Science of Nanotechnology

THE SCIENCE OF NANOTECHNOLOGY: AN INTRODUCTORY TEXT

THE SCIENCE OF NANOTECHNOLOGY: AN INTRODUCTORY TEXT

LUANNE TILSTRA S. ALLEN BROUGHTON ROBIN S. TANKE DANIEL JELSKI VALENTINA FRENCH GUOPING ZHANG ALEXANDER K. POPOV ARTHUR B. WESTERN AND

THOMAS F. GEORGE

Nova Science Publishers, Inc. New York

Copyright © 2008 by Nova Science Publishers, Inc.

All rights reserved. No part of this book may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, electrostatic, magnetic, tape, mechanical photocopying, recording or otherwise without the written permission of the Publisher. For permission to use material from this book please contact us: Telephone 631-231-7269; Fax 631-231-8175 Web Site: http://www.novapublishers.com NOTICE TO THE READER The Publisher has taken reasonable care in the preparation of this book, but makes no expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of information contained in this book. The Publisher shall not be liable for any special, consequential, or exemplary damages resulting, in whole or in part, from the readers’ use of, or reliance upon, this material. Independent verification should be sought for any data, advice or recommendations contained in this book. In addition, no responsibility is assumed by the publisher for any injury and/or damage to persons or property arising from any methods, products, instructions, ideas or otherwise contained in this publication. This publication is designed to provide accurate and authoritative information with regard to the subject matter covered herein. It is sold with the clear understanding that the Publisher is not engaged in rendering legal or any other professional services. If legal or any other expert assistance is required, the services of a competent person should be sought. FROM A DECLARATION OF PARTICIPANTS JOINTLY ADOPTED BY A COMMITTEE OF THE AMERICAN BAR ASSOCIATION AND A COMMITTEE OF PUBLISHERS. LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA George, Thomas F., 1947Science of nanotechnology : an introductory text / Thomas F. George. p. cm. Includes index. ISBN-13: 978-1-60692-870-7 1. Nanotechnology--Textbooks. I. Title. T174.7.G46 2006 620'.5--dc22 2006030796

Published by Nova Science Publishers, Inc.

New York

CONTENTS Preface

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Chapter 1

The Nanoscale World

1

Chapter 2

Investigating the Nanoscale

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Chapter 3

Making the Nanoworld

49

Chapter 4

Describing the Geometry of the Carbon NanoFamily

67

Chapter 5

Mechanical and Magnetic Properties of Nanoparticles

85

Chapter 6

Optical Properties

103

Appendix:

Activities for Nanotechnology

143

Glossary

155

References

163

Index

169

PREFACE This book arose from the desire of a group of chemistry, physics and mathematics faculty to bring nanotechnology into the undergraduate classroom. We were fortunate to secure funding that made the project possible. Our initial effort was to teach one-credit classes at the three campuses where we work: Rose-Hulman Institute of Technology, Indiana State University and University of Wisconsin−Stevens Point. To teach these classes, we worked together to create course materials appropriate for sophomore science majors. Those lecture notes have evolved into this book. Any book with nine co-authors is a complicated project. We decided early on that we did not simply want to produce an edited volume, but instead to create a textbook. The goal is teaching rather than monographs, and the intent is that there be a progression from one chapter to the next, so that the book can usefully be read from cover to cover. At the same time, the expertise represented by our group varied widely: experimentalists and theoreticians; mathematicians and laboratory chemists; and much in between. There is no point in trying to hide this fact, and hence, while we’ve tried to create a coherent text, we have made no effort to produce an homogeneous one. The casual reader will note variations in style and content that reflect the personalities and interests of the principal authors of that chapter. It is assumed that all students reading this book will have completed general chemistry. Hence, terms like stoichiometry and Ångstrom are used with abandon. It is supposed that students are completely familiar with metric and SI units. Concepts such as molecular orbital theory are described in more detail, but it is still assumed that the student has seen some of this before. For some chapters, familiarity with calculus will prove useful. Chapter One serves as an introduction and discusses scales, sizes and some history of nanoparticles. Chapter Two concentrates on optical methods for studying nanoparticles, especially absorption, light scattering and diffraction methods. Chapter Three discusses various ways to make nanoparticles, including laser ablation, chemical vapor deposition and self-assembly techniques. These three chapters can be considered as introductory material and should be covered by any student using this text. Anyone with a general chemistry background will readily understand the material.

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Chapter Four concerns the structure of carbon nanotubes. The primary author is a mathematician, and thus mathematically-inclined students will find it most rewarding. However, the prerequisite knowledge for this chapter is minimal—a good knowledge of trigonometry and vector algebra will be useful. Chapter Five is about the mechanical and magnetic properties of nanoparticles, and will be of greatest interest to those who may intend to be engineers. A year of physics will also be helpful before reading this chapter, as is some familiarity with calculus. Chapter Six, covering optical properties, is the most difficult chapter in the book, and definitely requires a good background in general physics. Arguably, it is more appropriate for senior students than sophomores, but the well-prepared or hard-working sophomore will find it rewarding. The book contains exercises and hands-on activities. The latter, some of which may be considered laboratory experiments, are collected in an appendix. As with most textbooks, a comprehensive literature review is not provided, but the principal references and articles that may be of further interest to students are cited at the end of the book. There is a comprehensive glossary. Terms in the text are italicized if they appear in the glossary. The authors acknowledge the National Science Foundation for funding under Grant No. DMR-0304487. We thank Rose-Hulman sophomore Ross Poland for assistance in developing the hands-on projects. And finally, we acknowledge our copy editor, Dr. Bob Rich (www.bobswriting.com), for technical assistance, wise counsel and good friendship. For a book with nine authors, his efforts were crucial in bringing this text to fruition. There are a great many diagrams within this book. Some were created by the authors. Other figures were copied or adapted from various sources. Each such source is cited within the relevant figure caption. The copyright holders of all these drawings have kindly given permission to have their material reproduced.

SOME USEFUL CONSTANTS Speed of light Boltzmann constant Gas constant Planck’s constant Avogadro’s Number Bohr magneton

c = 2.9979 × 108 m/s kB = 1.3807 × 10-23 J/K R = 8.3145 J/mol K h = 6.6261 × 10-34 J s NA = 6.0221 × 1023 1/mol μB = 9.27 x 10-24 A m2 109 nm = 106 μm = 103 mm = 1 m

Chapter 1

THE NANOSCALE WORLD 1.1. A MATTER OF SCALE It’s all a Matter of Scale Beginning around 1600, people began to design instruments. The pendulum clock was invented by Huygens Christiaan in 1656. Pendulum clocks were rather large and not especially portable (think of your grandmother’s grandfather clock). They also had to stay upright in order to function properly, which rendered them useless for shipboard navigation. The invention of spring-driven clocks changed this by making clocks both smaller and more portable. The most important immediate application was the development of the marine chronometer. This accurate clock permitted the determination of longitude by comparing local time with Greenwich Mean Time, read from the chronometer. During the 19th century, people manufactured exceedingly fine chronometers, easily accurate to the nearest second. Today this technology exists only as a luxury item, in the form of elegant Swiss watches. The development of clocks, and the desire to make them as small and as portable as possible, required the ability to manipulate very small objects. Fingers were too big and so forceps were created. Fine machining was developed—think of all the little screws, springs and hinges that are necessary for a mechanical wristwatch. But the key limitation was human eyesight. In those days it was impossible to manipulate things too small to see—and this indeed defined the scale of the technology—millimeter scale. Just for fun, let’s call it “millitechnology”. While we no longer use mechanical clocks, we still use a lot of millitechnology— engines, toasters and pianos, for example, along with the moving parts of all sorts of items you would never associate with the 19th century: CD players, computer keyboards and photocopiers, to name just a few. Millitechnology continues to be important to this very day. Not all millitechnology has served useful purposes; some of it is done simply for fun. Think of the ship models built in bottles, or model train sets. These entertaining though impractical endeavors demonstrate just how proficient 19th century millitechnologists were. One of the most important products of the millimeter era was the invention of the microscope. A Dutch clockmaker (and millitechnologist) named Anton Van Leeuwenhoek invented one of the earliest microscopes near the end of the 17th century. We normally associate this invention with developments in medicine, and certainly those are important, but for our purposes here the microscope takes on a larger (or smaller?) meaning, namely

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removing the limitation on human eyesight. In principle, it permitted technology 1000 times smaller than a millimeter: on the order of a micrometer, μm, frequently referred to as a micron. Microtechnology was born... but it took a long time to develop. Of course the famous Swiss watchmakers used magnifying lenses in their work from early on. Elegant binoculars, opera glasses, and cameras were manufactured; the famous German optics firm, Zeiss, was founded in 1846. But none of this is really microtechnology; it is simply the application of simple optics to millimeter-scale problems. So what was the hang-up? To actually do microtechnology requires not only being able to see at the micron scale, but also to be able to manipulate objects at that scale. A pair of forceps no longer works. Oddly enough, the solution to this problem evolved from another crucial invention of the millimeter age—lithography. While type-setting required manipulating individual letters (using forceps) into position to make lines of words, lithography involved using available materials and a clever application of simple chemistry. Lithography involves five steps. (1) the image is laid down on a print block (originally limestone) with an oil-based medium. (2) The block is etched with an acid and gum arabic (a highly branched carbohydrate whose constitutive monomers are primarily D-galactose and salts of D-glucuronic acid). No etching occurs where the image is laid down. (3) The oilbased medium is washed off with turpentine. A raised salt matrix remains that is the ‘negative’ of the image. (4) An oil-based ink is rolled over the moist print block, filling the recessed areas where the image was laid down. (5) Paper is pressed on the block to produce multiple copies of the same image. The ink in step 4 can be any available color, and so this process allows production of multiple copies of multi-colored prints. In 1948 William Shockley, John Bardeen and Walter Brattain invented the solid state transistor; this led the way to integrated circuits that make up today’s microtechnology. A modern computer chip contains roughly 100,000 transistors, connected by “wires” that are roughly 0.5 to 1.0 μm in width. The process by which these transistors are connected uses photolithography. Fundamentally similar to lithography, this process allows micrometer-level precision when positioning transistors and their connectors. The components of a microchip can be readily discerned using an optical microscope—this really is microtechnology. Another early invention of microtechnology (1939) was the electron microscope. Optical microscopes are limited because of the wave nature of light—visible light has a wavelength on the order of half a micron. To see objects much smaller than that, one needs to “look” at them with something having a much shorter wavelength. It turns out that electrons have a wavelength on the order of one one-millionth of a micron. This permits objects of that size to become “visible”. The invention of the electron microscope, though not realized at the time, was as important in its own way as the invention of the optical microscope. Whereas the optical microscope increased resolution over the naked eye by a factor of 1000 or so, the electron microscope increased resolution over the optical microscope by an additional factor of 100,000. Thus a new distance scale is in order: a nanometer, abbreviated nm, is 10-9 m in size. The prefix “nano” denotes objects on this scale, and nano-objects are a hundred million times smaller than what can be seen with the naked eye. The electron microscope allows one to look at nanoscale objects—nanotechnology becomes possible. It’s taking a long time. As with the development of microtechnology, actually doing nanotechnology requires the ability to manipulate nanoscale objects. Development of these skills is very much in the forefront of current research and engineering, and constitutes the

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major topic of this book. However, it is now necessary to introduce another strand of the tale, specifically, chemistry.

1.1.1. Chemistry and Nanotechnology Parallel to the history just described, similar progress was being made in chemistry. The reader is probably familiar with Dalton’s Laws, formulated in 1808, that postulated the existence of “atoms”, and stated the empirically demonstrated laws of definite and multiple proportions. In 1828, Friedrich Wöhler published a paper in which he reported the synthesis of urea from inorganic molecules. He reported the stoichiometry of that substance as follows: Nitrogen Carbon Hydrogen Oxygen

46.78 20.19 6.59 26.24 99.80

4 atoms 2 atoms 8 atoms 2 atoms

Thus even in Wöhler’s time the term “atom” was widely used. So how big is an atom? Chemists usually think in terms of Ångstroms, where an Ångstrom is 1 × 10-10 m = 0.1 nm (nanometers). Thus it seems that chemists have been doing better than nanotechnology for nearly two centuries now—at least since 1808! They’ve been doing Ångstrom-technology, and furthermore, they are very good at it. So what’s the big deal? Why do we treat nanotechnology as if it is something new and important? There are two answers to this question. The first, and less significant one, is that the meaning of the word “atom” has changed. For Dalton and Wöhler, “atom” simply meant “basic chemical unit”, rather like we use “aliquot” or “portion” today. They did not necessarily believe in the actual physical existence of particles called “atoms”, and they certainly had no conception of atomic structure as we understand it today. For Dalton, an “atom” was simply what permitted the laws of definite and multiple proportions. This is also the way Wöhler thought of it; indeed, he even mentions the water atom. The very existence of atoms was controversial even into more modern times. Ludwig Boltzmann, who near the end of the 19th century developed statistical mechanics on the assumption that atoms really existed, committed suicide in 1906 in despair that atoms didn’t really exist and his life’s work was for naught. Only a few years later (1909), Jean Perrin was the first to measure Avogadro’s number and thus decisively prove the existence of atoms. The moral is this: it is hard to give early chemists credit for Ångstrom-technology if they didn’t believe in the existence of atoms. The second reason nanotechnology is really important is that nanotechnology is not chemistry, at least not as understood by Dalton or Wöhler. Nanotechnology derives not from chemistry, but rather from the spirit of the clock makers of yore. Imagine, for example, if Christiaan Huygens had attempted to synthesize a clock using the tools of chemistry: Mix 3 moles of screws, 2 moles of hinges and 0.5 moles of springs in a container with suitable solvent. Heat to 350°C stirring continuously for 48 hours. Extract the product. Air dry, and add an excess of clock-faces… This procedure results in a 5% yield of clocks, albeit with two enantiomers—half of them run counter-clockwise.

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Of course not! Clocks are manufactured one at a time with nearly 100% yield. Even if a chemical synthesis could be devised, it would be so inefficient as to be not worth doing. Put another way, the entropy cost of manufacturing clocks occurs in the human brain and on the factory floor, not in the chemical reaction chamber. And nanotechnologists live in the spirit of clockmakers and microchip makers—they want nothing less than to produce their molecules one at a time, with 100% yield, and with whatever custom-made appurtenances the customer may desire. This is as different from traditional chemistry as it possibly could be, and this is why nanotechnology is such a big deal. Nanotechnology really is technology, and is in some ways more akin to mechanical engineering than traditional chemistry. Indeed, the goal of nanotechnology is to make oldfashioned, synthetic chemistry obsolete. Big words, that. Unfortunately it hasn’t come about—yet. In the current state of the art, nanotechnology still has to use a lot of chemistry, but it isn’t by choice. An example illustrates: In the following pages you will read much about carbon nanotubes, strips of graphite rolled up into a tube. These tubes have many characteristics, the details of which you will learn, but for the moment we simply mention that important variables include tube length, radius, chirality (whether it has a right- or left-hand twist) and purity. Figure 1-1 shows a big jumble of nanotubes that were synthesized using chemistry. Recently a research group from Rice University took such a jumble of nanotubes and separated them from each other by sonication (shaking up with sound waves). A detergent was added to the tube suspension so that a single nanotube was in each bubble. The scientists were then able to do spectroscopy on individual nanotubes by looking at individual soap bubbles. This is nanotechnology, because instead of looking at a mole of particles, or even particles in parts per million concentration, they examined and were able to characterize individual nanotubes. Additional results of manipulation of individual nanoparticles are shown in figures 1-2 and 13. Figure 1-4 is not really at the nanometer scale, but illustrates the desired precision in fabrication.

Figure 1-1. A Scanning Electron Microscope photo of nanotubes, from www.iljinnanotech.co.kr/en/material/r-4-1.htm.

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Figure 1-2. A Scanning Electron Microscope photo of iron atoms on a copper surface. These are the Japanese (Kanji) letters spelling “atom.” The colors are created by the artist, but the resolution and placement of the individual atoms is real. (From http://www.almaden.ibm.com/vis/stm/atomo.html).

Figure 1-3. (From http://www.ipt.arc.nasa.gov/nanoflag_lowres.html) Caption included in figure.

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Figure 1-4. A nanotube farm, though note the large scale.

To be considered nanotechnology, the substance must be produced with 100% yield and there must be an absolute control of the structure. Nanostructures are built one atom at a time, as described in Feynman’s speech (Exercise 1.1). The current state of the art is not very far developed, and the actual implementation of the technology is still mostly in the future. Work is proceeding on two fronts. In the first case, we are trying to improve our ability to do the nanoengineering, and in the second case we are looking for possible applications of nanoparticles. A very clear definition comes from M. Meyyappan of Ames Labs, “Nanotechnology is the creation of USEFUL/FUNCTIONAL materials, devices and systems through control of matter on the nanometer length scale and exploitation of novel phenomena and properties (physical, chemical, biological) at that length scale,” (Meyyappan, http://ipt.arc.nasa.gov/nanotechnology.html). Having provided a sense of what nanotechnology is, it is appropriate to introduce you to some specific nanoparticles. Nanoparticles can be roughly divided into carbon-based, and not carbon-based. The following sections will introduce you to these materials, a brief history of their development, and some applications—anticipated and realized.

1.2. CARBON-BASED NANOPARTICLES To understand some of the features of carbon-based nanoparticles, it is useful to review some features of the different forms, or allotropes, of pure carbon. The most stable allotrope of carbon is graphite, shown in figure 1-5a. Graphite, such as found in pencil lead, has a large number of such sheets stacked on top of each other. It is, however, fairly straightforward to isolate a single sheet of graphite, known as graphene. In graphite, the carbon atoms have trigonal planar geometry. You may recall from your general chemistry course that this means the orbitals are sp2 hybridized to form the planar structure. Another well-known allotrope of carbon is diamond, shown in figure 1-5b. In diamond, each atom has four nearest neighbors located at tetrahedral positions; the orbitals are sp3 hybridized and the resulting structure is not planar. Although difficult to see, the carbon atoms of diamond exhibit a regular repeating pattern in three dimensions. Both graphite and diamond are pure carbon, yet they have very

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different properties and appearance. Carbon-based nanoparticles can be considered to be additional allotropes of carbon; not surprisingly, they have unique and sometimes amazing physical and chemical properties.

Figure 1-5. Two allotropes of carbon. Each dot is a carbon atom. (a) graphite; the dotted lines identify a single unit cell (see Chapter 2). This sketch shows portions of three parallel graphene sheets. (b) diamond: one unit cell is shown. From www.chem.wisc.edu/~newtrad/CurrRef/BDGTopic/BDGtext/BDGGraph.html

1.2.1. Bucky Ball Bucky ball, short for buckminsterfullerene, which in turn is the name for the C60 molecule shown in figure 1-6, plays an important historical role in the development of nanotechnology. C60, as the chemical formula implies, contains 60 carbon atoms arranged in the form of a soccer ball. All atoms are chemically identical, i.e., they will show up in the same place on an NMR (nuclear magnetic resonance) spectrum. C60 is historically important for a couple of reasons: arguably, it was the first molecule to be explicitly denoted as “nano”. Also, the discovery of C60 led within a couple of years to the discovery of nanotubes, which are now an integral part of nanotechnology. At the time of its discovery, C60 was described as another allotrope of carbon, distinct from graphite or diamond. Today this picture is muddier—there is a whole class of molecules known as fullerenes, and yet another class of molecules known as carbon nanotubes or onions. The story of buckminsterfullerene began when a British astrochemist, Harry Kroto, wanted to test the hypothesis that small carbon particles existed in interstellar dust clouds. Our data from such dust clouds is necessarily spectroscopic, and the species are identified by comparing such spectra with those generated by molecules on earth. Kroto learned that a group at Rice University in Houston headed by Richard Smalley was able to experimentally reproduce the environment of an interstellar dust cloud. Smalley’s group had designed their experiment for other purposes, but eventually Kroto was able to prevail on them to attempt to generate carbon clusters.

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Figure 1-6. A schematic diagram of buckminsterfullerene. Each vertex on the surface of the ball is the location of a carbon atom. The lines represent bonds between carbon atoms.

The result was published in a now famous paper in 1985 (Kroto et. al., 1985). Figures 1-7 and 1-8 are reproduced from that paper. As pointed out in the caption to figure 1-8, the C60 structure appears to be relatively stable. This means that as carbon clusters are placed in an environment where they are more able to exchange energy with their surroundings and to collide with other carbon clusters, then C60 will be the predominant product. On the other hand, at low helium pressures as shown in figure 1-8c, where there is less interaction with the surroundings, a variety of carbon fragments are formed.

Figure 1-7. Schematic diagram of the pulsed supersonic nozzle used to generate carbon cluster beams. The integrating cup can be removed at the indicated line. The vaporization laser beam (30-40 mJ at 532 nm in a 5 ns pulse) is focused through the nozzle striking a graphite disk which is rotated slowly to produce a smooth vaporization surface. The pulsed nozzle passes high-density helium over this vaporization zone. This helium carrier gas provides the thermalizing collisions necessary to cool, react and cluster the species in the vaporized graphite plasma, and the wind necessary to carry the cluster products through the remainder of the nozzle. Free expansion of this cluster-laden gas at the end of the nozzle forms a supersonic beam which is probed 1.3 m downstream with a time-of-flight mass spectrometer. Figure and caption from Kroto et. al, (1985).

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Figure 1-8. Time-of-flight mass spectra of carbon clusters prepared by laser vaporization of graphite and cooled in a supersonic beam. Ionization was effected by direct one-photon excitation with an Ar-F excimer laser (6.4 eV, 1 mJ cm-2). The three spectra shown differ in the extent of helium collisions occurring in the supersonic nozzle. In c, the effective helium density over the graphite target was less than 10 torr - the observed cluster distribution here is believed to be due simply to pieces of the graphite sheet ejected in the vaporization process. The spectrum in b was obtained when roughly 760 torr helium was present over the graphite target at the time of laser vaporization. The enhancement of C60 and C70 is believed to be due to gasphase reactions at these higher clustering conditions. The spectrum in a was obtained by maximizing these cluster thermalization and cluster - cluster reactions in the “integration cup” shown in figure 2 (figure 1-7). The concentration of cluster species in the especially C60 form is the prime experimental observation of this study. Figure and caption from Kroto, et. al, (1985).

The other noticeable fact about figure 1-8 is that carbon clusters with an even number of atoms are found. This was the crucial structural clue that led to the hypothesis that the clusters formed closed polyhedral cages. It is easy to show that such cages must have an even number

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of atoms, and further, there is no reason why graphite or diamond fragments should necessarily have an even number of atoms. So Kroto et al’s hypothesis, subsequently verified, was that these small carbon clusters formed polyhedral structures with five- and six-membered rings. For carbon, the sixmembered, hexagonal ring is most stable, whereas the five-membered, pentagonal ring is less stable. It turns out that 60 atoms is the smallest such polyhedron that can be made where pentagonal rings are not adjacent to each other. This, the authors suggested, is what leads to the unique stability of C60. Further, for species larger than 60 atoms, the next smallest structure with no adjacent pentagonal rings is C70, which shows up as the second largest peak in all spectra in figure 1-8. These hypotheses imply that a large class of fullerenes will exist, with stable ones having even numbers of carbon atoms with 60, 70 or more atoms. A fullerene is any closed polyhedron made up of carbon atoms. This has turned out to be true, and fullerenes with 84, 92 and 96 atoms are now known to exist. For several years, the only evidence for fullerenes was the squiggly lines generated by a mass spectroscope, as shown in figure 1-8. Needless to say, the very existence of C60 was controversial. This changed in 1990 when a group in Switzerland synthesized C60 in bulk quantities (Krätschmer et. al., 1990). They did this in a remarkably simple way: they took graphite and vaporized it in an inert atmosphere. C60 was deposited on the walls of the container and could be isolated by dissolving it in toluene. The result was a flowering of research on fullerenes and fullerene-like molecules. Science magazine chose C60 as the “Molecule of the Year” in 1991. When they were first discovered, much importance was ascribed to fullerenes. They were hailed as 3-dimensional molecules that potentially opened up a brand new functional group for organic chemistry. Much of this hype has proved disappointing—there are to date few practical applications for C60. However, the discovery of C60 has directly led to the development of nanotechnology, and so the historical importance of the molecule is immense.

1.2.2. Nanotubes Shortly after the synthesis of fullerenes, Japanese scientists used a scanning tunneling electron microscope and found nanotubes (Iijima, 1991). To envision a nanotube, take a bucky ball and cut it in half. Now roll up a graphene sheet and insert it between the two halves; the result is a nanotube. The actual geometry of nanotubes is considerably more complicated and will be considered in detail in Chapter 4. Some pictures are shown in figure 1-9, and here it is seen that one can put nanotubes inside of other nanotubes—sort of like stacks of graphite rolled up. Thus one can distinguish between multiwalled nanotubes (MWNT) and singlewalled nanotubes (SWNT).

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Figure 1-9. Electron micrographs of microtubules of graphitic carbon. Parallel dark lines correspond to the (002) lattice images of graphite. A cross-section of each tubule is illustrated. a. Tube consisting of five graphitic sheets, diameter 6.7 nm. b. Two-sheet tube, diameter 5.5 nm. c. Seven-sheet tube, diameter 6.5 nm, which has the smallest hollow diameter (2.2 nm). Figure and caption from Iijima (1991).

Depending on the specific geometry, carbon nanotubes can conduct electricity, in which case they are known as metallic nanotubes, or they can be semiconducting. A quantity known as chiral angle, discussed in Chapter 4, which measures the twisting of a nanotube, partially determines the conductivity of carbon nanotubes. “Chirality” refers to the fact that the structure can occur with a right or left hand twist. Semiconducting nanotubes are potentially important for electronic applications. Unfortunately, as of this writing, it is only possible to make chiral mixtures of nanotubes, though semiconducting and metallic tubes are fairly easily separated. Most nanotubes are MWNTs—these tend to be rigid. They can easily be grown with reproducible length, diameter and location, though the metallic or semiconducting properties are not yet controllable. Figure 1-10 shows the state of the art as of 1998—it is more advanced now. SWNTs are harder to manufacture. Because they are not as rigid, they tend to stick to surfaces and form spaghetti. Nevertheless, it is now possible to control more carefully the structure of SWNTs. It has recently been reported that an SWNT with a 1 nm diameter has been grown to a length of 1.5 cm!

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Figure 1-10. Images of MWNT’s as produced at a laboratory at Boston College. Since these photos were taken, the laboratory has been able to make more uniform samples with greater control. From Ren et al (1998).

Carbon nanotubes have already found some important applications. They serve as efficient catalysts in Ni/Cd batteries, extending the duty cycle by several multiples. They play a similar role in the venerable lead/acid battery used in your car—new car batteries should last longer. They form the tips in AFM instruments. They have the greatest tensile strength of any substance known. Unlike C60, there are already commercial applications for nanotubes, and private companies are manufacturing them to user-defined specifications. Although the ability to control the diameter, length and number of walls in nanotubes exists, we are not yet able to control the chirality. As alluded to earlier, a chiral molecule is one which has a distinct mirror image, in the same way that your left and right hands are mirror images of each other. Conversely, a ball is not chiral because its mirror image is identical to the original ball, i.e., it is not distinct. A molecule that has a distinct mirror image is said to be chiral, or to have the property of chirality. Manufacturing nanotubes in precisely reproducible ways is the hallmark of nanotechnology. Ultimately, we want to be able to mass-produce nanotubes just like we mass-produce clocks or cars—with near 100% yield and to precise specification. This is the world of nanoengineering.

1.3. NON-CARBON BASED NANOPARTICLES Inorganic (non-carbon) substances have also been used to make nanotubes. In particular WS2 (that’s right—tungsten disulfide) has been formed into nanotube structures. In principle, any substance that forms a two-dimensional lattice is a candidate to make a nanotube. Most

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non-carbon based nanoparticles are not nanotubes, but rather nanosize particles of metals or semiconductors. Like buckyballs, these non-carbon based nanoparticles were synthesized and studied by chemists before there was a real awareness of their potential applications. In 1856, Michael Faraday at the Royal Institution of Great Britain prepared gold “fluids” that were ruby, blue or purple in color by the reduction of gold salts with phosphorous. Faraday found that these “fluids” were like solutions in that they did not settle readily over time, but unlike solutions, the “fluids” dispersed light as suspensions as shown in figure 1-11. Faraday is credited as the discoverer of metallic colloids, particles from 0.5-500 nm that do not readily settle out from solution. Unfortunately, the microscopic tools available to Faraday did not allow him to “see” the gold particles and consequently he could not answer questions about their behavior. Nevertheless, Faraday described a method for preparing metallic nanoparticles and suggested that changes in particle size or shape may influence the properties of particles. These methods (described in Chapter 3) allow preparation of nanoparticles that are within rigid size parameters.

Figure 1-11. A beam of light passes through a solution dispersed and a colloidal mixture. Photo taken by Ryan D. Tweney, Bowling Green State University. Permission to take this image was kindly given by the Royal Institution of Great Britain.

In addition to the nanoparticles of pure metals, nanocrystals of semiconducting materials such as CdS and GaAs have been prepared with sizes ranging from 1000 nm to 10 nm. These nanosize fragments of semiconductors are called quantum dots. Conductivity and color all

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vary as the size of these particles is reduced from the macroscopic crystal to the molecular regime. The electrical and optical properties of quantum dots depend strongly on the size of the fragments because of a phenomenon known as quantum confinement, which will be discussed in Chapter 2. The special topic of the optical properties of nanoparticles is discussed in Chapter 6. For now, it is sufficient to mention that the electrical properties of quantum dots allows the development of tunable LEDs (light emitting diodes), optical switches, and maybe even quantum lasers (Alivisatos, 1996). Because nanoparticles have a very low heat capacity, they are being studied for a possible role in cancer treatments. Gold nanoparticles are bound to antibodies that are selective for proteins found only on the membranes of cancerous cells. The energy of a brief laser pulse, tuned to the gold nanoparticles, is absorbed. The low heat capacity results in very localized extreme heating that in turn kills cells with gold nanoparticles attached to their membrane. Many physical properties are dramatically altered when inorganic materials are clustered in nanosize particles. Figure 1-12 presents results of how the melting temperature (and the heat capacity) of gold varies with particle size. There is clearly a dramatic change as one enters the nanoscale regime. In addition, the mechanical properties of nanoscale materials are modified. Tungsten carbide, tantalum carbide, and titanium carbide are much harder, more wear-resistant, and more erosion resistant than their large-grain counterparts. It is not surprising, then, that they are currently used as cutting tools and may become part of new spark plug designs for automobiles. The special mechanical and magnetic properties of nanomaterials are discussed in Chapter 5.

Figure 1-12. The melting point of gold depends on the radius of gold particle size most noticeably when articles have a radius smaller than 4 nm. From Koper and Winecki, (2001).

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1.4. SPECIAL FEATURES OF NANOPARTICLES 1.4.1. Dimensionality In our earlier discussion of the allotropes of carbon, we mentioned that diamond has a three-dimensional regular repeating pattern, but graphene—a single sheet of graphite—is flat. Being the thickness of only one atom of carbon, a sheet of graphene can be said to be nanoscale in one dimension. Alternatively, we can say that in the macroscopic world, graphene is a two-dimensional structure, i.e., its dimensionality is 2. In a similar fashion, nanotubes—whether they are made of carbon or any other material—are nanoscale in two dimensions. They are one-dimensional in the macroscopic world. It is not a large stretch to imagine a material that is nanoscale in three dimensions, e.g., a bucky ball. Particles that are nanoscale in three dimension are said to be 0-D structures in the macroscopic sense. This does not mean the particles occupy no volume, but rather that they are very, very small scale structures. The macroscopic properties of materials depend on their nanoscale structure, and dimensionality is one way of describing that structure. Diamond has a dimensionality of three, graphite has a dimensionality of two. Diamond is hard; graphite is soft. Diamond is an electrical insulator, graphite is a conductor. While defining dimensionality is not equivalent to defining the macroscopic properties, defining the dimensionality does introduce possible sets of macroscopic behavior to study.

1.4.2. Surface Effects Surfaces are unstable. This is because matter is almost always attractive, and hence atoms and molecules are lower in energy when surrounded by neighbors. You may recall the old chemistry expression “like likes like.” This means that similar substances will dissolve in one another, whereas dissimilar substances will segregate. The ultimate separation is a welldefined surface, which further suggests that surfaces are unstable. Nanosize particles have an inordinately large surface area to volume ratio, so surface effects are very important for nanoscale materials. We now spend some time discussing their properties. Surfaces are usually stabilized in some way. To illustrate, consider a diamond crystal, shown in figure 1-5b. Each atom has four nearest neighbors (we say it has a coordination number of 4), located at tetrahedral positions. For a diamond crystal of the size you might put on your ring, the typical atom is very far away from the surface. However, at the surface, the atoms no longer have nearest neighbors and are therefore unstable. There are two ways to stabilize them: passivation—that is, to provide material for surface atoms to bond to, and surface rearrangement (also known as surface reconstruction). Saturation is a term taken from organic chemistry, and generally means filling all dangling bonds with hydrogens. An example of saturation is given by figure 1-13a, and shows that saturated surfaces tend to be more stable. An extreme example of saturation is Teflon. That surface is so stable that almost nothing sticks to it at all. Typically, the surfaces on a diamond ring are saturated, though perhaps not only with hydrogen atoms. A surface may be passified by organic compounds, hydroxyl or amino groups, or whatever else is scavenged from the environment.

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A clean surface refers to one where the saturation molecules are removed. A clean surface can usually only exist in a vacuum or in an inert atmosphere. Since a clean surface cannot be stabilized via saturation, then surface rearrangement occurs. In this case, surface atoms will bond with each other to tie up the dangling bonds, or in the case of diamond, they may form multiply-bonded structures, i.e., double and triple bonds. Thus, the geometry around each atom at the surface will no longer be tetrahedral or sp3. Some elements, such as clean silicon, form consistent and well-characterized rearrangements. A rearranged surface is usually unstable when exposed to the atmosphere—bonds will tend to saturate, reducing the strain energy implicit in rearrangement. An example of a possible rearrangement of a diamond surface is shown in figure 1-13b, which shows that the surface assumes a graphitelike structure. Surfaces are very important and will affect optical and chemical properties. Nanostructures have a large surface area per unit mass, and thus for nanoparticles the properties of surfaces is crucial. It doesn’t matter if it is a diamond-air surface or a diamondaluminum surface—there still will be surface effects.

Figure 1-13a. The effect of surface saturation. The purpose of this study was to determine the effect of surface saturation on a diamond-aluminum interface. The gray balls represent diamond, while the darker ones are aluminum. For an unsaturated surface the circumstance is as depicted in (b). When the diamond surface is saturated with (smaller) hydrogens, the situation is as depicted in (c). Note that saturation stabilizes the diamond surface, which destabilizes diamond-aluminum interactions, forcing the aluminum further away. From Qi and Hector (2003).

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Figure 1-13b. This shows the reconstruction that takes place at a diamond surface. The dark balls represent surface atoms that are four-fold coordinated, as is bulk diamond. The lighter balls on the surface are only three-fold coordinated, and look more like graphite. The graphitic-like structure stabilizes the surface. From Petukhov et. al., (2000).

A graphite sheet has two kinds of surfaces. The surface of the sheet is relatively stable— there are no dangling bonds. Graphite, however, is reactive in the sense that free radical species can relatively easily attack the aromatic rings that make up the sheet. For this reason, graphite readily burns at elevated temperatures; it is a primary constituent of charcoal. Nevertheless, the planar surface of graphite may be considered stable under atmospheric conditions at room temperature. The other kind of surface is the edge of the sheet. Here there are dangling bonds, and these must be saturated or rearranged as described with diamond. Nevertheless, clean graphite is less reactive than clean diamond, simply because only the edge atoms require saturation or rearrangement.

1.4.3. Optical and Electrical Properties A complete understanding of the effect of existence in the nanoscale regime requires a review of quantum mechanics. You may recall from General Chemistry that quantum mechanics only becomes important when one is dealing with material within the size/mass regime of electrons. This is the nanoscale regime. The purpose of this section is to introduce you to what the special properties are without providing a justification. First, nanoparticles have unique electrical conductivity properties. This is particularly noticeable for nanocrystals of semi-conductors. As will be demonstrated in Chapter 2, the

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ability of a semiconductor to elevate electrons to higher energy levels decreases as the particles get smaller. This means that regulating particle size may result in very small tunable laser systems. On another front—and as has already been mentioned—the conductivity of carbon nanotubes depends on their chirality. What this means, and the nature of this relationship, will be spelled out in Chapter 4. Secondly, the reflectivity and/or color of particles depends on their size in the nanoscale regime. This is apparent from the changing color of gold colloids already mentioned. Although metals tend to be good conductors all the way down to the nanoscale, the confinement of the electrons to the nanoparticle results in a lower heat capacity than the metal would have in the bulk. Any energy put into the nanoparticles can not be readily dissipated and so the temperature of the particles rises dramatically with a relatively small influx of energy. This is the source of the utility of gold nanoparticles for cancer cell death described earlier in this chapter. The purpose of this chapter has been to introduce you to the possibilities of a world filled with nanotechnology. To really understand how and why nanoparticles have the properties they have, you’ll need to dig into the following chapters. Some of it will seem straightforward and some of it will be confusing. It’s going to take some time, but considering the developments we’ve experienced in going from millitechnology to microtechnology and the beginning of great benefits we see from nanotechnology, it’ll be worth the effort.

EXERCISES Exercise 1-1: After you have read the transcript of the speech printed at http://www.zyvex.com/nanotech/feynman.html, choose one of Feynman’s examples of nanotechnology and write a paragraph that elaborates on a possible application. Exercise 1-2: Suppose atoms are spherical with a radius of 1 Å. Suppose a collection of such atoms is arranged in a spherical ball that has a radius of 1 μm. Estimate the fraction of atoms located at the surface of the ball. Repeat this calculation for a ball with a 1 nm radius.

Chapter 2

INVESTIGATING THE NANOSCALE 2.1. INTRODUCTION One take-home message from the first chapter is that nanoparticles are really small. So, how can scientists ‘see’ what they’ve made? The electron microscope mentioned in Chapter 1 allows scientists to observe materials on the nanometer scale, however there are several additional methods that have been developed to look at individual molecules. These techniques are described in this chapter with enough detail that, when you read about results, you will both understand them and accept their validity. Most of the principles described in this chapter require at least a basic understanding of quantum mechanics. Quantum theory is also necessary for understanding the properties of nanoparticles; and so quantum mechanics is also introduced in this chapter. The purpose of this chapter is to describe methods that can be used to investigate nanosize materials. All of the methods involve, in some way, the interaction of energy and matter. It is useful, then, to first present some fundamental ideas associated with the nature of energy and of matter. Let us first look at energy.

2.1.1. The Nature of Energy Energy is transmitted as a wave. Consider the nature of light and the extended electromagnetic spectrum shown in figure 2-1. The term ‘electromagnetic’ arises because the waves described in figure 2-1 are comprised of an electric field component and a magnetic field component. Electromagnetic radiation is the propagation of energy in the form of electromagnetic waves. Included in the types of electromagnetic radiation are x-rays, ultraviolet rays, visible light, infrared light, microwaves and radio waves. As can be seen by looking at figure 2-1, the wavelength of these various types of electromagnetic radiation is inversely related to their frequency. Expressing wavelength in meters (m) and frequency in Hz (s-1), the speed of light (3 x 108 m/s) is the proportionality constant ν = c/λ

(2.1)

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Figure 2-1. The electromagnetic spectrum. From Rubinson and Rubinson, (1998), page 317.

If all the waves emanating from a source hit their peak at the same point in time, then the waves are said to be ‘in phase’. In other words, the waves are coherent. When waves are not coherent, then it is possible for destructive interference to occur. Two waves that are perfectly out of phase, that is one reaches its maximum while the other reaches its minimum, will interfere with each other, resulting in a ‘wave’ with zero magnitude at all points in space. If two waves are coherent, their constructive interference will yield a wave with maxima that has a magnitude equal to the sum of the two original waves. Understanding of the nature of electromagnetic energy is made more complicated with the realization, first proposed by the German physicist Max Planck, that light has a particulate nature. In 1900, Planck proposed that energy must be quantized; the small, discrete units of energy were called quanta (singular: quantum). Later, Albert Einstein proposed the name photon to describe a quantum of light. The energy of photons is proportional to their frequency E = hν = hc/λ.

(2.2)

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where h, known as Planck’s constant, has the value 6.626 x 10-34 Joules. It is instructive to look at the electromagnetic spectrum from the point of view of the magnitude of energy. From equation 2.2, it is apparent that small wavelength is associated with large energy. In units of J per event (J), chemical reactions produce energy on the order of 10-19 J (which translates to about 10,000 J/mole of substance reacted), whereas nuclear reactions are roughly 10-12 J or higher in energy. The energy of X-rays is in between these two values: 1-100 x 10-16 J. Electromagnetic energy isn’t the only kind of energy that has both wave and particulate nature. The thermal energy of an atom in a solid is also quantized. Manifested as elastic vibrations of a particle around its equilibrium position in a solid, these vibrational waves are excited spontaneously in a crystal by the thermal agitation of atoms. Their amplitude increases as temperature rises. Phonon is the name given to a quantum of vibrational energy hν for a frequency ν. Another commonly used notation for this quantum of energy is ħω for a frequency ω; where ħ = h/2π and ω = 2πν. The maximum frequency of a phonon is around 1012 Hz. While this corresponds to the frequency of infrared light, the velocity of phonons is considerably less than the velocity of light. The velocity of propagation for these elastic waves is of the order of 5000 m/s.

2.1.2. The Nature of Matter Most of our understanding of matter comes from our own observations: matter has mass, occupies space, when in motion it tends to stay in motion. These observations have been clearly defined in the laws of Classical Mechanics. There’s just one hitch: as the mass of particles gets smaller and smaller, classical mechanics begins to fail. ‘Particles’ begin to behave like waves. In 1924, the French physicist Louis de Broglie suggested that the wavelength of a particle, λ, must be inversely related to its mass, m, and velocity, v. λ = h/(mv)

(2.3)

This equation suggests that for massive particles like baseballs, the wavelength is very small and the wave nature is difficult to discern. However, for particles with very small mass (e.g., electrons), the wave nature is a significant part of their behavior. The behavior of a photon of green light is well described by equations of wave mechanics. Until 1900, energy and light were thought to be entirely wave-like in nature. Indeed, their behavior is mostly wave-like; the theories and equations of wave mechanics are sufficient to describe and explain most observations about light. Electrons, having a mass of 9.1 x 10-31 kg (rest mass), exhibit both wave and particle nature. The only way to explain the behavior and properties of electrons is to use a theory that includes both particle and wave properties. The theories and equations of quantum mechanics must be used to describe and explain observations about electrons.

2.1.2.1. Quantum Mechanics During the 1920s, Erwin Schrödinger found a way to combine the two fields of classical mechanics and wave mechanics in an equation named after him.

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(2.4)

In this equation, Ĥ is called the Hamiltonian operator and E is the energy of the wavefunction Ψ. The solutions to the Schrödinger equation are the wave functions Ψ and the corresponding energies E that describe the state of a particle. From these solutions came an understanding of how electrons exist around the nuclei of atoms. As you may recall from your General Chemistry course, orbitals (s, p, d, f, g, etc.) describe the three-dimensional regions of space around the nucleus where it is most likely that the electrons exist. Each orbital is correlated with one solution to equation 2.4. Orbitals have a shape defined by squaring the wave function Ψ and the energy of an orbital is the energy E associated with the wave function Ψ of that orbital.

2.1.2.2. Molecular Orbital Theory and Band Theory Something interesting happens when two atoms, each with their own sets of orbitals, approach each other. As the wave functions overlap in space, they interfere with each other, resulting in the formation of new wave functions. These new wave functions have different shapes and different energies than the wave functions of the isolated atoms. They are called molecular orbitals (MO). According to Molecular Orbital Theory, when two atomic orbitals overlap, two molecular orbitals will form. One of the molecular orbitals will have lower energy than the atomic orbitals and the other will have higher energy. In the ground (lowest energy) state, electrons occupy the lowest energy orbitals possible. If occupied, the lower energy molecular orbital would lower the energy of a system relative to the energy of the isolated atoms; it is called a bonding MO. The higher energy molecular orbital is called an antibonding MO. These are represented in figure 2-2a for a diatomic of copper atoms. Because it is reasonable that only the orbitals that are furthest away from the nucleus will have significant overlap with orbitals from another atom, figure 2-2 presents only the valence atomic orbital of copper (4s) which—in the copper atom’s ground state—has one electron.

Figure 2-2. As copper atoms approach each other, their valence orbitals overlap, resulting in the formation of molecular orbitals. Bonding molecular orbitals are represented with a solid line, and antibonding molecular orbitals are represented with a broken line. (a) If two atoms have overlapping atomic orbitals, the resulting molecular orbitals each have a single defined energy. However, as more and more atoms approach each other (b) the molecular orbitals have a distribution of energies manifested as a band. The width of the band widens as the number of atoms increases.

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Based on figure 2-2a, it is apparent that diatomic copper has lower energy than a copper atom, yet diatomic copper does not exist. We know, from our own experience, that copper exists as a metal, i.e., many copper atoms held together. In order to explain why, we continue our trip across figure 2-2 and introduce Band Theory. One way to understand why the MOs have different energies from the atomic orbitals is to recognize that the bonding MO feels the nuclear charge from both of the atoms and the antibonding MO feels less nuclear charge than the original atomic orbitals. (To convince yourself of this, check out the three-dimensional shape of MOs in a general chemistry textbook.) When many atoms are near each other, the MOs that form experience forces from many more sources than just two nuclei. The variation in the magnitude of these forces results in the formation of MOs with a distribution of energy levels rather than the two, defined energies that result when only two atoms bond. The distribution of energy levels results in what are known as ‘bands’ of energy. It turns out that the stronger the interactions between neighboring atoms, the wider the distribution. Additionally, the greater the number of nearest neighbors, the stronger their interactions will be. The combination of these effects results in what is shown in the rest of figure 2-2; namely, as the number of particles increases, the width of the bands increases. In the case of metals, the wider bands overlap. The result is one continuous band, the lower half of which is completely occupied in the ground state of the metal. The occupied level with the maximum energy is known as the Fermi level. For metals, the Fermi level is in the middle of a continuous state, even at relatively small cluster sizes (tens or hundreds of atoms) (Alivisatos, 1996). One practical consequence of this is that the electrons can readily move about. Because of the mobility of their electrons, metals are good conductors. The picture is somewhat altered for non-metals. Diamond crystals, for example, contain many carbon atoms, therefore the MOs must have a distribution of energies. But diamond does not conduct a current. This is because the bands do not overlap. The distribution of energy for the bonding MOs, also known as the valence band, is energetically separated from the distribution of energy for the antibonding MOs, also know as the conducting band. There is a forbidden region between the two bands. Electrons with energy between the valence band and conducting band cannot exist in diamond. The Fermi level is at the top of the valence band. The valence band is full, so electrons cannot readily move. Nor can they readily attain the energy of the conducting band. Diamond is an insulator. In the case of diamond, the energy difference between the two bands is large, > 1 eV. There also exist materials for which the energy difference between the two bands is not very big. These substances are called semiconductors. A semiconductor has an energy gap of less than 1 eV between the valence and conducting band. Adding energy to a semiconductor, whether by increasing the temperature or some other means, will promote an electron from the valence band to the conducting band. Electrons in the conducting band can move freely and so the material can conduct, albeit not as well as a metal; there are not as many mobile electrons in a semiconductor. Silicon and germanium are two examples of semiconductors.

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Figure 2-3. Comparison of the energy gaps between valence band and conduction band in a conductor, semiconductor, and insulator. In a conductor the energy gap is virtually non-existent, which means that when an electrical potential is applied across the material, electrons can move easily. In a semi-conductor the energy gap is small, so that some electrons may be promoted to the conduction band to become mobile upon application of an electrical potential. However, in an insulator the energy gap is very large; electrons are not promoted to the conduction band and remain immobile.

One method that has been used to enhance the conductivity of semiconductors is a process called doping. Consider the semiconductor silicon. Silicon forms crystals that are very similar to diamond. Each silicon atom is bonded to four other silicon atoms so that the four are at the corners of a tetrahedron. Although complex, this is a regular repeating pattern in the atomic-level structure of silicon. You may recall that the repeat pattern of a crystalline solid is called a unit cell. It turns out that if a few silicon atoms in this regular repeating structure are replaced with a similarly sized atom, such as arsenic, there is no effect on the structure. There is also no effect on the energies of the valence band or of the conducting band. However, arsenic atoms have one more valence electron than silicon does. Because the valence band is full, that electron must go into the conducting band (see figure 2-4). The few electrons in the conducting band (as many as arsenic atoms have been incorporated) are very mobile and so the conductivity is enhanced. Doping a semiconductor with atoms that have a greater number of valence electrons results in what is called an n-type semiconductor. Alternatively, silicon atoms can be replaced with an atom with one fewer electron such as aluminum. This results in an empty spot known as a ‘hole’ in the valence band. Figure 2-4 represents a system in which three of the silicon atoms have been replaced by atoms with three valence electrons. The presence of a hole (is that an oxymoron?) means the electrons in the valence band are more mobile. Doping a semiconductor with atoms that have fewer valence electrons results in what is called a p-type semiconductor. If too many silicon atoms are replaced by aluminum atoms, the result will be aluminum metal with a few silicon atoms in it. This material is not a semiconductor.

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Figure 2-4. Semiconductors can be doped by replacing atoms in the matrix with other atoms that have more valence electrons (n-type) or fewer valence electrons (p-type). Because most of the atoms that form the matrix are identical, the energy of the bands is not affected when the semiconductor is doped. The additional electrons in the system for the n-type semiconductor must therefore occupy the conducting band. The p-type semiconductor is said to have ‘holes’ in the valence band.

2.1.2.3. Quantum Dots As the size of semiconductors is reduced, the band gap gets wider and wider (see figure 2-2). In semiconductors, the Fermi level lies between the valence band and the conducting band. Consequently, the electrical transport properties of semiconductor nanoparticles depends strongly on size as do their optical properties. Quantum dots are fragments of semiconductors consisting of hundreds to thousands of atoms having the same unit cell they have in macroscale materials. Among the interesting properties of quantum dots is the fact that their electrons are constrained to stay within the nanoparticles. If an electron in the valence band is somehow excited to the conducting band, it leaves an empty spot called a hole in the valence band. This excited electron-hole pair is called an exciton. When the electron returns to the valence band, it returns to the hole from which it came. This means that when there is a collection of nanoparticles of the same (or very similar) size, the energy emitted after an excitation event will be exactly (or very nearly so) the same for all of the particles. At the very worst the energy will have an extremely narrow distribution. This has marvelous applications for optics. 2.1.2.4. Types of Molecular Energy Within the bands discussed above, the energy levels of electrons are so closely spaced that they form a continuum. This does not remove the fact that the energy of electrons is quantized. The existence of a forbidden region between the valence band and conducting band in insulators and semiconductors attests to the requirement that electrons exist as wavefunctions with defined energies. When we talk about the energy of matter, it is convenient to define some specific types of energies in terms of the molecules. The discrete energy levels observed for electrons associated with particular atoms and molecules are presented schematically in figure 2-5. The bold lines represent electronic

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energy levels; these energies are associated with the atomic and molecular orbitals reviewed in the previous section. The narrower lines above the bold lines represent vibrational energy levels.

Figure 2-5. Energy can only be absorbed by a substance if the energy matches the spacing between the energy levels of the particle. Once energy has been absorbed (a), the substance can return to its ground state through (b) collisional deactivation, (c) intersystem crossing, or (d) emission. Energy can be emitted as (d1) fluorescence or (d2) phosphorescence.

Molecular vibrations, i.e., fluctuations in interatomic distances between atoms of a molecule, occur at defined frequencies that are a function of bond length, bond strength, and atomic mass. Gas-phase atoms do not have vibrational energy; gas phase molecules, e.g., O2, do have vibrational energy. The energy difference between vibrational energy levels (ΔEvib) is proportional to the difference between the frequencies of the two vibrational modes (Δν = νvib1 - νvib0). The proportionality constant is Planck’s constant, h (see equation 2-2). One can also consider the rotational energy levels of particles if the particles are not spherically symmetrical, however analysis of rotational quantum states is beyond the scope (and need) of this book. The energy associated with the movement of a particle through space is called translational energy. For most particles in containers that are larger than nanoscale in at least one dimension, the translational energy levels are so close to each other, the apparent translational energy is a continuum. An electron confined to the space of an orbital has large spacing between energy levels because of the small volume of the orbital. The mathematical justification for this is presented in section 2.1.5.

2.1.3. When Matter and Energy Interact Any attempt to examine the nature of particles on the nanoscale requires a consideration of the nature of the interaction of energy and the particles. When energy impinges on a material it can be transmitted, reflected, absorbed, or diffracted (scattered). A stop light looks red through a car’s windshield because the glass transmits red light. Grass looks green

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because chlorophyll pigments in the grass absorb many wavelengths, but reflect green light. Finally, the rainbow after a thunderstorm appears because the water droplets remaining in the sky scatter or diffract light of different wavelengths at different angles. Which of these phenomena occur, and to what degree, depends both on the wavelength of the incident energy and the nature of the material. Consequently, monitoring the effect of interactions of energy with particles reveals a great deal about the structure and/or appearance of the material.

2.1.3.1. Absorption When the electrons of a particle are all in the lowest possible energy levels, the particle is said to be in its ground state. When energy strikes the particle, it may interact in such a way as to increase the energy of the electrons. However, the only energy that will be absorbed by a substance (path a in figure 2-5) is energy that corresponds to the spacing between two energy levels. The absorption of a photon to increase the vibrational energy of atoms in a solid is an example of photon-phonon interaction; consistent with the frequency of phonons, the vibrational modes of solids are best determined using infrared light. Measuring the frequency of the energy absorbed reveals information about the spacing between the levels depicted in figure 2-5. Energy that is not absorbed is transmitted, scattered, or reflected. Electrons that are in an excited state may return to their ground state by collisional deactivation, emission of a photon, or intersystem crossing. A return to the ground state by way of collisions with other particles usually does not result in the emission of photons and so the only observable phenomenon is absorption of incident energy. If the photon is emitted from the lowest vibrational level of the excited electronic state, the phenomenon is called fluorescence (path d1). In this case, the energy of the emitted photon is somewhat less than the energy of excitation. Intersystem crossing (path c), which means there is a change in the spin state of the particle, is not—according to the ‘rules’ of quantum mechanics—allowed. However, in quantum mechanics, this really means it is improbable and/or it takes a long time to occur. If a photon is emitted after intersystem crossing occurs, the phenomenon is called phosphorescence (path d2). As with fluorescence, the energy of the emitted photon is less than the energy of excitation. But while fluorescence occurs within nanoseconds of the excitation event, phosphorescence may occur hours after excitation. Fluorescence and phosphorescence spectra reveal details about the vibrational energy levels in the ground and excited electronic states. 2.1.3.2. Scattering Frequently, the energy that impinges on a substance is not of a frequency that exactly matches any of the transitions described in the previous paragraph. Whether absorbed or not, energy interacts with matter. The electrons of atoms and molecules are held in the vicinity of their particle by the attractive forces of the nucleus (or nuclei). A molecule has a dipole moment if the electron density is larger at one end of the molecule than at the other. Electrons feel an effective nuclear charge. The smaller this is, the less rigidly the electrons are held in place; the particle is said to have a large polarizability. The electrons will respond to an external electric field. The oscillating electric field of electromagnetic radiation that impinges on a particle may interact with the electrons of a particle, resulting in an oscillating dipole moment. The magnitude of this oscillating dipole moment will be proportional to the polarizability of the particle and the strength of the oscillating field. One might say that the particle is in a virtual electronic state, where the energy of the particle with an oscillating

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dipole does not correspond to any of the energy levels presented in figure 2-5. The oscillating dipole radiates light at all angles, a phenomenon called scattering. If the frequency of the scattered light is the same as the frequency of the incident light, the scattering is said to be elastic. The intensity of the scattered light is a quantifiable function of the angle of observation (relative to the incident light) and the mass of the particle.

2.1.3.3. Rayleigh Scattering When light is scattered by particles that are much smaller than the wavelength of the incident radiation, the phenomenon is called Rayleigh scattering. The intensity of scattered light increases as wavelength decreases, consequently short wavelength radiation is scattered more intensely than long wavelength radiation. The sky appears blue because particles in the atmosphere scatter the shorter wavelength blue light more intensely than the longer wavelength red light. Another property of Rayleigh scattering is that the intensity of the scattered light is proportional to the size of the particle. Additionally, intensity varies with the angle at which the scattered light is observed. When the size of the particle is comparable to the wavelength of the incident light, scattering may occur from different sites of the same molecule. Frequently, scattering measurements are done on solutions of particles, and the fact that not all solutions behave ideally results in a modification of the observed scattering. Nevertheless, light scattering experiments can reveal useful information about the size and shape of particles that are close to the size of the wavelength of the exciting light. The size of particles detected, therefore, depends on the excitation source wavelength. Clearly, if the scattering of x-rays is being monitored, information will be learned about particles that are considerably smaller than if visible light scattering is monitored. 2.1.3.4. Raman Scattering As molecules vibrate, their interatomic distances change. In some cases, this results in a change of the polarizability of the molecule. We have said that the oscillating electric field of incident radiation induces an oscillating dipole moment in the particle. The size of this depends on the polarizability of the particle. If the polarizability changes while the dipole is oscillating, then the magnitude of the oscillating dipole moment will also change. The light radiated by the oscillating dipole will be at a different frequency than the incident light. This phenomenon is called Raman scattering. Because the frequency of the radiated light is different that the frequency of the incident light, Raman scattering is said to be inelastic. Because these are rare incidents, Raman scattering typically has very low intensity; if there is any fluorescence, Raman scattering is masked. Raman scattering reveals details about the vibrational modes of particles. 2.1.3.5. X-Ray Diffraction When the wavelength of incident light is approximately the same as the spacing between atoms in a solid, the light reflected off the surface experiences constructive and destructive interference. X-ray diffraction takes advantage of the fact that the X-ray wavelength is approximately the same as the spacing between atoms in a solid. Thus, when X-rays are reflected off a solid, an array of dots is formed that is directly related to the orientation of the particles relative to each other. To illustrate the method, consider a two-dimensional system in which the particles (which are represented as dots) are arranged in a regular repeating

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pattern. It is possible to envision sets of parallel lines to represent planes of particles; for the following discussion, consider the horizontal planes.

Figure 2-6. Diffraction of an x-ray by two parallel planes of particles. The text defines θ as the angle between the source and the horizontal plane. Note that, because DB is perpendicular to the planes defined by ‘a’ and ‘b’, both