -0.700
The solution
V versus
band electrode electrode
sents idealized
anodic
was electrolyzed
from a solution
results.
rule integration
determine
A tuhular stripped
By integration,
of the solution
nano-
off the
electrode.
Y~u can do a
with ExeeT.49 From
from which the silver was
deposited. Potential,
organisms. \ Throughout
measurements
photocurrent
tionalto
analytes at low concentrations.
Current, nA
0.000 -0.02
-0.123
- 1.10
of implementations
-0.\0
used for studying a variety of biological systems.2 These
-0.40
-0.001
-0.\15
-0.30
-0.\0
-0.09
-0.65
of extracellular
-0.25
-0.20
-0.08 -0.065
-0.20
-0.30 -0.44
-0.52 -0.37
tion resulting from stimulation
-0.22
-0.22
ments, it is useful to consider Figure IA4-1, which shows
-0.18
-0.67
-0.05 -0.D25
-0.12
some of the processes that produce extracellular
-0175
0.00
-·0.05
-0.168
-0.80 -1.00
0.05
-0.03
acidification. For example, when membrane-bound
-0.16
- 1.18
0.\0
-0.15
1.34
0.15
-OJJ2 -O.lX15
-l.28
-0.135 (c)
Suggest
(d)
Would
experiments
the deposition (c)
Describe method.
it matter
all the Ag'
was reduced
to Ag(s)
in
step.
an alternative
of metabolic processes in
method
were not a hemisphere" against
Why or why not
0
which you might test the proposed
surr;unding
species.
230-6). LEOs are then positioned opposite each of the areas as shown in Figure IA4-2 so that by alter-
nately switching on each light source, photocurrents
corre-
sponding to each of selected species may be recorded in receptors bind
turn. Response curves such as those in Figure IA4-3 are recorded for each of the ionophores
to produce acidic
dressed sequentially, they can also be addressed simultane-
as a result. These exmicrophysiometer
of other important
ionic
to calibrate the instru-
ment for each detected species, Although the three sensor areas of the LAPS can be ad-
ion and chloride ion are ex-
used to monitor these pH changes and can also measure changes in the concentrations
(and resulting voltage change ~V). The LAPS
photocurrent
ionophoric
ligands, metabolic processes such as res-
the cdl. The LAPS-based
indicates a bias voltage that is appro-
to different areas of the surface of the device (see Section
ously using the arrangement
change processes cause a decrease in the pH of the solution
if the droplet
"'as
is made selective for other species by applying ionophores
the significance of such measure-
changed across the celt memhrane
was
for two different buffers.
The verticaillne
waste products inside the cell. Protons are exchanged with
to show whether
shown, the
priate for measuring changes in pH from the change in the
and changes in ionic composi-
sodium ions, and bicarbonate
for data storage and
LAPS was exposed to a buffer, and the photocurrent then repeated
devices have been especially useful for real·time monitoring
piration or glycolysis are stimulated
to a computer
The response of the LAPS to changes in pH
recorded as a function of bias voltage; the experiment
of this device, and they have been
-0.80 -\'OO
to appropriate
produces a voltage prop or-
is shown in Figure fA4-3. In the experiments
One
or LAPS (see Section 23F-2). There have been a number
living cells. To understand
(eE)
(WE). The current-to-voltage
pH that is then passed to a lock-in amplifier whose
manipulation.
sensor,
Potential, V
acidification
is used to hias the
(RE). When light from
output is recorded with a digital oscilloscope. The oscillo-
and devices capable of rapidly and potentiometric
of H-'-,
appears between the counter electrode
converter of the potentiostat
on living
Section 4, we have explored many electro-
such device is the light addressable
of a LAPS chip de-
the concentrations
the LAPS chip is selective for H'.
and the working electrode
scope is interfaced
chemical instruments
is produced that is pro-
one of the LEOs falls on the surface of the biased chip, a
are
Current, nA
-0.50 -0.45
to the pH of the solution. Figure IA4-2 shows the
chip versus a reference electrode
to provide rapid, real-time, high-through-
accurately determining V
experimen-
being developed to aid in drug discovery and medical diag-
put~ accurate, multivariate
portional
As shown in Figure IA4-2, a potentiostat
tal design, genomics, and analytical chemistry, models of
instrumentation
total
a photocurrent
Without modification.
By bringing to bear knowledge and tools from diverse
biochemical and genetic interactions
electrode,
signed to monitor simultaneously Ca2", and K +.l
years, the emergent field of systems hiology has approached
intracellular
at a certain bias voltage versus a
reference
basic elements of one implementation
In recent
nosis. These models strongly depend on the availability of
table repre-
determine.the
or do the integration
the volume
that was
for 30 min at a potential
to strip the silver from the tubular
Simpson's
the charge,
was Ag(s)
rate of 0.10 Vis. The following
stripping
face, which is maintained
the problem from the top down rather than the bottom up.
22-8), derive the ahove equation
was used. The silver was then anodically
required
manual
F is the faraday,
electrolysis.
a gold top layer as a pseudoreference.
using a linear sweep
often ob-
the detailed inter-
fields, such as systems analysis, computation,
In one experiment,
charge
per mole of analyte,
law (see Equation
device that is pH sensitive. When light impinges on its sur-
tained at widely different times and many different places,
actions of living things with their environments.
n is the numher
As described in Section 23F-2, the LAPS is a semiconductor
on the details of com-
scientists have sought to develop models of complex sys-
V=~ , nFC where
How the System Works
the biological sdences, biomedical sciences,
and indeed science ltself have relied on chemical analysis
is
shown in Figure IA4-2. In this
scheme, the three LEOs corresponding are modulated
independently
to K', Ca
by a signal generator
2 ••
and Hwith
three frequency outputs: 3 kHz. 3.5 kHz, and 4 kHz Concentration information
for each of the species is encoded in one
2.5
'"=r
1.5
""~~
'?
< FIGURE IA4-3 The response of the LAPS to changes in bias voltage for two buffer solutions. The change in output voltage .1.V of the system at a constant bias voltage of 0.25 V is proportional to the change in pH on the surface of the LAPS. (Adapted from W. Yicong et aI., Biosens. Bioeleetron., 2001,16,277. With permission.)
of these frequency components.
0.5
For example. K +- is encoded
trum, and its inverse transform provides a mea~ure of the
at 3 kHz, Ca 2' is encoded at 3.5 kHz, and H is encoded at
concentration
4 kHz. The signal at the output of the potentiostat
rate of 100 kHz, each 1024-point time-domain
-I-
for a solu-
quired in about 10 ms. For experiments
tion containing all three species is shown in Figure IA4-4a. FIGURE IA4-1 The cell biology of extracellular acidification. When a receptor is stimulated, signal transduction pathways are induced. Adenosine triphosphate (ATP) consumption is then compensated by the increased uptake and metabolism of glucose, which results In an increase in the excretion of acid waste products. The extracellular acidification is measured by the LAPS. (From F. Hafner, B/osens. B/oeiectron., 2000, 15, 149. With permission.)
of the selected species. At a data acquisition
This complex waveform is then subjected to Fourier trans-
trations of the three species are to be monitored
formation and digitalliltering
of time, time-domain
(see Section 5C-2) to produce
the frequency spectrum of Figure IA4-4h. The amplitude of
hard drive of the computer for subsequent ting of the results.
analysis and plot-
~' 41~)
" -3300
~
200
Frequency,
Hz
X
10-3
(bl
FIGURE IA4-2 Schematic diagram of a LAPS-based system for monitOring changes in extracellular H', Ca 2 • and K - concentrations in studies of the effects of drugs on living cells. RE ~ reference electrode. CE ~ counter electrode. WE ~ working electrode, PC personal computer. D/A -- digltal-to-analog converter. (Adapted from W Yicong et al. BlOsens. B/oe/eetron .. 2001, 76.277. With permission.)
as a function
signals are acquired and stored on the
the signal for each species is then extracted from the spec-
~
signal is ac-
in which the concen-
FIGURE IA4-4 (a) Time-domain LAPS output for a solution containing K " Ca 2', and H '. The signal was sampled at 100 kHz, and the time-domain signal contained 1024 points. (b) Fourier transform of the signal in (a). (Adapted from W Ylcong et aI., Biosens. B/oe/eetran., 2001, 76, 277. With permission.)
The LAPS system described in the previous paragraphs
can
1.2
be used to study the effects of drugs on living cells placed directly on the sensor, as shown in Figure IA4-2. Two peri-
t.R
staltic pumps, wbich are controlled by the system computer, cause either or both of two solutions to flow past the cells to the active area of the LAPS. The first solution is RPMI 1640
>
culture medium (CM), and the other solution contains the
~ ~
drug being studied, which in this example is phenobarbital (PB). In a typical experiment,
rat cardiac muscle cells were
placed in the LAPS flow channel, and CM and PB were alternately
1.4
,g 0
"-
passed over the cells and across the active area
of the LAPS for 3-minute periods. Results from the LAPS data analysis are shown in Figure IA4-5, in which concentrations of K +, Ca 2+. and H+ are plotted versus time. First, CM is passed over the cells for 3 minutes. During
0.6
0.2 12
0
15
18
this time, all three ions generally decrease in concentration. Then, PB is passed over the cells for 3 minutes. About halfway through the PB period, Ca"
and H' concentrations
begin to increase and K + begins to decrease. These changes continue into the second eM period, and the change reverses for all three ions beginning at about the same point during the period. Subsequent
FIGURE IA4-S Results of LAPS monitoring of K 'or Ca", and H ' while administering phenobarbital to rat cardiac muscle cells. (Adapted from W. Yicong et aI., Biosens. Bioe/ectron., 2001, 16,277. With permission.)
periods repeat the same
behavior as CM and PB are alternately cells.
The photo show", a ":itate-of-the-arr LC :iy.srem. On the right from top to bottom are .:iol\'f>nrresen·oirs, an automated samplt>.r area, and 1"\vo pump:,; that cau he u,;ed to produce a hi nary gradient. At the top left is the tiwnl1o:italtl'd columu area. A diodt>-array trV -visibk detector i...; .-;hOWll on dlt' hottom left. (Courte:'iy of Perkin-Elmer. Illc .. Sheltoll. CT.;
he method., describcd in this section arc ased
T
to separate carious components of ana~l·tical
samples prior to t!Jei,. determination
passed over the multivariate experimental data on the production of ions on the surface of living cells. This example.j shows how micro-
introdurtion
drugs, and the physiological responses of the cells were
miniaturization,
graphic separations u:ith an elnpltasis
compared.
sors, and modern data-acquisition
In similar experiments,
cells were exposed to other
Drugs that produce similar physiological
advances in solid-state transducers and -manipulation
responses arc presumed to operate by similar mechanisms.
ods continue to provide new tools for investigations
Dilantin, for example, produces a somewhat different re-
forefront of chemistry, biology, biochemistry,
sponse pattern for the three monitored
ions, which suggests
iflstru-
ogy, and other biosciences.
and senmeth~ at the
systems biol-
of experimentall'ariahles quantitatil'c thorough
analpis,
disCflj'Sl~Oll
The LAPS microphysiometer
combines several interest-
the maiasta"
ing teChnologies and measurement
strategies to produce
ject o(Chapler
Oll
vptimization
ji,r ,,{jicient qualitatil'e and n,is Ircatment is follrJleed by a
of the (lIror)' and practice of gas Chapter 2;, Liquid chromatography,
o( "aal,·t i",d chromatograph",
is the suh-
2~. Chapter 29 describes the techniqucs
ofsllpereritical.fluid fluid
WI
to the termirlOlo[.Q·and theor.l· of chromato-
chrorrwtograplll'ia
that a different mechanism is active.
q}'
mental methorfs, Chapter 2(, hegins this section trith
chromatograph)'
aad superceitiral
e.rtractiOfl. TILl:) section cOrlclud(~.s 1-l'itlt (l discussion
in Chapter -30 of the emergia.!!:/ielrls o( mpillan' tropllOre.,-i."capdlar,· clectrochrofllatogruphl: j[ou'j;'actio!lali()!l.
:lpplicatiuflS
(~r('{Jch method
iarluded ia the "1'!iT"'!iT'ia!c,.ha!,!cr.
eler"ndjieldare
An Introduction to
Chrom~tograp!llc Separations '
here ,-
are veryfew, ifany, methodSfor chemical analysis that are specificfor!l single chemical species, At ~est, analytical meth-
ods aeorenselectivetlfoCtOhfew spef.~s o~;th~'it* ofl,.;e:'~J Cles. . .sequen y, e separ"j~on oJ;irza",e .
Chromatography is a powerful separation method that finds applications in all branches of science, Chromato_ graphy was invented and named by the Russian botanist Mikhail Tswett shortly after the turn of the last century, He employed the technique to separate various plant pigments such as chlorophylls and xanthophylls by passing solutions of these compounds through a glass column packed with finely divided calcium carbonate, The separated species appeared as colored bands on the column, which accounts for the name he chose for the method (Greek chroma meaning "color" and graphein meaning "writing"), , The applications of chromatography have grown explosively in the last half century, due not only to the development of several new types of chromatographic techniques but also to the growing need by scientists for better methods for characterizing complex mixtures. The tremendous impact of these methods on science is attested by the 1952 Nobel Prize in Chemistry that was awarded to A. J P, Martin and R. L M, Synge for their discoveries in the field, Many of't~ Nobel Prizes awarded since that time have been based on work in which chromatography played a vital role.
26A
r..
GENERAL DESCRIPTION OF CHROMATOGRAPHY
from potential inteterences~~uite ofte~;a vitnl " ,:,t.,.~,•., step in onalyticalprocedures::~ntil the~~dle ofxfi:
Chromatography encompasses a diverse and important group of methods that allow the separation, identificathe twentieth centyty' anafyt~l sepa~'i[!rzs w<e,.e~.2i,i.; tion, and determination of closely related components largely carried out by such ~sical m';iXddsas",; of complex mixtures; many of these separations are impossible by other means.' In all chromatographic precipitation, distilll1tion,an~.extractid~Today, '> separations the sample is dissolved in a mobile phase, however,onalyticalseparaue~ are mO~9omwhich may be a gas, a liquid, or a supercritical fluid. This monly carried oU/by chromamgraphydtlji elec- ~:~~ mobile phase is then forced through an immiscible statrophoresis,particu.farly witiJ'fsamplest&¥are:;,,~ tionary phase, which is fixed in place in a column or on multicomponent and complex;' "'-'1' a solid surface. The two phases are chosen so that the ;;~,components of the sample distribute themselves be
Although the distribution constant is fundamental to chromatographic separations, it is not readily measured. Instead, we can measure a quantity called the retention time that is a function of K" To see how this is done, let us refer to Figure 26-4, a simple chromatogram made up of two peaks. The small peak on the left is for a species that is not retained by the column. Often, the sample or the mobile phase contains an unretained species. When it does not, such a species may be added to aid in peak identification. The time t" fol' the unretained species to reach the detector is sometitnes called the dead, or void, time. The dead time provides a measure of the average rate of migration of the mobile phase and is an important parameter in identifying analyte peaks. All components spend time tM in the mobile phase. The larger peak on the right in Figure 26-4 is that of an analyte species. The time required for this zone to reach the detector after sample injection is called the retention time and is given the symbol tR. The analyte has been retained because it spends a time ts in the stationary phase. The retention time is then
bular column, F is related to the linear velocity at the column outlet Uo
where A is the cross-sectional area of the tube (7Tr'). For a packed column, the entire column volume is not available to the liquid and so Equation 26-6 must be modified to
The average linear rate of solute migration through the column Ii (usually cm/s) is _
X
CMVM CMVM
--
To relate the rate of migration of a solute to its distribution constant, we express the rate as a fraction of the velocity of the mobile phase:
The retention factor k is an important experimental quantity widely used to compare the migration rates of solutes in columns' The reason that k is so useful is that it does not depend on column geometry or on volumetric flow rate. This means that for a given combination of solute, mobile phase, and stationary phase any column of any geometry operated at any mobilephase flow rate will give the same retention factor. For solute A, the retention factor kA is defined as
moles of solute in mobile phase total moles of solute
The total numher of moles of solute in the mobile phase is equal to the molar concentration, cM, of the solute in that phase multiplied by its volume. v,,,. Similarly. the number of moles of solute in the stationary phase is given by the product of the concentration, cs, of the solute in the stationary phase and its volume. Vs. Therefore.
...A.
_..
1 + csV,lcMVM
26B-5 The Rate of Solute Migration: The Retention Factor
v=uX
Experimentally, in chromatography the mobile-phase flow is usually characterized by th" volumetric flo" rate F (em '/min) at the column outlet. For an open tu-
X
U
Substitution of Equation 26-2 into this equation gives an expression for the rate of solute migration as a function of its distribution constant as well as a function of the volumes of the stationary and mobile phases:
kA
26B-3 The Relationship between Volumetric Flow Rate and Linear Flow Velocity
=
+ e,;Vs
26B-4 The Relationship between Retention Time and Distribution Constant
This fraction, however, equals the average number of moles of solute in the mohile phase at any instant divided by the total number of moles of solute in the column:
where L is the length of the column packing. Similarly, the average linear velocity u of the mobile-phase molecules is
iI = u
The two volumes can be estimated from the method by which the column is prepared.
mobile phase)
v =tR
component mixture. The small peak on the left represents a solute that is not retained on the column and so reaches the detector almost immediately after elution is begun. Thus, its retention time tM is approximately equal to the time required for a molecule of the mobile phase to pass through the column.
where E: is the fraction of the total column volume available to the liquid (column porosity).
iI = u X (fraction of time solute spends in
L
FIGURE 26-4 A typical chromatogram for a two-
KAVS
=~VM
where KA is the distribution constant for solute A. Substitution of Equation 26-9 into 26-8 yields _
v=UX---.
1
I
+
kA
410 the older literature. this constant was calkd the capacity factor and symbolized by k'. In 1993, bowever, the lUPAC Commission on Analytical Nomenclature recommeoded that this constant be termed (he relention facror and symbolized by k.
_
To show how kA can be derived from a chromatogram, we substitute Equations 26-4 and 26-5 into Equation 26-10:
two solutes into Equation 26-14 gives an expression that permits the determination of " from an experimental chromatogram:
L L I -=-x---tR tM 1+ kA
a=
(tR)B - tM (tR)A - tM
In Scction 260-2, we show how we use the selectivity and retention factors to compute the resolving power of a column. Note that the time spent in the stationary phase, tR - tM, is sometimes called the adjusted retention time and given the symbol t". As shown in Figure 26-4, tR and tM are readily obtained from a chromatogram. The retention factor is then found from these quantities and Equation 26-12. A retention factor much less than unity means that the solute emerges from the column at a time near that of the void time. When the retention factor is larger than perhaps 20 to 30, elution times become inordinately long. Ideally, separations are performed under conditions in which the retention factors for the solutes in a mixture lie in the range between I and 10. Optimization of separations (see Section 260) is then done by optimizing k values for the components of interest.
268-6 Relative Migration Rates: The Selectivity Factor The selectivity factor a of a column for the two solutes A and B is defined as
where KB is the distribution constant for the more strongly retained species Band KA is the constant for the less strongly held or more rapidly eluted species A. According to this definition, " is always greater than unity. Substitution of Equation 26-9 and the analogous equation for solute B into Equation 26-13 provides a relationship between the selectivity factor for two solutes and their retention factors:
where kB and kA are the retention factors for Band A. respectively. Substitution of Equation 26-l2 for the
26C
BAND BROADENING AND COLUMN EFFICIENCY
The efficiency of a chromatographic column is affected by the amount of band broadening that occurs as a compound passes through the column. Before defining column efficiency in more quantitative terms, let us examine the reasons that bands become broader 'as they move down a column. ' 26C-1 The Rate Theory of Chromatography The rate theory of chromatography describes the shapes and breadths of elution bands in quantitative terms based on a random-walk mechanism for the migration of molecules through a column. A detailed discussion of the rate theory is beyond the scope of this text. We can, however, give a qualitative picture of why bands broaden and what variables improve column efficiency.s If you examine the chromatograms shown in this and the next chapter, you will see that the elution peaks look very much like the Gaussian or normal error curves (see Appendix I). As shown in Appendix I, Section a I B-1, normal error curves are rationalized by assuming that the uncertainty associated with any si~gle meas~rement is the summation of a much larger number of small, individually undetectable and random uncertainties, each of which has an equal probability of being positive or negative. In a similar way, the typical Gaussian shape of a chromatographic band can be attributed to the additive combination of the random motions of the various molecules as they move down the column. We assume in the following discussion that a narro\\ zone has been introduced so that
the injection width is not the limiting factor determining the overall width of the band that elutes. It \S Important to realize that the widths of eluti~g bands can never be narrower than the width of the IllJectlon zone. It is instructive to consider a single solute molecule as it undergoes many thousands of transfers between the stationary and the mobile phases during elution. Residence time in either phase is highly irregular. Transfer from one phase to the other requires energy, and the molecule must acquire this energy from its surroundings. Thus, the residence time in a given phase may be transitory after some transfers and relatively long after others. Recall that movement down the column can occur only while the molecule is in the mobile phase. As a consequence, certain particles travel rapidly by virtue of their accidental inclUSIOnIIIthe mobIle phase for most of the time whereas others lag because they happen to be incorporated in the statIonary phase for a greater -than-average length of time. The result of these random individual processes is a symmetric spread of velocities around the mean value, which represents the behavior of the average analyte molecule. The breadth of a zone increases as it moves down the column because more time is allowed for spreading to occur. Thus, the zone breadth is dircctly related to residence time in the column and inversely related to the velocity of the mobile-phase flow. As shown in Figure 26-5, some chromatographic peaks are nonideal and exhibit tailing or fronting. In the former case the tail of the peak, appearing to the right on the chromatogram, is drawn out and the front is steepened. With fronting, the reverse is the case. A common cause of tailing and fronting is a distribution constant that varies with concentration. Fronting also arises when the amount of sample introduced onto a column is too largc. Distortions of this kind are undcsirable because they lead to poorer separations and less reproducible elution times. In the discussion that follows, tailing and fronting are assumed to be mmlmal.
26C-2 A Quantitative Description of Column Efficiency Two related terms are widely used as quantitative measures of chromatographic column efficiency: (I) plate heighr Hand (2) plare counr, or number of theorecical plares, N. The two are related by the equation
FIGURE 26-5 Illustration of fronting and tailing in chroma-
tographic peaks. where t is the length (usually in centimeters ) of the column packing. The efficiency of chromatographic columns increases as the plate count N becomes greater and as the plate height H becomes smaller. Enormous differences in efficiencies are encountered in columns as a result of differences in column type and in mobile and stationary phases. Efficiencies in terms of plate numbers can vary from a few hundred to several hundred thousand; plate heights ranging from a few tenths to one thousandth of a centimeter or smaller are not uncommon.
The genesis of the terms "plate height" and "number of theoretical plates" is a pioneering theoretical study of Martin and Synge in which they treated a chromatographic column as if it were similar to a distillation column made up of numerous discrete but contIguous narrOw layers called theorerical plates6 At each plate, equilibration of the solute between the mobile and stationary phases was assumed to take place. Movement of the solute down the column was then treated as a stepwise transfer of equilibrated mobile phase from one plate to the next.
t~
bands are often assumed to be Gaussian in shape, it is convenient to define the efficiency of a column in terms of variance per unit length of column. That is the plate height H is given by ,
Analyte profile at end of packing
] (b)
-0 E
(L
+ lu)
lI'
H=L
'0
..,~ E
H=~
i
L L
Distance
~_.
migrated
pac:in_g __
~_J== -.-.-
FIGURE 26-6 Definitionof plate height H = u'lL.
In (a) the column length is shown as the distance from the sample entrance point to the detector. In (b) the Gaussian distribution of sample molecules is shown. The plate theory successfully accounts for the Gaussian shape of chromatographic peaks and their rate of movement down a column. The theory was ultimately abandoned in favor of the rate theory, however, because it fails to account for peak broadening in a mechanistic way. Nevertheless, the original terms for efficiency have been carried over to the rate theory. This nomenclature is perhaps unfortunate because it tends to perpetuate the myth that a column contains plates where equilibrium conditions exist. In fact, the equilibrium state can never be realized with the mobile phase in constant motion. The Definition
of Plate Height
As shown in Section a lB-l of Appendix 1, the breadth of a Gaussian curve is described by its standard deviation II or its variance II '. Because chromatographic
This definition of column efficiency is illustrated in Figure 26-6a, which shows a column having a packing L em In length. Above this schematic (Figure 26-6b) is a plot showing the distribution of molecules along the length of the column at the moment the analyte peak reaches the end of the packing (that is, at the retention time). The curve is Gaussian, and the locations of L + 1lI and L - 1lI are indicated as broken vertical lines. Note that L carries units of centimeters and lI' units of centimeters squared; thus H represents a linear distance in centimeters as well (Equation 26-17). In fact, the plate height can be thought of as the length of column that contains a fraction of the analyte.that lies between Land L - lI. Because the area under a normal error curve bounded by plus or minus one standard deviation (2:llI) is about 68% of the total area, the plate height, as defined, contains approximately 34% of the analyte. The Experimental
Evaluation
of Hand N
Figure 26-7 is a typical chromatogram with time as the abscissa. The variance of the solute peak, which can be obtained by a straightforward graphical procedure, has units of seconds squared and is usually designated as T' to distinguish it from lIZ, which has units of centimeters squared. The two standard deviations T and (J are related by a T=--
LltR
where LlrRis the average linear velocity;; of the solute in centimeters per second (Equation 26-4). Figure 26-7 illustrates a method for approximating T and (J from an experimental chromatogram. Tangents at the inflection points on the two sides of the chromatographic peak are extended to form a triangle with the baseline of the chromatogram. The area of this triangle can be shown to be approximately 96% of the total area under the peak if the peak is Gaussian. In Section alB-l of Appendix 1 it is shown that about 96 % of the area under a Gaussian peak is included within plus or minus two standard deviations (2:2lI) of its maximum. Thus, the intercepts shown in Figure 26-7 occur at approximately plus or minus two standard deviations of the solute peak (:':2T) from the maximum, and W = 4T, where W is the magnitude of the base of the triangle. Substituting this relationship into Equation 26-18 and rearranging yields lI=--
LW 4tR
Substitution of this equation for gives
II
into Equation 26-17
LW' H=16t~ To obtain N, we substitute into Equation 26-16 and rearrange to get
Thus, N can be calculated from two time measurements, tR and W; to obtain H, the length of the column packing L must also be known. Note that these calculations are only approximate and assume Gaussian peak shapes. Another method for approximating N, which some workers believe to be more reliable, is to determine Wl/" the width of the peak at half its maximum height. The plate count is then given by N =
5.54(~)2 W1i2
r
FIGURE 26-7 Detennination of the number of plates N =
16(~
Because the experimental determinations of H and N described here are based on Gaussian chromatographic peaks, the calculations are considered estimates. More accurate methods for dealing with skewed Gaussian peaks have been described in the literature; they are based on finding the variance of the peaks using statistical second-moment calculations. 7
Symbol
Variable
Usual Urnts
Linear velocity of mobile phase Diffusion coefficientin mobile phase*
u
D M**
cms-t cm2s~1
Diffusion coefficient in stationary
D,
cm2s-1
k
unitless
dp
cm cm
phase* Retention factor (&jnation 26-12) Diameter of packing particles Thickness of liquid coating on stationary phase *Increases as temperature
d(
increases and viscosity decreases.
*"'In liquids, DM values for small and medium-size molecules are on the order of 10 -5 em! s -1; for gases, DM values are -~10 5 times larger.
The plate count N and the plate height H are widely used in the literature and by instrument manufacturers. They can be quite useful quantities in comparing separating power and efficiencies among columns. However, for these numbers to be meaningful in comparing columns, it is essential that they be determined with the same compound. 26C-3 Kinetic Affecting
Variables
Column
Efficiency
Band broadening reflects a loss of column efficiency. The slower the rate of mass-transfer processes occurring while a solute migrates through a column, the broader the band at the column exit. Some of the variables that affect mass-transfer rates are controllable and can be exploited to improve separations. Table 26-2 lists the most important of these variables. Their effects on column efficiency, as measured by plate height H, arc described in the paragraphs that follow. The Effect of Mobile-Phase
Flow Rate
The extent of band broadening depends on the length of time the mobile phase is in contact with the stationary phase, which in turn depends on the flow rate of the mobile phase. For this reason, efficiency studies have generally been carried oul by determining H (by means ~1. P. foley and 1. G. Dorsey, Anal. Chern., 1983.55,730: I Chrnmatogr Sci .. tqs.t, 22, 40. For a spreadsheet approach tll nonideal peak shapes. see S. R. Crouch and F. 1. Holler, Applicaciulls of ',,/icro:wti' Excel in Allulytil:tll Chemistry. Rdm 2000). (Adapted from High Performance Liquid Chromafography, 2nd ed., S. Lindsay and J. Barnes, eds., New York:Wiley,1992. With permission.)
Figure 28·1 reveals that the various liquid chromatographic procedures are complementary in their application. Thus, for solutes having molecular masses greater than 10,000, size-exclusion chromatography is often used, although it is now becoming possible to handle such compounds by reversed-phase chromatography as well. For lower-molecular-mass ionic species, ion-exchange chromatography is widely used. Small polar but nonionic species are best handled by reversed-phase methods. In addition, this procedure is frequently useful for separating members of a homologous series. Adsorption chromatography was once used for separating nonpolar species, structural isomers, and compound classes such as aliphatic hydrocarbons from aliphatic alcohols. Because of problems with retention reproducibility and irreversible adsorption, adsorption chromatography with solid stationary phases has been largely replaced by normal-phase (bonded-phase) chromatography. Among the special. ized forms of LC, affinity chromatography is widely used for isolation and preparation of biomolecules, and chiral chromatography is employed for separating enantiomers.
The discussion on band broadening in Section 26C- 3 is generally applicable to LC. Here, we illustrate the important effect of stationary-phase particle size and describe two additional sources of zone spreading that are sometimes of considerable importance in LC. 288-1 Effects of Particle Size of Packings The mobile-phase mass-transfer coefficient (see Table 26-3) reveals that eM in Equation 26-23 is directly related to the square of the diameter dp of the particles making up a packing. Because of this, the efficiency of an LC column should improve dramatically as the particle size decreases. Figure 28-2 is an experimental demonstration of this effect, where it is seen that a reduction of particle size from 45 to 6 j.1mresults in a tenfold or more decrease in plate height. Note that none of the plots in this figure exhibits the minimum that is predicted by Equation 26·23. Such minima are, in fact, observable in LC (see Figure 26-8a) but usually at flow rates too low for most practical applications.
2.0 Linear velocity.
em/s
Effect of particle size of packing and flow rate on plate height H in LC.Column dImensIons: 30 cm x 2.4 mm. Solute: N,N'-diethyl-p-aminoazobenzene. Mobile phase: mixture of hexane, methylene chloride, isopropyl alcohol. (From R. E. Majors, J. Chromatogr. SCI., 1973, 11,88. With permission.) FIGURE
28-2
FIGURE 28-3
28B-2 Extracolumn Band Broadening in LC In LC. significant band broadening sometimes occurs outside the column packing itself. This extracolumn band broadening occurs as the solute is carried through open tubes such as those found in the injection system, the detector region, and the piping connecting the various components of the system. Here, broadening arises from differences in flow rates between layers of liquid adjacent to the wall and the center of the tube. As a result, the center part of a solute band moves more rapidly than the peripheral part. In GC, extracolumn spreading ISlargely offset by diffusion. Diffusion in liquids. however, is significantly slower, and band broadening of this type often becomes noticeable. It has been shown that the contribution of extracolumn effects H" to the total plate height is given by' H
,
=
"
7rr-u 24D M
(28-1)
where u is the linear-flow velocity (cm/s), r is the radius of the tube (cm), and DM is the diffusion coefficient of the solute in the mobile phasc (cm2/s). Extracolumn broadening can become quite serious when small-bore columns are used. Here, the radius of the extracolumn components should be reduced to
o.o!O inch or less, and the length of extracolumn tubing made as small as feasible to minimize this source of broadening.
Pumping pressures of several hundred atmospheres are required to achieve reasonable flow rates with packings of 3 to !O 11m,which are common in modern LC. Because of these high pressures, the equipment for HPLC tends to be more elaborate and expensive than equipment for other types of chromatography. FIgure 28-3 is a diagram showing the important components of a typical LC instrument. 28C-1 Mobile-Phase Reservoirs and Solvent Treatment Systems A modern LC apparatus is equipped with one or more glass reservoirs, each of which contains SOO mL or more of a solvent. Provisions are often included to remove dissolved gases and dust from the liquids. Dissolved gases can lead to irreproducible flow rates and band spreading; in addition, both bubbles and dust interfere with the performance of most detectors. Degassers may consist of a vacuum pumping system, a distillation system, a device for heating and stirring, or as
Block diagram showing components of a typical apparatus for HPLC. (Courtesy
of Perkin-ElmerCorp., Norwalk, Cl). shown in Figure 28-3, a system for sparging, in which the dissolved gases are swept out of solution by fine bubbles of an inert gas that is not soluble in the mobile phase. Often the systems also contain a means of filtering dust and particulate matter from the solvents to prevent these particles from damaging the pumping or injection systems or clogging the column. It is not necessary that the degassers and filters be integral parts of the HPLC system as shown in Figure 28-3. For example, a convenient way of treating solvents before introduction into the reservoir is to filter them through a millipore filter under vacuum. This treatment removes gases as well as suspended matter. An elution with a single solvent or solvent mixture of constant composition is termed an isocratic elution. In gradient elution, two (and sometimes more) solvent systems that differ significantly in polarity are used and varied in composition during the separation. The ratio of the two solvents is varied in a preprogrammed way, sometimes continuously and sometimes in a series of steps. Modern HPLC instruments are often equipped with proportioning valves that introduce liquids from two or more reservoirs at ratios that can be varied continuously (Figure 28-3). The volume ratio of the solvents can be altered linearly or exponentially with time.
Figure 28-4 illustrates the advantage of a gradient eluent in the separation of a mixture of chlorobenzenes. Isocratic elution with a SO:SO (v/v) methanolwater solution yielded the curve in Figure 28-4b. The curve in Figure 28-4a is for gradient elution, which was initiated with a 40:60 mixture of the two solvents; the methanol concentration was then increased at the rate of 8%/min. Note that gradient elution shortened the time of separation significantly without sacrificing the resolution of the early peaks. Note also that gradient elution produces effects similar to those produced by temperature programming in gas chromatography (see Figure 27-7). 28C-2 Pumping Systems The requirements for liquid chromatographic pumps include (1) the generation of pressures of up to 6000 psi (lb/in.'), or 414 bar, (2) pulse-free output, (3) flow rates ranging from 0.1 to 10 mUmin, (4) flow reproducibilities of O.S% relative or better, and (S) resistance to corrosion by a variety of solvents. The high pressurcs
f7I lQ.J
Simularion: Learn more about liquid chromatography.
Two major types of pumps are used in LC: the serew-dnven synnge type and the reciprocating pump. ReCIprocatIng pumps are used in almost all modern commercial chromatographs.
dition. the output is pulse free. Disadvantages include limited solvent capacity (- 250 mL) and considerable inconvenience when solvents must be changed. Flow Control and Programming
Reciprocating I. Benzene 2. Monochlorobenzene 3. Orthodichlorobenzene 4. 1,2,3-trichlorobenzene 5. 1,3,5-trichlorohenzene
6. 1.2.4-trichlorobenzene 7. 1,2,3,4-tetrachlorobenzene
8. l,2,4.5-tetrachlorobenzene 9. Pentachlorobenzene 10. Hexachlorobenzene
Pumps
Reciprocating pumps usually consist of a small chamber in which the solvent is pumped by the back and forth motion of a motor-driven pis Ion (see Figure 28-5). Two ball check valves, which open and close alternatelv. control the /low of solvent into and out of a cylinde~. The solvent is in direct contact with the piston. As an alternative, pressure may he transmitted to the solvent via a /lexible diaphragm. which in turn is hydraulically pumped by a reciprocating piston. Reciprocating pumps have the dIsadvantage of producing a pulsed /low, which must be damped because the pulses appear as baseline noise on the chromatogram. Modern LC instruments use dual pump heads or elliptical cams to minimize such pulsations. The advantagesy! reciprocatIng pumps include their small internal volume (35 to 400 flL). their high output pressures (up to 10.000 psi). thelf adaptabIlity to gradient elution. their large solvent capacities. and their constant /low rates. which are largely independent of column back pressure and solvent viscosity. Displacement
Pumps
Displacement pumps usually consist of large, syringelIke chambers equipped with a plunger activated by a screw-driven mechanism powered by a stepping motor. DIsplacement pumps also produce a flow that tends to be independent of viscosity and back pressure. In adFIGURE28-4 Improvement in separation effectiveness by gradient elution. Column: 1 m x 2.1 mm inside-diameter. precision-bore slainless steel; packing: 1% Permaphase" ODS (C,al.Sample: 5 ~Lof chlorinated benzenes in isopropanol. Detector: UV photometer (254 nm). Conditions: temperature. 60°C. pressure. 1200 psi. (From J. J. Kirkland. Modem Practice of LiqUid Chromatography. p. 88. New
York:Interscience. 1971. Reprinted by permission of John Wiley& Sons. Inc.) generated by liquid chromatographic pumps are not an explosion hazard because liquids are not verv compressible. Thus. rupture of a component results ~nlv in solvent leakage. However. such leakage may constitute a fire or environmental hazard with some solvents.
Systems
As part of their pumping systems, many commercial instruments are equipped with computer-controlled devices for measuring the flow rate hy determining the pressure drop across a restrictor located at the pump outlet. Any difference in signal from a preset value is then used to increase or decrease the speed of the pump motor. Most instruments also have a means for varying the composition of the solvent either continuously or in a stepwise fashion. For example. the instrument shown in Figure 28-3 contains a proportioning valve that permits mixing of up to four solvents in a pre programmed and continuously variable way.
28C-3 Sample-Injection
Systems
Often. the limiting factor in the precision of liquid chromatographic measurements is the reproducibility with which samples can he introduced onto the column packing. The problem is exacerbated hy band broadening, which accompanies a lengthy sample injection plug. Thus, sample volumes must be very small- a few tenths of a microliter to perhaps 500 flL. Furthermore, it is convenient to he able to introduce the sample without depressurizing the system. The most widely used method of sample introduction in LC is based on sampling loops, such as that shown in Figures 28-6 and 27-5. These devices are often an integral part of liquid-chromatographic equipment and have interchangeable loops providing a choice of sample sizes from 1 flL to 100 flL or more. Sampling loops of this type permit the introduction of samples at pressures up to 7000 psi with relative standard deviations of a few tenths of a percent. Most chromatographs today are sold with autoinjectors. Such units are capable of injecting samples into the LC [rom vials on a sample carousel or from microtiter plates. They usually contain sampling loops and a syringe pump for injection volumes from less than I flL to more than 1 mL. Some have controlledtemperature environments that allow for sample storage and for carrying out derivatization reactions prior to injection. Most are programma hIe to allow for unattended injections into the LC system.
FIGURE28-6 A sampling loop for Le. With the valve handle as shown on the left, the loop is filledfrom the syringe. and the mobile phase flows from pump to column. When the valve is placed in the position on the right. the loop is inserted between the pump and the column so that the mobile phase sweeps the sample onto the column. (Courtesy at Beckman-Coulter. Inc.)
Liquid-chromatographic columns' are usually constructed from smooth-bore stainless steel tubing. HPLC columns are sometimes made from heavywalled glass tubing and polymer tubing, such as polyetheretherketone (PEEK). In addition, stainless steel columns lined with glass or PEEK are also available. Hundreds of packed columns differing in size and packing are available. The cost of standard-sized. nonspeciality columns ranges from $200 to more than $500. Specialized columns, such as chiral columns, can cost more than $1000.
'For more mfdrmathHl. s K' > NH," > Na' > H' > Li'. For divalent cations, the order is Ba" > Pb" > Sr" > Ca" > Ni" > Cd'- > Cu2+ > Co" > Zn" > Mg" > VO,". For anions, K" for a strong-base resill decreases in the order sol' > C,O/- > 1-> NO] - > Iir" > CI- > HCO, - > CH,CO, - > OH" > F . This sequence somewhat depends on the type of resin and reaction conditions and should thus be considered only approximate.
(28-6) 28F-2
Here, [RSO] -B -], and [RSO, -H-L arc concentrations (strictiy activities) of B' and H' in the solid phase. Rearranging yields
During the elution, the aqueous concentration of hydrogen ions is much larger than the concentration of the singly charged B' ions in the mobile phase. Also, the exchanger has an enormous number of exchange sites relative to the number of B ' ions being retained. Thus, the overall concentrations [H'Lq and [RSOJ-H'l, arc not affected signilicantly by shifts in the equilibrium 28-5 Therefore, when [RSO, - H' j, 'b [RSOJ -B 'L and [H'Lq 'b [B 'laq, the right-hand side of Equation 2X-7is substantially constant. and we ean write
where K is a constant that corresponds to the distribution constant as defined by Equations 26-1 and 26-2. All of the equations in Table 26-5 (Section 26E) can then bc applied to ion-exchange chromatography in
lon-Exchange
Packings
Historically, ion-exchange chromatography was performed on small, porous beads formed during emulsion copolymerization of styrene and divinylbenzene. The presence of divinylbenzene (usually -8%) results in cross-linking, which makes the beads mechanically stable. To make the polymer active toward ions, acidic or basic functional groups are bonded chcmieally to the structure. The most common groups are sulfonic acid and quaternary amines. Figure 28-22 shows the structure of a strong acid resin. Note the cross-linking that holds the linear polystyrene molecules together. The other types of resins have similar structures except for the active functional group. Porous polymeric particles are not entirely satisfactory for chromatographic packings because of the slow rate of diffusion of analyte molecules through the micropores of the polymer matrix and because of the compressibility of the matrix. To overcome this problem, two ncwer types of packings have been developed and arc in more general use than the porous polymer type. One is a polymeric bead packing in which the bead surface is coated with a synthetic ion-exchange
28-22 Structure of a cross-linked polystyrene ion-exchange resin. Similar resins are used in which the -SO, -H' group is replaced by -COO 'W, ~NH;OH', and -N(CH,), +OH groups.
FIGURE
resin. A second type of packing is prepared by coating porous mieroparticles of silica, such as those used m adsorption chromatography, With a thm film of the exchanger. Particle diameters are typically 3-10 J.lm. With either type, faster diffusion in the polymer film leads to enhanced efficiency. Polymer-based packmgs have higher capacity than silica-based packings and can bc used over a broad pH range. Silica-based ,on exchangers give higher efficiencies, but suffer from a limitcd pH range of stability and an incompatiblhty WIth suppressor-based detection (see next sectIOn). 28F-3
Inorganic-Ion
Chromatography
The mobile phase in ion-exchange chromatography must have the same general properties required for other types of chromatography. That is, it must dissolve the sample, have a solvent strength that leads to reasonable retention times (appropriate k values), and mteract with solutes in such a way as to lead to selectivity (suitable" values). The mohile phases in ion-exchange chromatography arc aqueous solutions that may contain moderate amounts of methanol or other watermiscible organic solvents; these mobile phases also contain ionic species, often in the form of a buffer. Solvent strength and selectivity are determined by the kmd and concentration of these added ingredients. In general, the ions of the mobile phase compete with analyte ions for the active sites on the ion-exchange packing. Two types of ion chromatography are currently in use: suppressor,based and sillgle-columll. They differ in the method used to prevent the conductivity of the eluting electrolyte from interfering with the measurement of analyte conductivities.
.,.
Ion Chromatography
Based on Suppressors
As noted earlier, the widespread application of ion chromatography for the determination of inorganic species was inhibited by the lack of a good general detector, which would permit quantitative determmallon of ions on the basis of chromatographic peak areas, Conductivity detectors are an obvious choice for this task. Thev can be highly sensitive, they are unIversal for charg~d species, and as a general rule, they respond in a predictable way to concentration changes: Furthermore, such detectors are simple, inexpenSive to construct and maintain, easy to miniaturize, and ordInarily give prolonged, trouble-free service. The only limitation to conductivity detectors proved to be a serious one, which delayed their general use. This limitation arises from the high electrolyte concentration required to elute most analyte ions in a reasonablc time. As a result, the conductivity from the mobIle-phase components tends to swamp that from analyte ions, which greatly reduces the detector sensitivity. In 1975 the problem created by the high conductance of eluents was solved by the introduction of an eluent suppressor columll immediately following. the ionexchange column." The suppressor column IS packed with a second ion-exchange resin that effectIvely converts the ions of the eluting solvent to a molecular species of limited ionization without affecting the conductivity due to analyte ions. Forexample, when cations are being separated and determined, hydrochlortc aCId IS chosen as the eluting reagent, and the suppressor column is an anion-exchange resin in the hydroxide form.
The product of the reaction in the supprcssor is water. That is H+(aq)
+ CI (aq) + rcsin-OH
(s)-.
resin' CI
(s)
+ ficO
The analyte cations are not retained by this second column. For anion separations. the suppressor packing is the acid form of a cation-exchange resin and sodium bicarbonate or carbonate is the eluting agent. The reaction in the suppressor is Na+(aq)
+ HCO
j
(aq)
+ resin'H;
Concentrations. P-
ppm 3
Formate BrO,' Ct'
S 10 4
NO,' HPO,'
III 30
Br 1';0,' S0.s:-
30 30 25
Concentrations, Ca2+ t
ppm J
Mg: Sr:"!+
J 10
Ba2+
25
~ ~~
Qualitative
TLC
The data from a single chromatogram usually do not provide sufficient information to permit identification of the various species present in a mixture because of
~
s
\:. 4
o.ij
Two-dimensional thin-layer chromatogram (silicagel) of some amino acids. Solvent A: toluene, 2-chloroethanol, pyridine. Solvent B: chloroform, benzyl alcohol, acetic acid. Amino acids: (1)aspartic acid, (2)glutamic acid, (3)serine, (4)l3-alanine,(5)glycine, (6)alanine. (7)methionine, (8)valine, (9) isoleucine, (10)cysteine.
FIGURE 28-31
of their positions with those of standards. Imaging techniques have been used for quantitative analysis of twodimensional separations.'" Quantitative
Analysis
A semiquantitative estimate of the amount of a componen t present can be obtained by comparing the area of a spot with that of a standard. More accurate results can be obtained by scraping the spot from the plate, extracting the analyte from the stationary-phase solid, and measuring the analyte by a suitable physical or chemical method. In a third method, a scanning densitometer can be used to measure fluorescence or absorption of the spot.
•Answers are provided at the end of the book for problems marked with an asterisk.
28-1
,,)
:u'
of Thin-Layer
~
~~"'-~
8 ~
50
C
~
c..
FIGURE29-11 Comparison of extraction efficiencies obtained by using CO, and CO, modified with methanol. A soil sample was used. Allextractions were for 30 min. Diuron is a common herbicide that is an aromatic substituted derivative of urea. TCDDis 2,3,7,8-tetrachlorodibenzo-p-dioxin. LASis linear alkylbenzenesulfonate detergent.
Two types of methods have been used to collect analytes after extraction: off-line and on-line. In off-line collection, which is the simpler of the two, the analytes are collected by immersing the restrictor in a few milliliters of solvent and allowing the gaseous supercritical fluid to escape into the atmosphere (see Fig-
Material
Analyte*
Soils River sediments Smoke, urban dust Railroad bed soil Foods Spices, bubble gum Serum Coal, flyash Polymers Animal tissue
Pesticides PAHs PAHs PCBs,PAHs Fats Aromas and fragrances Cholesterol PCBs, dioxins Additivesand oligomers Drug residues
ure 29-10). Analytes have also been collected on adsorbents, such as silica. The adsorbed analytes are then eluted with a small volume of a liquid solvent. In either case the separated analytes are then identified by any of several optical, electrochemical, or chromatographic methods. In the on-line method, the effluent from the restrictor, after depressurization, is transferred directly to a chromatograph system. In most cases the latter is a GC or an SFC instrument, although occasionally an HPLC system has been used. The principal advantages of an on-line system are the elimination of sample handling between the extraction and the measurement and the
* Answers ~
Supercritical Fluid
Extradion Time, Off-line (1),
CO, CO,15%MeOH
CO, CO,lMeOH CO,lMeOH
CO, CO, CO, CO, CO,
min
On-line (2)
20 120 15 45 12 10 30 15 15
1 1 2 1 1 2 1 2 2 1
9
potential for enhanced sensitivity because no dilution of the analyte occurs. 29C-5 Typical
Applications
of SFE
Hundreds of applications of SFE have appeared in the literature. Most applications are for the analysis of environmental samples. Others have been for the analysis of foods, biomedical samples, and industrial samples. Table 29-3 provides a few typical applications of off-line and on-line SFE. In addition to the analytical uses of SFE, there are many preparative and isolation uses in the pharmaceutical and polymer industries.
are provided at the end of the book for problems marked with an asterisk.
Problems with this icon are best solved using spreadsheets.
29·1 Define (a) critical temperature and critical pressure of a gas. (b) supercritical fluid. 29-2 What properties of a supercritical fluid are important in chromatography? 29-3 How do instruments for SFC differ from those for (a) HPLC and (b) GC? 29-4 Describe the effect of pressure on supercritical fluid chromatograms. 29-5 List some of the advantageous properties of supercritical CO, as a mobile phase for chromatographic separations.
29-6 Compare SFC with other column chromatographic
;'/;'
~J;.£:::~::: .:~.::/;
29-7 For supercritical carbon dioxide, predict the effect that the following changes will have on the elution time in an SFC experiment: (a) increasing the flow rate (at constant temperature and pressure). (b) increasing the pressure (at constant temperature and flow rate). (c) increasing the temperature (at constant pressurc and flow rate). 29-8 For SFE, differentiate between (a) on-line and off-line processes. (b) static and dynamic extractions. 29-9 List the advantages and any disadvantages of SFE compared to liquid-liquid extractions.
[n capillary electrophoresis and electrochromatography, separations occur in a buffer-filled capillary tube under the influence of an electric field as seen in the schematic of Figure 30-1. Separations in field-flow fractionation, on the other hand, occur in a thin ribbon-like flow channel under the influence of a sedimentation. electrical, or thermal field applied perpendicular to the flow direction.
30A
Challenge Problem
29-11 In a recent paper, Zheng and coworkers (J. Zheng, L. T. Taylor, J. D. Pinkston, and M. L. Mangels, J. Chromatogr. A, 2005, 1082, 220) discuss the elution of polar and ionic compounds in SFC. (a) Why are highly polar or ionic compounds usuallv not eluted in SFC? (b) What types of mobile-phase additives have been' used to improve, the elution of highly polar or ionic compounds? . (c) Why is ion-pairing SFC not often used? (d) Why arc ammonium salts sometimes added as mobile-phase modifiers in SFC? (e) The authors describe an SFC system that uses mass spectrometry (MS) as a detector. Discuss the interfacing of an SFC unit to a mass spectrometer. Compare the compatibility of SFC with MS to that of HPLC and GC with MS. (f) The authors studied the effect of column outlet pressure on the elution of sodium 4-dodecylbenzene sulfonate on three different stationary phases with five mobile-phase additives. What effect was observed, and what was the explanation for the effect? (g) What elution mechanisms were considered by thc authors? (h) Which mobile-phase additive gave the fastest elution of the sulfonate salts? Which provided the longest retention times? (i) Did a silica column give results similar to or different from a cyano bondedphase column?
·'~K~
:r,:
>,,{:i::'
AN OVERVIEW OF ELECTROPHORESIS
Electrophoresis is a separation method based on the differential rate of migration of charged species in ao applied dc electric field. This separation technique was first developed by the Swedish chemist Arne Tiselius in the 1930s for the study of serum proteins; he was awarded the 1948 Nobel Prize in Chemistry for this work. Electrophoresis on a macro scale has been applied to a variety of difficult analytical separation problems: inorganic anions and cations, amino acids, catecholamines, drugs, vitamins, carbohydrates, peptides, proteins, nucleic acids, nucleotides, polynucleotides, and numerous other species. A particular strength of electrophoresis is its unique ability to separate charged macromolecules of interest in biochemical, biological, and biomedical research and the biotechnology industry. For many years, electrophoresis has been the powerhouse method for separating proteins (enzymes, hormones, antibodies) and nucleic acids (DNA, RNA) with unparalleled resolution. For example, to sequence DNA it is necessary to distinguish between long-chain polynucleotides that have as many as perhaps 200 to 500 bases and that differ by only a single nucleotide. Only electrophoresis has sufficient resolving power to handle this problem. Without electrophoresis, for example, the Human Genome Project would have been nearly impossible because human DNA contains some three billion nucleotides. An electrophoretic separation is performed by injecting a small band of the sample into an aqueous buffer solution contained in a narrow tube or on a flat porous support medium such as paper or a semisolid gel. A high voltage is applied across the length of the buffer by means of a pair of electrodcs located at each
.~~~::r~~~~~~~:~~~~~~~:;~ .thomson~u.com/ch~~/sl< interactive.t\!torials, s4iit!1ations,
g YOlltg ,exercise&i:t·
~i:::"
species are eluted from one cnd of the capillary. so quantitative detectors, similar to those found in highperformance liquid chromatography (HPLC), can bc used instead of the cumbersome staining techniqucs of slab electrophoresis. I
FIGURE30-1 Schematic of a capillary electrophoresis system.
30B-1 Migration Rates in CE end of the buffer. This field causes ions of the sample to migrate toward one or the other of the electrodes. The rate of migration of a given species depends on its charge and its size. Separations are then based on differences in charge-to-size ratios for the various analytes in a sample. The larger this ratio, the faster an ion migrates in the electric field.
Electrophoretic separations are currently performed in two quite different formats: one is called slab electrophoresis and the other capillary electrophoresis. The first is the classical method that has been used for many years to separate complex, high-molecular-mass species of biological and biochemical interest. Slab separations are carried out on a thin flat layer or slab of a porous semisolid gel containing an aqueous buffer solution within its pores. This slab has dimensions of a few centimeters on a side and, like a chromatographic thinlayer plate, is capable of separating several samples simultaneously. Samples are introduced as spots or bands on the slab, and a dc electric field is applied across the slab for a fixed period. When the separations are complete, the field is discontinued and the separated species are visualized by staining in much the same way as was described for thin-layer chromatography in Section 281-2. Slab electrophoresis is now the most widely used separation tool in biochemistry and biology. Monographs, textbooks, and journals in the life sciences contain hundreds of photographs of developed electrophoretic slabs. Capillary electrophoresis, which is an instrumental version of electrophoresis, was dcveloped in the mid-to-late 1980s. It has bccome an important tool for a wide variety of analytical separation problems. In many cases, this new method of performing electrophorctic separations is a satisfactory substitute for slab electrophoresis with several important advantages that are described later in this chapter.
30A·2 The Basis for Electrophoretic Separations The migration rate v of an ion (cm/s) in an electric field is equal to the product of the field strength E (V cm '1) and the electrophoretic mobility M, (cm2 V-I S'I). That is,
The electrophoretic mobility is in turn proportional to the ionic charge on the analyte and inversely proportional to frictional retarding factors. The electric field acts on only ions. If two species dil'fej cither in charge or in the frictional forces they experience while moving through the buffer, they will be separated from each other. Neutral spccies are not separated. The frictional retarding force on an analyte ion is determined by the size and shape of the ion and the viscosity of the migration medium. For ions of the same size, the greater the charge, the greater the driving force and the faster the rate of migration. For ions of the same charge, the smaller the ion, the smaller the frictional forces and the faster the rate of migration. The ion's charge-to-size ratio combines these two effects. Note that in contrast to chromatography, only one phase is involved in an electrophoretic separation.
As Equation 30-1 shows, the migration rate of an ion v depends on the electric field strength. The electric field in turn is proportional to the magnitude of the applied voltage V and inversely proportional to the length L over which it is applied. Thus
This relationship indicates that high applied voltagcs are desirable to achieve rapid ionic migration and a fast separation. It is desirable to have rapid separations, but it is even more important to achieve highresolution separations. So we must examine the factors that determine resolution in electrophoresis. 30B-2 Plate Heights in CE In chromatography, both longitudinal diffusion and mass-transfer resistance contribute to band broadening. However, because only a single phase is used in electrophoresis, in theory only longitudinal diffusion needs to be considered. In practice, however, Joule heating can add variance as well as the injection process. Although CE is not a chromatographic process, separations are often described in a manncr similar to chromatography. For example, in electrophoresis, we caleulate the plate count N by MeV
N=W As useful as conventional slab electrophoresis is, this type of electrophoretic separation is typically slow, labor intensive, and difficult to automate. Slab electrophoresis does not yield very precise quantitative information. During the mid-to-late 1980s, there was explosive growth in research and application of electrophoresis performed in capillary tubes, and several commercial instruments appeared. Capillary electrophoresis (CE) yields high-speed, high-resolution separations on exceptionally small sample volumes (0.1 to 10nL in contrast to slab electrophoresis, which requires samples in the flL rangc). Additionally, the separated
where D is the diffusion coefficient of the solute (cm' S'I). Because resolution increases as the plate count increases, it is desirable to use high applied voltages to For additional discussion of CE, see Analysis and Detection by Capillllr.r Electrophoresis, M. L. Marina, A. Rios. and M. Valcarcel, eds., Vol. 45 of Comprehensive Analytical Chemistry, D. Barcelo. ed., Amsterdam: Elsevier, 2005; Capillary Electrophoresis of Proteins and Peptides. M. A Strege and A. L L.agu. eds., Totowa. NJ: Humana Press. 2004; Clinical and Forensic Applications of Capil1ary Electrophoresis. J. R. Petersen and A. A. Mohamad, eds .. Totowa. NJ: Humana Press. 2001; R. Weinberger. Practical Capillary Electrophoresis. 2nd ed .. New York: Academic Press. 2000: High Performance Capillar)' Electrophoresis. M. G. Khaledi. ed .. I
New York: Wiley. 1998.
achieve high-resolution separations. Note that for electrophoresis, contrary to the situation in chromatography, the plate count does not increase with the length of the column. With gel slab electrophoresis, joule heating limits the magnitude of the applied voltage to about 500 V. Here, one of the strengths of the capillary format compared with the slab format is realized. Bccause the capillary is quite long and has a small cross-sectional area, the solution resistance through the capillary is exceptionally high. Because power dissipation is inversely proportional to resistance (P = [2/R), much higher voltages can be applied to capillaries than to slabs for the same amount of heating. Additionally, the high surface-to-volume ratio of the capillary provides efficient cooling. As a result of these two factors, band broadening due to thermally driven convective mixing does not occur to a significant extent in capillaries. Electric fields of 100-400 V/cm are typically used. High-voltage power supplies of 10-25 kV are normal. The high fields lead to corresponding improvements in speed and resolution over those seen in the slab format. CE peak widths often approach the theoretical limit set by longitudinal diffusion. CE normally yields plate counts in the range of 100,000 to 200,000, compared to the 5,000 to 20,000 plates typical for HPLC. Platc counts of 3,000,000 have been reported for capillary zone electrophoresis of dansylated amino acids,' and plate counts of 10,000,000 have been reported for capillary gel electrophoresis of polynucleotides.'
A unique feature of CE is electroosmotic flow. When a high voltage is applied across a fused-silica capillary tubc containing a buffer solution, electroosmotic flow usually occurs, in which the bulk liquid migrates toward the cathode. The rate of migration can be substantial. For example. a 50 mM pH 8 buffer flows through a 50-cm capillary toward the cathode at approximately 5 cm/min with an applied voltage of25 kV4 As shown in Figure 30-2, the cause of electroosmotic flow is the electric double layer that develops at the silica-solution interface. At pH values higher than 3, the ~R. D. Smith.J. A. Olivares, N. T. Nguyen. and H. R. Udseth,A/laL
Chern .•
1988,60.436 J A. GUltman. A. S. Cohen. D. N. Hciger, and R. L Karger. Anal. Chern .. 1990.62,137 ~J. D. Olechno. J M. Y. Tso. 1. Thayer, and A. \\/ainright. Amer. Lab., 1990,22(171.51
The number of theoretical plates in the presence of electroosmotic flow can be found from an expression analogous to Equation 26-21:
+1
N =
FIGURE 30-2 Charge distribution at a
silica-capillary interface and resulting electroosmotic flow. (From A. G. Ewing, R. A. Wallingford,and T. M Olefirowicz, Anal. Chern., 1989, 61, 298A. Copyright 1989 American Chemical Society.)
inside wall of a silica capillary is negatively charged because of ionization of the surface silanol groups (Si-OH). Buffer cations congregate in the electrical double layer adjacent to the negative surface of the silica capillary. The cations in the diffuse outer layer of the double layer are attracted toward the cathode, or negative electrode, and because they are solvated, they drag the bulk solvent along with them. As shown in Figure 30-3, electroosmosis leads to bulk solution flow that has a flat profile across the tube because flow originates at the walls of the tubing. This profile is in contrast to the laminar (parabolic) profile observed with the pressure-driven flow encountered in HPLC. Because the profile is essentially flat, electroosmotic flow does not contribute significantly to band broadening the way pressure-driven flow does in liquid chromatography. The rate of electroosmotic flow is generally greater than the electrophoretic migration velocities of the individual ions and effectively becomes the mobile-phase pump of CEo Even though analytes migrate according to their charges within the capillary, the electroosmotic flow rate is usually sufficient to sweep all positive, neutral, and even negative species toward the same end of the capillary, so all can be detected as they pass by a common point (see Figure 30-4). The resulting electropherogram looks like a chromatogram but with narrower peaks.
The electroosmotic flow velocity v is given by an equation similar to Equation 30-1. That is,
16(~Y
where W, as in chromatography, is the peak width measured at the base of the peak. It is possible to reverse the direction of the normal electroosmotic flow by adding a cationic surfactant to the buffer. The surfactant adsorbs on the capillary wall and makes the wall positively charged. Now buffer anions congregate near the wall and are swept toward the cathode, or positive electrode. This ploy is often used to speed up the separation of anions. Electroosmosis is often desirable in certain types of CE, but in other types it is not. Electroosmotic flow
In the presence of electroosmosis, the velocity of an ion is the sum of its migration velocity ahQ. the electroosmotic flow velocity. Thus,
As a result of electroosmosis, order of elution in a typical electrophoretic separation is, first, the fastest cation followed by successively slower cations, then all the neutrals in a single zone, and finally the slowest anion followed by successively faster anions (see Figure 30-4). In some instances, the rate of electroosmotic flow may not be great enough to surpass the rate at which some of the anions move toward the anode, in which case these species move in that direction instead of toward the cathode. The migration time tm in CE is the time it takes for a solute to migrate from the point of introduction to the detector. If a capillary of total length L is used and the length to the detector is I, the migration time is tm
=
I (J-Le + J-Leofi
As shown in Figure 30-1, the instrumentation for CE is relatively simple5 A buffer-filled fused-silica capillary, typically 10 to 100 flm in internal diameter and 30 to 100 cm long, extends between two buffer reservoirs that also hold platinum electrodes. Like the capillary tubes used in gas chromatography (GC), the outside walls of the fused-silica capillary are typically coated with polyimide for durability, flexibility, and stability. The sample is introduced at one end and detection occurs at the other. A voltage of 5 to 30 kV dc is applied across the two electrodes. The polarity of this high voltage can be as indicated in Figure 3D-lor can be reversed to allow rapid separation of anions. Highvoltage electrophoresis compartments are usually safety interlocked to protect the user. Although the instrumentation is conceptually simple, significant experimental difficulties in sample introduction and detection arise due to the very small volumes involved. Because the volume of a normal capillary is 4 to 5 flL, injection and detection volumes must be on the order of a few nanoliters or less. Sample Introduction
IL
= (J-L, + J-LwlV
can be minimized by modifying the inside capillary walls with a reagent like trimethylchlorosilane that bonds to the surface and reduces the number of surface silanol groups (see Section 280-1).
FIGURE 30-4 Velocitiesin the presence of electroosmotic flow.The length of the arrow next to an ion indicates the magnitude of its velocity;the direction of the arrow indicates the direction of motion. The negative electrode is to the right and the positive electrode to the left of this section of solution.
Simulation: Learn more about capillary electrophoresis.
The most common sample-introduction methods are electrokinetic injection and pressure injection. With electrokinetic injection, one end of the capillary and its electrode are removed from their buffer compartment and placed in a small cup containing the sample. A voltage is then applied for a measured time, causing the sample to enter the capillary by a combination of ionic migration and electroosmotic flow. The capillary end and electrode are then returned to the regular buffer solution for the duration of the separation. This injection technique discriminates by injecting larger amounts of the more mobile ions relative to the slowermoving ions. In pressure injection, the sample-introduction end of the capillary is also placed in a small cup containing the sample, but here a pressure difference drives the sample solution into the capillary. The pressure difference can be produced by applying a vacuum at the de-
tector end, by pressurizing the sample, or by elevating the sample end (hydrodynamic injection). Pressure injection does not discriminate because of ion mobility, but it cannot be used in gel-filled capillaries. For both electrokinetic injection and pressure injection, the volume injected is controlled by the duration of the injection. Injections of 5 to 50 nL are common, and volumes below 100 pL have been reported. For a buffer with density and viscosity near the values for water, a height differential of 5 cm for 10 s injects about 6 nL with a 75-!lm inside-diameter capillary. Microinjection tips constructed from capillaries drawn to very small diameters allow sampling from picoliter environments such as single cells or substructures within single cells. This technique has been used to study amino acids and neurotransmitters from single cells. Other novel injection techniques have been described in the literature6 Commercial CE systems are available with thermos tatted multiposition carousels for automated sampling.
75-J.L1ll capillary
Spectrometry Absorption' Fluorescence
1-1000 1-0.01
Thermal lens'
10
Ramant Chemiluminescence
t
Mass spectrometry Electrochemical Conductivity' Potentiometry t Amperometry
1000 1':0.0001 1-0.01
Because the separated analytes move past a common point in most types of CE, detectors are similar in design and function to those described for HPLC. Table 30-1 lists several of the detection methods that have been reported for CEo The second column of the table shows representative detection limits for these detectors. Absorption Methods. Both fluorescence and absorption detectors are widely used in CE, although absorption methods are more common because they are more generally applicable. To keep the detection volume on the nanoliter scale or smaller, detection is performed on-column. In this case a small section of the protective polyimide coating is removed from the exterior of the capillary by burning or etching. That section of the capillary then serves as the detector cell. Unfortunately, the path length for such measurements is no more than 50 to 100 !1m,which restricts detection limits in concentration terms; because such small volumes are involved, however, mass detection limits are equal to or better than those for HPLC. Several cell designs have been used for increasing the measurement path length to improve the sensitivity of absorption methods. Three of these are shown in
Shim with 300-p.m hole
Capillary
"~
\ 0
ce
30-5 Three types of cells for improving the sensitivity of absorption measurements in CEo(a) a 3-mm z cell, (b) a 150-~m bubble cell, (c) a multireflection cell.
FIGURE
/-/
B. Huang. 1. J. Li, L. Zhang, 1. K. Cheng, Anal. Chern., 1996, 68.2366; S. C. Beale, Anal. Chern., 1998, 70, 279R. S. N. Krylov and N. 1. Dovichi, Anal. Chern., 2000, 72, III R; S. Hu and N. 1. Dovichi. Anal. Chern., 2002, 74, 2833.
Sources:
* Detection limits quoted have been determined with injoction volumes ranging from IX pL to 10 nL.
Detection
/
Representative Deteetion Limit * (attomoles detected)
t Mass detection limit converted from concentration using a I-nL injection volume
dete~tion limit
Figure 30-5. In the commercial detector shown in Figure 30-5a, the end of the capillary is bent into a Z shape, which produces a path length as long as ten times the capillary diameter. Increases in path length can lead to decreases in peak efficiency and thus resolution. In some cases, special lenses, such as spherical ball lenses, are inserted between the source and the z cell and between the cell and the detector.' Such lenses improve sensitivity by focusing the light into the cell and onto the detector. Figure 30-5b shows a second way to increase the absorption path length. In this example, a bubble is formed near the end of the capillary. In the commercial version of this technique, the bubble for a 50-!lm capillary has an inside diameter of 150 !1m,which gives a threefold increase in path length. A third method for increasing the path length of radiation by reflection is shown in Figure 30-5c. In this technique, a reflective coating of silver is deposited on the end of the capillary. The source radiation then undergoes multiple reflections during its transit through the capillary, which significantly increase the path length.
Source
Silver coating
-\N\J&'ZsDetector
Commercial CE systems are available with diode array detectors that allow spectra to be collected over the UV -visible range in less than 1 s. Indirect Detection. Indirect absorbance detection has been used for species of low molar absorptivity that are difficult to detect without derivatization. An ionic chromophore is placed in the electrophoresis buffer. The detector then receives a constant signal due to the presence of this substance. The analyte displaces some of these ions, just as in ion-exchange chromatography, so that the detector signal decreases during the passage of an analyte band through the detector. The analyte is then determined from the decrease In absorbance. The electropherogram in Figure 30-6 was generated by using indirect absorbance detection with 4-mM chromate ion as the chromophore; this ion absorbs radiation strongly at 254 nm in the buffer. Although the peaks obtained are negative (decreasing A) peaks, they appear as positive peaks in Figure 30-6 because the detector polarity was reversed. Fluorescence Detection. Just as in HPLC, fluorescence detection yields increased sensitivity and selec, tivity for fluorescent analytes or fluorescent derivatives.
Laser-based instrumentation is preferred to focus the excitation radiation on the small capillary and to achieve the low detection limits available from intense sources. Laser-induced-fluoreseence attachments are
30-6 Electropherogram of a six-anion mixture by indirect detection with 4-mM chromate ion at 254 nm. Peak: (1)bromide (4 ppm), (2) chloride (2 ppm). (3)sulfate (4 ppm), (4)nitrate (4 ppm), (5)fluoride (1 ppm), (6)phosphate (6 ppm).
FIGURE
sections that follow illustrate typical applications of each of these techniques. LOO-em-Iong, i.d. fused-silica
\
lOO-l'm· capillary
~£2'
1)
/~~ Melahz~fused silica
SampLe High-voltage (interlocked automated
III
r
/
30C-1 Capillary
h"~'f=
Electron
==r=:
multiplier To data system
Cryo pump
CE buffer region with injection)
FIGURE30-7 An instrument for CE/MS. The high-voltage (anode) end was maintained at 3050 kVin an electrically isolated. interlocked box. Electrical contact at the low-voltage (cathode) end was made by silver deposited on the capillary and a stainless steel sheath. This electrical contact was at 3 to 5 kVwith respect to common, which also charged the electrospray. The flow of nitrogen at -70'C for desolvation was 3 to 6 Llmin. (From R. D. Smith, J. A. Olivares, N, T. Nguyen, and H. R. Udseth, Anal. Chern., 1988, 60, 436, With permission.)
available that couple with commercial CE instruments. Laser-induced fluorescence has allowed detection of as little as 10 zeptomoles, or 6000 molecules." Electrochemical Detection. Two types of electrochemical detection have been used with CEo conductivity and amperometry. One of the problems with electrochemical detection has been that of isolating the detector electrodes from the high voltage required for the separation. One method for isolation involves inserting a porous glass or graphite joint between the end of the capillary and a second capillary containing the detector electrodes. Mass Spectrometric Detection. The very small volumetric flow rates of less than I flL/min from electrophoresis capillaries make it feasible to couple the effluent directly to the ionization source of a mass spectrometer. The most common sample-introduction and ionization interface for this purpose is currently electrospray (Section 20B-4), although fast atom bombardment, matrix-assisted laser desorption-ionization (MALDI) spectrometry, and inductively coupled plasma mass spectrometry (ICPMS) have also been used. Because the liquid sample must be vaporized before entering the mass spectrometry (MS) system,
it is important that volatile buffers be used. Capillary electrophoresis-mass spectrometry (CE/MS) systems have become quite important in the life sciences for determining large biomolecules that occur in nature, such as proteins, DNA fragments, and pep tides.' Figure 30-7 is a schematic of a typical electrospray interface coupled to a quadrupole mass spectrometer. Note that the capillary is positioned between the isolated high-voltage region and the electrospray source. The high-voltage end of the capillary was at 30 to 50 k V with respect to common. The low-voltage end was maintained at 3- 5 k V and charged the droplets. Similar electrospray instruments are available commercially coupled with either quadrupole or ion-trap mass spectrometerslO Ion-trap mass spectrometers can allow CE IMS I MS or CE I MS n operation. Figure 30-8 shows the electrospray mass spectrum obtained for vasotocin, a polypeptide having a molecular mass of 1050. Note the presence of doubly and triply charged species. With higher-molecular-mass species, ions are often observed with charges of + 12 or more. Ions with such large charges make it possible to detect high-molecular-mass analytes with a quadru"For more information on mass spectromctnc detectIOn, see 1. C Seyas and R. D. Smith, in Handbook ofCapiliary Electrophoresis, 2nd ed., 1. P. Landers, ed., Chap. 28, Boca Raton, FL: CRC Press, 1997. 10 Agilent Technologies, Wilmington, DE; Beckman Coulter, Inc .. Fullerton,CA.
200 400 600 800 1000 1200
Zone Electrophoresis
In capillary zone electrophoresis (CZE), the buffer composition is constant throughout the region of the separation. The applied field causes each of the different ionic components of the mixture to migrate according to its own mobility and to separate into zones that may be completely resolved or that may be partially overlapped. Completely resolved zones have regions of buffer between them as illustrated in Figure 30-9a. The situation is analogous to elution column chromatography, where regions of mobile phase are located between zones containing separated analytes.
ml';.
FIGURE30-8 Electrospray ionization mass spectrum for vasotocin. (From R. D. Smith, J. A. Olivares. N. 1. Nguyen, and H. R. Udseth, Anal. Chern., 1988. 60. 436. With permission.)
pole instrument with a relatively modest mass range. Typical detection limits for CE/MS are ofa few tens of fcmtomoles for molecules with molecular masses of 100,000 or more. Commercial
CE Systems
Currently, fewer than ten companies worldwide manufacture CE instruments. Some two dozen companies offer supplies and accessories for CEo The initial cost of equipment and the expense of maintenance for CE are generally significantly lower than those for ion chromatographic and atomic spectroscopic instruments. Thus, commercial CE instruments with standard absorption or fluorescencc detectors cost $10.000 to $65,0001l Addition of mass spectrometric detection can raise the cost significantly.
Capillary electrophoretic separations can be performed in several different modes. These include capillarv zone electrophoresis, capillary gel electrophoresis. capillary isoelectric focusing, capillary isotachophoresis. and micellar electrokinetic chromatography. The
Separation of Small Ions
For most electrophoretic separations of small ions, the smallest analysis time occurs when the analyte ions move in the same direction as the electroosmotic flow. Thus. for cation separations, the walls of the capillary are untreated and the electroosmotic flow and the cation movement are toward the cathode. For the separation of anions, on the other hand, the electroosmotic flow is usually reversed by treating the walls of the capillary with an alkyl ammonium salt, such as cetyl trimethylammonium bromide. The positively charged ammonium ions become attached to the silica surface, yielding a positively charged. immobile surface layer. This, in turn, creates a negatively charged, mobile solution layer, which is attracted toward the anode, reversing the electroosmotic flow. In the past, the most common method for analysis of small anions has been ion chromatography. For cations, the preferred techniques have been atomic absorption spectroscopy and ICPMS. Figure 30-10 illustrates the speed and resolution of electrophoretic separations of small anions. Here, thirty anions were separated cleanly in just more than 3 minutes. Typically, an ionexchange separation of only three or four anions can be accomplished in this brief period. Figure 30-11 further illustrates the speed at which separations can be carried out. In this example, nineteen cations were separatcd in less than 2 minutes. CE methods were once predicted to replace the more established methods because of lower equipment costs, smaller-sample-size requirements. and shorter analysis times. However, because variations in electroosmotic flow rates make reproducing CE separations difficult, LC methods and
ILl VI ;;;'J1.IE
Samples are typically contained in sample pans made of platinum, aluminum, or alumina. Platinum is most often used because of its inertness and ease of cleaning. Thc volumes of sample pans range from 40 flL to more than 500 flL. Autosamplers are available as attachments for most TGA systems. With the majority of these units, all aspects are automated under software control. The sample-pan taring, loading, and weighing; the furnace heating and cooling; and the pan unloading are totally automatic.
Temperature
Control and Data Processing
The temperature recorded in a thermogram is ideally the actual temperature of the sample. This temperature can, in principle, be obtained by immersing a small thermocoup~e directly in the sample. Such a procedure is seldom followed. however, because of possible catalytic decomposition of samples, potential contamination of samples, and weighing errors resulting from the thermocouple leads. Because of these problems, recorded temperatures are generally measured with a small thermocouple located as close as possible to the sample container. The recorded temperatures then generally lag or lead the actual sample temperature. Modern TGA systems use a computerized temperature control routine that automatically compares the voltage output of the thermocouple with a voltageversus-temperature table stored in computer memory. The computer uses the difference between the temperature of the thermocouple and the temperature specified to adjust the voltage to the heater. In some systems the same thermocouple behaves as the heating element and the temperature sensor. With modern control systems, it is possible to achieve excellent agreement between the specified temperature program and the temperature of the sample. Typical runto-run reproducibility for a particular program falls within 2°C throughout an instrument's entire operating range. Combined
Thermal Instruments
Several manufacturers offer systems that provide simultaneous measurement of heat flow (see Section 31C for differential scanning calorimetry) and mass change (that is, TGA) or of energy change (see Section 31B for differential thermal analysis) and mass change. Such instruments can not only track the loss of material or a vaporization phenomenon with temperature but also reveal transitions associated with these processes. These combination units can eliminate the effects of changes in sample size, homogeneity, and geometry. Many TGA systems produce the derivative of the thermogram as well as the thermogram itself. Such derivative plots are not true differential thermograms as produced in differential thermal analysis, but they provide similar qualitative information. They are often called single differential thermal analysis (SDTA) plots.
Tutorial: Learn more about thermogra,imetric
analysis.
l: __~ _ ;;:
o
100
200
300
400
500
600
700
800
75% Polyethylene
25'7c Carbon black
N2tO,
--.L.....:
Temperature,OC 250
Thermograms for some common polymeric materials. PVC = polyvinylchloride; PMMA= polymethylmethacrylate; LOPE = low-density polyethylene; PTFE = poly1etrafluoroethylene;PI ~ aromatic polypyromelitimide. (From J. Chiu, in Thermoanafysis of Fiber-Forming Polymers, R. F.Schwenker, ed., New York:Wiley,1966.)
500
FIGURE 31-3
TGA/MS and TGAfFTlR
TGA is used to determine the loss in mass"J.tparticular temperatures, but TGA cannot identify the species responsible. To obtain this type of information, the output of a thermogravimetric analyzer is often connected to a Fourier transform infrared (FTIR) or a mass spectrometer (MS). Several instrument companies offer devices to interface the TGA unit to a spectrometer. Some even claim true integration of the software and hardware of the TGA/MS orTGA/FTIR systems. High-Resolution
TGA
In high-resolution TGA, the sample heating rate fluctuates so that the sample is heated more rapidly during periods of constant mass than during periods when mass changes occur. This allows higher resolution to be obtained during the interesting periods and reduces the time of inactivity.
Because TGA monitors the mass of the analyte with temperature, the information provided is quantitative, but limited to decomposition and oxidation reactions and to such physical processes as vaporization, sublimation, and desorption. Among the most important applications of TGA 2 are compositional analysis and decomposition profiles of multicomponcnt systems. For a discussion of applications of thermal methods. see A. 1. Pasztor, in Handbook of Instrumental Techniques for Analytical Chemistry. F. Settle. ed., Upper Saddle River. NJ: Prentice-Hall. 1997, Chap. 50. 2
Thennogravimetric determination of carbon black in polyethylene. (From J. Gibbons, Amer. Lab., 1981, 13 (1),33. Copyright 1981 by International Scientific Communications, Inc.)
FIGURE 31-4
In polymer studies, thermograms provide information about decomposition mechanisms for various polymeric preparations. In addition, the decomposition patterns are characteristic for each kind of polymer and can sometimes be used for identification purposes. Figure 31-3 shows decomposition patterns for five polymers obtained by thermogravimetry. Figure 31-4 illustrates how a thermogram is used for compositional analysis of a polymeric material. The sample is a polyethylene that has been formulated with fine carbon-black particles to inhibit degradation from exposure to sunlight. This analysis would be difficult by most other analytical methods. Figure 31-5 is a recorded thermogram obtained by increasing the temperature of pure CaC,O,' H20 at a rate of 5°C/min. The clearly defined horizontal regions correspond to temperature ranges in which the indi-
cated calcium compounds are stable. This figure illustrates the use of TGA in defining the thermal conditions needed to produce a pure species. Figure 31-6a illustrates an application ofTGA to the quantitative analysis of a mixture of caleium, strontium, and barium ions. The three are first precipitated as the monohydrated oxalates. The mass in the temperature range between 320°C and 400°C is that of the three anhydrous compounds, CaCzO" SrC,O" and BaCzO" and the mass between about 580°C and 620°C corresponds to the three carbonates. The mass change in the next two steps results from the loss of carbon dioxide, as first CaO and then SrO are formed. Sufficient data are available in the thermogram to calculate the mass of each of the three elements present in the sample. Figure 31-6b is the derivative of the thermogram shown in (a). The derivative curve can sometimes reveal information that is not detectable in the ordinary thermogram. For example, the three peaks at 140°C, IS0°C, and 205°C suggest that the three hydrates lose moisture at different temperatures. However, all appear to lose carbon monoxide simultaneously and thus yield a single sharp peak at 450°C. Because TGA can provide quantitative information, determination of moisture levels is another important application. Levels of 0.5% and sometimes less can be determined.
Differential thermal analysis (DTA) is a technique in which the difference in temperature between a substance and a reference material is measured as a function of temperature while the substance and reference material are subjected to a controlled temperature program. Usually, the temperature program involves
31-5 Thermogram for decomposition of CaC20, ' H20 in an inert atmosphere. (From S. Peltier and C. Duval,Anal. Chim. Acta, 1947,1,345. With permission.)
FIGURE
~20
-->MC,O,
is used as the x-axis of the differential thermogram. The output across the sample and reference thermocouples flE is amplified and converted to a temperature difference fl T, which serves as the y-axis of the thermogram. Generally, the sample and reference chamber in DTA are designed to permit the circulation of an inert gas, such as nitrogen, or a reactive gas, such as oxygen or air. Some systems also have the capability of operating at high and low pressures.
+ H20
318-2 Temperature,OC (a) Thermogram
FIGURE 31-7 Differentialthermogram showing types of
changes encountered with polymericmaterials. (From R. M.Schutken Jr., R. E. Roy Jr., and R. H. Cox, J. Polymer Sci., Part C, 1964,6,18. Reprinted by permission of John Wiley& Sons, Inc.) heated furnace. The reference material is an inert substance such as alumina, silicon carbide, glass beads. The digitized output voltage E, from the sample thermocouple is the input to a computer. The computer controls the current input to the furnace in such a way that the sample temperature increases linearly and at a predetermined rate. The sample thermocouple signal is also converted to temperature T" which
ot
Temperature,OC (b) Differential
thermogram
FIGURE 31-6 Decomposition of CaCzO, . HzO.
srCzO,· HzO.and BaCzO,· HzO.From L. Erdey, G. Liptay. With permission.)
Sample
G. Svehla. and F. Paulike, Ta/anla, 1962,9,490.
heating the sample and reference material in such a way that the temperature of the sample T, increases linearly with time. The difference in temperature fl T between the sample temperature and the reference temperature T, (flT = T, - T,) is then monitored and plotted against sample temperature to give a differential thermogram such as that shown in Figure 31-7. (The significance of the various parts of this curve is given in Section 3IB-2.)
atmosphere
Sample
TC Figure 31-8 is a sehematic of the furnace compartment of a differential thermal analyzer. A few milligrams of the sample (S) and an inert reference substance (R) are contained in small aluminum dishes located above sample and reference thermocouples in an electrically
TC II I l.l..-.-!1E-J II I ....II-. I
\ Furnace heater leads
E,
FIGURE 31-8 Schematic diagram of a typical instrument
for DTA.TC = thermocouple.
General
Principles
Figure 31-7 is an idealized differential thermogram obtained by heating a polymer over a sufficient temperalure range to cause its ultimate decomposition. The initial decrease in flT is due to the glass transition, a phenomenon observed in the initial segments of many differential thermograms of polymers. The glass transition temperature Tg is the characteristic temperature at which glassy amorphous polymers become flexible or rubberlike because of the onset of the concerted motion of large segments of the polymer molecules. When heated to the glass transition temperature Tg, the polymer changes from a glass to a rubber. Such a transition involves no absorption or evolution of heat so that no change in enthalpy results - that is, flH = O. The heat capacity of the rubber is, however, different from that of the glass, which results in the lowering of the baseline, as shown in the figure. No peak appears during this transition, however, because of the zero enthalpy change. Two maxima and a minimum are observed in the thermogram in Figure 31-7. The two maxima are the result of exothermic processes in which heat is evolved from the sample, thus causing its temperature to rise. The minimum labeled "melting" is the result of an endothermic process in which heat is absorbed by the analyte. When heated to a characteristic temperature, many amorphous polymers begin to crystallize as microcrystals, giving off heat in the process. Crystal formation is responsible for the first exothermic peak shown in Figure 31· 7. The second peak in the figure is endothermic and involves melting of the microcrystals formed in thc initial exothermic process. The third peak is exothermic and is encountered only if the heating is performed in the presence of air or oxygen. This peak is the result of the exothermic oxidation of the polymer. The final negative
r::!?I
leJ
Tutori~/: Learn more about differential thermal analySIS.
change in fl Tresults from the endothermic decomposition of the polymer to produce a variety of products. As suggested in Figure 31-7, DTA peaks result from both physical changes and chemical reactions induced by temperature changes in the sample. Physical processes that are endothermic include fusion, vaporization, sublimation, absorption, and desorption. Adsorption and crystallization are generally exothermic. Chemical reactions may also be exothermic or endothermic. Endothermic reactions include dehydration, reduction in a gaseous atmosphere, and decomposition. Exothermic reactions include oxidation in air or oxygen, polymerization, and catalytic reactions.
[n general, DTA is considered a qualitative technique. Although able to measure the temperatures at which various changes occur, DTA is unable to measure the energy associated with each event. DTA is a widely used tool for studying and characterizing polymers. Figure 31-7 illustrates the types of physical and chemical changes in polymeric materials that can be studied by differential thermal methods. Note that thermal transitions for a polymer often take place over an extended temperature range because even a pure polymer is a mixture of homo logs and not a single chemical species. DTA is also widely used in the ceramics and metals industry. The technique is capable of studying hightemperature processes (up to 2400'C for some units) and relatively large sample sizes (hundreds of milligrams). For such materials, DTA is used to study decomposition temperatures, phase transitions, melting and crystallization points, and thermal stability. An important use of DTA is for the generation of phase diagrams and the study of phase transitions. An example is shown in Figure 31-9, which is a differential thermogram of sulfur, in which the peak at 113'C corresponds to the solid-phase change from the rhombic to the monoclinic form. The peak at 124'C corresponds to the melting point of the element. Liquid sulfur is known to exist in at least three forms, and the peak at 179cC apparently involves these transitions, whereas the peak at 446 C corresponds to the boiling point of sulfur. The DTA method also provides a simple and accurate way of determining the melting, boiling, and decomposition points of organic compounds. Generally, the data appear to be more consistent and reproducible than those obtained with a hot stage or a capillary tube. Q
a specified
rate
(e.g., 5°C/min)
given temperature.
The instrument
measures
to be a quantitative
technique,
in con-
FIGURE
Figure
31-10 shows
atmospheric
thermograms
pressure
peak corresponds
for benzoic
There
acid at
are three
point
Power-Compensated
and the second
31C DIFFERENTIAL SCANNING CALORIMETRY
often used thermal of its speed,
calorimetry
analysis
simplicity,
method, and
(DSC)
is the most
both temperatures
are increased
The power needed
to maintain
primarily
availability.
holder
because In DSC
independent a
Ambient
.c '0 >
..
In an initial counting period, the counting rate for a partleular sample was found to be 453 cpm (counts per mmute). In a second experiment performed 420 min later, the same sample exhibited a counting rate of 285 cpm. If it can be assumed that all counts are the result of the decay of a single radionuclidc, what is the half-life of that radionuclide?
Equation 32-8 can be used to calculate the decay constant, A,
0.693
285 cpm
dt
=
Here, c is a. constant called the absolute detection effiCIency, which depends on the nature of the detector the geometric arrangement of sample and detector, and other factors. The dccay law given by Equation 32-4 can then be written in the form
=
453 cpm
=
-A(420 min)
A = 1.10
I
. 0
>:
120
25
FIGURE 32-1 Expected frequency of deviations from the true average count (x, - /-,) versus the deviations. Although smooth curves are shown, the Poisson function is defined only for integer values shown as the circled points.
~ 100 '"~ ~ 80
§ 0
"0
~ >< '"
e-A("Omio!
60
OIl
X
20
10-3 min-!
10
tV2
AN
Activity is given in units of reciprocal seconds. The becquere! (Bq) corresponds to one decay per second. That is, 1 Bq = 1 S-I. An older, but still widely used, unit of activity is the curie (Ci), which was originally defined as the activity of 1 g of radium-226. One curie is exactly equal to 3.7 X 1010 Bq. In analytical radiochemistrv activities of analytes typically range from a nanocuri~ or less to a few microcuries. In the laboratory, absolute activities are seldom measured because detection efficiencies are seldom 100%. Instead, the counting rate R is used, where R = cA. Substituting this relationship into Equation 32-6 yields
A (11~ 5) 140
40
285 cpm) In ( 453 cpm
In 2
dN
160
4
u
Half-lives of radioactive species range from small fractions of a second to many billions of years. The activity A of a radionuclide is defined as its disintegration rate. Thus, from Equation 32-2, we may wnte
= -
200
180
= -At
ln~
A
the use of the decay rate
=A
0.693 1.10 x 10 3 mini
=
32A-4 Counting
Deviation
=
Statistics
Counts
1 2 3
180
187 166 173
4
5 6 Total counts
Minute
170
164 =0
=
i
=
167.
15
(Xi - Ji)
168
9
173 132 154 167
170
period.' Table 32-2 shows typical dccay data obtained by successive I-minute measurements of a radioactive source. Because the decay process is random, considerable variation among the data is observed. Thus, in Table 32-2, the rates range from a low of 132 to a high of 187 counts per minute (cpm). Although radioactive decay is random, the data, particularly for low number of counts, are not distributed according to Equation a1-14 (Appendix 1), because the decay process does not follow Gaussian behavior. The reason that decay data are not normally distributed is that radioactivity consists of a series of discrete events that cannot vary continuously as can the indeterminate errors for which the Gaussian distribution applies. Furthermore, negative numbers of counts are not possible. Therefore, the data cannot be distributed symmetrically about the mean. To describe accurately the behavior of a radioactive source, it is necessary to assume a Poisson distribution, which is given by the equation For a more complete discussion, see G. Friedlander, 1. W. Kennedv, E. S. Macias, and 1. M. Miller, l\'uclear and Radiochemistry, 3rd ed .. Chap. 9. New York: Wiley. 1981.
4
2004.
Average counts/min
Connts
7 8 10 11 12
count,
630 min
As will be shown in Section 32B, radioactivity is measured by means of a detector that produces an electronic pulse, or count, each time radiation strikcs the detector. Quantitative information about decay rates is obtained by counting these pulses for a sp'ccified
Minute
from {rue average
where y is the frequency of occurrence of a given count Xi and J1 is the mean for a large set of counting data.' The data plotted in Figure 32-1 were obtained with the aid of Equation 32-9. These curves show the deviation (Xi - J1) from the true average value that would be expected if WOO replicate observations were made on the same sample. Curve A gives the distribution for a substance for which the true average count J1 for a selected period is 5; curves Band C correspond to samples having true means of 15 and 35. Note that the absolute deviations become greater with increases in J1, but the relative deviations become smaller. Note also the lack of symmetry about the mean for the two smaller count numbers. .;In the derivation of Equation 32-9, it is assumed that the counting period is short with respect to the half-life so that no significant change in the number of radioactive atoms occurs. Further restrictions include a detector that responds to the decay of a single radionuclide only and an invariant counting geometry so that the detector responds to a constant fraction of the decay events that occur.
Standard Deviation of Counting Data
ThUS,there are 95 chances in 100 that the true rate for
In contrast to Equation al-14 (Appendix 1) for a Gaussian distribution, Equation 32-9 for a Poisson distribution contains no corresponding standard deviation term. It can be shown that the breadth of curves such as those in Figure 32-1 depend only on the total number of counts for any given period.' That is,
R (for the average of 12 min of counting) lies bctween
(a) Applying Equation O'R
=
VM -1-
=
=
L
160 and 174 counts/min. For the single count in part (a), 95 out of 100 times, the truc rate will lie between 154 and 206 counts/min.
v180 I min
=
13.4 cpm
13.4 cpm 180cpm x 100%
O'R
R
32-12 gives
=
7.4%
(b) For the entire set. where M is the number of counts for any given period and 0' M is the standard deviation for a Poisson distribution. The relative standard deviation O'MIM is given by O'M
=
O'R
V2OO4 = u=
O'R
3.73 cpm
=
3.7 cpm
3.73
R = 167 x
100%
=
M
Background
VM
M
Confidence Interval for Counts
O'k
YO'~ + (aa~YO';
= (;~
Generally, time can be measured with such high precision that a? = O. The partial derivative of R with respect to Mis 111.Thus, 2~ fIR
=
(2
In Section alB-2 (Appendix 1), the confidence interval for a measurement is defincd as the limits around a measured quantity within which the true mean can be expected to fall with a stated probability. When the measured standard deviation is believed to 'be a good approximation of the true standard deviation (s --> 0'), the confidence interval CI is given by Equation a 1-20: CI for
JL =
x
:t ZO'
For counting rates, this equation takes the form CI for R = R
:t
ZO'R
(32-14)
where z depends on the desired level of confidence. Some values for z are given in Table al-3. Example 32-3 illustratcs the ealculation of confidence intervals.
Taking the square root of this equation and substituting Equation 32-10 gives O'R
= VM = v'Ri = -Vif1l I
I
:;=V:=ff Example 32-2 illustrates the usc of these equations for counting statistics.
Calculate the 95% confidence interval for (a) the first entry in Table 32-2 and (b) the mean of all the data in the table.
(a) In Example 32-2, we found that O'R = 13.4 cpm. Table al-3 (Appendix 3) reveals that z = 1.96 at the 95 % confidence level. Thus, for R 95% CI
Calculate the absolute and relative standard deviations in the counting rate for (a) the first entry in Table 32-2 and (b) the mean of all of the data in the table.
=
180 cpm :t (1.96 x 13.4 cpm)
= 180 :t 26 cpm
(b) In this instance 95% CI for R
O'R
= =
Substituting leads to
Equation
32-12 into this equation
2.2%
Vii!.. = _1_
Thus, although the standard deviation increases with the number of counts, the relative standard deviation decreases. The counting rate R is equal to Mil. To obtain the standard deviation in R, we apply Equation al-29 (Appendix 1), which gives
Figure 32-2 illustrates the relationship between total counts and tolerable levels of uncertainty as calculated from Equation 32-14. Note that the horizontal axis is logarithmic. Thus, a decrease in the relative uncertainty by a factor of 10 requires that the number of counts be increased by a faetor of 100.
where R, is the corrected counting rate and Rx and Rb are the rates for the sample and the background, respectively. The standard deviation of the corrected counting rate can be obtained by application of Equation (1) in Table al-6 (Appendix 1). Thus,
was found to be 3.73 cpm and 167 cpm :t (1.96 x 3.73 cpm) 167 :t 7 cpm
Corrections
The number of counts recorded in a radiochemical analysis includes a contribution from sources other than the sample. Background activity can be traced to the presence of minute quantities of radon radionuc1ides in the atmosphere, to the materials used in construction of the laboratory, to accidental contamination within the laboratory, to cosmic radiation, and to the release of radioactive materials into the Earth's atmosphere. To obtain an accurate determination, then, it is necessary to correct the measured counting rate for background contributions. The counting period required to establish the background correction frequently differs from the counting period for the sample. As a result, it is more convenient to employ counting rates as shown in Equation 32-15.
A sample yielded 1800 counts in a lO-min period. Background was found to be 80 counts in 4 min. Calculate the absolute uncertainty in the corrected counting rate at the 95% confidence level. Solution
Rx = Rb
O'R,
=
1800
10 = 180cpm 80
="4 = 20cpm
180
80
10 +"4 =
6.2cpm
32B-1 Measurement
CL for R, = (180 - 20) :!: 1.96 x 6.2 = 160:!: 12cpm Here, the chances are 95 in 1()()that the true count lies between 148 and 172 cpm. Note that the inclusion of background contributions invariably leads to an increase in the reported uncertalllty of the determination.
Radiation from radioactive sources can be detected and measured in essentially the same way as X-radiation (Sections 12B-4 and 12B-5). Gas-filled chambers scintillation counters, and semiconductor detecto:s are all sensitive to alpha and beta particles and to gamma rays because absorption of these particles produces 101llzallon or photoelectrons, which can in turn produce thousands of ion pairs. A detectable electrical pulse is thus produced for each particle reaching the transducer.
of Alpha Particles
To minimize self-absorption, alpha-emitting samples are generally counted as thin deposits prepared by electrodeposillon or by vaporization. Often, these deposits are then sealed with thin layers of material and counted III wllldowiess gas-flow proportional counters or ionizatlOn chambers. Alternatively, they are placed immediately adjacent to a solid-state detector, often in a vacuum for counting. Liquid scintillation counting (see next secllon) IS becoming increasingly important for counting alpha emitters because of the ease of sample preparation and the higher sensitivity for alpha-particle detecllon. Because alpha-particle spectra consist of characteristic, discrete energy peaks, they are quite useful for identification. Pulse-height analyzers (Section 12B-5) permIt the recording of alpha-particle spectra.
1.2
x 10"
1.0
x to'
1---._-
"':
-
L
----
~
---
._--- --
---
!
~
,
! , i
I
-b,
~
~I -~--
!
!
I
"'lilol !
llc +
bn
cal generator consists of an ion source that delivers deuterium ions to an area where they are accelerated by a potential difference of a few hundred kV to a target containing tritium adsorbed on titanium or zirconium. The reaction is ;H + jH --> jHe +
bn
The higher-energy neutrons produced in this way are particularly useful for activating the lighter elements.
+ 5.7 MeV
To produce thermal neutrons, paraffin is typically employed as a moderator. Accelerators
Benchtop charged particle accelerators are commercially available for the generation of neutrons. A typi"
The basic characteristics of neutrons are given in Table 32-1. Free neutrons are not stable, and they decay with a half-life of about 10.2 min to give protons and electrons. Free neutrons do not, however, generally exist long enough to disintegrate in this way
because of their great tendency to react with ambient material. The high reactivity of neutrons arises from their lack of charge, which permits them to approach charged nuclei without interference from coulombic forces. Neutron capture is the most important reaction for activation methods, Here, a neutron is captured by the analyte nucleus to give an isotope with the same atomic number, but with a mass number that is greater by 1. The new nuclide is in a highly excited state because it has acquired several Me V of energy by binding the neutron. This excess energy is released by prompt gamma-ray emission or emission of one or more nuclear particles, such as protons or alpha particles. An example of a reaction that produces prompt gamma rays is HNa +
6n
-+ iiNa
+
y
dN* ----;;t=
Ncf>(J'- AN*
Ncf>(J' N* = -A-[I - exp(-At)] If we substitute term, we obtain
Equation 32-5 into the exponential
N* = Ncf>(J'[l _ exp(-
0.693t)]
A
tll2
The last equation can be rearranged to give the product AN*, which is the activity A (see Equation 32-6), Thus, A = AN* = Ncf>(J'[I - exp( - 0,~:3t) ] "': Ncf>(J'S
FIGURE 32-7 The effect of neutron flux density and time on the activity induced in a sample,
(32'17)
ijNa(n, y)iiNa
where S is the saturation factor, which is equal to 1 minus the exponential term, Equation 32-17 can be written in terms of experimental rate measurements by substituting Equation 32-7 to give
mass of analyte is directly proportional to the counting rate, If we use the subscripts x and s to represent sample and standard, respectively, we can write (32-19) (32-20)
R When exposed to neutrons, the rate of formation of radioactive nuclei from a single isotope is given by dN* ----;;t=Ncf>(J' where dN*ldt is the reaction rate (S'I), N is the number of stable target atoms, cf> is the average flux density (n cm -I S·I), and (J' is the capture cross section (cm'). The capture cross section is a measure of the probability of the nuclei reacting with a neutron at the neutron energy employed, Tables of reaction cross sections for thermal neutrons list values for (J' in barns b, where I b = 10.24 cm'. Once formed, the radioactive nuclei decay at a rate -dN*ldt given by Equation 32-2, That is, -
dN* -dt
= AN*
=
cNcf>(J'[ I - exp( - 0,~:3t) ]
=
Ncf>(J'cS
Figure 32-7 is a plot of this relationship at three levels of neutron flux density, The abscissa is the ratio of the irradiation time to the half-life of the isotope (tltll2). In each case, the counting rate approaches a constant value where the rates of formation and disintegration of the radionuclide approach one another. Clearly, irradiation for periods beyond four or five half-lives for an isotope will result in little improvement in sensitivity. In many analyses, irradiation of the samples and standards is carried out for a long enough period to reach saturation so that S approaches unity. Under this circumstance, all of the terms except N on the right side of Equation 32-18 are constant, and the number of analyte radionuclides is directly proportional to the counting rate, If the parent, or target, nuclide is naturally occurring, the mass of the analyte m can be obtained from N by multiplying it by Avogadro's number, the natural abundance of the analyte nuclide, and the atomic mass. Because all of these are constants, the
Experimental
in Activation
Integrating this equation from time 0 to t, gives
Usually, equations of this type are written in the abbreviated form
The prompt gamma rays formed by capture reactions are of analytical interest in some cases, but the radionuclide produced (24Na) and its decay radiations are more often used in NAA.
32C-4
Thus, during irradiation with a uniform flux of neutrons, the net rate of formation of active particles is
where k is a proportionality constant. Dividing one equation by the other and rearranging leads to the basic equation for computing the mass of analyte in an unknown:
samples
of
Cooling
and
period
standards
Figure 32-8 is a block diagram showing the flow of sample and standards in the two most common types of activation mcthods, destructive and nondestructive, In both procedures the sample and one or more standards are irradiated simultaneously with neutrons (or other types of radiation), The samples may be solids, liquids, or gases, although the first two are more common. The standards should physically and chemically approximate the sample as closely as possible. Generally, the samples and standards are contained in small polyethylene vials; heat-scaled quartz vials are also used on occasion. Care must be taken to ensure that the samples and standards are exposed to the same neutron flux. The time of irradiation depends on a variety of factors and often is determined empirically. Frequently, an exposure time of roughly three to five times the half-life of the analyte product is used (see Figure 32-7). Irradiation times generally vary from a few minutes to several hours. After irradiation is terminated, the samples and standards are often allowed to decay (or "cool") for a period that again varies from a few minutes to several hours or more, During cooling, short-lived interferences decay so that they do not affect the outcome of the analysis. Another reason for allowing an irradiated sample to cool is to reduce the health hazard associated with higher levels of radioactivity. Nondestructive
Methods
As shown in Figure 32-8, in the nondestructive method the sample and standards are counted directly after cooling. Here, the ability of a gamma-ray spec-
Data
Simultaneous irradiation
Considerations
Methods
processing and display
trometer to discriminate among the radiations of different energies provides selectivity. Equation 32-21 is then used to calculate the amount of analyte in the unknown as shown in Example 32-5.
Two 5.oo-mL aliquots of river water were taken for NAA. Exactly 1.00 mL of a standard solution containing 1.00 Ilg of Al J+ was added to one aliquot, and 1.00 mL of deionized water was introduced into the other. The two samples were then irradiated simultaneously in a homogeneous neutron flux. After a brief cooling period, the gamma radiation from the decay of 28 Al was counted for each sample. The solution diluted with water gave a counting rate of 2315 cpm, whereas the solution containing the added Al J+ gave 4197 cpm. Calculate the mass of Al in the 5.00-mL sample.
Here, we are dealing with a simple standard-addition problem that can be solved by substituting into Equations 32-19 and 32-20. Thus, 2315 = kmx 4197 = k(mx + m,) = k(mx + 1.00) Solving these two equations leads to mx = 1.231lg
As shown in the lower pathway in Figure 32-8, a destructive method requires that the analyte be separated from the other components of the sample prior to counting. If a chemical separation method is used, this technique is called radiochemical neutron activation. In this case a known amount of the irradiated sample is dissolved and the analyte separated by precipitation, extraction, ion exchange, or chromatography. The isolated material or a known fraction thereof is then counted for its gamma - or beta - activity. As in the nondestructive method, standards may be irradiated simultaneously and treated in an identical way. Equation 32-21 is then used to calculate the results of the analysis.
- - 2 Oi -x x - -x s x x
.,
Destructive Methods u.,
I
I
N
- G -x en
~.~
-
~.Nx or." 0
or.
or.
"2
x x ~, v;
E
I
""
x
~.
-
-
.D
"-
I
- '7 "1 -x 0 -:::x x - bx sx - ~. ~. -
eo eo
1 "1 o ~ ~
0
:t
b
~x
Neutron activation methods offer several advantages, including high sensitivity, minimal sample preparation, and ease of calibration. Often, these proc~dures are nondestructive and for this reason are applied to the analysis of art objects, coins, forensic samples, and archaeo~ogical specimens. The major disadvantages of activation methods are their need for large and expensive equipment and special facilities for handling and disposing of radioactive materials. Another shortcoming is the long time required to complete analyses when long-lived radionuclides are used.
--
z
S
"2
~.
0
""
v;
x v;
x
e.
0
N
I
1 "1
..:(
-
s
x
x
"I
0;
"1
.c 0::
0
~.v;
~. "- ~. b 1 S '" x
U
-
"1
eo
0
"2
X
X
X
0
S
X
X V;
I
-
-- b
;> :::
X
~. X
b i=
b
X
X
or,
V;
U
-
;;:
"
0::
X
~.
X
V;
0 X
~.
"2
U
;;:
X
V;
, .D
Z
N
0
~ X
X
X
- '! b - ~X
~,
X V;
- - :;: I
,
"
..J
X
e
0
0
x
X V;
-
- ~ -x '"" x 0
~ 0
V;
X
V;
..
c. >.: -
0
X
X
X
~,
V;
X
-
V;
or,
V;
x
'k
"2
-
b
~
1 1
::l:=: S Ul
x x ~,
S ~ S bX
0 0
e
"'::: S
x or,
I
-X
-
or,
"I
en
N
X
0
Scope
U
o
"I
or,
~
X
-0
or,
0 0 N
;;:
, , S S
"
::: 0 x x or, v;
-,- b u.," cr, 0:: x x 0 x - 1 ~ X
X
~,
I
X
eo 1eo '" x x :t .r. v; -
""
x U x
, 1 - ~gNi + X (b) !~p -> !~Si + X (c) 'lipb -> 'liBi + X (d) '~lu+ 'i]1 + X (f) ~Cu + x -> tjNi Potassium-42 is a f3 emitter with a half-life of 12.36 h. Calculate the fraction of this radionuclide remaining in a sample after 1, 10. 20, 30,40.50,60,70, and 100 h. Plot
..
the fraction remaining versus time. Determine the time required for the fraction to fall to 1%. ~
32-3 Calculate the fraction of each of the following radionuclides that remains after 1 day, 2 days, 3 days, and 4 days (half-lives are given in parentheses): iron-59 (44.51 days), titanium-45 (3.078 h), calcium-47 (4.536 days), and phosphorus-33 (25.3 days). *32-4 A PbSO, sample contains 1 microcurie of Pb-200 (cliZ = 21.5 h). What storage period is needed to assure that its activity is less than 0.01 microcucie" *32-5 Estimate the standard deviation and the relative standard deviation associated with counts of (a) 100, (b) 750, (c) 7.00 X 103. (d) 2.00 X 10'. *32-6 Estimate involving (a) 90% (b) 95% (c) 99 %
the absolute and relative uncertainty associated with a measurement 800 counts at the confidence level. confidence level. confidence level.
*32-7 For a particular radioactive sample, the total counting rate (sample plus background) was 450 cpm, and this value was obtained over a 15.0-min counting period. The background was counted for 2.0 min and gave 7 cpm. Estimate (a) the corrected counting rate Roo (b) the standard deviation associated with the corrected counting rate (c) the 95% confidence interval associated with the corrected counting r~te.
IT;.
*32-8 The background counting rate of a laboratory was found to be approximately 9 cpm when measured over a 3-min period. The goal is to keep the relative standard deviation of the corrected counting rate at less than 5% (ITRlR, < 0.05). What total number of counts should be collected if the total coun'ting rate is (a) 70 cpm and (b) 400 cpm? *32-9 A sample of "'Cu exhibits 3250 cpm. After 10.0 h, the same sample gave 2230 cpm. Calculate the half-life of "'Cu. *32-10 One half of the total activity in a particular sample is due to 38et (cll2 = 87.2 min). The other half of the activity is due to "S (e1l2 = 37.5 days). The beta emission of "s must be measured because this nuclide emits no gamma photons. Therefore, it is desirable to wait until the activity of the 38et has decreased to a negligible level. How much time must elapse before the activity of the 38CIhas decreased to only 0.1 % of the remaining activity because of "S" 32-11 Prove that the relative standard deviation of the counting rate ITR/R is simply M-lI2, where M is the number of counts. 32-U Under what conditions can the second term in Equation 32-23 be ignored? *32-13 A 2.00-mL solution containing 0.120 microcurie per milliliter of tritium was injected into the bloodstream of a dog. After allowing time for homogenization, a 1.00-mL sample of the blood was found to have a counting rate of 15.8 counts per sccond (cps). Calculate the blood volume of the animal. *32-14 The penicillin in a mixture was determined by adding 0.981 mg of the I'C-Iabeled compound having a specific activity of 5.42 X 10' cpm/mg. After
equilibration, 0.406 mg of pure crystalline penicillin was isolated. This material had a net activity of 343 cpm. Calculate the mass in milligrams of penicillin in the sample. *32-15 In an isotope dilution experiment, chloride was determincd by adding 5.0 mg of sodium chloride containing 38et (e1l2 = 37.3 min) to a sample. The specific activity of the added NaCl was 4.0 X 10' cps/mg. What was the total amount of chloride present in the original sample if 400 mg of pure AgCI was isolated and if this material had a counting rate of 35 cps above background 148 min after the addition of the radiotracer? 32-16 A 1O.0-gsample of protein was hydrolyzed. A 3.0-mg portion of I'C-labeled threonine, with specific activity of 1000 cpm/mg, was added to the hydrolysate. After mixing, 11.5 mg of pure threonine was isolated and found to have a specific activity of 20 cpm/mg. (a) What percentage of this protein is threonine? (b) Had llC (e1l2 = 20.3 min) been used instead of I'C, how would the answer change? Assume all numerical values are the same as in part (a) and that the elapsed time between' the two specific activity measurements was 32 min. *32-17 The streptomycin in 500 g of a broth was determined by addition of 1.34 mg of the pure antibiotic containing 14c. The specific activity of this preparation was found to be 223 cpm/mg for a 30-min count. From the mixture, 0.Il2 mg of purified streptomycin was isolated, which produced 654 counts in 60.0 min. Calculate the concentration in parts per million streptomycin in the sample. 32-18 Show, via a calculation, that the average kinetic energy of a population of thermal neutrons is approximately 0.04 eV. 32-19 Naturally occurring manganese is 100% "Mn. This nuclide has a thermal neutron capture cross section of 13.3 X 10-24 cm'. The product of neutron capture is 56Mn, which is a beta and gamma emitter with a 2.50-h half-life. When Figure 32-9 was produced, it was assumed that the sample was irradiated for 1 h at a neutron flux of 1.8 X 1012 neutrons/(cm2 s) and that 10 cpm above background could be detected. (a) Calculate the minimum mass of manganese that could be detected. (b) Suggest why the calculated value is lower than the tabulated value. Challenge Problem
32-20 (a) By referring to a reference on NAA or by using an Internet search engine to find the information, describe in some detail the instrumental and radIOchemical differences between prompt gamma-ray neutron activation and delayed gamma-ray neutron activation. (b) What are the types of elements for which prompt gamma-ray activation analysis is most applicable? (c) Why is delayed gamma-ray emission most often used in NAA? (d) Why is NAA considered to bc a very selective and sensitive method? (e) A crvstal of potassium fluoride is to be studied via NAA. The following tabl~ summarizes the behavior of all naturally occurring isotopes in the crystal.
100% 93% 0.01%
I;F (n, y)'gF
:;K (n, y)::it' :;:K (n,y\~K :;K (n, y);;K
19F,2oNe. 39K. "K, and 42Ca are stable, and we will assume that 40Kis also stable because it has a half-life of 1.3 x 109 years. What sort of irradiation and detection sequcnce would you use if you wanted to base your analysis on fluorine? What sort of irradiation and detection sequence would you use if you wanted to base the analysis on potassium? Refer to part (e) and calculate the activity due to 2°F and 42Kin a 58-mg (l.O-millimole) sample of pure potassium fluoride that has been irradiated for 60 s. The thermal neutron cross sections for "F and 41K are 0.0090 X 10-24 cm 2 and 1.1 X 10-24 cm 2, respectively. Assume a flux density of 1.0 x 1013 neutrons cm-' S-I. Find a method in the literature that describes the use of NAA for determining selenium in freshwater ecosystems. Describe the method in detail. Include the neutron source, the irradiation time, and the calculations used. Give the advantages and disadvantages of the method over other inltlytieal techniques.
Automated Methods of
Analysis
m fl.e.of the m atJ..·.ordevetO'P·. in adecades na.lytical chemistry during the.. enis lGdtfew O.
automated
ha.~ been the appearance
of co,w"ercial
analytical systems, Which provide ana -
l)'tical and control information with a minimum of operator intervention.~utomatedsy-stemsfirst species areroutinel.y4itermine4for screening pwposes.
ap-
.where thirty '!rmore
peared in clinicallabo[atories,
diagfl9stic and
LaI;JOratorymutomation
There are many definitions of automation, but the practical meaning is the performance of operations without human intervention. In the context of analytical chemistry, automation may involve operations like the preparation of samples, the measurement of responses, and the calculation of resultsl Figure 33-1 illustrates the common steps in a typical chemical analysis and the automation methods used. In some cases, one or more of the steps shown on the left of the figure can be omitted. For example, if the sample is already a liquid, the dissolution step can be omitted. Likewise, if the method is highly selective, the separation step may be unnecessary. The steps listed in Figure 33-1 are sometimes called unit operations. We discuss in this chapter analyzers that are highly automated, such as flow injection and discrete analyzers. In addition, laboratory robotic systems that are becoming more and more commonplace for sample handling and preparation are also described. The latest advances in automation involve the development of microfluidic systems, which are sometimes called labon-a-chip or micro total analysis systems. These recent developments are also described here. It is important to note that the same principles of automatic analysis discussed here also apply to process control systems, which analyze the current state of a process and then use feedback to alter experimental variables in such a way that the current state and the desired state are nearly identical.
soon
spread to industrial process cOf1tr'01and laterto
33A-1 Advantages
pharmaceutical,
of Automated
environmental,jorensic,
15.0vern-
mental, and university research laboratories. Toda)', man)' routine determinations of the most demanding
anal)'ses are made with to-
tally or partial!;y automated
rYl
as well as man)'
s)'stems.
Throughout this chapter, this logo indicates an opportunity for online self-study at www .thomsonedu.com/chemistry/skoog, linking you to interactive tutorials, simulations, and exercises.
lQ.J
and Disadvantages
Analyses
Automated instruments can offer a major economic advantage because of their savings in labor costs. This advantage is realized when the volume of work is large enough to offset the original capital investment. For clinical and testing laboratories, in which large numbers of routine analyses are performed daily, the savings achieved by automation can be very large. A second major advantage of automated instruments is that the number of determinations per day (throughput) can be much higher than with manual For monographs on laboratory automation. see Laboratory Automation in (he Chemical Industries, D. G. Cork and T. Sugawara, eds., New York Dekker, 2002; Auwmarion in the Laborawry. 'W:. 1. Hurst. ed .. :'-JewYork: Wiley, 1995; V Cerda and G. Ramis, An inrroduction £0 Laboratory Auw1
mation. New York: Wiley.lWO
Robotics, gas or liquid sampling
Flow injection automated
system
or discrete
analyzer
FIGURE 33-1 Steps in the analytical process showing possible automation methods. L1MS= laboratory information management system.
methods. In some cases, this is due to the speed of an automated analyzer being significantly greater than that of the equivalent manual device. In other cases, the increased throughput arises because the automated instrument can be used many more hours per day than can a human employee. Indeed, the higher throughput often makes possible the continuous monitoring of the composition of products as they are being manufactured. This information in turn permits alteration of conditions to improve quality or yield. Continuous monitoring is also useful in medicine, where analytical results can be used to determine patients' current conditions and their response to therapy, and in environmental monitoring, where the results can be used to measure the effectiveness of clean-up procedures. A third advantage of automation is that a welldesigned analyzer often provides more reproducible results over a long period than can an operator using a
manual instrument. Two reasons can be cited for the higher precision of an automated device. First, machines do not suffer from fatigue or boredom, which have been demonstrated to affect adversely results obtained manually. A more important contributing factor to precision is the high reproducibility of the timing sequences of automated instruments, which can seldom be matched in manual operations. For example, automatic analyzers permit the use of colorimetric reactions that are incomplete or that yield products whose stabilities are inadequate for manual measurement. Similarly, separation techniques, such as solvent extraction or dialysis, where analyte recoveries arc incomplete, are still applicable when automated systems are used. In both instances, the high reproducibility of the timing of the operational sequences assures that samples and standards arc processed in the same way and for the same length of time. Other advantages of automation include the ability to process samples in situations that would be dangerous for humans, the minimization of calculatiqn errors, and the direct recording of results in databases and archival storage systems. In some cases procedures that arc more lengthy and more complicated than those performed manually can be used with automated systems. In the early days of automation in laboratories, it was thought that automated instruments would replace human analysts or downgrade their role. It has been found, however, that the role of the analytical chemist has not been downgraded in automated laboratories but merely revised. Analytical chemists are ultimately rcsponsible for the status and quality of the laboratory results. This means the analyst must be fully aware of the strengths and weaknesses of the automated methods employed and be intimately familiar with calibration and validation methods. In fact, modern analytical chemists are now responsible not only for data quality but also for specifying new instrumentation, for adapting or modifying procedures, and for investigating new methods for handling samples, separating interferences, and assessing data reliability - a different, but still vitally important, role. 33A-2 Types of Automatic
Systems
Automatic analytical systems are of two general types: discrete analyzers and continuous flow analyzers; occasionally, the two are combined. [n a discrete instrument, individual samples are maintained as separate entities and kept in separate vessels throughout each
unit operation listed in Figure 33-1. In continuous flow systems, in contrast, the sample becomes a part of a flowing stream where several of the steps take place as the sample is carried from the injection or sample introduction point to a flow-through measuring unit and thence to waste. Both discrete and continuous flow instruments are generally computer controlled. Because discrete instruments use individual containers, cross-contamination among samples is totally eliminated. On the other hand, interactions among samples are always a concern in continuous flow systems, particularly as sample throughput increases. Here, special precautions are required to minimize sample contamination. Modern continuous flow analyzers are generally mechanically simpler and less expensive than their discrete counterparts. Indeed, in many continuous flow systems, the only moving parts are pumps and switching valves. Both of these components are inexpensive and reliable. In contrast, discrete systems often have a number of moving parts such as syringes, valves, and mechanical devices for transporting samples or packets of reagents from one part of the system to another. In the most sophisticated discrete systems, unit operations are performed by versatile computerized robots, in much the same way human operators would. Some unit operations are not possible with continuous flow systems because such systems are capable of handling only fluid samples, Thus, when solid materials are to be analyzed or when grinding, weighing, ignition, fusion, or filtration is required in an analysis, automation is possible only by using discrete systems or by combining robotics with a continuous flow unit. In this chapter, we first discuss flow injection analysis (FIA), a recent and important type of continuous flow method. We next consider microfluidic systems, which are miniaturized types of continuous flow units. We then describe several types of discrete automatic systems, several of which are based on laboratory robotics.
Flow injection methods were first described by Ruzicka and Hansen in Denmark and Stewart and coworkers in the United States in the mid-1970s-' Flow injection
methods are an outgrowth of segmented-flow procedures, which were widely used in clinical laboratories in the 1960s and 1970s for automatic routine determination of a variety of species in blood and urine samples for medical diagnostic purposes. [n segmented-flow systems, samples were carried through the system to a detector by a flowing aqueous solution that contained closely spaced air bubbles. The purpose of the air bubbles was to minimize sample dispersion, to promote mixing of samples and reagents, and to prevent erosscontamination between successive samples. The air bubbles had to be removed prior to detection by using a debubbler or the effects of the bubbles had to be removed electronically. The discoverers of flow injection analysis found, however, that continuous flow systems could be greatly simplified by leaving out thc air bubbles and by employing reproducible timing through injection of the sample into a flowing stream.' Such systems could be designed with minimal crosscontamination of successive samples. The absence of air bubbles imparts several important advantages to flow injection measurements, including (I) higher analysis rates (typically 100 to 300 samples/h), (2) enhanced response times (often less than 1 min between sample injection and detector response), (3) much more rapid start-up and shutdown times (less than 5 min for each), and (4) except for the injection system, simpler and more flexible equipment. The last two advantages are particularly important because they make it feasible and economic to apply automated measurements to a relatively few samples of a nonroutine kind. That is, continuous flow methods are no longer restricted to situations where the numbcr of samples is large and the analytical method highly routine. In addition, the precise timing in flow injection leads to controlled dispersion, which can be advantageous in promoting reproducible mixing, producing sample or reagent concentration gradients, and minimizing reagent consumption. Because of these advantages, many segmented-flow systems have been replaced by flow injection methods (and also by discrete systems based on robotics). Complete FlA instruments arc now available from several different companies. Fur monographs on flow injection analysis. see M. Trojano'l.-icz, Flaw Injection Analysis. River Edge, NJ: World Scientific Publishing Co .. 2C~:XJ; B. Karlbcrg and G. F. Pacey. Flok" Injection Analvsls. A Praclical GUIde. New )"ark: Flst.'\"icr. 1989; 1. Ruzicka and E. H. Hansen, Flow frljeCll.nn Anahsis. 2nd ed .. New York: Wile\,. 1988; M. Vakarcel and M. D. Luque d.: Castro, FluK Injection Analy;is: Principles and Applicaliom, Chichester. UK: EllIS Hm\\'ood. 1987. J
Diagram showing one channel of a peristaltic pump. Several additional tubes may be located under the one shown (below the plane of the diagram) to carry multiple channels of reagent or sample. (From B. Karlberg and G. E. Pacey, Flow Injection Analysis: A PractIcal Guide, p. 34, New York:Elsevier, 1989. With permission of Elsevier Science Publishers.)
FIGURE 33-3 Peristaltic pump
Sample Reactor
mLirnin Reagent
Hg(SCN~2 ~ Feh
0.8
I
/
Photometer
coil SOcm D
To \\'aste
Bypass
of the sample and reagent, both of which lead to more symmctric peaks.
Flow injection determination of chloride: (a)flow diagram; (b) recorder traces for standards containing 5 to 75 ppm chloride ion (left)and fast scan of two of the standards to demonstrate the low analyte carryover (less than 1%) from run to run (right).Note that the point marked 1% corresponds to where the response would just begin for a sample injected at time S2' (From J. Ruzicka and E. H. Hansen, Flow Injection Methods, 2nd ed., p. 16, New York: Wiley,1988. Reprinted by permission of John Wiley& Sons, Inc.) FIGURE 33-2
Sample and Reagent Transport System
Figure 33-2a is a flow diagram of a basic tlow injection system. Here, a peristaltic pump moves colorimetric reagent for chloride ion directly into a valve that permits injection of samples into the flowing stream. The sample and reagent then pass through a 50-cm reaclor coil where the reagent diffuses into the sample plug and produces a colored product by the sequence of reactions Hg(SCN),(aq) + 2Cl- ~ Fe'+ + SCN- ~
HgCI,(aq) + 2SCW Fe(SCN)"
From the reactor coil, the solution passes into a flowthrough photometer equipped with a 480-nm interference filter. The signal output from this system for a series of standards containing from 5 to 75 ppm chloride is shown on the left of Figure 33-2b. Note that four injections of each standard were made to demonstrate the reproducibility of the system. The two curves to the right are high-speed scans of one of the samples containing 30 ppm (R,o) and another containing 75 ppm (R75) chloride. These curves demonstrate that cross-contamination is minimal in an unsegmented stream. Thus, less than I% of the first analyte is present in the flow cell after 28 s, the time of the next injection (5,). This system has been successfully used for the routine determination of chloride ion in brackish and waste waters as well as in serum samples.
Sample Injectors and Detectors
,
The solution in a flow injection analysis is usually pumped through flexible tubing in the system by a peristaltic pump, a device in which a fluid (liquid or gas) is squeezed through plastic tubing by rollers. Figure 33-3 illustrates the operating principle of the peristaltic pump. Here, the spring-loaded cam, or band, pinches the tubing against two or more of the rollers at all times, thus forcing a continuous flow of fluid through the tubing. Modern pumps generally have eight to ten rollers, arranged in a circular configuration so that half are squeezing the tube at any instant. This design leads to a flow that is relatively pulse free. The flow rate is controlled by the speed of the motor, which should be greater than 30 rpm, and the inside diameter (i.d.) of the tube. A wide variety of tube sizes (i.d. = 0.25 to 4 mm) are available commercially that permit flow rates as small as 0.0005 mUmin and as great as 40 mUmin. Flow injection manifolds have been miniaturized through the use of fused silica capillaries (i.d. = 25 -100 flm) or through lab-on-a-chip technology (see Section 33C). The rollers of typical commercial peristaltic pumps are long enough so that several reagent and sample streams can be pumped simultaneously. Syringe pumps and electroosmosis are also used to induce flow in flow injection systems. As shown in Figure 33-2a, flow injection systems often contain a coiled section of tubing (typical coil diameters are about 1 cm or less) whose purpose is to enhance axial dispersion and to increase radial mixing
The injectors and detectors employed in flow injection analysis are similar in kind and performance requirements to those used in high-performance liquid chromatography (HPLC). Sample sizes for flow injection procedures range from less than 1 flL to 200 flL, with 10 to 30 flL being typical for most applications. For a successful analysis, it is vital that the sample solution be injected rapidly as a pulse or plug of liquid; in addition, the injcctions must not disturb the tlow of the carrier stream. The most useful and convenient injector systems arc based on sampling loops similar to those used in chromatography (see, for example, Figures 27-5 and 28-6). The method of operation of the sampling loop is illustrated in Figure 33-2a. With the sampling valve in the position shown, reagents flow through the bypass. When a sample has been injected into the loop and the valve turned 90', the sample enters the flow as a single, well-defined zone. For all practical purposes, flow through the bypass ceases with the valve in this position because the diameter of the sample loop is significantly greater than that of the bypass tubing. The most common detectors in flow injection are spectrophotometers, photometers, and fluorometers. Electrochemical, chemiluminescence, atomic emission, and atomic absorption detectors have also been used.
Dialysis and Gas Diffusion, Dialysis is often used in continuous flow methods to separate inorganic ions, such as chloride or sodium, or small organic molecules, such as glucose, from high-molecular-mass species, such as proteins. Small ions and molecules diffuse relatively rapidly through hydrophilic membranes of cellulose acetate or nitrate but large molecules do not. Dialysis usually precedes the determination of ions and small molecules in whole blood or serum. Figure 33-4 is a diagram of a dialysis module in which analyte ions or small molecules diffuse from the sample solution through a membrane into a reagent stream, which often contains a species that reacts with the analyte to form a colored species, which can then be determined photometrically. Large molecules that interfere with the dctermination remain in the original stream and are carried to waste. The membranc is supported between two Teflon plates in which com-
To Reagent
in
detector
t
~ Membrane
-
-
Separations in FIA
Separations by dialysis, by liquid-liquid extraction, and by gaseous diffusion are easily accomplished automatically with tlow injection systems'
"
t
Sample In
'F(J[ a review of applications of rIA for sample preparation and separatIOns. See G. D. Clark. D. A. Whitman, G. D. Christian. and 1. Ruzicka, Cril. Rel'. Anal. Chern., 1990. 21151. 35Y.
tTo waste
dialysis flow module. The membrane is supported between two grooved Teflonblocks. FIGURE 33-4
A
Aqueous
to waste
Organic
Fe Detector Sample
liquid ~
To waste
_L
t
Jl
solution~
>
c .~
Organic to detection system
~ =8 1!.
-;
~L (a) Flow diagram of a flow injection system containing an extraction module (ABC). (b) Details of A, the organic injector system. (c) Details of C, the separator. (Adapted from J. Ruzicka and E. H. Hansen, Flow Injection Analysis, 2nd ed., New York:Wiley,1988. With permission of John Wiley& Sons.)
_
FIGURE 33-5
plementary channels have been cut to accommodate the two streams on opposite sides of the membrane. The transfer of smaller species through the membrane is usually incomplete (often less than 50%). Thus, successful quantitative analysis requires close control of temperature and flow rates for both samples and standards. Such control is easily accomplished in automated flow injection systems. Gas diffusion from a donor stream containing a gaseous analyte to an acceptor stream containing a reagent that permits its determination is a highly selective technique that is often used in flow injection analysis. The separations are carried out in a module similar to that shown in Figure 33-4. In this application, however, the membrane is usually a hydrophobic microporous material, such as Teflon or isotactic polypropylene. The determination of total carbonate in an aqueous solution is an example of this type of separation technique. Here, the sample is injected into a carrier stream of dilute sulfuric acid, which is then directed into a gas-diffusion module, where the liberated carbon dioxide diffuses into an acceptor stream containing an acid-base indicator. This stream then passes through a photometric detector that yields a signal proportional to the carbonate content of the sample. Solvent Extraction. Solvent extraction is another common separation technique that can be easily adapted to continuous flow methods. Figure 33-5a shows a flow diagram for a system for the colorimetric determination of an inorganic cation by extracting an aqueous solution of the sample with chloroform containing a complexing agent, such as 8-hydroxyquinoline. At
point A, the organic solution is injected into the samplecontaining carrier stream. Figure 33-5b shows \hat the stream becomes segmented at this point anClis madc up of successive bubbles of the aqueous solution and the organic solvent. Extraction of the metal complex occurs in the reactor coil. Separation of the immiscible liquids takes place in the T-shape separator shown in Figure 33-5c. The separator contains a Teflon strip or fiber that guides the heavier organic layer out of the lower arm of the T, where it then flows through the detector labeled Fe in Figure 33-5a. This type of separator can be used for low-density liquids by inverting the separator. It is important to reiterate that none of the separation procedures in FIA methods are complete. Bccause unknowns and standards are treated identically, incomplete separation is unimportant. Reproducible timing in FIA ensures that, even though separations are incomplete, there is no loss of precision and accuracy as would occur with manual operations.
Effect of convection and diffusion on concentration profiles of analytes at the detector: (a) no dispersion, (b) dispersion by convection, (c) dispersion by convection and radial diffusion, and (d) dispersion by diffusion. (Reprinted with permission from D. Betteridge, Anal. Chern., 1978,50, 836A. Copyright 1978 American Chemical Society.) FIGURE 33-6
the fluid moves more rapidly than the liquid adjacent to the walls, creating the parabolic front and the skewed zone profile shown in Figure 33-6b. Diffusion also causes broadening. Two types of diffusion can, in principle, occur: radial, which is perpendicular to the flow direction, and longitudinal, which is parallel to the flow. It has been shown that longitudinal diffusion is insignificant in narrow tubing, and radial diffusion is much more important. In fact, at low flow rates, radial diffusion is the major source of dispersion. Under such conditions, the symmetrical distribution shown in Figure 33-6d is approached. In fact, flow injection analyses are usually performed under conditions in which dispersion by both convection and radial diffusion occurs; peaks like that in Figure 33-6c are then obtained. Here, the radial dispersion from the walls toward the center essentially frees the walls of analyte and nearly eliminates cross-contamination between samples. Dispersion
Immediately after injection with a sampling valve, the sample zone in a flow-injection apparatus has the rectangular concentration profile shown in Figure 33-6a. As it moves through the tubing, band broadening, or dispersion. takes place. The shape of the resulting zone is determined by two phenomena. The first is convection arising from laminar flow in which the center of Animation: Learn mOre about flow injection analysis.
Dispersion D is defined by the equation
where Co is the analyte concentration of the injected sample and c is the peak concentration at the detcctor (see Figure 33-6a and c). Dispersion is measured by injecting a dye solution of known concentration Co and then recording the absorbance in a flow-through cell. After calibration. c is calculated-from Beer's law.
Dispersion is influenced by three interrelated and controllable variables: sample volume, tubing length, and flow rate. The effect of sample volume on dispersion is shown in Figure 33-7a, where tubing length and flow rate are constant. Note that at large sample volumes, the dispersion becomes unity. Under these circumstances, no appreciable mixing of sample and carrier takes place, and thus no sample dilution has occurred. Most flow injection analyses, however, involve interaction of the sample with the carrier or an injected rcagent. Here, a dispersion value greater than unity is necessary. For example, a dispersion value of 2 is required to mix sample and carrier in a 1: 1 ratio. The dramatic effect of sample volume on peak height shown in Figure 33-7a emphasizes the need for highly reproducible injection volumes when D values of 2 and greater are used. Other conditions also must be closely controlled for good precision. Figure 33-7b demonstrates the effect of tubing length on dispersion when sample size and now rate are constant. Here, the number above each peak gives the length of sample travel in centimeters.
33B-3 Applications of FIA Flow injection applications tend to fall into three categories: low dispersion, medium dispersion, and large d;spersion.
11 .20-
A
j\ \/ "
V
50 em
= 2.0
"E
~
;5
u
=" .2
B
~L sample
II
~ Bypass
\
~iPh~otometer
V
100 em
= 4.0
0.25
~
• To waste
I
Recorder
.~
~
:;:
5
~ 0.3
~
1:
'?
. 0.2
_--Qr;j~,(
FIGURE 33-17 Sketch of Caliper Staccato Replication System. The unit is a ninety-six-channel device designed to handle loading and unloading of microtiter plates and deep wellplates. Itcan accommodate various reagent reservoirs, pipette tips, and waste disposal units. (Courtesy of Caliper LifeSciences, Hopkinton, MA.)
Master laboratory with fraction collection Dispense,
station turntable
dilute. and extract
In addition to general-purpose laboratory robots, robotic units are designed for specific tasks such as loading and unloading of mierotiter and deep well plates. The system shown in Figure 33-17 can dispense ninety-six channels simultaneously at volumes of 2 to 200 ilL. The robot dispenser is a cylindrical design that can access a wide variety of storage racks arranged in a circular pattern. The dispensing head remains stationary while the well holder rotates to selectable positions.
FIGURE 33:16 A robotic laboratory system: (a)robot arm and hand; (b)total system. (Courtesy of Caliper LifeSCiences, Hopkinton, MA.)
device is its ability to change hands. Thus, the robot can leave its tonged hand on the table and attach a svringe in its place for pipetting liquids. . The robotic system is controlled by a computer that can be user programmed. Thus, the instrument can be instructed to bring samples to the master laboratory station where they can be diluted. filtered, parti-
tioned, ground, centrifuged, homogenized, extracted, and treated with reagents. The device can also be instructed to heat and shake samples, dispense measured volumes of liquids, inject samples into a chromatographic column, and collect fractions from a column. In addition, the robot can be interfaced with an automatic electronic balance for weighing samples.
Clinical instruments have long been the focus for laboratory automation. Indeed, the Technicon AutoAnalyzer, an air-segmented continuous flow system,15 was the first truly automated instrument for a clinical laboratory. In 1968 DuPont introduced the ACA (Automated Clinical Analyzer), the first totally automated discrete analyzer. The analyzer was based on prepack-
ged reagents and a conveyor-belt operation in which n aliquot of the sample was obtained, mixed with ppropriate reagents, reacted, and moved to a pho"meter for measurement of absorbance. Later disrete analyzers were based on multilayer tilms (Kodak 'ktaehem) or on the use of a centrifuge to mix the amples and reagents (centrifugal fast analyzers). Today, a wide variety of discrete analyzers are availble for clinical laboratories. Some of these are genral purpose and capable of performing many different eterminations, often on a random access basis. Othrs are of more limited use intended for one or a few pecifie determinations. Many of the general-purpose nalyzers use a combination of traditional chemical ~sts and immunoassays in which antibody-antigen lteractions are used in the determination. Several eneral-purpose analyzers are capable of performing lore than 100 tests, including the determinations hown in Table 33-1. With some of the analyzers, routine tests can be llerrupted to do stat testing (stat is an abbreviation ,f the Latin word statim, meaning "immediately"). In other cases, instruments dedicated to a few highfrequency tests arc used for stat measurements. Many modern analyzers use a closed-tube technology to minimize exposure to biohazards and to reduce manual manipulations. Samples and reagents are dispensed automatically, the measurements made by photometry or ion-selective electrodes, and the results computed. Most have bar-coding capabilities to reduce errors from incorrect patient identification. A typical chemistry-immunochemistry automated analyzer is shown in Figure 33-18. Many dedicated immunoehemical analyzers use microtiter plates or wells in which the reagents are immobilized. Adding the sample begins the immunochemical reaction. A well or microplate reader is then used to measure absorbance or in some cases fluorescence. Automatic loading and unloading via robotic dispensing units (see Section 33D-2) is available with most systems. Several companies now make automated DNA sequencers for clinical and forensic applications. Sequencing is accomplished by incorporating labeled nucleotides into a copy of the DNA piece. The sequence can then be obtained from the positions of the labeled nucleotides. An enzyme is used to make complementary copies of the strands containing the labeled nucleotides. The strands are tben separated by gel electrophoresis.
Radioactive nucleotides were traditionally used for this DNA sequencing, but these have been largely replaced by alternative labeling procedures, such as fluorescence labeling. Laser-excited fluorescence is then used to read the sequence. Commercial instruments can be partially or fully automated. With fully automated systems, a sample tray is loaded with template DNA. All the labeling and analysis steps are performed automatically. Many new techniques, such as tandem mass spectrometry, are under development for simplifying and further automating DNA sequencing. Special-purpose clinical instruments are available for the most-often-used diagnostic tests (glucose, blood gases, urea nitrogen, etc.). Many clinical analyzers have now been miniaturized to the point where they can be used in the field, at a patient's bedside, or at home. Figure 33-19 shows a glucose monitoring system for in-home use. Immobilized glucose oxidase reacts with glucose to produce products that can be detected electrochemically16 Electrodes are' screen-printed using ink-jet printing technology. The meters have memory so that results can be averaged and stored for later recall. The glucose monitor shown in Figure 33-19 is available for about $50.
Blood
Albumin Amylase Bicarbonate
Alcohol Amphetamine
Ammonia
Acetaminophen
C-reactive protein
Caffeine
Barbiturate
Digoxin
Bilirubin Calcium Chloride Cholesterol Cholinesterase
Cannabinoids
Glucose-6-phosphate dehydrogenase Immunoglobulin A Immunoglobulin G Immunoglobulin M Lactate Microalbumin Rheumatoid factor Thyroid (T4)
Creatinine
Glucose HDL cholesterol Phosphate Iron LDL cholesterol Lithium Magnesium Potassium Sodium Total protein Triglyceride Urea nitrogen Uric acid
Cocaine metabolite
LSD Methadone Methaqualone Opiates PCP Urine bleach
Lidocaine
Phenobarbital Primidone
Quinidine Salicylate Theophylline Vancomycin
Urine chromate Urine nitrates
Urine pH Urine specificgravity
330-4
Automatic
Elemental
Organic
Analyzers
Several manufacturers produce automatic instruments for analyzing organic compounds for one or more of the common elements, including carbon, hydrogen, oxygen, sulfur, and nitrogen. All of these instruments are based on high-temperature oxidation of the organic compounds, which converts the elements of interest to gaseous molecules. In some instruments, the gases are separated on a chromatographic column, and in others separations are based on specific absorbents. In most instruments, thermal conductivity detection completes the determinations. Often, these instruments are equipped with devices that automatically load the weighed samples into the combustion area. Figure 33-20 is a schematic of a commercial automatic instrument for the determination of carbon, hydrogen, and nitrogen. In this instrument, samples are oxidized at 900°C under static conditions in a pure oxygen environment that produces a gaseous mixture of carbon dioxide, carbon monoxide, water, elemental FIGURE 33·18 Picture of integrated chemistry-immunochemistry testing system. (Courtesy of
Beckman Coulter, Inc., Fullerton, CA.)
«.1
FIGURE 33-19 Photograph of a blood glucose monitor for in-home use. The meter (a) contains the electronics and display. A droplet of blood is placed on a test strip (b), which is placed at the top of the meter. The test strip contains immobilized glucose oxidase and electrodes for the amperometric detection system. (Courtesy of LifeScan, Inc., Milpitas, CA.)
nitrogen, and oxides of nitrogen. After 2 to 6 min in the oxygen environment, the products are swept with a stream of helium through a 750"C tube furnace where hot copper reduces the oxides of nitrogen to the element and also removes the oxygen as copper oxide. Additional copper oxide is also present to convert carbon monoxide to the dioxide. Halogens are removed by a silver wool packing.
Combustion
Reduction
Sample i~i"I~'l"1
\O;J&;.\I,.',,-;~
Mixing volume ..
33-2 Sketch a flow injection system that could be used for the determination of phosphate in a river water sample by means of the molybdenum blue reaction (phosphate + molybdate + ascorbic acid in acid solution give phosphomolybdenum blue, which absorbs at 660 nm). 33-3 Design a flow injection system for determining lead in the aqueous effluent from an industrial plant based on the extraction of lead ions with a carbon tetrachloride solution of dithizone, which reacts with Pb" to form an intensely colored product.
FIGURE 33-20 An automatic C, H, and N
analyzer. (Courtesy of Perkin-ElmerCorp., Norwalk, CT.)
33-4 Compare and contrast continuous flow and discrete automated systems. Give the advantages and disadvantages of each type of automated system. 0,
He
t The products from the reaction furnace pass into a mixing chamber where they are brought to a constant temperature. The resulting homogeneous mixture is then analyzed by passing it through a series of three precision thermal conductivity detectors, each detector consisting of a pair of sensing cells. Between the first pair of cells is a magnesium perchlorate absorption trap that removes water. The differential signal then serves as a measure of the hydrogen in the sample. Carbon dioxide is removed in a second absorption trap. Again, the differential signal between the second pair of cells is a meaSure of carbon in the sample. The remaining gas, consisting of helium and nitrogen, passes through the third detector cell. The output of this cell is compared to that of a reference cell through which pure helium flows. The voltage difference across this pair of cells is related to the amount of nitrogen in the sample. For oxygen determinations, the reaction tube is replaced by a quartz tube filled with platinized carbon. When the sample is pyrolyzed in helium and swept
* Answers ~
through this tube, all of the oxygen is converted to carbon monoxide, which is then converted to carbon dioxide by passage over hot copper oxide. The remainder of the procedure is the same as just described, with the oxygen concentration being related, to the differential signal before and after absorption orthe carbon dioxide. For a sulfur determination, the sample is combusted in an oxygen atmosphere in a tube packed with tungsten(VI) oxide or copper oxide. Water is removed by a dehydrating reagent located in the cool zone of the same tube. The dry sulfur dioxide is then separated and determined by the differential signal at what is normally the hydrogen detection cell. In this instance, however, the sulfur dioxide is absorbed by a silver oxide reagent. The instrument shown in Figure 33-20 can be fully automated. In this version up to sixty weighed samples contained in small capsules are loaded into a carousel sample tray for automatic sampling.
are provided at the end of the book for problems marked with an asterisk.
Problems with this icon are best solved using spreadsheets.
33-1 List sequentially a set of laboratory unit operations that might be used to (a) ascertain the presence or absence of lead in flakes of dry paint. (b) determine the iron content of multiple-vitamin and mineral tablets. (c) determine the glucose concentration in a patient's blood.
33-5 Give the advantages and disadvantages of sequential injection analyzers compared to traditional flow injection analyzers. 33-6 Lab-on-a-chip technology is used in several analyzers made by Agilent Technologies. Use a search engine such as Google to find such an analyzer. Describe in detail the use of microfluidies in one Agilent analyzer. Discuss the types of determinations possible and the advantages and limitations of lab-on-a-chip technology as applied to the analyzer chosen. 33-7 Sketch a flow injection apparatus for the determination ous samples.
of sodium sulfite in aque-
33-8 Sketch a flow diagram (indicating columns, detectors, and switching valves) designed to satisfy the following requirements. First, the solvent peak must be rapidly separated from two analytes of much lower volatility than the solvent. Second, the solvent peak should not pass into the analytical column. Third, the two analytes, which differ considerably in polarity, must be separated and ultimately determined quantitatively. Challenge
Problem
33-9 Lawrence, Deo, and Wang (Anal. Chern., 2004, 76,3735) have described an electrochemical biosensor for determining glucose based on a carbon paste electrode. (a) What electrochemical technique is used with the enzyme electrodes described? (b) What are the advantages of incorporating an enzyme in a carbon paste electrode matrix? (c) What is a mediator and how is it used with these biosensors? (d) What is the advantage of using a mediating paste liquid instead of a conventional carbon paste electrode? (e) Give the enzyme and mediator reactions. (f) What was cyclic voltammetry used for in the Lawrence, Deo, and Wang study? (g) What are the approximate response times for these electrodes? (h) Which of the new mediators gave the highest sensitivity? Which gave the wider linear dynamic range? (i) Discuss in detail how the current measured with these biosensors is related to the glucose reaction rate. How was the Michaelis constant Km determined?
34A INTRODUCTION TO PARTICLE SIZE ANALYSIS
Particle Size Determination
R
article size information
portant formanx
is extremely im-
research projects and ine
..dustrial processes. Several analytical
tech-
niques give particle size informatioa. Some give onlX a raean size, whereas others give a complete particle size distributiofL Hence, the first step in performing
a particle size anal,ysis is to choose the
appropriate
analxtical
technique.
We examine in
this chapter some of the considerations
that influ-
ence this choice and then focus On three techniques: low-angle
laser light scattering,
scattering,
and photosedimentation,
dynamic
light
techniques
that we have not yet discussed in this book. The specific particle sizing method chosen depends on the t.vpe of size information needed and the chemical and physical properties of the sample. In addition to the three techniques discussed here, molecular sieving, electrical conductance, copy, capillary hydrodynamic light obscuration
counting, fieldllow
Doppler anemometry,
micros-
chromatography, fractionation,
and ultrasonic spectrometry
are commonly applied. Each of the particle sizing methods has its advantages and drawbacks for particular
samples and anal,yses.
r::;;l
Throughout this chapter, this logo indicates an opportunity for online self-study at www .thomsonedu.com/chemistry/skoog, linking you to
l2J
interactive
tutorials,
simulations,
and exercises.
Particle size analysis presents a particular dilemma.l In general, we try to describe the particle size by a single quantity, such as a diameter, volume. or surface area. The particle size distribution is a plot of the number of particles having a particular value of the chosen quantity versus that quantity or a cumulative distribution representing the fraction of particles bigger or smaller than a particular size. The dilemma arises because the particles being described are three dimensional. The only three-dimensional object that can be described by a single quantity is a sphere. Given the diameter of a sphere, we can calculate its surface area and volume exactly. If we know the density of a spherical particle, we can also calculate its mass . How then do we deal with nonspherical particles? The usual approaches are to assume the particles are spherical and then to proceed as we would with'spherical particles, or we can convert the measured' '¥oIantity into that of an equivalent sphere. For example, if we obtain the mass m of a particle, we can convert this into the mass of a sphere because m = (4/3)7Tr3p, where I' is the particle radius and p is its density. This allows the particle size to be described by only its diameter (d = 21'). This diameter then represents the diameter of a sphere of the same mass as the particle of interest. Similar conversions can be made with other measured quantities, such as surface area or volume. Another basic problem with particle size measurements is that different techniques often give different results for three-dimensional particles. Even if the particle diameter were to be measured directly with a microscope, what dimension is measured? If the particle were cubic, three different dimensions (lengths) could be taken as the diameter. For example, the maximum length could be taken as the diameter. This is equivalent to saying that the particle is a sphere of this diameter. Or the minimum length could be taken as the diameter. Alternatively, the volume or surface area could be used to calculate the diameter of the equivalent sphere. All the results obtained by this single technique, microscopy, will be different but correct for the quantity being measured. It is thus not surprising that For additional information, see T. Allen. Particle Size .\1easuremenr. 5th ed., Vol. 1, London: Chapman & Hall. 1997; S. P. Wood and G. A. Von Wald, in Handbook of Instrumental Techniques for Anahtical Chemislrv F. Settle, ed .. Upper Saddle Rin~r, NJ: Pr~ntice-Hall. 1997: H. G Banh. '\fodern Methods of Particle Size Analvsls'. New York: Wik~,198-t.
different techniques can give different results for particle sizes or particle size distributions. The onlv reasonable solution to the size quandary is to use the' same measuring technique and measured quantity for comparisons of particle sizes and particle size distributions. Comparisons between instruments that use different measuring procedures are sometimes made but are generally considered to be qualitative. Some measurement techniques also require physical characteristics, such as density and refractive index. For example. refractive-index information is usually needed for methods based on light scattering, but densities are generally required for those based on sedimentation. Often, assumptions are made about these quantities unless measured values are available. These assumptions can again lead to discrepancies in measured particle sizes. Before choosing a particle sizing technique, examination of the samples under a microscope is usually wise bec'\use the range of sizes and shapes present can then be estimated. Most particle size methods are sensitive to particle shape and all are limited with respect to the particle size range. Particles with approximately spherical shapes are measured most accurately. Needles and other shapes that differ significantly from spherical are often analyzed by microscopy. For many techniques, particle sizes are best obtained by suspending the particles in a fluid in which the particles are insoluble. The fluid can produce a suspension that is homogeneous in concentration and fairly uniform in size for introduction to the particle sizing instrument. Fluid suspensions also disrupt any cohesive forces that could lead to coagulation or agglomeration of the particles. The fluids chosen must be chemically inert toward the materials contacted in the instrument.
348
LOW-ANGLE LASER LIGHT SCATTERING
The laser low-angle laser light scattering (LALLS)' technique, also called laser diffraction, is one of the most commonly used methods for measuring particle sizes and size distributions from 0.1 f1mto 2000 f1m.The
l
"See 1. D. Ingle Jr, and S R. Crouch, Spectrochemical Analysis, Upper Saddle River. NJ: Prentice-Hall, 1988, pp. 518-19; P. E. PlanlZ, in Modem \/elhoc4. ofPartic{e Size Analysis. H. G. Barth, ed., New York: Wiley, 198~, Chap 6
technique is popular because of its wide dynamic range. its precision, its ease of use, and its adaptability to samples in various forms. The measurements are made by exposing the sample to a beam of light and sensing the angular patterns of light scattered by particles of different sizes. Because the patterns produced arc highly characteristic of the particle size, a mathematical analysis of the light scattering patterns can produce an accurate, reproducible measurement of the size distribution.
A typical laser diffraction apparatus is shown in Figure 34-1. The beam from a continuous-wave (CW) laser, usually a He-Ne laser, is collimated and passed through the sample, where scattering from particles occurs. The beam is then focused on a detector array where the scattering pattern, shown in Figure 34-1 as a diffraction pattern, is measured. The scattering pattern is then analyzed according to theoretical models to give the particle size distribution. Some instruments monitor the concentration of particles in the beam by means of an obscuration detector located at the focal point of the lens. If no particles are present in the beam, all the light falls on the obscuration detector. As soon as particles enter the beam, they block some of the light and scatter light onto the elements of the detector array. The fraction of the light attenuated by scattering, absorption, or both is related to the concentration of particles in the beam (see Section 340). Instrument manufacturers provide several different accessories for sample introduction. For example, some introduce the sample directly into the laser beam as an aerosol. Samples can also be passed through a sample cell with transparent windows or suspended in a cuvette while being agitated. Dry powders can be blown through the beam or allowed to fall through the beam by gravity. Particles in a suspension can be recirculated through the beam by means of a pump.
Most commercial instruments use optical models in their analvsis software that are based on Mie scattering theory or' Fraunhofer diffraction. Mie [heary provides a co~plete solution to the problem of light scattering by a sphere, including the effects of transmitted and absorbed light. On the other hand, the Fraunhofer dif-
FIGURE 34-2 Scattering from particles of different sizes. (a) Largeparticle scattering showing interference. Rays emitted in a backward direction observed at point Dean destructively interfere because of the large path difference between the route SXD and the route SYD. Rays emitted in the forward direction observed at position D' and traveling routes SXD' and SYD' are more likely to constructively interfere because of the much smaller path difference. (b)The distributions of scattered light are shown for three particle sizes, corresponding to Rayleigh scattering, Debye scattering, and Mie scattering. Scattering angle 8 is the angle between the incident and scattered rays with radiant powers Po and P" respectively. Thus, 8 is 0' for forward scattering and 180' for scattering in the backward direction.
D'
FIGURE 34-1 Laser diffraction apparatus. When a particle enters a laser beam, light is scattered at an angle related to the particle size. The scattered light is collected by a detector and the resulting scattering pattern is analyzed. The scattering pattern of a group of different-size particles is, within limits,the summation of the patterns of the individualparticles.
model is much simpler to implement. This model treats particles as opaque, circular apertures obstructing the beam of light.
fraction
Mie Theory
[n the Mie theory, particles are considered to be finite objects instead of point scatterers. Scattering centers are found in various regions of the particles. When such particles scatter light, the scattering centers are far enough apart that some interference is likely between the rays emitted from one area of the particle and those from another. This condition leads to an intensity distribution that is quite different from the distribution observed from small particles. The scattering that occurs with particles much smaller than the wavelength of the light (d < 0.05A) is termed Rayleigh scattering. Figure 34-2a illustrates the interference that can occur in large-particle scattering. As a result, the intensity distribution pattern shifts to one showing predominantly forward scattering as depicted in Figure 34-2b. Scattering from particles with diameters near the wavelength of light (0.05A < d < A) is sometimes termed Debye scattering. Mie scatterill[; occurs for particles with diameters larger than the wavelength of the incident light (d > A). Note in Figure 34-2 that the envelopes for Debye and Mie scattering are similar to Rayleigh scattering in the
forward direction but quite different in the reverse direction. Often, Debye scattering is omitted as a separate class and Mie scattering is considered to occur for particles with diameters close to the wavelength of the light and larger. When the particle size is small compared to the incident wavelength, the scattered light shifts toward the side and rear and finally spreads in all directions (Rayleigh scattering). [n the Rayleigh scattering limit, the intensity distribution of the front scattering is nearly constant and independent of particle size. Before the advent of powerful desktop computers, the rigorous Mie theory was difficult to implement for the determination of particle size distributions in laser diffraction systems. The theory assumes that the particles are isotropic and spherical with a smooth surface. Even if these conditions hold, a complex materialdependent Mie parameter must be known. Finally, Mie theory is not applicable for mixtures of different components. Fraunhofer Diffraction
Theory
Fraunhofer theory is a simplification that considers the particles to be transparent, spherical, and much larger than the wavelength of the incident beam. Absorption and interference effects are not considered as they are in Mie theorv. Thus. the particle behaves like a circular
aperture and scattering from it results in a diffraction pattern, known as an Airy pattern. The Airy pattern ean be expressed as a function of x = 211"rs/Af, where r is the radius of the particle, s is the radial distanee measured from the optical axis, A is the wavelength of the incident radiation, and f the focal length of the lens (see Figure 34-1). The Airy funetion can be written as
_ (2ib))'
1-/0
--
x
where lis the scattered intensity, 10 is the intensity at the center of the pattern. and i[ is the first-order spherical primary Bessel function. A plot of the Airy function is shown in Figure 34-3. The inset shows an expansion of the y-axis to allow the extrema to be seen more clearly. Note the positions of the maxima and minima. The Airy patterns are different for different particle radii. Figure 34-4 shows the patterns for particles of radii r. 2r. and 0.5r. Note that the pattern is broader for particles of smaller size and narrower for larger particles. Note also that the extrema shift to higher values of x as' the particle size decreases. When particles of
different sizes are present, the intensity pattern can be considered to be the summation of the Airy patterns for individual particles. Particle Size Distribution
Analysis
[n actuality, particles of various sizes are present in any real sample, and the intensity distribution of the scattered light is used to calculate the particle size distribution. The relationship between the intensity distribution of the scattered light and the particle size distribution for the case of Fraunhofer diffraction is I(x)
= 10
r Ci~X))
2
f(d)dd
where I(x) is the intensity distribution of the scattered light.f(d) the particle size distribution coefficient, and d the particle diameter. We can write Equation 34-2 in terms of the scattering angle 0 and a size parameter a
=
211"r1A
=
11"d/A
1(0)
=
10
i (2J(ao))' X
0
~
f(d)dd
100 90 80 70 rj
'"
The Airyfunction showing a plot of intensity 1 relative to the central intensity 10as a function of the variable x (see text). The inset shows an expansion of the y-axis to show the maxima and minima more clearly. FIGURE 34-3
.§
60
~ '3 ~
50
"
40
>
E~ U
30 20
This equation can bc solved in matrix form or by iterative methods. In most modern instruments, the measurement is performed by an array of N detectors. Also, Mie scattering theory is used in many instrumcnts instead of Fraunhofer diffraction theory. In one popular approach the particles are divided into size intervals and each interval is assumed to generate an intensity distribution according to the average sizc. In this case, the preceding equation becomes N
giN) =
:L K(N,di)f(d,)!l.d i=l
where giN) is the output of the Nth detector, K(N, d,) is the response coefficient of the Nth detector, di is the ith diameter, and !l.d is the particle size inter~a~ number. The particle size distribution f(d,) is calculated from the relationship between the output of the dctector and its response function. The distrihution is usually calculated on the basis of volume. Figure 34-5 shows a plot of the cumulative undersize distribution. The value at each particle diameter represents the percentage of particles having diameters less than or equal to the expressed value. A frequency distribution showing the percentage of particles having a particular particle diameter or range of diameters is also com-
10 0 0.1
manly given. These can be plotted either as histograms or as continuous distributions.
Since the initial introduction of laser diffraction instrumentation in the 1970s, many different applications to particle size analysis have been reported.3 These have included measurements of size distributions of radioactive tracer particles, ink particles used in photocopy machines, zirconia fibers, alumina particles, droplets from electronic fuel injectors, crystal growth particles, coal powders, cosmetics, soils, resins, pharmaceuticals, metal catalysts, electronic materials, photographic emulsions, organic pigments, and ceramics. About a dozen instrument companies now produce LALLS instruments. Some LALLS instruments have become popular as detectors for size-exclusion chromatography.
·'See. for example. B. B. Weiner, in Modern Method, of Panicle Size Analysis. H. G. Barth, ed .. New York: Wiley, 1984, Chap. 5; P. E. Plantz, ibilL Ch~p. 6
Dynamic light scattering (DLS), also known as photon correlation spectroscopy (peS) and quasi-elastic light scattering (QELS), is a powerful technique for probing solution dynamics and for measuring particle sizes.' The DLS technique can obtain size information in a few minutes for particles with diameters ranging from a few nanometers to about 5 f1m. Thc DLS technique involves measurement of the Doppler broadening of the Rayleigh-scattered light as a result of Brownian motion (translational diffusion) of the particles. This thermal motion causes time fluctuations in the scattering intensity and a broadening of the Rayleigh line. The Rayleigh line has a Lorentzian line shape. In macromolecular solutions, concentration -1For additional information. see 1. D. Ingle Jr. and S. R Crouch. Spectrochemical Analysis. Upper Saddle RIver. NJ: Prentice-Hall, 1988. Chap. 16; N. C. Ford. in Measurements of Suspended Partides by Quasi·elastic Light Scattering, B. E. Dahenke. ed .. New York: \\/iley. 1983; M. L. McConnelL Anal. Chern., 1981, 53. 1007:\: B. 1. Berne and R. Pecora, D.\'namic Light Scattering with Applications to Chemistry. Blulogy and Physics, Nc:w York: Wiley. IY76, reprinted by Dover Publications. fne .. N.::w 'York.
averaged product is obtained at various delay times and plotted against the delay time. The autocorrelation function is the Fourier transform of the power spectrum. Because the scattered radiation has a Lorentzian line shape. its Fourier transform should be an exponential decal', as illustrated in Figure 34-6b. According to the thco~v of DLS, the time constant of the exponential decav T i; directly related to the translational diffusion coefficient of the isotropic. spherical particles in Brownian motion.
fiuctuations arc usually dominant. Under these conditions, the width of the Rayleigh line is directly proportional to the translational diffusion coetJicient Dr. The DLS method uses optical mixing techniques and correlation analysis to obtain these diffusion coefficients. The line widths (1 Hz to I MHz) are too small to be measured bv conventional spectrometers and even interferometers.
The sample in a DLS experiment is well-dispersed in a suspending medium. [n a typical DLS experiment, the sample is illuminated by a single-wavelength laser beam. To measure the Doppler widths, the DLS instrument uses optical mixing or light-beating techniques to translate the optical frequencies (-6 X 10" Hz with the 488-nm line of an Ar' laser) to frequencies near 0 Hz (dc) that can be easily measured. [n most DLS instruments, a photomultiplier tube (PMT) is uscd as a nonlinear mixer because its output is proportional to the square of the electric field falling on its photosensitive surface. To see how the PMT acts as a mixer, let us assume that thc scattered radiation contains sine wavcs of two frequencies WIand w,. The elcctric field vector E can be written as
where E, and E, are the amplitudes of the two waves. The PMT output signal S(w) is proportional to the square of the electric field and can be expressed as S(w)
A(Elsin'WII" Eisin'w21 + E,E,[cos(w, - WI)I - COS(W2+ WI)IJ} =
(34-6)
wherc A is a proportionality constant. The PMT cannot respond directly to frequencies and or the sum term because these are greater than 10" Hz for visible radiation. The PMT can respond, however, to the difference frequency term (w, - WI)'which can be as small as a few Hz. When multiple frequencies are present, a difference spectrum is generated that is centered at o Hz. The time dependence of the intensity fluctuations is then used to obtain the particle size information. Optical mixing is accomplished by beating thc scattered light against a small portion of the source bcam (hetcro-
w,
It]
w,
Tutorial: Learn more about particle size anal)'sis
Timt' la)
kT ds = h-T/DT
(h)
from an aqueous solution of 2 .02-~m (diameter) polystyrene spheres; (b) autocorrelation function of intensity fluctuations. dyne detection) or by beating the scattered light against itself (self-beating). The PMT output signal is proportional to the scattered radiation intensity. Bccause the dispersed particles are in continuous thermal motion, the observed scattered intensity 1(1) fluctuates with time. The intensity-versus-time trace resemhles a noise pattern as shown in Figurc 34-6a. Small particles cause thc intensity to fiuctuate more rapidly than large particles. The next step in the process is to determinc the autocorrelation function of the signal. With autocorrelation, the signal is multiplied hy a delayed version of itself, and the product is time-averaged. The time-
__
L_a,_ is the Stokes diameter at time t. Let us now consider a small change in absorbance AA, as the sedimentation time changes from t to t + A. Here, the average Stokes diameter in the beam is di, and we can write AA,
-K,
= kcbnidi
2
6Horiha., Ltd Notice for CAPA-SOO, U.S. Version, Code {)-1. 169-1.00 , December 1993: see aho sections 7.13 and 8.6.1 of T. Allen, Particle Si:.e ,I,feasurement, Vol. L 5th ed" London: Chapman & Hall, 1997; H. 1. Karnack, 11nal. Chern., 1951, 23, 8+4. 'See T. Allen, Particle Si:.e Measurement, Vol. I. 5th ed , London: Chapman &
Hall..1997. pp 269-327.
340-3
Applications
Photosedimentation has been used to determine particle sizes of polymers, dye materials, pharmaceutical preparations, and biological materials. It is used in quality control during the production of paints, foods, and ceramics. In the pharmaceutical industry. for example, one of the current areas of interest is the delivery of medicine via inhalation powders. For these, fine particles are prepared and used in an inhaler as dry powders to deliver medicine directly to the lungs (pulmonary delivery). Some preparation processes use supercritical fluids to control powder formation from a wide ran"e of chemicals, such as inorgal1lc and orgal1lc material; polymers. peptides. and proteins. For dry powders to be used as inhalants, the particle size must be within a quite limited range. Hence. techmques such
as photosedimentation are used to monitor particle sizes during the preparation process or for quality control purposes. With dry powder inhalation. protein-based drugs can be delivered without being decomposed by the digestive system before entering the blood stream. Delivering medication in dry powder form thus has advan-
Challenge Problem
tages over intravenous injection for several types of pharmaceutical prcparations. Pulmonary delivery of drugs to treat diabetes (insulin), multiple sclerosis, cystic fibrosis, anemia, asthma, and several other diseases have been implemented or arc currently under development. Particle size analysis is playing a significant role in these advances.
34-15 (a) Use an Internet search engine to find laser diffraction instruments made by a commercial company (try Malvern, Sympatec, Shimadzu, Beckman Coulter, or Horiba). Choose a specific instrument and describe its operation. What laser is used' What is the detection system" Give typical values of accuracy and precision. . (b) What ranges of particle sizes can the chosen instrument determme? (c) What types of sampling accessories are available for the instrumenP What sample cells are available' (d) What is the size of the instrument? (e) What models does the software use to determine particle sizes' (0 Are any options available to automate particle size analysis? . (g) Use a search e"gine to find a paper in the literature that uses las~r dIffraction to determine particle sizes. Describe the application in detat!.
*Answers are provided at the end of the book for problems marked with an asterisk. ~
Problems with this icon are best solved using spreadsheets. 34-1 What is a normal particle size distribution') What is a cumulative particle size distribution? 34-2 What is the major problem presented by particle size analysis? 34-3 What quantities are used to describe particle size? 34-4 How are nonspherical particles dealt with in particle size analysis? 34-5 Why are comparisons of particle sizes between different instrumental techniques only qualitative? 34-6 Define Mie scattering. For what particle sizes does Mie theory apply? 34-7 What is an Airy pattern? How does it arise in diffraction' 34-8 What is a cumulative undersize particle distribution? 34-9 Discuss the major differences between DLS and LALLS.
*34-10 The translational diffusion coefficient of the cnzyme aspartatc transcarbamylase in dilute aqueous solution was found to be 3.75 x 10-7 cm 2 s -[ at 20"C (1) = 1.002 cPl. What is the hydrodynamic diameter of the particles? What does the hydrodynamic diameter mean if the particles are nonspherical? *34-11 A protein molecule is approximately spherical and has a hydrodynamic diameter of 35 llm. What is the translational diffusion coefficient of the protein at 20°C in dilute aqueous solution? *34-12 In a particular batch of polystyrene microspheres, their diameter is 10.0 llm and density 1.05 g cm-'. In 20"C water (PF = 0.998 g cm-'), what will be the settling velocity of these particles in a I G gravitational field? What time will it take for the particles to sediment 10 mOl? *34-13 For polystyrene spheres of 10.0 11mdiameter in water at 20°e, how long will it take the particles to move from an initial radius of 70 mOl to an analytical radius of 80 mOl in a centrifugal field of 10,000 rpm? What is the centrifugal acceleration in G at 10,000 rpm" *34-14 A polystyrene particle settles, moving from a starting radius of 70 mOl to an analytical radius of 80 mOl in 2.9 s in a centrifugal field of 9000 G. If the particle is in an aqueous solution at 20°C, what is the Stokes diameter'
j :+'$
Instrumental Analysis in Action
'
The John Vollman case in New Brunswick. Canada, in 1958 was the first murder case in which neutron activation analy-
some chocolate from a local restaurant.
sis (NAA), then labeled in the press as "atomic evidence,"
she \\'as seen talking to the driver of a light-green Pontiac
played a major role in the outcome. Since then. NAA has
with Maine license plates. About an hour later, two friends saw her seated in a green Pontiac. Another witness saw a
been widely used and accepted in forensic science for determining trace elements.
the court shifted so dramatically against Vollman that he changed his plea to guilty of manslaughter. He admitted to
The next day Gaetane 's movements in the hours leading up to her murder were retraced. At 4 p.m., she purchased
killing Gaetane.
A short time later,
found him guilty as charged. He was scntenc~d to death, a sentence that was later commuted
death to the mul-
In May 1958, a 16-year-old girl, Gaetane home in lale afternoon
Bouchard, left her
Brunswick town of Edmundston.
When she failed to return
home by 8 p.m., her father telephoned mentioned
friend, John Vollman, who lived across the border in Madawaska,
Maine. Mr. Bouchard drove across the border
and met with the 20-year-old Vollman who worked a night shift at a printing plant. Vollman claimed that he and Gaetane were no longer seeing each other and that he was now engaged to another woman. When Bouchard
returned to Edmundston,
he called the
police and then began searching for his daughter. friends advised him to search an abandoned
gravel pit out-
over 2 inches long. Detectives immediately surmised that Gaetane had pulled the hair from the murderer as she mine whether the hair found had come from Vollman.
a
A few minutes
ity in forensic science. The major reason, of course. is that NAA is expensive and requires access to a nuclear reactor. finge;~rinting.'
in hair analysis by DNA
The amount of DNA found at the root of
o~e human hair is sufficient for DNA fingerprinting.
found clutched in the girl's hand when she was aut~psied. Entwined in her fingers was a strand of human hair, a Ilttle
neutron activation analysis has never gained great popular-
Todav NAA has been superseded
piece of evidence, however, ~as
spot
for young couples. Bouchard's flashlight soon illuminated suede shoe that he recognized as Gaetanc's.
Books, 2000.)
The most important
was a
struggled to free herself. The challenge now was to deter-
Some
side of town. The pit was often a popular "make-out"
half-eaten bar of chocolate, identical to the type that Gaetane had purchased at the restaurant.
even more evidence. Inside the glove compartment
that she might have been with a former boy-
Although capable of incredible sensitivity and selectivity. FIGURE IA6-1 SEM photomicrograph of a human hair (left thinner strand) compared with a cat hair. (From D. Owen, Hidden Evidence: 40 True Crimes and How Forensic Science Helped Solve Them. Buffalo, NY: Firefly
scopically - the missing paint particle. The car revealed
friends, asking if Ihey knew where she was. Some friends
Neutron Activation Analysis in Forensic Science
piece of paint missing from just
below the passenger door. The paint chip found at the crime scene matched perfectly - both visually and later micro-
several of her
the new technique of neutron activation analysis.
Vollman at his workplace
and examined his recently purchased green 1952 Pontiac. They found a heart-Shaped
to go shopping in the small New
to life imprisonment.
John Vollman became the first criminal to be convicted by
tiple stabbings and put the time of death no later than 7 p.m. Detectives then interviewed
He claimed that she
suffered a blackout. The jury did not believe his story and
green car parked by the gravel pit sometime belween 5 and 6 p.m. The medical examiner attributed
but not intentionally.
had i~itially encouraged his advances. but latcr changed her mind. As a struggle broke out, Vollman said that he had
techniques hand. To identify the hair, the ratio of the gamma ray intensitv of sulfur to phosphorus
(SIP) was measured.
In the case
Such
are much less expensive and morc readily avail-
able than neutron activation analysis. Neutron activation analysis has been quite useful. how-
of~thc victim, the ratio was found to be 2.02. The sample
ever, in special forensic situations. For example, NAA has
found in Gaelane's hand had an SIP intensity ratio of 1.02,
been used to determine
while that from VoUman registered
surements. it was concluded that the hair dad nol come from
residues from the hands of suspects and metal fragments taken from the wounds of victims. During the investigation
Gaetane. but was a close match to that from the suspect.
of the assassination
l.07. From these mea-
t
trace amounts of metals in gunshot
of President John F. Kennedy, for ex-
To establish whether the hair found in Gaetane's hand came
Scanning electron microscopic evidence, similar to that
ample, forensic scientists used NAA to determine
later, he found the body of his daughter. She had been re-
from the suspect, investigators
shown in Figure IA6-1. was also consistent with the hair
antimony in the recovered bullets and in metal fragments
peatedly stabbed in the chest and back and then dragged off
duced and somewhat controversial
being that of the suspect.
from the wounds of President Kennedy and Governor John
to die. The police were notified, and the pit was secured as a crime scene.
tivation analysis. Neutron activation analysis can identify
Connally. The concentrations
and determine
significantly from one bullet to the next, but are quite simi-
turned to the recently introtechnique of neutron ac-
trace amounts of as many as 14 different ele-
ments in a single hair. Theoretical that the probability same concentrations
calculations have shown
of two different individuals having the of nine of these clements is about one
The Trial in
19:\0. He pleaded not guilty and seemed very
indicated that a single bullet had wounded both men. The second bullet had struck President Kennedy only. It was
Police searching the pit soon found a dark pool of blood
in a million. [n many cases, the ratios of two element con-
confident that the ·'atomic evidence" would not be allowed.
also concluded
and tire tracks where Gactane's assault had begun. While
centrations
Despite the vigorous objections of the defense, however, . the NAA evidence v,:asadmitted. Scientists eager to explalO
fired by the same gun.'
are strongly indicative of hair from a particular
making plaster casts of the tire tracks. one of the police offi-
person. Neutron activation analysis has also been used to
cers noted two tiny slivers of green paint possibly chipped off the car by rocks as the car sped off. One of the paint
determine the presence of poisons. such as arsenic, in the hair of victims.
chips was no larger than the head of a pin. wbile the second was a larger heart-shaped piece.
the victim were compared
In the Vollman case, hair samples from the suspect and with the hair found in Gaetane's
the NAA procedure
took the witness stand. The mood of
C. Evans, The CIJ._"ebookof Forensic Detection: Hal'" Science Solved 100 (.(the H'orld's ..Hoyt Baffling Crimes. N~w York: Wiley, 1996
I
of these trace elements vary
lar in pieces of metal from a single bullet. The NAA results
John Vollman stood trial for murder in Edmundston November
silver and
that the two bullets were almost certainly
2D. Owen, Hidden E~'idence: 40 True Crimes and How Forensic Science Helped Soh'e Them. Buffalo, NY: Firefly Books, 2000 Jp. Moore, The Fvrensics Handbook..- The Secrets of Crime Scene Investigation. New York: Hames & Noble Books, 2004
This appendix describes the types of errors that are encountered in analytical chemistry and how their magnitudes are estimated and reported.' Estimation of the probable accuracy of results is a vital part of any analysis because data of unknown reliability are essentially worthless.
procedure that yields results that are within:+: 10% of the correct amount of mercury in an are that contains 20% of the metal would usually be deemed unacceptably inaccurate. Accuracy is expressed in terms of either absolute error or relative error. The absolute error E of the mean (or average) x of a small set of replicate analyses is given by the relationship
Two terms are widely used in discussions of the reliability of data: precision and accuracy.
where x, is the true or accepted value of the quantity being measured. Often, it is useful to express the accuracy in terms of the relative error En where
Precision describes the reproducibility of results, that is, the agreement between numerical values for two Or more replicate measurements, or measurements that have been made in exactly the same way. Generally, the precision of an analytical method is readily obtained by simply repeating the measurement. Three terms are widely used to describe the precision of a set of replicate data: standard deviation, variance, and coefficient of variation. These terms have statistical significance and are defined in Section a18-1.
a1A-2 Accuracy
Accuracy describes the correctness of an experimental result expressed as the closeness of the measurement to the true or accepted value. Accuracy is a relative term in the sense that what is an accurate or inaccurate method very much depends on the needs of the scientist and the difficulty of the analytical problem. For example. an analytical method that yields results that are within:+: 10%, or 1 part per billion, of the correct amount of mercury in a sample of fish tissue that contains 10 parts per billion of the metal would usually be considered to be reasonably accurate. In contrast, a
For more d.:tails. _\e~D. A. Skoog, D. M. West, F J Holler, and S. R Crouch. FundamenwL~ of Analrrical Chemistr.\', 8th ed., Belmont. CA: Brooks/Cf?le.2004 I
Frequently, the relative error is expressed as a percentage as shown; in other cases, the quotient is multiplied by 1000 instead of by 100% to give the error in parts per thousand (ppt). Note that both absolute and relative errors bear a sign, a positive sign indicating that the measured result is greater than its true value and a negative sign indicating the reverse. We will be concerned with two types of errors, random errors, often called indeterminate errors, and systematic errors, often called determinant errors2 We will give random error the symbol Ed and systematic error the symbol E,. The error in the mean of a set of replicate measurements is then the sum of these two types of errors:
Random Errors Whenever analytical measurements are repeated on the same sample, a scatter of data such as that shown in Table al-I are obtained because of the presence ~A third type of error that is eocounkred occasionally is gross error, which arises in most instances from a human error. Typical sources indude transposition of numbers in recording. data, spill Lng of a sampk. using the wrong sealm., 1982,54, 1226A; see also http://v.'ww,msLgo\ For example, in the clinical and hiological sciences a~ea. see Sigma Ch~m. ical Co., 3050 Spruce St., St. Louis. MO 63103 and Blo-Rad Lahoratow::'>,
Because N in this case is a finite number, x often differs somewhat from the population mean /l, and thus the true value, of the quantity being measured. The use of a different symbol for the sample mean emphasizes this important distinction. Population Standard Deviation (..,.) and Population Variance (..,.'), The population standard dC\'latlon and the population \'ariance provide statisticallY' SIgnificant
measures of the precision of a population of data. The population standard deviation is given by the equation ,r----,,,,-,
!
\I
2; (x, -
JL)' lim c.~ __ ._ N
V.\'-+"
where x, is again the value of the ith measurement. Note that the population standard deviation is the root mean square of the individual deviations from the mean for the population. The precision of data is often expressed in terms of the variance (IT '), which is the square of the standard deviation. For independent sources of random error in a system, variances are often additive. That is, if there are n independent sources, the total variance IT; IS given by IT;
where IT;, IT), error sources.
...
=
, IT~
deviations ..The relative standard deviation of a data sample ISgIven by
----
,r; +
IT)
+.
+ IT~
(al-9)
are the individual variances of the
Note that the standard deviation has the same units as the data, whereas the variance has the units of the data squared. Scientists tend to use standard deviation rather than variance as a measure of precision. It is easier to relate a measurement and its precision if they both have the same units. Sa,mple Standard Deviation (sl and Sample Variance (s-). The standard deviation of a sample of data that is of limited size is given by the equation
When z = 2, the relative standard deviation is given as a percent; when it is 3, the deviation is reported in parts per thousand. The relative standard deviation expressed as a percent is also known as the coefficient of variatIOn (CV) for the data. That is, CV = ~ x
Lxi ~ 2.844t45
3.771
Xi
N
Other Ways to Calculate Standard Deviations, Scientific calculators usually have the standard deviation function built in. Many can find the population standard deviation IT as well as the sample standard rdevia_ tion s. For any small set of data, the sample standard deviation should be used. To find s with a calculator that does not have a standard deviation key, the following rearrangement of Equation al-IO is easier to use than Equation al-1O Itself:
'"
( Xi
2
-
2; N
Xi )' -
,~I --N---
N -1
'By definition. the number of degrees of freedom is the numher of values thar remain indcpel~dent when s is calculated. \\-'hen the sample mean is ~ed In the calcul.allOn, only .v ~ I values are independent. because one \alue can be obtamed from the mean and the other values.
3.77t
= 0.754 ppm Pb
14.2~0441
= 2.8440882
The Normal Error Law
In Gaussian statistics, the results of replicate meaSUrements arising from indeterminate errors are assumed to be distributed according to the normal error law, which states that the fraction of a population of observations, dNIN, whose values lie in the region x to (x + dx) is given by
5
Substituting into Equation al-13 leads to
i~
Relative Standard Deviation (RSD) and Coefficient of Variation (CVI. Relative standard deviations are often more informative than are absolute standard
2;
0.565504 0.57t536 0.565504 0.564001 0.577600
=-N = 5 = 0.7542
In dealing with a population of data, IT and JL are used In place of s and x in Equations al-11 and al-12.
N
Note that the sample standard deviation differs in three ways from the population standard deviation as defined by Equation al-8. First, IT is replaced by s in order to emphasize the difference between the two terms. Second, the true mean JL is replaced by:t, the sample mean. FInally, (N - I). which is defined as the number of degrees of freedom, appears in the denominator rather thanN7
x
=
(2; x,)' = (3.771)2 =
100%
X
LX,
0.752 0.756 0.752 0.75t 0.760
calculations, these programs can be used to carry out least-squares analysis, nonlinear regression, and many advanced functions.
Example al-2 illustrates the use of Equation a 1-13 to finds.
The following results were obtained in the replicate determination of the lead content of a blood sample: 0.752,0.756,0.752,0.751, and 0.760 ppm Pb. Calculate the mean, the standard deviation, and the coefficient of variation for the data. Solution
x
To apply Equation (Lx,)'IN.
al-l3,
we calculate
LX!
and
2.844145 - 2.8440882 5-1
s=
(D.()()()()4
\j-
568
= 0.00377 = 0.004 ppm Pb s
CV
=:f
X
]00%
=
0.00377
0.7542
X
100%
= 0.5%
Note in Example a 1-2 that the difference between LX; and (Lx,)'1 N is very small. If we had rounded these numbers before subtracting them, a serious error would have appeared in the computed value of s. To avoid this source of error, never round a standard deviation calculation until the very end. Furthermore, and for the same reason, never use Equation al-13 to calculate the standard deviation of numbers containing five or more digils. Use Equation al-IO instead.' Many calculators and computers with a standard deviation function use a version of Equation al-13 internally in the calculation. You should always be alert for roundoff errors when calculating the standard deviation of values that have five or more significant ligures. In addition to calculators, computer software is widely used for statistical calculations. Spreadsheet software, such as Microsoft'· Excel, can readily obtain a variety of statistical quantities9 Some popular dedicated statistics programs include MINITAB, SAS, SYSTAT, Origin, STATISTICA, SigmaStat, SPSS, and STATGRAPHICS Plus. In addition to normal statistics most cases, the first two or three digits in a set of data arc identical to each other. As an alternative, then, to using Equation a 1-10, these identical digits can be dropped and the remaining digits used with Equation a 1-13 For example. the standard deviation for the data in Example al-2 could he based on 0.052, 0.056, 0.052. and so forth (or even 52, 56, 52. etc.). ~S_R. Crouch and E 1- Holler, Applicmions {If Microsoft]; Excel in Anahtical Chemistry. Belmont. CA: Brooks/Cole. 2004 1I10
Here, JL and IT are the population mean and the standard deviation, and N is the number of observations. The two curves shown in Figure al-3a are plots of Equation al-14. The standard deviation for the data in curve B is twice that for the data in curve A. Note that (x - JL) in Equation al-14 is the absolute deviation ofrhe individual values ofx from the mean in whatever units are used in the measurement. Often, however, it is more convenient to express the deviations from the mean in units of the variable z, where x-I-'
z=-IT
Note that z is the deviation of a data point from the mean relative to one standard deviation. That is, when x - JL = ,
"" ~ 0
r
0.2
j
samples, each containing N results, is taken randomly from a population of data, the means of samples will show less and less scatter as N increases. The standard deviation of the means of the samples is known as the standard error of the mean and is denoted by a m' It can be shown that the standard error is inversely proportional to the square root of the number of data points N used to calculate the means. That is, IT
:i!
=--
IT
Areas under Regions of the Normal Error Curve. The area under the curve in Figure al-3b is the integral of EquatIOn al-17 and is determined as follows:
0.1
AN N 0-----_ Deviation
from mean, x -
-
f
a
~
1
\/2; e
(aV2)
dz = erf -
\/Fi
For data in which the sample standard deviation s is calculated, Equation al-18 can be written as
2
s
=-m
where erf(b) is the error function given by
N
Relative error in the sample standard deviation s as a function of the number of measurements N. FIGURE
a1-4
s
VN
1.J
erf(b) =
0.3
"" ~
N
0
cr'
~ 0.2 ~ ~ 0
>
01
a1-3 Normalerror Curves.The standard deviation of B is twice that of A; that is, fIB ~ 2fIk (a)The abscissa is the deviation from the mean in the units of the measurement. (b)The abscissa is the deviation from the mean relative to fI. Thus, A and B produce identical curves when the abscissa is z = (x - iL)/ fI
Iov7T b
-
2
, e-rdx
The fraction of the population between any Specified limits is given by the area under the curve between these limits. For example, the area under the curve between z = -1 and z = + 1 is given by the definite integral
--/::"N =
0>,
FIGURE
-,'/2
m
fl 1 _, --=e
_1V27T
(V2)
,(2dz = erf -
2'
= 0683
Thus, ANIN = 0.683, which means that 68.3% of a populahon of data lie within ±llT of the mean value. For similar calculations with z = 2 and z = 3, we find that 95.4% lie within ±2lT and 99.7% within ±3lT. Valucs for (x - iL) corresponding to ±llT, ±2lT, and ±3lT are indicated by blue vertical lines in Figure al-3. The properties of the normal error curve are useful bccause they permit statements to be made about the probable magnitude of the net random error in a given measurement or set of measurements provided the standard deviation is known. Thus, one can sav that it is 68.3 % probable that the random error asso~iated with any single measurement is within ± IlT, that it is 95.4% probable that the error is within ±2lT, and so forth. The standard deviation is clearly a useful quantitv for estimating and reporting the probable net rando~ error of an analytical method. Standard Error of the Mean. The probability figures for thc Gaussian distribution just cited refer to the probable error of a single measurement. If a set of
where .I'm is the sample standard deviation of the mean. The mean and the standard deviation ofa set of data are statistics of primary importance in all types of science and engineering. The mean is important because it usually provides the best estimate of the variable of interest. The standard deviation of the mean is equally important because it provides information about the precision and thus the random error associated with the measurement. Methods
to Obtain a Good Estimate
of
IT
To apply a statistical relationship directly to finite samples of data, it is nccessary to know that the sample standard deviation s for the data is a good approximation of the population standard deviation IT. Otherwise, statistical inferences must be modified to take into account thc uncertainty in s. In this section, we consider methods for obtaining reliable estimates of a from small samples of data.
Performing Preliminary Experiments. Uncertainty in the calculated value for s decreases as the number of measurements N in Equation al-IO increases. Figure al-4 shows the relative error in s as a function of N. Note that when N is greater than about 20, sand IT can be assumed. for most purposes. to be identical. Thus, when a method of measurement is not excessively timeconsuming and when an adcquate supply of sample is available, it is sometimes feasiblc and economical to carry out preliminary experiments whose sole
purpose is to obtain a reliable standard deviation for the method. For example, if the pH of numerous solutions is to be measured in the course of an investigation, it is useful to evaluate 5 in a series of preliminary experiments. This measurement isstraigbtforward, requiring only that a pair of rinsed and dried electrodes be immersed in the test solution and the pH read from a scale or a display. To determine 5, 20 to 30 portions of a buffer solution of fixed pH Can be measured with all steps of the procedure being followed exactly. Normally, it is safe to assume that the random error in this test is the same as that in subsequent measurements. Tbe value of .I' calculated from Equation al-lO is then a good estimator of the population value, a. Pooling Data. lfwe have sevcral subsets of data, we can get a better estimate of tbe population standard deviation by pooling (combining) the data than by using only a single data set. Again, we must assume the same sources of random error in all the measurements. This assumption is usually valid if the samples have similar compositions and have been analyzed in exactly the same way. We must also assume that the samples are randomly drawn from the same population and thus have a common value of IT. The pooled estimate of a, which we call Spoolod, is a weighted average of the individual estimatcs. To calculate Spookd' deviations from the mean for each subset are squared: the squares of the deviations of all subsets are then summed and divided by the appropriate number of degrees of freedom. The pooled S is obtained by
taking the square root of the resulting number. One degree of freedom is lost for each subset. Thus, the number of degrees of freedom for the pooled S is equal to the total number of measurements minus the number of subsets nt:
For the first month. the sum of the squares in the next to last column was calculated as follows: Sum of squares ~ (1108 - 1100.3)' + (1122 -1100.3)' + (1075 - 1100.3)' + (1099 - 1100.3)' + (1115 - 1100.3)' + (1083 - 1100.3)' + (1100 -- 1100.3)' = 1687.43 The other sums of squares were obtained similarly. The pooled standard deviation is then _
Here, the indices i, j, and k refer to the data in each subset, N" N" N3, ••. , Nn, are the numbers of results in each subset. Example al-3 illustrates the calculation and application of the pooled standard deviation.
Glucose levels are routinely monitored in patients suffering from diabetes. The glucose concentrations in a patient with mildly elevated glucose levels were determined in different months by a spectrophotometric analytical method. The patient was placed on a low-sugar diet to reduce the glucose levels. The following results were obtained during a study to determine the effectiveness of the diet. Calculate a pooled estimate of the standard deviation for the method. Glucose
Time
Month I
Month2
Month3
Month4
Sumor
Concentration,
mg/L 1108,1122, 1075,1099, 1115,1083, 1100 992.975, 1022,1001. 991 788,805. 779,822, 800 799,745, 750,774, 777.800. 758
1100.3
1687.43
16.8
996.2
1182.80
17.2
798.S
1086.80
16.5
771.9
295086
22.2
Note: Total number of measurements squares = 6907.89.
Mean Glucose,
Squares of Deviations
mg/L
Standard
from Mean
Deviation
Spooled
-
V
!69078'!. _ _ = 24 _ 4 - 18.)8 19m9/L
-I
0 ;:=~ (J
In most of the situations encountered in chemical analysis, the true value of the mean JL cannot be determined because a huge number of measurements (approaching infinity) would be required. With statistics, however, we can establish an interval surrounding an experimentally determined mean x within which the population mean JL is expected to lie with a certain degree of probability. This interval is known as the confidence interval. For example, we might say that it is 99% probable that the true population mean for a set of potassium measurements lies in the interval 7.25 :!: 0.15% K. Thus, the mean should lie in the interval from 7.10 to 7.40% K with 99% probability. The size of the confidence interval, which is computed from the sample standard deviation, depends on how well the sample standard deviation s estimates the population standard deviation iT. If s is a good approximation of iT, the confidence interval can be significantly narrower than if the estimate of J1.o and J1. < J1.a. These are called one-Iailed lests. For example, suppose we are interested in determining whether the concentration of lead in an industrial wastewater discharge exceeds the maximum permissible amount of 0.05 ppm (J1.o = 0.05 ppm). Our hypothesis test would be written as follows: HiI: J1.
=
H,: J1.
> 0.05 ppm
0.05 ppm
and the test would be one tailed.
Now suppose instead that experiments over a period of several years have determined that the mean lead level is J1.o = 0.02 ppm. Recently, changes in the industrial process have been made and we suspect that the mean lead level is now different from 0.02 ppm. Here we do not care whether it is higher or lower than 0.02 ppm. Our hypothesis test would be written as HtI:
J1.
=
0.02 ppm
H,: J1. *0.02 ppm
and the test is a two-tailed test. In order to carry out the statistical test, a test procedure must be implemented. The crucial elements of a test procedure are the formation of an appropriate test statistic and the identification of a rejection region. The test statistic is formulated from the data on which we will base the decision to accept or reject Ho. The rejection region consists of all the values of the test statistic for which Ha will be rejected. The null hypothesis should be rejected if the test statistic lies within thc rejection region. For tests concerning one or t'w., means, the test statistic can be the z statistic, if we have a large number of measurements or if we know 0'. Alternatively, we must use the 1 statistic for small numbers with unknown 0'. When in doubt, the 1 statistic should be used. For the 1 statistic, the procedure is as follows: 1. State the null hypothesis: Ho: J1. = J1.0' ..
2. Form the test statistIc:
In testing for bias, we do not know initially whether the difference between the experimental mean and the accepted value is due to random error or to an actual systematic error. The I test is used to determine the signilicance of the difference as illustrated in Example a I-I O.
A new procedure for the rapid determination of sulfur in kerosenes was tested on a sample known from its method of preparation to contain 0.123% (J1.() = 0.123%) S. The results were % S = 0.112,0.118,0.115, and 0.119. Do the data indicate that there is a bias in the method at the 95% confidence level? Solution
The null hypothesis is Ho: J1. = 0.123% S, and the alternative hypothesis is H,: J1. * 0.123% S. = 0.112
~Xi
sl
~ xl
= =
We can illustrate the procedure by considering a test for systematic error in an analytical method as illustrated in Figure al-2. Determination of the analyte in this case gives an experimental mean that is an estimate of the population mean. If the analytical method had no systematic error, or bias. random errors would give the frequency distribution shown by curve A in Figure al-2 and J1.A = J1.o. the true value. Method B has some systematic error so that xR, which estimates J1.b differs from the accepted value J1.(). The bias is given by
=
=
0.464
0.116% S
0.012544 + 0.013924 + 0.013225 + 0.014161 0.53854 0.053854 - (0.464)'/4
~----
--_."_._---~
4-1 =
V1ii'
3. State the alternative hypothesis H, and determine the rejection region. Here the critical value of t, I"i. is the value found from the tables of the 1 statistic. For Ha: J.L *- Mo, reject Ho if t 2: tcrit or if l :::; --lcrit (two-tailed test). For H,: J1. > J1.o. reject Htl if 12: I"" (one-tailed test). For H,: J1. < J1.o, reject Ho if 10'0-I"i. (one-tailed test).
+ 0.118 + 0.115 + 0.119
i = 0.464/4
X-/Lo 1=
error in the outcome." The significance level (0.05, 0.01, O.OO!. etc.) is the probability of making an error by rejecting the nullilypothesis. Hypothesis testing is widely used in science and engineering.13 Comparison of one or two samples is carried out as described here. The principles can, however, be extended to comparisons among more than two population means. Multiple comparisons fall under the general category of IlIllllysis of variance (ANaYA)." These methods use a single test to determine whether there is a difference among the population means rather than pairwise oomparisons as is done with the 1 test. After ANaYA indicates a potential difference, mulliple comparison procedures can be used to identify which specific population means differ from the others. Experimenlaldesign melhods take advantage of ANaYA in planning and performing experiments.
x -
)0.000030 3
J1.o
s/V1ii
=
0.0032%S
0.116 - 0.123 0.032/V4
=
-4.375
From Table al-5, we find that the critical value of 1 for 3 degrees of freedom and the 95% confidence level is 3.18. Because 1 0'0 - 3.18, we conclude that there is a significant difference at the 95 % confidence level and, thus, bias in the method. Note that if we were to carry out this test at the 99% confidence level, Iw• = 5.84 (Table al-5). Because -5.84 < -4.375, we would accept the null hypothesis at the 99% confidence levcl and conclude there is no difference between tbe experimental and the accepted values.
Note that in this example the outcome depends on the confidence level that is used. The choice of confiden-ce level depends on our willingness to accept an
Most analytical metbods are based on a calibration curve in which a measured quantity y is plotted as a function of the known concentration x of a series of standards. Figure al ~shows a typical calibration curve, which was computed for the chromatographic determination of isooctane in hydrocarbon samples. The ordinate (the dependent variable) is the area under the chromatographic peak for isooctane, and the abscissa (the independent variable) is the mole percent of isooctane. As is typical, the plot approximates a straight line. Note, however, that not all the data fall exactly on the line becausc of the random errors in the measurement process. Thus, we must try to find the "best" straight line through the points. Regression analysis provides the means for objectively obtaining such a line and also for specifying the uncertainties associated with its subsequent use. We consider here only the basic melhod of kaSI squares for two-dimensional data.
12 For a discussion of errors" hypothesis testing. see J L Devore, Prohabilil}' and Statistics fur En~eering and the Sciences, 6th ed., Chap. 8, Pacific Gran:. CA: Duxbury Press at Brooks/Cole, 2004. llSee D. A. Skoog, D. M. West, F. 1. HoUer. and S. R. Crouch, Fundamen· [Ills of Analrllcal Chemistry. 8th ed .. Chap. 7. Belmont, CA: Brooks/CoI.::, 2(1(}4:S. R. Crouch and F J. Holler. Applications of Microsoft'" Excel in AnalYflcal Chemistry, BelmoBt, CA: Brooks/Cole, 20041Jfor a discussion of ANOVA methods, see D. A- Skoog. D. M. West, F.1. Hnlkr, and S. R Crouch. Fllltdamentais of Analytical Chemistry, 8th ed., Sec. 7C Belmont, CA: Broots/Colc, 2004
calculator
basic. linear analvsis may not' gIve t h e best I . least-squares . stralg It. line. In such a case. a more campi ex corre IaltOn . ana II'SIS may be . . necessarv . . In add't'I Ion, simple least-
ing used. Six useful
squ~res analvSIs may not be appropriate when the uncertdmtles In the y values varv. significantl Y Wit ,. h x. In h"
.
.
t IS case, II may be necessarv Ing factors to the points squares analysis.
50
J' to appl"
and perform
without
a built-in
quantities
40
Finding
As illustrated each
"§
The Ime generated th t .. . one a mlllllllIzes
C 3.0
~ a
y
~ ~ ~ 2.0 ~,;,
fll between
line is called
by the least-squares In addition
the experimental
Ime, the method The
least:squares
cordmg
1.0
method
of the residuals
finds
to the minimization
The value of 55""d is found =
SS""d
deviation
x, Concentration
FIGURE a1-6 Calibration In hydrocarbon mixtures.
1.5
of isooctane,
where
mol %
curve for determining
N is the number
Assumptions
Least-Squares
technique
Two assumptions squares.
2: (Xi
tionship
between
standard
analyte
relationship
x)'
-
are made in using the method the
is actually
measured
concentration
that describes
2: (x, -
respo~se Y and the x. The mathematical as
three
6. The
=
2:Yi - (2:;,)'
(al-32)
x)(,v,' _ .y)
the number
of paIrS and x and yare
ues for x and y; that is, x where b is the y intercept
(the value ofywhenx
mlS the slope of the line. We also assume ation
of the mdlvldual
anses
from error
points
from
'" ,,:.XiYi
-
2: N2: Xi
is 0) and
that any devi-
the straight
in the measurement. That
line
is. we as-
=
2: x,l Nand
the average
y=
s, = Equation
tIOns al-31
through
shown
al-33
of these
for many
analytical
whenever
there
assumptions
methods,
is significant
are appropriate
but bear uncertainty
in mind
that
in the x data.
XiYi,
computed
with their sums appearing Note that the number
al-39
for results
valas the of dig-
obtained
y, of
S"
the standard
a set of M replicate
when a calibration
val-
that the slope
parameters,
2: y,I N.
viations
are measured
2: [y,
i= 1
j
_.~
2:
XiYi _
_
and
(2:Ny.l' (12.51)' - -5-
2: x~2:
= 5.07748
Yi
158199 _ 5.365 x 12.51 = 966 . 2 5 2.3 9
s, (Equa-
a 1-7 Calibration Data for the Chromatographic Determination of Isooctane in a Hydrocarbon Mixture
TABLE
Mole Percent Isooctane,
Xi
Peak Area,y;
x~
not from the mean of Y (as is the line that results
The value of
'N--------liThe procedure involves dillerCTlliating; SSr."J with respect to first m and then b and setting the dcnvatl~'es equal 10 O. This vie Ids two equat called normal ctjuatlons, In the (wo unknowns m a~d b. These are ~~I:~ solved!o gl\e lh~ least-squares best estimates of these parameters
arc in-
for Y when the de-
to SS""d by
when a
=
de-
true.
regression
deviation
prediction.
al-32,
analy-
and intercept
about
usual case), but from the straight the least-squares
al-31,
curve that contains
which is not strictly
deviation
tion a 1-36) is the standard
l
,,:.),
from
rt-i--C)i, - y)' + N + m'Sxx
imate and assumes
values should
into Equations
= 36.3775
allows us to calculate
The standard
= '" YY
curve, so:
from the mean
dependent
in the computed
S
N points is used; recall that y is the mean value of Y for the N calibration points. This equation is only approx-
sume there is no error in x values of the points (concenBoth
al-7
and obtain
1
on the far right in Equa-
are more convenient
of Table
al-6.
3, 4, and 5 of the table contain
xi, yi, and
(2: x,)'j 2: xi
-;;-V M
ses of unknowns Yi
Note that S" and S" arc the sums of the squares of the deViatIOns from the mean for individual values of x and y. The expressions
I
deviation
s, (al-31)
where x, and Yi are individu
.
.~
The relationship between the activity ax of a species and its molar concentration [Xl is given by the expression
a2A
PROPERTIES OF ACTIVITY COEFFICIENTS
Ca2-'-
0.4
=
::;"
0.2
AIJ+ Fe(CN)64'
0 0.1
0
where Yx is a dimensionless quantity called the activity coefficient. The activity coefficient, and thus the activity of X, varies with the ionic strength of a solution such that the use of ax instead of [XI in an electrode potential calculation, or in equilibrium calculations, renders the numerical value obtained independent of the ionic strength. Here, the ionic strength J.1. is defined by the equation
where Cb C" c], ... represent the molar concentration of the various ions in the solution and Zb Z2' 2], ... are their respective charges. Note that an ionic strength calculation requires taking account of all ionic species in a solution, not just the reactive ones.
Calculate the ionic strength of a solution that is 0.0100 M in NaNO] and 0.0200 M in Mg(NO]),. Solution
Here, we will neglect the contribution of Ht and OH to the ionic strength because their concentrations are so low compared with those of the two salts. The molarities of Na', NO] -, and Mg" are 0.0100, 0.0500, and 0.0200, respectively. Then CN,+X (I)'
= 0.0100
x I
= 0.0100
CNO,- x (1)2 = 0.0500 x I = 0.0500 CMg" x (2)'
=
0.0200 x 2' Sum
I
J.1.
= "2
x 0.1400
=
= 0.0800 =
0.14(Xl
00700
1. The activity coefficient of a species can be thought of as a measure of the effectiveness with which that species influences an equilibrium in which it is a participant. In very dilute solutions, where the ionic strength is minimal, ions are sufficiently far apart that they do not influence one another's behavior. Here, the effectiveness of a common ion on the position of equilibrium becomes dependent ollly on its molar concentration and independent of,other ions. Undcr these circumstances, the activity 'e~efficient becomes equal to unity and [Xl and a in Equation a2-1 are identical. As the ionic strength becomes greater, the behavior of an individual ion is influenced by its nearby neighbors. Thc result is a decrease in effectiveness of the ion in altering the position of chemical equilibria. Its activity coefficient then becomes less than unity. We may summarize this behavior in terms of Equation a2-1. At moderate ionic strengths, Yx < I; as the solution approaches infinite dilution (J.1. ....• 0), Yx ....•1 and thus ax"'"
[X].
At high ionic strengths, the activity coefficients for some species increase and may even become greater than 1. The behavior of such solutions is difficult to interpret; we shall confine our discussion to regions of low to moderate ionic strengths (i.e., where J.1. < 0.1). The variation of typical activity coefficients as a function of ionic strength is shown in Figure a2-1. 2. In dilute solutions, the activity coefficient for a given species is independent of the specific nature of the electrolyte and depends only on the ionic strength. 3. For a given ionic strength, the activity coefficient of an ion departs further from unity as the charge carried by the species increases. This effect is shown in Figure a2-1. Thc activity coefficient of an uncharged molecule is approximately I, regardless of ionic strength.
0.2 J.i
0.3
0.4
where YAand YB....•I), we could obtain K;p- A second solubility measurement at some ionic strength, J.1.,. would give values for [A] and [BJ. These data would then permit the calculation of YAYB= y':".n, for ionic strength J.1.l'It is important to understand that there are insufficient experimental data to permit the calculation of the individual quantities YAand YR.however. and that there appears to be no additional experimental information that would permit evaluation of these quantities. This situation is general; the experimental determination of individual activity coefficients appears to be impossible.
FIGURE a2-1 Effect of ionic strength on activity
coefficients.
4. Activity coeflicients for ions of the same charge are approximately the same at any given ionic strength. The small variations that do exist can be correlated with the effective diameter of the hydrated ions. 5. The product of the activity coefficient and molar concentration of a given ion describes its effective behavior in all equilibria in which it participates.
a2B
EXPERIMENTAL EVALUATION OF ACTIVITY COEFFICIENTS
In 1923, P. Debye and E. Hiiekel derived the following theoretical expression. which permits the calculation of activity coefficients of ions:l -logYA
0.509Z~ Vj" =
. r
1 + 3.28v_by65flVfor+iimitandv_>v.by75flY for~ limit
5-12 (SIN)o = 3.9(S/NIA
Chapter 6 v ~ -1.80 X 1017 Hz: £ ~ 3.18 10" eV
6-3
v ~
6-4
A ~
6~5
Vs~ci~s
8.52-1 10-:1.1 J
=
2.75
= 540
X
10-10 J: E ~ 1.99
X
9-11
104 mm
9-12
10" so': " ~ 28-13 em ': E ~ 5.648 x
X
81.5 cm: E ~ 5AO x 10
Asp'1,171. 231. 34'1. ionization detector) 402 - 405. -107(sa also (free induction decay) in NMR. Electronic transitions) 505.508-510.521. 522. nuclei, NMR, ')03-505 535. 538, 540. S4 I. 543 states. 147, 1-18.152-1')4, 156 Field Exclusion limit. size-exclusion centrifugal, 884. 959, '161 chromatograrhy, H46, 847 desorption sources, 552. 55'1, 5S5 Exit slit. monochromator, 181. 184. gradient. magnetic resonance 187-18'1.203,204,21>0. imaging, 538-')40 261,285 gravitational, 959-961 Exothermic process, thermal ionization sources. 558, 559 analysis, 898-'104 secondary in NMR, 51.1-51') Expression, mass-balance, 246, 381>, Field-effect transistors, 40 -48 387,390 Field-flow fractionation. 88-1-888 Extracellular acidification, 757. 758 Field-frequency lock. NMR, 525 Extracolumn band hroadening, LC, Filter 81S instruments, fR. 447, 474 Extraction rhotometers. UV -visible, 204, cell, 863, 864 354. 380. 824 solid-rhase. 8'10.'140 Filtering, digital, 120. 121 solvent. 930, 934, 936 Filters supercritical fiuid. 850. 8')7. absorption. 180 862-806 correlation analyzers, 448 for electrical signals, 40. 41, SO, Fabry-Perot etalon, 176 -I 77 73.113,115,117.122 Factor, retardation, in thin-layer interference, 176,177,180 chromatography, 849, 850 for luminescence spectroscopy, Faradaic 411-413,424 currents, 632, 633, 742, 743, 7')1 for X-rays, 311, 326-328 impedance. 722, 723 First-order spectra, NMR, 517. ') 18 Faraday cur, for mass Flame spectrometry, 285-287 ahsorrtion profiles, 232 Far-IR sreetroscory, 470 atomization. 230, 232. 233. 241, Fast 248 atom hombardment, sources for chemiluminescence, 425 MS,562-563 neutrons. 918. 922 Fellgett advantage, 206 Ferrocene in electrochemistry, 721. 740.741,745 FFF (field-fiow fractionation), 884-888 FlA. 247. 933-935. 939-941. See a/so Flow injection analysis
Flicker noise. 112. 113.115,206 Flight times. time-of-flight mass sreetrometry. 290. 569 F1ir-fiops.85 Flow
injection analysis, 225, 247. 383. 931-1)35.937, '138 (see also HA)
meter for Gc, 78'1, 7'10 rates e1ectroosmotic. 870, 875 FIA, 932, '134-931> flame. 231. 233 mobile phase. 77 I-774.778. 78'1.790. S19, H21 volumetric, 761>,767.7'10. 846 turbulent in electrochemistry. 726 Flow cells FlA. '132, '136. '137 LC, S23 voltammetry,731 Flow FFI'~887 Fluorescence,S. 6, 148. 156 atomic (see Atomic fiuorescence spect roseopy ) bands,402,403,411 detection, LC, 414, 421,825. H73 emission,S, 402, 405, 407, 408, 411,412,414,417.419, 422,494 instrumentation, 411, 413, 414 intensity, 407, 409, 410, 412 lifetime measurements, 421 molecular, 150. 157,399,400, 483 quantum efficiency of, 406-408, 428 radiation. 155, 156, 169 resonance, 219, -100 emission spectroscopy, 168,399,422 srectroscopy. 230-233, 246, srectrum, 219, 311, 410. 415. 425 248.273 theory of, 40()- 409 spectrum.21H ionization detector. 7'13. 794. 7'10. Fluoride determination of, 688, 689. 746 797.800.85'1,861 electrode. 672 rhotometers.273 Fluorometers. 5. 6. 204, 411-415 photometric detectors in F-numher, 185 chromatograrhy. 7'17.859
Focal length of monochromator. 185, 186 of optical element, 185 plane mass spectrometer, 285, 286, 291,568 optical spectrometer, 181, 182, 185, 187, 188, 194, 196, 203,260,261,270,353,361 Follower current, 63, 64, 66, 67, 75 voltage, 62, 63, 65, 67, 71, 114, 684 Force constant, 434-436 Formal potential, 645, 997-1000 Formation constant, of complexes, 384-390 Forward biasing, of semiconductor diodes, 45-46 Fourier transform instruments, UV-visible, 259, 265,266 IR spectrometers, 438, 439, 474, 476,824 mass spectrometers, 571-573, 584,604,800 measurements, 206, 499, 572 NMR, 521, 529 Raman spectrometers, 491 spectroscopy, principles, 204-207,209,211 Four-level system, lasers, 171-173 Fragmentation, mass spectrometry, 551,552,554,555, 557-560,562,574,576, 578,580 Frame of reference, rotating in NMR, 505, 508 Frequency of absorbed radiation, 153 bandwidth, electronics, 112, 115 carrier in NMR, 524, 525 chopping, 115, 116 components, 120,524,745,759 cyclotron, 571 domain, 7, 207, 209, 508 - 510 exchange NMR, 520 fundamental vibrational, 436, 437 lock system, NMR, 543
meter, 9, 85, 86 natural, 434 precession in NMR, 539, 540 proton, 521, 523, 532 range, 65,207,211, 524, 722 resonant of crystal, 10,87 response, electrical circuits, 41, 64,65,120 spectrum, 210, 211, 759 sum, 606 sweep signal, 571 synthesizers, NMR, 522, 524 Frequency distribution, of data, 968-970 Frequency-domain spectrum, 121, 207, 209, 522, 525 Frequency-doubling system for laser, 175 Fronting of chromatographic peaks, 769 FT voltammetry, 745 FTIR spectrometers, 439-443, 451, 453,454,466,467,470, 471,473,474,477. See also Fourier transform, IR spectrometers FT-NMR spectrometers, 498, 522, See also Fourier transform, NMR FT-Raman instrument, 488, 491, 492. See also Fourier transform, Raman spectrometers Fuel, combustion flames, 221, 230, 231,233,241 Function autocorrelation in dynamic lightscattering, 956, 957 work, 145, 146,593 Functional group detection IR, 438, 459, 460, 464, 474, 493 mass spectrometry, 552, 578 NMR, 512, 513, 515, 516, 526, 529,533 Raman, 493 surface analysis, 596, 602, 620, 621 UV-visible, 369, 373, 374
groups, and fluorescence, 405, 420,425 Furnaces atomic spectrometry, 234, 235, 243,245,247,256,257 thermal analysis, 894, 895, 898 GaAs photovoltaic cell, 192 Gain of amplifier, 41,60,63-65,67,70 bandwidth product, operational amplifier, 65 of BJT, 47
of PMT or electron multiplier, 285 Galvanic cell, 629-631, 638-640, 645,647 Gamma radiation, 303, 306, 612, 910, 911, 916-918,922 rays, prompt, 918-920 , Gamma-ray spectrometers, 9[6, 917 Gas chromatographic columns, 8tll-805 chromatography, 582, 788-804, 806-810,890,891 chromatography/mass spectrometry, 582, 761 sensor, electrochemistry, 677, 681 Gases dissolved, 677-679, 818 in electrochemistry, 677-679 in HPLC, 818, 819 purge in thermal analysis, 894, 895,903 Gas-filled detectors, X-ray analysis, 314,315 Gas-permeable membranes, 677, 678 Gas-sensing probes, 677-680 Gas-solid chromatography, 788, 810 Gaussian distributions chromatograms, 768, 770, 771 random errors, 768, 968, 969, 977, 978 Gaussian statistics, 973, 989 GC,788-81O
GDOES, See Glow discharge optical emission spectroscopy Geiger tubes, 314, 315 Gel filtration, 817, 845, 847 Gels electrophoresis, 877, 878, 892 size-exclusion chromatography, 844,845,847 General elution problem, chromatography, 780 - 781 Generation, sum frequency, 591, 604 Generator electrode, coulomctry, 707 Glass electrode acid error, 671, 689 alkaline error, 670, 671, 689 asymmetry potential, 669 hygroscopicity, 668 membranes, 665-670 transition, 899, 901, 904 GLC See Gas chromatography Globar,450 Glow discharge optical emission spectroscopy, 273, 274 Gold electrode, cyclic voltammetry, 740,741 Goniometer, X-ray analysis, 312 Gradient elution, chromatography, 781,819-820 Graphite furnace, atomic spectroscopy, 234 Grating, 179-181, 184-187, 189 concave, 184,261,262,359 echelle,186 echellette, 183, 184, 186 instruments, 358, 440, 474, 476, 477 master, 182, 183 monochromators, 181, 182, 184, 185, 188, 189,260,359, 360,413,415,438,476,825 Gravitational sedimentation, 960 Ground state, 147, 148, 151-156 vibrational states, 149,401 Ground-state analyte atoms, 274 Group frequencies. 459-461, 464
GSC See Gas-solid chromatography Guard columns, HPLC, 822 Hair, analysis of. 584, 964. 965 Half cycle, 116, 117,243,271.272 Half-celL 630, 635 -640,645,649, 659,660 potentials, 639, 642, 644, 646. 659 reactions, 630, 631, 635, 640, 641, 648, 649 (see also Halfreaction) Half-life, 307, 912, 919-921 Half-reaction, 635 -646 Half-wave potential, 722, 727-730, 746, 749 rectifier, 50 Hall electrolytic conductivity detector, 796 Hanging mercu£y drop electrodc, 719-720. See also HMDE Harmonic oscillator, 433-435 Heat capacity component, modulated DSC, 901,903 determinations, 903 thermal analysis, 901-904 transducers, 201, 451 flow, differential scanning calorimetry, 900-904 flow signal, reversing, 901 Heavy-atom effect, 404-405 Helium-neon laser, 172,483 Hertz (Hz), 33 Heteronuclear decoupling, NMR, 529 Hexacyanoferrate, 371, 636, 738, 745 High-pass filter, 40, 41,115 mass filter, 288, 289 High-performance liquid chromatography, 816-848 High-pressure gas flow, Bernoulli effect, 225, 226 High-purity germanium detector, 916,917,922
High-resolution mass spectrometers, 282 High-resolution NMR, 509-510 spectrometers, 498, 515, 521 High-resolution TGA, 896 High-speed voltammetry, 745 HMDE (hanging mcrcury drop electrodc), 719, 720, 742, 744, 749 Holes, in semiconductors, 44-46, 48,191,193,194,198,316 Hollow-cathodc lamps, 238-244, 250 Holographic grating, 184 Homonuclear decoupling, NMR, 520 Hooke's law, 434 HPLC,816-848 HPLC detectors, 823-828 Human Genome Project, 867, 878 Hydride generation tcchniques, atomic spectroscopy, 226 Hydrodynamic voltammetry, 722-737 Hydrogen electrode, 636-638, 641, 659, 660 ion activities, glass electrode, 641, 668. 669 concentration, 684, 688 ions, generation of, 708-709 peroxide, 375, 399, 425, 679, 730, 733,737 Hydroxide ions, generation of, 708, 709 Hyper Raman effect, 495 Hyphenated methods, 283, 582, 800 Hypothesis testing, 983~985 ICP emission spectrometry, 255-258, 266-269 sources, 255-259, 263, 266-269, 276,291-294 ICPMS, 282, 291-299 Image current, ion-cyclotron resonance, 571,572 Immobilized enzyme, 679-680, 733 Immunosensors.733
Impedance, 39-42, 63, 71, 72 measurements, 42 Incandescent wire source, IR spectroscopy, 450 Incident electron beam, surface analysis, 611,612 frequencies, sum-frequency generation, 605 Incoherence, of electromagnetic radiation, 140 Indeterminate errors. See Random errors Indicator electrode, 659, 660, 662, 664,665,686,687,691 Indicators, Beer's law deviations of, 339,340 Inductively coupled plasma mass spectrometry (see ICPMS) See ICP Inductors, 34, 35 Inert electrodes, 664, 749 Information digital, 5, 7, 8, 80 flow of, 3, 5, II5 sampling-interval interferometry, 440 spectral, multichannel instruments, 199, 204 Infrared absorption spectrometry, 430-452,454,455-477 detectors, LC, 824 radiation, 134, 149, 155, 172, 174, 180,182,191,201-203, 209,213,364 Initial rate, 382, 383 - Injection in chromatography, 783, 791, 801. 821 electrokinetic in capillary electrophoresis, 871, 872 in FlA, 864, 871,872,877,887, 931,933,934 Inlet on-column for capillary GC, 791 system, mass spectrometry, 283, 563-565 Inorganic species absorption by, 370, 371. 419
chemiluminescence of, 419, 424, 425 far-IR applications to, 476 fluorometric determination of, 419-420 Raman spectra of, 419, 492 Input difference voltage, 59, 62 frequency, digital circuits, 85-87 transducer, 5, 81, 111 (see also Detector) Input-output systems, for computers, 95 Instructions, for computers, 91, 92, 94 Instrument components, 3, 4 control mass spectrometry, 318, 576, 577 software for, 99 thermal analysis, 894 response, 6, 11, 15, 16,248 standardization, luminescence, 418 Instrumental deviations, from Beer's law, 338, 340 -342, 466 limitations, in IR spectrometry, 464,465 methods, 1-3 calibration of, 11- I 7 noise, 111 effects on spectrophotometric analysis, 343-345 precision, 344 procedures, 2, 3 Instrumentation amplifiers, 114, 115,201 voltammetric,718-721 Instruments automated, 127,326,736,929, 930,945 calibration of, 11-17 cold-vapor atomic fluorescence, 333 commercial CE, 874, 875 components of optical, 164,249, 310,411 computerized coulometric. 706
double-beam, 241, 346, 351-353, 358-360, 441, 444 energy-dispersive X-ray, 310. 318-320,322 Fourier transform, 265, 266, 430, 443 gas chromatographic, 789 multinuclear NMR, 534 nondispersive atomic fluorescence, 250 IR, 431, 447, 448 portable, 193, 315, 354, 415, 809 pulsed NMR, 499 sector for mass spectrometry, 566,575 sequential for atomic spectrometry, 259-261 single-channel X-ray, 318 tandem-in-spaee mass spectrometers, 575, 5:J6 virtual, 102, 103 wavelength-dispersive for X:;'ay analysis, 310,318 Integration, operational amplifiers for, 71-73 Integrators boxcar, 120 for eoulometry, 706 Intensity distribution, light scattering, 952-954 of electromagnetic radiation, 134 t1uctuations, light scattering, 956 reflected, 142, 470, 605 Interaction volume, SEM, 611, 612 Interactions, analyte-ligand in affinity chromatography, 848 Intercept, of calibration curve, 12-17 Interfaces electrode-solution, 632, 703, 723, 727 liquid-liquid, 605, 606, 774 Interfacial methods, 652, 653 Interference filters, 176, 177, 179,350,355, 41-\,430 fringes, 458 pattern, 178, 179, 184,209,210
Interferences atomic spectroscopy, 219, 239, 2-\1-247,250,266,267, 269 chemical, 2-\4, 248. 254, 258, 269 general, 2, 13,21,22 ICPMS,294-296 isobaric, mass spectrometry, 294, 300 plasma emission spectroscopy, 269 spectral, 241. 242, 248, 269 Interferograms, 209-2II, 439, 440, 442,443,466, 467 Interferometer, 208-210, 440-443, 492 Internal conversion
luminescence, 402- 404 nuclear, 911 resistance of glass electrode, 30, 31, 55, 57,62,66,67,71,124,649, 655,684 loading and, 30, 31, 62, 66, 67 solution indicator electrodes, 668, 669, 675,677-679 reference electrode, 662 standard method, 17, 18,98 for chromatography, 783, 807 for emission spectroscopy, 98, 272 Intersystem crossing, 404, 405, 407, 409,421 Inverse Raman spectroscopy, 495 Inverting input, operational amplifier, 61-63,67,71,74,705 voltage amplifier, 64 Ion chromatography, 839-844, 852, 875 applications of, 841, 842 single-column, 843 cyclotron resonance, 571-572 detector elcctrooptical, 285, 286 mass spectrometry, 574, 828 microprobe, 603, 624
simultaneous detection of in sources, mass spectrometry, 283, mass spectrometry, 286. 288, 290, 294, 551. 287 552-563,564 trapped, 570, 572 spectroscopic techniques, Ion-selective 602-604 electrodes, 664-675, 680, 683 trap analyzers, 569-571 field effect transistor (ISFET), Ion-exclusion chromatography, 675-677 843-844 membrane electrodes, 286,576, Ionic strength, 641, 642, 646, 647, 664-675 687, 688, 848, 994 - 996 Ion-trap mass spectrometer, 570 Ionization IR chemical, 552, 553, 557, 558 absorption spectrometry, degrees of in atomic 431-452,455-469 (see spectroscopy, 246 also Infrared absorption electron-impact, 554-557,558, spectrometry) 559,563,581 active transitions. mutual electrospray, 552, 560, 562 exclusion principle, 486 region, mass spectrometry, 557, detectors, 440, 477, 825 (see also 565 Infrared detectors) source, 565, 566, 570, 573, 583 filter hard, 552, 553 correlation analyzer, 449 soft, 552, 553, 574, 575 photometers, 447, 469 suppressor, atomic spectroscopy, instrumentation, 438-449 246 instruments, dispersive, 445, 446, lon-molecule collisions, 555 465 Ionophores, 674, 675 liquid cells, 457 Ion-pair chromatography, 836, 838 radiation, 166, 167,430-432 (see Ions also Infrared radiation) alkali-metal, effect on glass sources, 449 - 451, 477 electrodes, 689 spectra, 432, 437, 438, 446, 459, energetic 464,466,467,481,482,485 mass spectrometry, 285, 287 spectral regions, 455 Rutherford backscattering, 603 spectrometry, applications of, excited, 276, 305, 307, 309, 593, 455-477 598 transducers, 451-452 nitrate, reduction of, 698,- 700 Irradiation, neutron activation organic solute in HPLC, 836 analysis, 909, 918, 920, primary in ion spectroscopic 921,924 methods, 603 ISFETs (ion-selective field effect product in tandem mass transistors), 675-677 spectrometry, 573-576 Isobaric profile, SFC, 294, 858 protonated matrix in MALDI, Isoelcctric 560 focusing, capillary. 880-882 reagent in mass spectrometry, point, 876, 880, 881 558 Isotope separation of by dilution, 924 -925 CE,875 ratio measurements, mass ion chromatography, 569, spectrometry, 299, 578, 839-844.875 580 mass spectrometry, 566 -577
ISS (ion-scattering spectroscopy), 591.603.604.622 IUPAC sign convention. cell potentials, 31, 639-640 Johnson noise, 111-112.344-345 Joule heating. capillary electrophoresis. 144, 146, 160,640.869 Junction pn, 44, 45, 47 potential, 630, 635, 665, 667, 668, 686-689 thermal, 201,452 Kinetic energy, photoelectron in photoelectric effect, 144-146 methods, 381-385 polarization, 697 Kirchhoff current law, 26-30 voltage law, 26-27,30,36,62 Lab-on-a-chip analyzers, 941 Laboratory electronic, 127-130 operations, in microfluidics, 940 paperless, 127 recorders, 52-53 LabVIEW, 99,102-103,745 LALLS (low-angle laser light scattering), 951-955 Laminar-flow burners, 233 LAN (local area network), !O5, 107 LAPS (light-addressable potentiometric sensor), 683-684,757-760 Larmor frequency, NMR, 502-509, 533 Laser ablation, 227, 292-294 beam detector, in AFM, 617 diodes, 173-175 Laser-fringe reference systems, 440, 441 Lasers, 168-175 carbon dioxide, 450
for desorption of sample in MALDI,560 in holographic grating fabrication, 184 microprobe, 274 as reference in FTIR spectrometer, 440 source
for atomic fluorescence, 250 in DLS, 957 in ellipsometry, 606 for excitation in on-column CE,879 in low-angle light scattering, 951 in nonlinear Raman spectroscopy, 495 in photoluminescence measurements, 413 for Raman spectroscopy, 488 LC detectors, 823, 828 LC instrumentation, 821-827 LC (liquid chromatography), 816-856 LCD (liquid crystal display), 54 Least-squares analysis, 15, 20 weighted, 12,279-280,331 method,985-988 polynomial smoothing, 120 -123 LEOs (light-emitting diodes), 54, 174,350,413,757,758,960 Level detector, operational amplifier, 74 L1BS (laser-induced breakdown spectroscopy),274-276 Lifetime measurements, fluorescence, 421-422 Light amplification, in lasers, 168-171, 174 scattering dynamic, 955, 957, 958 low-angle laser, 893, 950, 951, 953 Limiting current, 722 LlMS (laboratory information management systems), !O7, 127-130,692,930
Line sources, 168,237 spectrum, 150, 151,254.303,304, 311 X-ray, 304 -305 voltage, 49-50 widths, natural, 220, 221 Linear dispersion, of monochromator, 181, 185 -186 Linearity, 21 calibration curves, 248 departures from in absorption measurements, 341 from in fluorescence measurements, 408 from in ICP, 268 from in pH measurements, 671 Liquid chromatography, 816-848 junctions, 630-631, 635, 659, 690 cells without, 631- 632 mobile phases, chromatography, 774 -779,828-830,859 stationary phases, chromatography, 773-775, 801-S03,884 Liquid-membrane electrodes, 672-675 Liquid-solid chromatography, 837, 839 Lithium, salts as supporting electrolyte in organic voltammetry,747 Lithium-drifted silicon detectors for X-rays, 316 Loading errors, 30-32, 62, 66, 684 LOD (limit of detection), 20 conductivity detector, 796 fluorimetry, 420 nitrogen-specific chemiluminescence GC detector, 800 piezoelectric sensor, 10 sulfur chemiluminescence GC detector. 800
Logic level, S4 state, 84, 88, 94 LOL (limit of linearity), 21 Loop in electrical circuits. 26, 27, 29, 821 sampling for FlA, 933 for LC, 821 Low-pass filter, 40-41,115-117, 123
Luminescence methods, 399-419 Luminol, as chemiluminescent reagent, 425 Magic angle spinning, 533 Magnetic field absorption in, 155 electronic, relation to chemical shift, 511 energy levels in, NMR, 499 locking, NMR, 523 precession in, NMR, 502 strength, 499, 501, 567-568, 576 moment, 499-500, 502, 505-506 quantum numbers, 499, 501, 504, 542 Magnetic resonance imaging, 537-541 Magnetic sector analyzers, 566, 568 Magnetogyric ratios, 499-501,504, 529,534 Magnets, NMR, 522 Map, data-domain, 3-4, 7-8 Martian surfaces, 476, 917 Mass absorption coefficients, 308 analyzers, 283 double-focusing, 291 ion-trap, 570 secondary-ion, 602, 603 time-of-flight. 290, 798 change, in TGA, 896, 897 chromatograms, 799. 800 exact, 282, 566, 578 fraction, 308, 320
numbers, 281 reduced, 434 -436 spectra in GC/MS, 798 molecular mass from, 578 spectral data, presentation, 551, 580 libraries, 552, 577, 581 spectrometers atomic, 283, 290 molecular, 563 -577 spectrometry, 281-302, 550 -588, 798-874 accelerator, 301 applications, 583, 798 of molecular, 577-581 of tandem, 582 atomic, 281-302 detection limits, ICPMS, 297 detectors GC, 798, 809 LC,825 laser-microprobe, 604 molecular, 550-588 quantitative applications of, 583-584 secondary-ion, 602 spark source, 299 transfer in chromatography, 774, 830 in electrochemical cells, 633, 649 rate of in electrochemical cells, 628,774 transport, mechanisms of, 651 Mass-analyzed ion kinetic energy spectrometer (MIKES), 576 Mass-to-charge ratios in atomic mass spectrometry, 282 in mass spectrum, 551 in quadrupole MS, 289 Matrix effects, 325 in AA,241 in calibration, 13 enhancement in XRF, 322 in ICPMS, 296 in the internal-standard method, 17
minimizing in standard-addition methods, 13 in plasma sources, 269 in UV-visible spectrometry, 376 in XRF, 321 Mattauch-Herzog geometry, mass spectrometer, 291 Mean population, 971 sample, 967-969, 971,976 value, 967-969 Medium, lasing, 168-169, 172 Membrane electrode systems, types, 677 electrodes, 664 -665, 66S-671, 675-677,680,686, 692-695 ion-selective, 659, 665 ion-selective, 665, 683 properties of, 665 Memory, computer. 92-94 Mercury electrodes, 663-664, 719, 720 dropping, 716, 717, 737 film electrode, 720-721, 737, 740, 749 Metal sample plate, 560 Metallic indicator electrode, 662-663 Meter, DMM, 31 Meter, loading error, 31 Method of least squares, 985-988 Methods continuous flow, 3S3, 931, 933, 934 kinetic, 381-383, 385 Methyl protons, in NMR. 511-518 Micelles in MEKC, 882-883 in room-temperature phosphorescence, 421 Michelson interferometer. 208-210, 213,214,439,454, 491-492 Microchannel plates, 285-286 Microcomputers, 80, 90-92 Microelectrodes applications o[ 753 voltammelric, 751- 753
croprobe. electron. 328. 607. 610-612.624 icroscope. 1R. 477 icroscope. scanning electrochemical. 613. 753 probe. 613-621, 623. 753 tunneling, 613-616 1icrothermal analysis, 904-906 rlicrowave-induced plasma, 255, 797 Mid·J R absorption spectrometry, 457-467 Mie theory,.951-952 Migration of anions and cations in electrolytic conduction, 630 of cations in Geiger tube, 315 cessation of at isoelectric point in CE,881 in chromatography, rate theory, 768 in concentration polarization, 651 drifting of Li ions in SiLi detectors, 316 holes and electrons in pn junction, 44 in ion-selective membranes, 665 of majority carriers in a BIT, 47 mass transfer mechanism, 633, 651 minimizing in voltammetry with supporting electrolyte, 724 of mobile phase measured by dead time. 766 rate of in chromatography, 763 in electrophoresis, 868, 869 relation to concentration difference and diffusion coefficient, 774 to distribution constant, 767 varying to optimize column performance, 775 retardation of in CGE. 878 Mirrors, movable, in Michelson
interferometer. 208. 439-441,443,492 Mixers in microtluidics. 941 stopped-flow, 384 Mixtures, two-component, 377, 729, 767.787 l\lobile phase. in chromatography. 762 Mobile-phase veiocity, 772, 773. 775 Mooilities, ionic. 635 Modem, 9,106 Modes, normal. 437-438 Modulation, 115-116 refractive-index, 179, 214 Molar absorptivity, 158. 367, 375 Molecular absorption, 153. 155. 157,223, 237,431 ions, 282, 555 luminescence spectrometry, 399-429 mass spectrometry, 550-588 masses, 281 average, or chemical. 282 high-precision. 568 mass numocr, 282 from mass spectra, 578 in size-exclusion chromatography, 845 -848 Molecular-mass calibration standards, in sizeexclusion chromatography, 847 Molecular-selective electrode systems, 677- 683 Molyodenum target, X-ray, 304, 311 Momentum, angular, in NMR, 499 Monochromatic radiation Beer's law, 158 diode lasers, 173 incoherent, 169 Monochromator,18o-J89 dispersion. 185 echelle spectrograph, 21>I effect of slit width on resolution, 188 in tluorescence spectrometry, 411.413 in IR spectrometry. 444
light-gathering power. 185 performance characteristics, 181> in Raman spectrometry. 490 resolving power. 185 slits. 187 Monochromator. Spectronic 20, 357 Monochromator. X-ray. 311-312, 325 MOSFET.48 Moving average. 120. 125 MRI (magnetic resonance imaging), 537-542 MS (mass spectrometry). 281-302, 550-588 Mull, in IR spectroscopy. 459 Multichannel analyzer. 317, 319, 595. 603 electrode array detector, 707 emission spectrometers. 26(;-262 instruments, UV-visible. \ 353-354.30-361 photoelectric spectrometers, 271 Multidimensional NMR, 535-536 Multiplct peaks in NMR, 515-519 Multiplicity, 518 in internal conversion. 402 in intersystem crossing. 404 in NMR, 517-519 NAA. See Neutron activation analysis Nanoneedle electrode. 752 Natural line width. 220-221 Near-IR region. 455 Near·IR spectroscopy, 473-476 Nebulizer in atomic spectrometry, 224 -225. 256 in evaporative light-scattering detector, 826 Nernst diffusion layer. 726-727, 751 equation. 634, 640. 642. 644 calculation of half-cell potentials. 642, 643 effect of substituting concentration
for activity,
644 with formal potentials. 645
in voltammetric concentration protiles,724 glower. 449 - 450 Network, computer. 103-107 Neutralization titrations, hy coulometry. 709 Neutron
activation
analysis,
918-924 in the John Vollman case, %4-965 Nichrome wire sources. 450 NfR spectrometry, 473-474 NIST standard-reference pH solutions. 691 Nitrogen-specific chemiluminescence detector, 800 NMR (nuclear magnetic resonance spectroscopy). 498-549 applications of. 528-537 sample cell. 523 spectrometers. 521. 526 theory of, 499-509 Noise. 126 chemical. Ill. 582 effect on spectrophotometric analyses, 343 -346 electrical. 1>,1>62 shot.III-Il2, U5, 191.206.344 signals and, UO s~urces of in instrumental analysis, III Noise-power spectrum, 115 Nondestructive methods. NAA. 921-922 Nonelectrical domains. 3-4.6.8-9, 81 Nonfaradaic current. 633, 742-743 Noninverting input. operational amplifier. 61-63. 1>9.74, 114.706 Nonlinear regression, 388 semiconductor devices. 43 - 44 Nonpolarizcd electrodes, ideal. 641-;-649 Nonradiali\'c
t'\citation
147 Normal error curve, 976
91>1'1,
processe-;.
973, 974.
Normal-phase
scparalH ..H13.~,.._.
835.839 Notch filter. holographic, 179-180. 491-49~ Notehook, electronic laooratorY, 127-130 npn transistors. 46 - ,n n-type Si, 191>,199.311> Nuclear magnetic resonance spectroscopy. See NMR Nuclear Overhauser effect, 520,531 Nuclear quantum numhers, 499 Nuclei properties in NMR. 499-504 target. in NAA, 918-919 Null hypothesis. 984, 985 Nyquist frequency, 118-119.525 sampling theorem, 118-119,524
atomiC
SrtX':Uq".,,~ .. ,.
instruments.
components
of.
11>4-214 Optimization of column performance, 775-779 Oroitals in atomic spectra, 215 in charge-transfer complexes, 371 in K capture, 911 in molecular aosorption. 369, 370 splitting, 211> in valence band of semiconductors, 173 in X-ray spectra, 593, 598 Order of diffraction, 186 of interference, 139. 177 Organic solvents. effect on AA, 248 Off-resonance dccoupling. in NMR, voltammctric analysis. 747-748 529-531 Oscillator Ohmic potential drop, anharmonic. 436 electrochemical cell, 647 harmonic. 433 - 436 Ohm's law,S. 26-27, 30, 31>.38. 39, Output 1>3.69.73 impedances, operational On-column laser fluorescence amplifier. 59 - 63 detection system. 879 transducers, 6 One-tailed tests. 984 Overtones, 436. 473-474,481> On,line Overvoltage, 649 -652,697-700 operations. data collection. 92 pre-concentration. in MEKC, 883 Oxygen concentration. automated Open tubular columns determination of. '14k Gc. 801 dissolved, 409. 730 SFC, 859 determination of with Clar! Open-loop gain, 59. 1>4-1>5 electrode, 732 Operational amplifier effect on fluorescence. 407 applications of. 74 409 to mathematical operations, reduction of 71. 73 voltammetric wave. 730 to voltage and current control. voltammogram. 737 70 Ozone circuits, 62-1>3. 67. 1>9,73, 378. in chemiluminescence dete' 706 of sulfur. 800 difference amplifier. 69 determination of. 424 functions, 71 output voltage. 706 properties of. 59-61 yoltage follower. 62 l.cn)-crossing
detector.
Packed column 7-1-
ekctrochromatog SK3
((owilll/ed)
Packed
difference,
columns in column chromatography. 8(K)-801
in LC, 821
zone broadening Packings
Photoacoustic
sizes of in Le, 817-818 829, 83h
reversed-phase,
Paper chromatography, circuits,
Partial Particle
Photocathode,
848 diagrams,
152,
950-963 analysis,
Photodiodes,
in Ge,
954
Photoelectrorts,
950, 958, 961 828--836
of, 835 -837
Photometric
interferometer,
337
(photodiode
fringes,
458
arrays),
196-197
379-381
counting, emission, Photons,
Peak 33-34
voltage,
33, 39, 40
in photoelectric
Photosedimentation pholotubes,
surface
methods,
590 devices,
computer,
92-93 247, 760, 9_,2, 937,
941 663, 665
Polychromatic
radiation,
958
transducer,
inversion, mean, sample,
Planar
electrodes,
Planck's
constant,
146. 156,
171 ~l72
(see
ICp)
curves,
in a resistive
clement,
electron
in XI'S, 592 emission.
407
836
radiant,
2112,
35
- Raman
569, 575, 576
134
emission,
575 -577
absolutc.
32:i
909 methods,
activc transitions.
spectra, uf
group
microprobe. scattering.
el1icicnc) properties
909-928 common.
Raman in
4lJ4-4118, 418
144 -157
219, 404
for X-ray
Radionuclides. 9lO. 925 Radius, analytical. 959, 962
vield. 4114, 408. 423. See
radiation.
sources.
functional
lllso Quantum Ouantum-mechanical
148. 165, 17h
307
of lIV372 -374
analysis.
237
transitions,
RadiOisotopic source~,
tripk,
efficiency.
Radiationless
Radiochemical
828
467
191-201
methods.
MS. ';75
486
transducers,
Radioactivity.
visihle absorption
Ouantulll
115, 16:i, 166 -175 absorption. 303, :i94
MS. 3(Xl
291 -2'12
applications
Quantitative
4K6
background
in atomic synchrotron.
Radioactive
798
spectrometers,
Ouantum
law, 337
IR measurcment, capacitor,
201
RBS.604
X-ray, 308
of radiation. Beer's
287-290,
in tandem
900
502
transmitted.
spectroscopy. in DSe,
143, 486, 502
correction. 243
mass
in lCP-MS.
3S6,
147-149 near-infrared. 17S, 191 .. ,48, ,,50
source,6g,
170-172
in GC/MS.
monochromator,
of, 149 -152
in Raman spectroscopy,
transducers,
analyzers.
184-IS6
emission
170, 172
Quadrupole
178
energy of, units, 146, I:iS intensity of. 132,204,315,
in Zeeman
Qualitative
light -gathering,
164, 310, 9lO
in NMR,
317 -318
in LC/MS. beam
139-140,
detector,
polarized,
in glow discharge
Power, 63 dissipated
910-911
a charged
742 -743,748
451
691-692 70-71, 699, 70l, 704,
coherent,
interactions of with malter. 393
917
selectors,
686 - 690
of. 152 -1:i5
470,475
726
Pseudo-fIrst-order conditi()fis,
Pyroelectric
688
705, 730, 731. 757-759
iSTAT,
across spectrometry
for, Ih6
laser, 168-169,
gain, 63
difference
Plasma
direct,
IX7
Pumping
plot of vs. temperature
reaction,
182, 186
energy,
of fluorescence 971
Potential
499 emission
976, 978
971, 981
postcolumn
161-163.169,304.435,
356
681-6S2 Positron.
28
27
in lasers,
clinical analyzer,
724 - 726, 728,
53
659
calibration
deviations
deviation,
deviation,
variance,
divider,
titrations, Potentiostat,
971
standard Portable
752
737
due to, 340-342, Pooled standard Population
618 Pixel, 198-199
685 - 690
angle, 33
analyzers, 5, 9, 81, 41 I
66, 67,144,191-194
Piezoelectric
pH, 636, 670 Phase
716-717,
-lOX
of pH, 690
716-719
Polarography,
instrumental
photovoltaic cell, 192-193 pI. See Isoelectric point
in FlA, 932-933 p-funetion,
146
Prisms,
analysis, recorders,
measurements, 175
zone. 231-232
Pulse voltammetry.
Potentiometric
in voltammetry,
effect,
184, 683, 733
Phototransducer,
in spectroscopic
pump,
voltage
optical effects, 143-144
fluorescence.
comhustioll
Pulse-height
648, 649, 651
in nonlinear of radiation,
ahsorption.
voltammetry,
67
electrochemical, 697
bands of. 1.'2. 167,402,450
697
in laboratory
inNMR,533
absorption
Primary
in electrolysis,
laboratory,
157
132 -133
Preparative chiral separations. X()I
materials
electrode,
power.
Radiation,
ProlilL's. concentration-distance,
649, 651
Photosedimentation,958-961
Penetration depth in ATR,472
Peristaltic
194
Radiant
Prcdissociation, in fluurescence.
of, 641
charge-transfer, kinetic,
(PMTs),
195,202,313,491,957 148-149
Photoresist,
current,
curves,
Photomultiplier tubes Photon, 132, 144
209
IR from interference
titration
140
static, 409
748
determination
Potentiometer
or molecules,
dynamic.408-40tj
Precol1centration step. in stripping
in ('chelle monochrornalnrs.
tables of standard 997-](J(J()
144,652
of atoms
354, 355
839
143,484 - 486
Polarization,
6hl
potential)
index, 831-832,
Ouenching, 407-409, 417. 421 collisional. 408. 421. 428
SOI-S02
electrode
Standard
44 -45,48,50,54,·197,
Polarizability,
applications of, 418-421 Photometers, 354-355 double-beam,
in absorption measurements, Beer's law, 158
methods,
668
electrodes,
64 J, 645 (s 
