Sensors: a comprehensive survey

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Ursula E. Spichiger-Keller

Chemical Sensors and Biosensors for Medical and Biological Applications

@ WILEY-VCH

Further titles of interest: W. Gopel, J. Hesse, J. N. Zemel (eds.) Sensors - A Comprehensive Survey Volumes 1-9 ISBN 3-527-26538-4

New! The on-going series that keeps you up-to-date: H. Baltes, W. Gopel, J. Hesse (eds.) Sensors Update Volumes 1-3 ISSN 1432-2404

Ursula E. Spichiger-Keller

Chemical Sensors and Biosensors for Medical and Biological Applications

8WILEY-VCH Weinheim - New York . Chichester Brisbane - Singapore Toronto 4

Prof. Dr. Ursula Spichiger-Keller Zentrum fur Chemische Sensoren/Biosensoren und bioAnalytische Chemie Departement fur Pharmazie ETH-Technopark TechnoparkstraSe 1 CH-8005 Zurich

This book was carefully produced. Nevertheless, author and publisher do not warrant the information contained therein to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.

Library of Congress Card No. applied for A catalogue record for this book is available from the British Library Die Deutsche Bibliothek - CIP-Einheitsaufnahme Spichiger-Keller,Ursula E.: Chemical.sensors and biosensors for medical and biological applications / Ursula E. Spichiger-Keller. - Weinheim ; Wiley-VCH, 1998 ISBN 3-527-28855-4

0 WILEY-VCH Verlag GmbH, D-69469 Weinheim (Federal Republic of Germany), 1998

Printed on acid-free and low chlorine paper All rights reserved (including those of translation in other languages). No part of this book may be reproduced in any form - by photoprinting, microfilm, or any other means - nor transmitted or translated into machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law. Printing: strauss offsetdruck GmbH, D-69509 Morlenbach Bookbinding: Wilh. Osswald Co., D-67433 Neustadt Printed in the Federal Republic of Germany

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Preface

Chemical sensors are intended to solve analytical problems complementary to that provided by standard analytical instruments. In order to become commercially viable, chemical sensors have to be combined with an appropriate sampling device and electronics in such a way that the overall dimensions of the final device, the price and ease in handling, are acceptable. These parameters determine the profile of sensing devices in the vast range of applications in industrial and bio-process control, in environmental monitoring and in monitoring of toxic effluents (e.g. cyanide), in food technology, in field measurements, in emergency-care analysis, and point-of care testing (POCT) in medicine. An unexplored area is the use of chemical sensors in toxicology. In order to cope with various fields of applications, the brand "the Lab in the Bag" was coined specifying the trend of further developments. Several comprehensive volumes on chemical sensors had been published. However most of them are more focused on the development of the physical part, the transducers. This volume intends to provide an overview on the variety of chemical sensors focusing on analyticalchemical aspects generally, and on biological applications specifically. The field of chemical sensors could be depicted as a space which is spread by 3 coordinates: the biological or life sciences along one axis, physical-chemistry and chemistry along another, and mathematics and statistics along the third axis. This %pace'' reflects the complexity of the field. This volume tries to take sufficient account of each axis and gives an overview of the field with special focus on the developments in the goup of Prof. W. Simon, Laboratory for Organic Chemistry, involving the habilitation thesis of the author, and on developments in the Centre for Chemical Sensors/Biosensors and bioAnalytical Chemistry at ETH Ziirich-Technopark. Each chapter is devoted to a separate theme. So the references have been inserted after each thematic block or chapter, beginning with chapter 1. Each thematic block or section is closed by conclusions. In the first chapter, the question as to whether chemical sensors and biosensors have to be differenciated is discussed. In the course of this chapter, chemical sensors are defined and related to particular areas in analytical chemistry. A brief history of the field is given describing the development of chemical sensors. This is followed by a discussion of market trends and comments on possible future developments of the general situation in analytical laboratories. The second and third chapter sets out to give an overview on the chemical and physicochemical principles underlying the preparation of chemical and biochemical sensors. These chapters cope with the modelling of interactions, the investigation of interactions, and the basic theories underlying a reversible response which enables continuous monitoring. An understanding of these principles is assumed in chapter five and six, where some sensors developed and tested by the author's own research group are presented. In many cases, only a brief description is given, but this is compensated for by the provision of extensive references. A major subject of the author%research has been the investigation of the influence of the medium, the bulk of the sensing layer, incorporatingthe active compounds (chapter 4), and the development of the magnesium-selective electrode so that it can be routinely used in plasma and whole blood. Major efforts were devoted to the synthesis of the magnesium-selectiveionophore

VI

Preface

ETH 5506 in order to make this ligand accessible as ETHT 5506 to industrial production (appendix 10; ETHT means ETH-Technopark). The seventh chapter discusses the problems of reliability and interpretability of results. In all fields of analytical chemistry, these are at least as important as the development of new methods and procedures. Several sections focus on decision and discrimination problems analogous to analytical data treatment in medicine, in order to solve decision problems in general analytical chemistry. The author's experience with quality control and discrimination analysis is referred to. h the interests of completing this book, it has not been possible to go into great detail about the experimental conditions and fundamental explanations for all results presented. However, many of these can be found in the references provided. In selecting topics, I was governed by a desire to cover those which fill a gap in the existing comprehensivevolumes of other authors. In addition, these topics provide insights into the actions of specific sensors, which illustrate their characteristics in detail, and which show the differences of basic concepts. I would like to dedicate this book first to the memory of the late Prof. Wilhelm Simon in recognition of his outstanding contribution to the field. It was in his laboratory that I realised that productive research is, among other things, the reflection of personal and scientific discipline, the unguarded exchange of ideas and daily critical discussions. In writing the Habilitation thesis, I missed his critical comments and suggestions, and his sometimes strange, but always stimulating ideas. Secondly, I dedicate this book to those students and colleagues who are new to the field of chemical sensors and who will, I hope, find it a useful reference work. The appendices, in particular, are intended to be helpful for those involved in the development and in practical applications of chemical sensors. The appendices, specifically appendix 9, contain much information not easily available elsewhere. I would especially like to thank my assistants and my doctoral students for their collaboration and support. They contributed to the writing of this book in many ways, not least, through their knowledge and energy, and their humour and optimism. These are Angela Schmid, Ursula Wiesli, Remo Wild and Bruno Rusterholz; Gudrun Rumpf, Aiping Xu, Ruedi Eugster, Ulrich Schaller, Erika Haase, Ulrich Korell, Daniel Freiner, Mathias Nagele, Daniel Citterio, Jurg Muller, Caspar Demuth, Alphons Fakler, Wei Zhang, Michael Linnhoff, Thomas Roth. I am also grateful to my teachers, my colleagues and the postdoctoral fellows who had been working with me in the group, Dres. Maria Csosz, Maria Bochenska, Nik Chaniotakis, Kemin Wang, Honbing Li, Peter Holy, Eva Vaillo, Luzi Jenny, Stefan Rasonyi and Gerhard Mohr for their contributions. My special thanks go to Dr. Silvia Dingwall who checked my English professionally, and Dr.Markus Rothmaier who formatted this manuskript. This work was supported by the Swiss National Science Foundation, by the Swiss Commission for Technology and Innovation, the Swiss Priority Programmes "Optique" and "MIOS", by AVL LIST GmbH, 8020-Graz, Austria, and by Orion Research, Inc., Beverly, MA 02129, USA. Ursula E. Spichiger, August, 1997

Contents

Preface ...........................................................

v

1 Introduction ......................................................

1

.........................

1

.......................

6

1.1 Chemical Sensors as Alternative Analytical Tools

1.2 The Concept of Chemical and Biochemical Sensors

1.3 Recognition Processes and Sensor Technology: Milestones

.................

1.4 Goals for Future Developments and Trends ............................. 1.4.1 Trends .................................................... 1.4.2 Miniatuization. Nanotechnology ................................ 1.4.3 In Vivo and In Situ Monitoring ................................. 1.4.4 The Analytical Laboratory in the 21SfCentury ......................

10 13 13 16 21 25

...........................................................

27

2 Chemical and Biochemical Sensors ............................

33

References

2.1 Classification. Specification. and Nomenclatureof Chemical Sensors .......... 33 2 2 Molecular Recognition Processes for Ions and Neutral Species .............. 2.2.1 Introduction ................................................ 2.2.2 Molecular Interactions: Tools and Calculations ..................... 2.2.3 Molecular Recognition of Ions ................................. 2.2.4 Hydrogen Bonds ............................................ 2.2.5 Molecular Recognition of Enantiomers ........................... 2.2.6 Molecular Interactions within the Aqueous Medium ................. 2.2.7 Catalysis by Enzymes, Enzyme Mimics and Host-Reactands ......... 2.2.8 Catalytic Antibodies ......................................... 2.2.9 Multitopic Recognition of Immunological Systems ................. 2.2.10 Conclusions and Considerations for Ligand Design .................

References

...........................................................

38 38 41 48 56 58 59 63 70 71 74 76

VIII

3

Contents

Controlling Sensor Reactions ..................................

83

3.1 ThermodynamicallyControlled Sensor Reactions: Reversibility and ThermodynamicEquilibrium .......................... 83 3.1.1 The Chemical Potential and the Partition Equilibrium . . . . . . . . . . . . . . . 83 3.1.2 The Recognition and Transduction Process ........................ 93 3.1.3 The ElectrochemicalPotential and the @otentiometric) Sensor Response ............................................ 100 3.2 Thermodynamics of Nonequilibria: D f i s i o n and Steady-State ..........................................

104

3.3 Rate Controlled Sensor Reactions: Mediated Enzyme Reactions .........................................

106

3.4. Nonthermodynamic Assumptions .................................... 114 3.4.1 Activity Versus Concentrations ................................ 114 3.4.2 Ionic Strength and Estimates of Activity Coefficients ................ 118 3.4.3 Activity and Concentration of an Electrolyte: IFCC / TUPAC Definitions .................................... 121 124 3.4.4 The Osmotic Coefficient ...................................... 3.4.5 Calibration, Standardization. and Comparison with Definitive or Reference Procedures ........................................ 127 3.4.6 The Liquid Junction Potential under Physiological Conditions . . . . . . . . . 134 References

4

...........................................................

The Artificial Analyte-Selective Membrane . Limitations. Technological Precautions and Developments ................

136

139

.....................................................

139

4.2 Types of Membranes and Membrane Models ........................... 4.2.1 The BiologicalMembrane .................................... 4.2.2 MicialMembranes ........................................

140 140 144

4.1 Introduction

4.3 The Selectivity Coefficient

..........................................

155

Contents

IX

4.4 The Membrane Composition and the Membrane Medium . . . . . . . . . . . . . . . . . 161 4.4.1 The Influence of the Permittivity and of Plasticizers ................. 162 4.4.2 The Effect of Electron Pair Donor (EPD) and Acceptor (EPA). Properties of Solvents. SolubilizationProperties of the Membrane . . . . . . 169 4.4.3 The Influence of the Aqueous Sample Environment . . . . . . . . . . . . . . . . 170 4.4.4 The Influence of the Surface Tension ............................ 172 4.4.5 The Effect of Lipophilic Anionic Sites ........................... 173 4.4.6 The Effect of the Ligand Concentration .......................... 176 4.5 Response Behavior. Sensitivity and Detection Limit 4.6 Lifetime. Lipophilicity. and Immobilization

......................

.............................

179 182

4.7 Interactions by the Biological Matrix and Precautions ..................... 183 4.7.1 Biocompatibility ............................................ 183 4.7.2 Possible Mechanism of Protein Adsorption ...................... 185 4.7.3 Influence of Thrombocytes on Solvent Polymeric Membranes ........ 188 4.7.4 The Donnan Potential ........................................ 188 4.7.5 The Influence of Anticoagulants ................................ 191 References

..........................................................

193

5 Potentiometric Chemical Sensors and Biological Applications ....................................................

199

.................................

199

5.1 Principles of Ion-Selective Electrodes

5.2 The Symmetric Potentiometric Cell ................................... 203 5.2.1 The Asymmetry of ISE Membranes and Reference'Electrodes ........ 205 5.2.2 Analysis During Hemodialysis ................................. 211 5.2.3 How About Human Whole Blood? .............................. 214 5.3 The Magnesium-Selective Electrode ................................... 215 217 5.3.1 Characteristics of the Magnesium Ion ........................... 5.3.2 Analytical Techniques ....................................... 217 5.3.3 Natural Carriers ............................................ 222 5.3.4 Synthetic Carriers ........................................... 225 5.3.5 Applications ............................................... 237 5.3.6 Stop-Flow Analysis, the Continuous Flow System . . . . . . . . . . . . . . . . . . 239 5.3.7 Significance of Magnesium-SelectiveAssays ..................... 240 5.4 Microelectrodes for IntracellularMeasurements .......................... 5.4.1 The Nitrite-SelectiveMicroelectrode .............................

242 245

X

Contents

5.5 Miniaturized pH Probe for Intraluminal Monitoring of Gastric Juice

5.6 Chloride-Selective Measurements in Blood Serum and Urine

References

..........

. . . . . . . . . . . . . . . 248

..........................................................

6 Optical Sensors. Optodes

246

253

..........................................

6.1 Introduction and Medical Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

259

6.2 Sensors Based on Intrinsic Optical Effects of the Target Compound .......... 260 6.2.1 Sensors Based on Inherent Optical Characteristicsof a Specific M y t e .................................................... 260 6.2.2 Sensors Based on Inherent Optical Characteristics of a Host Responding to Analyte Quantity with an Optical Effect .............. 261 6.3 Sensors Based on a Labeled Host Compound or a Labeled Competitive Analyte

..........................................................

269

6.4 Chemical Sensors Based on a Second Component: "Simon Optodes" ......... 270 6.4.1 Chemical Principles of Operation .............................. 270 6.4.2 Optode Membranes for Cations ................................ 272 6.4.3 Optode Membranes for Anions ................................ 275 6.4.4 Optodes for Gases and Neutral Species .......................... 278 6.4.5 Principles of Reactions, Thermodynamic Equilibria and 282 Response Functions .......................................... 6.4.6 Medical Assays: Applications to Diluted Plasma . . . . . . . . . . . . . . . . . .285 6.4.7 Analytical Performance Parameters ............................. 289 6.5 The Optical TransductionProcess .................................... 299 6.5.1 Absorbance Measurements in Transmission Mode . . . . . . . . . . . . . . . . . 299 6.5.2 Optical Transducing Elements Based on Multiple Internal 300 Reflection(MIRE) ........................................... 6.6 Trend to Miniaturized Integrated Optical Sensors (MIOS) 6.7 NZR-Absorbing Dyes

. . . . . . . . . . . . . . . . . . 304

..............................................

309

6.8 Conclusions:Electrodes versus Optodes. Possibilities of Neutral Substrates . . . . . 312

References

..........................................................

3 14

Contents

7 Data Validation and Interpretation ............................

XI 321

7.1 Introduction: What Does "Data" Mean? What Does "Information" Mean? . . . . . 323 7.2 The Results of Analytical Tests: Random Numbers or Information Base? ...... 323 7.2.1 Information. Interpretation. and Decision Making . . . . . . . . . . . . . . . . . . 323 7.2.2 What Does Information Mean? ................................. 325 330 7.2.3 The Bayesian Approach ....................................... 7.2.4 General Validation of Clinical Tests and Analytical Results ........... 331 7.2.5 ROC Analysis (Receiver Operating Characteristics) . . . . . . . . . . . . . . . . 334 7.2.6 The Likelihood Ratio ........................................ 337 7.2.7 Multivariate and ClusteringProcedure ........................... 339 7.3 Goals in Analytical and Clinical Chemistry ............................. 343 7.3.1 Analytical Errors and Biological Variation ......... ;.............. 344 7.3.2 The Biological Scatterhg Range as the Dynamic Range ............. 348 7.3.3 Accuracy Assessment ....................................... 352 7.3.4 Conclusions and Recommendations for Planning Diagnostic Tests .... 354

...........................................................

355

Appendices ......................................................

359

Appendix 1: Milestones in the Development of Chemical and Biochemical Sensors .................................................

359

References

Appendix 2: Terminology for the DiagnosticPerformance of a Test Appendix 3: Biological Setting Points for Electrolytes

............. 361

.......................

Appendix 4: Allowable Analytical Errors for Electrolytes in Medical Assays

..... 365

Appendix 5: PhysicochemicalCharacteristicsof the Five Biologically Important Cations ......................................... Appendix 6: Structuresand Physical Data of Plasticizers

.....................

Appendix 7: Nomenclature and Molecular Masses of Plasticizers

363

367

369

. . . . . . . . . . . . . . 373

Appendix 8: Materials and Methods Used for Preparation of Ion-Selective Electrodes and Synthesis of Hydroxy-Poly(viny1chloride) .......... 376

Appendix 9: Required Logarithmic Selectivity Coefficients for Ion-Selective Electrodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

383

Appendix 10: Synthesis and Identity of the Ion-Selective Carriers ETH 7025. ETH 3832 and ETH 5506 used in this Work ....................

387

Appendix 11: List of Structures and Selectivity Coefficients of Investigated Magnesium-Selective Ligands ...............................

392

.....................

401

Appendix 12: IUPAC Units and Statistical Considerations

Index .............................................................

405

Chemical Sensors and Biosensors for Medical and BiologicalApplications Ursula E. Spichiger-Keller copyright 0 WILEY-VCH Verlag GmbH, 1998

1 Introduction 1.1 Chemical Sensors as Alternative Analytical Tools The technical potential of analytical chemistry has continued to grow over the past 30 years. It has evolved from being a field little more scientific than alchemy to becoming an exact science with almost no limits to its applications. Analytical chemistry is the chemist's way of answering the question: "What's in it?". The chemical components of a substance are determined through chemical analysis [11. The number of chemical components which are identified by the analytical method depends on its resolution or detection limit. For example, with detection limits in the range 10-g-10-12 moles L-l, the number of components in drinking water increases exponentially. In practice, therefore, analytical chemistry is mostly concerned with determining characteristic components of a substance in order to answer specific questions and to yield specific information. These characteristic components are known as "analytes" or "laboratoryparameters" when subjected to the analytical procedure and when listed in a report [2]. In what follows, the originally chosen, unchanged material is called the "specimen", whereas an appropriately representative portion of a substance, which is fed to the analytical instrument after adequate pretreatment, is called the "sample" [2]. For each specimen there are certain typical chemical components or analytes about which the analytical chemist seeks chemical information. In analytical chemistry today, it appears that the most important decision is to select an appropriate, highly capable instrument, together with the necessary hard- and software, and to .adapt the chemical procedure recommended by the standardization authorities. Ideally, the results flowing from the analyzer merely need to be collected and reported. Although this may seem extremely direct, the time spent on collecting, transporting, and pretreating specimens causes a bottleneck in most analytical processes; in many cases this is not seriously addressed, and needs to be reduced. Moreover, unstable analytes and analytes present at very low levels (ppb) are best analyzed on-site.As a result, the laboratory has to move closer to the source of the specimen, which means developing more user-friendly analytical instruments. Along with innovations in analytical chemistry, social pressures from the environmental movement, and economic pressures arising from health care reform, have been responsible for many new trends. Choice of the analytical instrument is important as it is the central element of the analytical procedure and is routinely handled by analytical chemists and chemists. The chemical and instrumental analysis is more likely to be limited by the chemistry of the specimen and its characteristic components than by the instrumental procedure. For example the biological matrix, specifically the protein content, has a crucial influence on the analytical procedure, owing to interactions with reagents and adsorption on surfaces. Special efforts are required to get rid of the effects of these interaction and to ensure that high-quality information is obtained by an appropriate analytical procedure. The term "high-quality information" is not restricted to the uncertainty of results and aspects of quality assessment, but is primarily concerned with getting

2

I

Introduction

Customer

/ Data Processing Quality Control

t I

Signal

I

-

Identification, Transport, Pretreatment

\

Sample

1 Analyte

Analytical Method

Figure 1-1.The analytical procedure and data evaluation process in a general analytical system and in a dedicated system, such as a chemical or biochemical sensor

the most essential and meaningful information. This information answers the question: which specific component or species involves the most useful and most relevant information in view of a decision about the quality of a substance, e.g., its biological activity or toxicity? Such a component might be one typical species, e.g., the fraction of the free, active electrolyte rather than the total concentration,or the free fraction of a single enantiomer rather than the racemate. Some very basic problems in standardizing quantitative information for typical species, and providing quality control specimens (e.g., to do with ion activity measurements)are currently still unsolved. Given this situation, an eclectic approach to chemical and instrumental specimen analysis seems most appropriate. Used well, it should: (a) allow immediate on-site measurements; (b) eliminate matrix effects; (c) achieve high selectivity and user-friendly handling; (d) allow screening based on c e d e d cut-off limits;(e) expand the application area; (f) allow modification of the methods or instruments.A novel concept in analytical chemistry needs to be governed by a strategy which involves and defines the necessary steps and procedures not the best possible. In addition, such a concept may not be oriented to increasing throughput, but, rather to increasing the efficacy of the analytical process (see below). Necessarily, such a concept must evolve not only from a profound and global insight into analytical processes, but also from a thorough understanding of the underlying chemical and physicochemical processes, and may be supplemented by chemometric approaches.


3

In conventional analytical chemistry, determining an analyte involves various steps (see also Figure 1-1and [31): 1. Define the problem; 2. collect the specimen; 3. identify the specimen; 4. transport the specimen to the laboratory; 5. select an appropriatemethod; 6. pretreat the specimen and prepare the sample; 7. perform the measurements; 8. compare with reference and quality control specimens; 9. calculate statistical parameters; 10. decide on the performanceand reliability of the analysis; 11. transform data to give an interpretablevalue; and, 12. present the data. The complete procedure is challenging for the analytical chemist as it normally requires considerable skill and a feeling for automation and robotics. Often it is necessary to use several different techniques and instruments in solving an analytical problem. In between identifying the analyte and presenting the results, additional steps may be necessary, e.g., choosing and evaluating sophisticated additional separation steps or chromatographic columns, connecting specific detectors, specifying a flow-cell, or eliminating interfering solutes and solvents. Despite the skill involved in carrying out the complete analytical process, more and more analytical tests can now be carried out on-site rather than in a central laboratory. Such front-line analysis has ecological and economic advantages, such as:

- Eliminating the need to transport specimens, which is particularly problematic with unstable -

analyteS Reducing the effort required to identify the analyte, and to interpret and transmit the results Providing immediate answers to a problem Avoiding queues in the high-tech, central laboratory Stimulating thinking in terms of eflcucy, which may be defined either the number of true positive results per total number of analyzed specimens or samples (positive efficacy) or the number of true negative results per total number of analyzed specimens or samples (negative efficacy), in contrast to eficiency, which is the number of correctly allocated specimens per total number of analyzed samples, and throughput (total number of analyzed specimens per unit time) (seesection 7.2.4 and Appendix 2)

In order to tackle an analytical problem, the customer and analyst must agree on the information needed, and the specimen and sampling required to obtain it. It is then up to the analyst to decide which procedure will be appropriate for dealing with the special properties of the specimen. The two triangles in Figure 1-1 denote communication between the customer and the analytical laboratory which is catalyzed by the analytical chemist in the middle of the sandwich. When applying biochemical or chemical sensors, the analytical process is straightline, since sensor technology allows the analyte in a specimen to be quantified directly. Thus, the analyst can avoid having to transport the specimen, pretreat it, and prepare a sample (at least steps 4 to 6 above). By using sensor technology, the steps in the first part of the data evaluation process can be reduced in principle to just one, namely, the interaction between the sensing element or sensor surface and the specimen. However, in many cases pH- and/or ionic strength buffering of the specimen (conditioning) is recommended in order to improve accuracy, which means making use of a continuous flow system. Instead of having to choose the chemical procedure and the detecting system, the required selectivity and detection limit have to be estimated, and the limiting operational conditions need to be considered when defining the

4

I Introduction

analytical problem. The more selective the sensor, the more dedicated the system, and, as a result, the cheaper and easier it is to use. If the technology applies a couple of poorly selective sensing elements arranged in a sensor array, it may be necessary to resort to sophisticated exterior data processing in order to interpret the measured values and to ensure that the sensing system was accurate. Sensor technology can be particularly useful and preferable to wellestablished analytical procedures in testing situations where: -

Continuous or periodical testing by laypeople is necessary

- There is a shortage of skilled manpower and/or natural resources Working with chemical reagents is avoided - The analytes are not stable and quick answers are required - Front-line screening saves on resources for economic and/or ecological reasons -

In order to improve the analytical methods involving sensor technology and the evaluation of their results, it will be necessary, in the future,to find ways of: (a) ensuring adequate sensitivity and accuracy; (b) validating the results reliably; (c) providing matrix independence and ruggedness of the analytical procedure; and (d) making the procedures user-friendly. Technological advances will involve: optimizing the performance over time (long-term stability), combining sensor techniques, designing modular and multidimensional sensing systems, and facilitating specific applications. Sensor technology is particularly appropriate in life sciences (biotechnology), in novel cultivation techniques, in the medical field, and in process monitoring, but there is considerableroom for improving applications in these areas. Chemical and biochemical sensors have attracted considerable attention because they can provide information about the active molality of the free fraction of an analyte. No other analytical techniques can do this. It is likely that, with future sensor technology, elemental analysis will be refined or replaced by the speciation of specific chemical fractions. This has already happened to some extent with a few inorganic and organic analytes. Unfortunately, there is still a tendency to evaluate total concentrations solely, especially in biology and medicine, although the activity of a metal ion is at least as relevant as the total concentration, and is, presumably, the most relevant fraction in toxicological studies. It is essential that the correlations between sensor outputs and the toxicity of a species should be investigated in tests using animals so that animal-free toxicology tests can be performed subsequently (see next section). There is also a growing need to determine active fractions for medical purposes, e.g., for electrolytes such as calcium and magnesium ions where the complexed fraction amounts to around 50% of the total concentration. Standard techniques in general analytical chemistry have very limited ways of dealing with the problem of direct, selective detection of a defined fraction of an analyte in the specimen or sample.

Biosensors Another very direct detecting system is the living organism. In response to the Toxic Substances Control Act (TSCA), the U.S. Environmental Protection Agency (EPA) was charged with the


5

responsibility of assessing the hazards particular chemicals posed for human health [4].For this purpose, whole-organism bioassays and physiological studies were used effectively in identifying potentially common modes of action, common analytical approaches, and in developing a knowledge base for an expert system designed to predict toxic mechanisms from the structure. A variety of organisms have been used in testing the toxicity of xenobiotics. Among these are protoma, especially ciliates such as Tetruhymena pyrifomzis, and various fish, in particular the rainbow trout. The assessment of the $sh acute toxicity syndrome (FATS) has been investigated through careful examination of the behavorial responses of trout, and associated variations in some commonly used diagnostic parameters which are correlated to the respiratory-cardiovascular toxic effects of xenobiotics dissolved in water [4]. Although using living organisms may seem a very simple and inexpensive technique, special care must be taken to ensure that the biochemical environment is controlled, usually by monitoring it electronically. The reliability of biological monitoring is sometimes impaired by individual variations in the inbuilt repair mechanisms of damage associated with resistance to different agents. However, the most relevant parameter in toxicological risk assessment is the lipophilicity of a xenobiotic and, therefore, the partition of the free species between water and the living organism. This suggests that at least some of the in vivo tests could be replaced by in vitro tests using chemical sensors. Some typical bulk membrane sensors, where the active component is incorporated into an apolar solvent polymeric layer, respond preferably to the lipophilicity of a target compound (see section 3.1). Currently one of the most interesting questions is whether the physicochemical activity of a xenobiotic correlates with its biological activity. Analytical experiments may help to answer this question for both charged and uncharged species. A living organism is a complex and sophisticated biosensing system. Some chemical senses in animal species as well as in plants are so exquisitely developed that communication can take place through "biochemical" reactions. Biosensor research has sought to mimic such natural . processes in the laboratory by fixing and connecting isolated cells and organs to a transducing and/or detecting system, usually an electrochemical receiver and amplifier [5, 61. In.one such study, the latent potential of living "bioreceptors", in this case the olfactory organs or the antennules of Hawaiian crabs, were treated so as to create an intact neuronal chemoreceptorbased biosensor called a receptrode [7]. This project involved confronting new aspects of detection and data processing. The various neurons of the antennular receptrodes generated action potentials with different amplitudes. The complex multiunit data were analyzed by employing an amplitude sorting program similar to that used in clinical encephalography. The amplitudes were associated with the selectivity of the olfactory organ, incorporating a multitude of different receptors, whereas the frequency of the depolarization and voltage change corresponded to the intensity of the stimulus by volatile amines (e.g., trimethylamine oxide). A chemoreceptor-based biosensor or receptrode like the one described above has some very desirable characteristics, such as: high specificity, extremely low detection limit, large dynamic range, and very short response time [7]. The major problem with using the antennules of Hawaiian crabs was they only had a short life-time of 48 h for the following reasons: 1. Autolytic processes destroy parts of the tissue 2. Neurons needed to be continually supplied with nutrients, electrolytes, and oxygen

6

I

Introduction

These conditions are difficult to reproduce in the laboratory, especially within the confines of a sensor tip. Other papers on receptrodes have looked at such things as the use of fish scales in optical devices [S] or of the taste receptor cells of the larval tiger salamander as electrochemical sensors [9]. Even if, so far, these studies have only resulted in rather unreliable devices, it is still essential to discover the fundamental properties of such sensors in order to create promising novel devices [lo]. In 1991, a very critical review on biosensors was published by G.A. Rechnitz Ell]. Since this time, several excellent overviews and books have appeared, the latest ones were edited by F.W.S. Scheller et al. [12], R.F. Taylor and J.S. Schultz [13]. Ludi et al. [14] have discussed possible applications of sensors in industry. Since both living organisms and isolated organs are selectively sensitive to agents and irritations, attempts have been made to develop artificial systems with comparable sensitivity. In these, enzymes incorporated in "biosensors"have been mainly used to mimic the recognition process [12c, 15, 161. In 1991 Schultz defined biosensors as: "Raflniertemoderne Pendants zu den Kanarienvogeln in Kohlebergwerken, deren Verhalten Hauer und Steiger vor gefahrlichen Ansammlungen von Grubengas warnte, basieren auf pflanzlichen oder tierischen Molekiilbausteinen"(they are refmed modem equivalentsto the caged canary used in coal mines to warn miners of dangerous collections of methane (mine gas) and are based on vegetable or animal molecular building blocks). Biosensors and chemical sensors differ in that they employ different recognition processes. In biosensors, natural materials are coupled to physical transducers. Excellent transducing elements are generally available, although the molecular recognition component is rarely satisfactory, owing to its short lifetime or the complexity of the signal. In chemical sensors, the recognition component is, in some cases, a fully synthetic, specially tailored molecule. The most successful chemical sensor involves incorporating valinomycin into a synthetic membrane. Since valinomycin is essentially a natural peptide, it is open to debate as to whether this may be considered to be a fully synthetic recognition model.

1.2 The Concept of Chemical and Biochemical Sensors It is not easy to distinguish clearly between a sensor and a complex analytical system. Integrated gas chromatographs, infrared and mass spectrometers may be called chemical sensors. However, a chemical sensor is typically more versatile and cheaper than traditional instrumentation. Some definitions of "chemical sensor" are given by ANSI, DIN, VDUVDE, ICE-Draft a.q. [17]. However confusing the range of definitions may be to the layperson, it is quite clear to experts what is meant. This is why only a rough and rather arbitrary definition is given here [181. Janata stresses that a chemical sensor must provide "a real time insight into the chemical composition of the system'' and couple "recognition and amplification" with a resulting electrical signal. One definition supported by the IUPAC commission in a provisional draft is [19a]:


7

Analytical chemical sensors are miniaturized transducers that selectively and reversibly respond to chemical compounds or ions and yield electrical signals which depend on the concentration. If this is interpreted strictly, reversibility must mean that successive concentration changes in both directions can be continuously monitored. As a consequence, sensors integrating antibodies which are regenerated by a washout process cannot be considered as chemical sensors according to this definition [20]. In another IUPAC paper, devices such as indicator tubes and test strips, which do not provide continuous signals, are considered to be dosimeters rather than sensors [21a]. However, the IUPAC definition does not take into account the fact that the signal yield is closely related to the molality of the free analyte in the sample, which might differ from the concentration. In addition to the very restricted definition, chemical sensors involve a broad spectrum of trumducing process performed optically, gravimetrically, calorimetrically, or in various other ways as shown in Figure 1-2. Remarkably, the transducing process, including coupling the chemical recognition element to the physical part of the sensor, may have a profound effect on chemical selectivity and analytical performance (see chapter 4). Those aspects were taken into account in a new draft by the IUPAC Commission on General Aspects of Analytical Chemistry. This draft provides a more detailed and more general definition and a broad discussion of chemical sensors which states in the f i t phrase[l9b]: A chemical sensor is a device that transforms chemical information, ranging from the concentration of a specific sample component to total composition analysis, into an analytically useful signal. At present, the final signal in a chemical sensor is still always electrical, but this may change with the development of optical computers. According to Figure 1-2, biosensors constitute a subgroup of chemical sensors where biological host molecules, such as natural or artificial antibodies, enzymes or receptors or their hybrids, are equivalent to synthetic ligands and are integrated into the chemical recognition process. Selectivity is related to specijkio. Selectivity means that an interfering species responds with the same type of signal, e.g., with the same wavelength or working potential, but with an intensity different from that of the target analyte. High selectivity means that the contribution of an interfering species to the signal relative to the primary analyte is minimal, although the active molality of both covers the same range (see chapters 3 and 4). Specificity, on the other hand, characterizes the unique property of a bioreceptor, e.g., an enzyme, which, in responding to a specific target substrate, generates a specific product. Therefore biosensors, in responding to that specific substrate or product, generate a specific signal or signal change. In the case where an enzyme shows cross-reactivity to an interfering substrate, it is assumed that it produces a different product which results in a sensor response clearly different from that of the primary substrate (e.g., different wavelength, different working potential). In practice, only two classes of

8

I Introduction

THERMAL ELECTRICAL MECHANICAL (MASS)

SPECIMEN

RECOGNITION

TRANSDUCTION

TRANSMISSION

SIGNAL AND COMPUTING TRANSPUTING

Figure 1-2. General model for chemical sensors, differentiating between molecular recognition, uansduction and data processing

enzymes are used in sensor technology, namely oxidases and dehydrogenases, which produce products such as hydrogen peroxide or NADH (nicotinamide adenine dinucleotide, reduced form) which are detected in a wide range of biosensors. Therefore the term "selectivity" has been used to describe the discriminative power of a biosensor in the same way as for other chemical sensors [22]. Generally, the selectivity of a biosensor allows for a mixed response to both the target analyte and the interfering species. Therefore, characterizing the selectivity coefficient for a typical application may be more relevant to the operation of such biosensors than relying on its Specificity [22]. Biosensors as a subgroup of chemical sensors are defined as operating with either high specificity or an exceptionally high natural selectivity, but with considerably restricted stability and lifetime in many cases. As a consequence, the lifetime of the sensor has to be sacrified in favour of the natural selectivity or specificity. The quantity detected is always a measure of the active molality of the analyte, whose calibration is strongly correlated with quantities such as: the active molality of the interfering species, the pH and temperature of the sample, and the ionic strength and osmolality relevant for both charged and uncharged analytes (see chapter 3). For biotechnological as well as medical applications, the analyte activity delivers only the biologically relevant information when measured in the specimen directly, preferably by a "realtime" approach. The most important features of chemical and biochemical sensors are shown in Table 1-1. Thermodynamic reversibility is important in ensuring continuous monitoring with chemical sensors. Individual sensor reactions include: thermodynamically reversible reactions, steadystate reactions and non-reversiblereactions in disposable sensors. Thermodynamics is central in understanding the principles involved in operating the individual devices. Chapter 3 is devoted to these reaction mechanisms. The key to the design of a chemical or biochemical sensor is the recognition process of an organic or inorganic substrate by a receptor-molecule generating a host-guest product (see


9

Table 1-1. Features and benefits of chemical and biochemical sensors

Features

Benefits

targeted specificity, selectivity

versatility, dedicated systems

selective assay in complex samples

ease of use, front-line analysis, reagent-free or reagent-poor operation

short response time

fast measurements and high sample throughput

electronic processing and electronic control of calibration

consumer friendliness, ensuring safety of the assay

reversibility

continuous measurements, low waste, no consumption of the analyte

enzymatic steady-state

enzymatictum-over of the analytehbstrate

availability, low cost

disposable or exchangeableelements

chapter 2). The sensing schemes of the molecular recognition element are based on bulk or surface interactions, on mechanisms where the analyte is adsorbed or where it partitions between the sample and the bulk phase (see section 2.1). The target analyte or substrate may be any organic or inorganic ion or any uncharged molecular species. In order for a sensor to detect an analyte successfully in a complex sample matrix containing some analogously reacting species, high selectivity is required. Selectivity may be achieved by using various designs of optical as well as electrochemical sensors furnished with synthetic carriers (see section 2.2), enzymesJ23-251, or antibodies [26281, or by using sensors based on competitive binding [29]. Enzymes are defined as reacting reversibly. In fact, what really happens is that they reach a stable steady state, assuming a constant mass transfer of substrates and products. In contrast, antigen-antibody reactions exhibiting high specificity are, in most cases, not reversible with a reasonable rate constant, owing to the exceptionally high affinity for their substrates associated with low detection limits. On reviewing the literature, it seems that an artificial recognition process can overcome the severe limitations of natural compounds [7,8]. One of the most outstanding recent developments has been the design of artificial enzymes or catalytic antibodies [30-321. The molecular recognition principles based on synthetic host compounds are more modest than those of artificial enzymes. When modelling host-guest

10

1 Introduction

interactions (see section 2.2), the shape of the analyte has to match the site of the host species. A broad range of electrodes specified for various anions and cations are available, and are routinely used with reasonable analytical performance in diagnostic instruments, in clinical analyzers [33, 341, and in environmental analysis. In clinical chemistry, highthroughput analyzers, preferably based on optical assays, produce 5000-15 000 results per hour. Furthermore, the use of ionselective electrodes (ISEs) in discrete analytical systems has increased throughput considerably. In the best case, the resident time of a sample in the ISE-module, which analyzes at least four parameters in series equivalent to four different typical ions, is 6 s. Although ligands and ligand c o c h l s are currently used worldwide, the approach developed by Simon for recognizing and sensing ions is not mentioned in any of the volumes on sensors [35, 361. The design of ligands for molecular recognition has been extended to include the recognition of uncharged species, such as: humidity (H20)[37,38], ethanol [39,40], glucose [41], creatinine [42], gases such as C02 [43], HSO3- and SO2 [44], and NH3 [45, 461. It offers exciting prospects for the optical translation and transduction of reversible host-guest interactions. The sensing system can, to a certain extent, be adapted and tailored to fit its applications. The detection limit, the selectivity, and the dynamic range may be shifted by modifying the ligand or the optical transducer and the surrounding bulk medium according to chemical or physicochemical principles (see chapters 4-6). Applications in various fields as different as medical analysis and biotechnology have been undertaken successfully r47-491. A survey evaluating optical assays is given in [50]. Strong competition in the field of sensor technology over the past 10 years has led to an increase in the number of models available. Nevertheless, only a few types of chemical and biochemical sensors appear to be viewed as reliable tools for analytical chemistry and to be used widely in this growing market sector. Physical sensors, on the other hand, have become wellestablished in a competitive market and are regularly used in different monitoring systems and devices. The concept of the chemical sensor is, however, not new. A brief history focusing on the development of chemical sensors, especially on aspects of commercial use, will be presented in the following section.

1.3 Recognition Processes and Sensor Technology: Milestones The technology of sensors and actuators has a long history. Wilhelm von Siemens built one of the first sensors in 1860. He made use of the temperature dependence of a resistor made of copper wire to measure temperature [51]. The fundamental principles behind physical sensors and transducers largely apply to chemical and biochemical sensors. The history of the development of chemical sensors for medical applications is summarized in Appendix 1 [52, 531. The first really significant event from the commercial point of view occurred around 1932, when Arnold Beckman developed the modern glass electrode [54]. In 1937, Kolthoff and Sanders [55] published a paper made use of solid-state electrodes, such as the silver halide and fluoride-selective electrodes (for an account of the development of solid-state and glasselectrodes, see Frant [54]).

1.3 Recognition Processes and Sensor Technology: Milestones

11

The key feature of carrier-based chemical sensors involves the recognition of the analyte by using a ligand tailored for the purpose. The sensing element is that critical part of the sensor where the primary transduction occurs and, as such, is vitally important in the operation of the whole sensor. The basic concept of chemical sensors owes much to the investigations of Moore and Pressman into the effects of naturally occurring neutral antibiotics on biological membrane systems in 1964-1965 [56]. Valinomycin (Figure 1-3) was reported to change the permeability of cells for potassium by a factor of 4 x 104. Two years later, the highly selective and reversible complexing properties for alkali metal ions were described by Stefanac and Simon [57]. In the meantime, Ross in the United States and Simon in Switzerland had both applied for a patent covering the K+-selectiveelectrode; the patent application of Simon was accorded priority [58]. Simon was certainly the first to introduce the class of chemical sensors based on neutral curriers. Subsequently, in 1970, Frant and Ross described how the valinomycin K+-selective electrode was first employed in serum measurements [59]. Orion received a licence under the Simon patent and developed a prototype electrolyte serum analyzer for NASA's Space Shuttle and, subsequently,the first commercialized sodiudpotassium analyzer SS-30 for whole blood. Ironically, spin-offs from the Orion project led to the business becoming commercially successful. In 1972, another clinical analyzer using a valinomycin-based sensor, namely the STAT-ION (Technicon/ Photovolt Corp., USA), was commercialized [60]. In 1967, the term "ionophore" was coined by Pressman et al. [61]. In the same year the structure of the first macrotetrolide-ion complex was elucidated (see Figures 1-3, and Appendix 1) [62]. The ionophores were, typically, lipid-soluble peptides with a relative molecular mass < 2000. Some of them, such as those in the valinomycin class, had in common molecular masses of 500-1500 and a curious alternation of D- and L- configurations of the participating aminoacids as well as a lack of ionizable groups. The structure of the K+-valinomycin complex was elucidated in 1969 by Pinkerton [63]. In contrast, the neutral ionophores with lower molecular mass were classified as "carriers". Today, the selectivity of valinomycin for potassium ions still seems striking, and compares favorably with the properties of other ligands developed later. After testing other naturally occurring antibiotics (macrotetrolides) with remarkable selectivities, Pedersen [66,67] ,Lehn [68,69], and Cram [70] began to study synthetic ligands (crown compounds, synthetic macrocyclic polyethers, macrohetero-bicyclic ligands, cyclophanes and others). Cram [71] uses the term host for the synthetic compounds that are the counterparts of acceptor sites in biological chemistry, and the term guest for compounds that are the counterparts of substrates or inhibitors in the acceptor sites, according to Kyba [72]. Pedersen, Cram, and Lehn were awarded the Nobel prize for these achievements in 1987. In the early development of the industrial electrode, organic ion exchangers were used in a solid configuration. Moody, Oke, and Thomas showed that incorporating the ligands into a plasticized PVC membrane prevents the membrane components from becoming fully hydrated and allows the active components to be sufficiently mobile [73]. This technique enabled ionselective electrodes to become not just practically, but also commercially feasible. The influence of ion-selective complexing agents on the ion selectivity of liquid membranes was discussed theoretically by Eisenman's school [74,75], by Covington [76], by Pungors' group [77] and by Sandblom [78] and Orme [79] and later by Buck [80] and by Wuhrmann, Morf and Simon [81,

12

1 Introduction

Figure 1-3. Constitution of valinomycin, as presented by [MI, and the macrotetrolideantibiotics monactin and nonacth [65]. The ligand-cationcomplexes are positively charged. The alkali- or ammonium ions are complexed by 5-8 polar oxygen atoms. The conformation of the complex is characterized by an outer nonpolar shell and the polar groups oriented towards the center. Thus the molecule is mobile within a nonpolar membrane phase. O* = coordinating oxygen atoms

821. Electrically neutral and electrically charged ligands were strongly debated. Eventually, charged ligands were shown not to work in nonpolar phases. The working priniciple and the functionaldistinction between charged and neutral ligands was accepted empirically rather than being rigurously defined and investigated. The complex formation was described for the interface between an aqueous phase and a relatively nonpolar membrane phase, where the selectivetransport of cations was to be expected. More than 12 years later, the first optical potassium test, based on dry reagent chemistry was evaluated by the author, and commercialized subsequently by the Ames Division. The evaluation of silicone rubber membranes for the valinomycin electrode (see Figure 1-3) has led to extensive collaborationbetween the groups of E. Pungor and W. Simon, within the context of a friendship which has not prevented occasional decisive discussions of fundamental issues [831. At the same time, the concept of the biosensor was proposed by L.C. Clark Jr. et al. in 1962 [84]. They measured pH, pC02, and PO;?for intravascularcontinuous monitoring (see section 1.4.3). Also in 1962, Enson, Briscoe, Polanyi, and Cournand [85] introduced intravascular reflection oximetry. Bergman [86] described the first oxygen fluorosensor in 1968, which was introduced into medicine by Lubbers and Opitz in 1975 [87, 881. At first it was thought that, unlike electrochemical sensors, optical sensors would not require a reference element. Satisfactory results were obtained by normalizing the optical signal of the analyte to a second reference wavelength, which involved evaluating relative intensity changes. Enson et al. [86] proposed the use of the isosbestic point as a reference.

1.4 Goals for Future Developments and Trends

13

Considerable progress in developing medical sensors has been made during the past few years [89-911. In nearly all cases of optode design sensitive to the chemical properties of the analyte, the optical detection principle is based on either quenching of luminescence by oxygen or on a change in luminescence intensity due to pH alteration. Pulse oximetry, as well as some other new approaches, are exceptions [12, 921. Different from other ions, pH is the unique parameter where the ion activity is measured and reported. Providing there is reliable calibration, pH assays are relatively unproblematic since no assumptions are necessary for calculating the concentration. For p02 measurements, the sensors are considerably more rugged than those used in the evaluation of enzymatically generated oxygen or quenching compounds such as S 0 2 , halides, etc. [91,92]. Thus, assays of most low-concentration analytes based on fluorescencequenching as well as pH evaluations demonstrate that these systems are too unreliable for direct monitoring in blood or in any biological sample. An element for selective recognition of the analyte, acting as a selective filter to take account of interfering entities, would ensure greater reliability. An important landmark was the introduction by D.W. Lubbers et al. [92] of immobilized indicators into the development of optical sensors for continuous monitoring in biological fluids. They introduced the term "optrode" by analogy with "electrode". The term "optrode", however, is etymologicallyincorrect; optode [93] would be more appropriate. Enumeration of all the scientists involved in developing combinations of sensing elements and transducers is beyond the scope of this study. Appendix 1 indicates some of the historic landmarks, whereas Table 1-3 shows some of the components and combinations that are possible in constructing chemical sensors and biosensors. Many of these have not yet been tested in real sensor configurations. Apart from the development of the recognition process, the transducers, actuators, or amplifiers have been improved considerably. In summary, the development of physical transducers is much more advanced than is that of the chemical recognition components as used in sensors [94]. At the Optical Meeting in The Hague 1991, the lack of innovation and development in this area was deplored.

1.4 Goals for Future Developments and Trends 1.4.1 Trends One of the catchier titles in the program of the 1991 Pittsburgh Conference was that of I.J. Higgins et al.: Biosensors: Philosopher's Stone or Fool's Gold? The authors presented statistical data and forecasts regarding the sensor market. Table 1-2 shows an extract from various reports on sales in the sensor market and their forecasts for the future [17,95-981. The first row shows figures taken from a report by Prognos AG (Basel, Switzerland) [17]. In 1988, the world market for sensors, physical and chemical, amounted to US$ 24.1 billion. Regional shares in the market reflect the strength of the sensor industries there: US$ 5.2 billion in both the United States and Western Europe, and US$ 3.0 billion in Japan [171. A wide variety of application-specific demands means that there is a fairly

14

I lntroducrion

Table 1-2. Overview of current sales in US$ X lo6 and forecasts of the sensor and biosensor market respecting different fields of applications (different references)

Year [reference]

Sensor class applications

Market

Sales figures US$ x 106

Predicted growth rate

1988 [17]

physical and chemical chemical sensors

worldwide worldwide

24100 1200

by 1998

1989 [95]

biosensors biosensors, processing environmentaland security applications

us us us

13.6 3.1 1.9

1994 [96]

chemical sensors, (biosensors excluded)

worldwide

500

1994 [961

* Projected in

biosensors biosensors, medical processing environmental

worldwide worldwide worldwide worldwide

400 ca. 200 (50%) 75 25

510%

by 1993 69 24.7 11.3 by 2004 * 1380 (9-1 1%) by 2004 * 1480 (10-15%) 950 250 75

1994 dollars (sales, contract research and development)

heterogeneous market for measuring parameters. According to the report cited, chemical parameters constituted only US$ 1.2 million of the total world market for sensors of US$ 24.1 billion in 1988. The report predicts an annual growth rate of 5 1 0 %for the next ten years. According to its forecasts, the United States will be the leading vendor and, maybe also consumer in the chemical sensor market by the year 2000 (US$ 14.5 billion), ahead of Western Europe (US$ 13.5 billion) and Japan (US$ 10 billion). This means that, relatively, Japan will have the highest growth rate. It is, however, to be expected that the regional market shares will change. Another report [95] estimated that the growth of the United States biosensor market would be from only US$ 3.1 million in 1989 reaching US$69 million by 1993. This report foresaw the application with the fastest growth during this time to be the monitoring and control of


15

process industries. It suggested that the largest market segment in 1993 would be in health care (US$29.4 million), and that it would consist mainly of single-analyte instruments. Depending on the source, the forecasts (Frost and Sullivan, Desjardin, Battelle, Market Intelligence Research) differ considerably. Whereas the figures for chemical sensors by Prognos AG include biosensors, the report by Taylor [96] clearly separates the two classes, so that the worldwide sales figures for chemical sensors and biosensors in 1994 have to be added together in order to compare them with the Prognos figures for 1988. Rather surprisingly, sales of chemical sensors and biosensors actually went down during the 6 years between 1988 and 1994, which might indicate some "cleaning" process in view of unsuccessful developments in chemical sensor technology. Notwithstanding this decline, a sharp upturn in the market, which may be entering the "take-off stage" [95], is predicted in both reports [95] and [96]. By way of comparison, in vitro diagnosticshad amarket of US$ 9 billion worldwide in 1992 [97]. 5% of this market consisted of consumer testing (US$ 450 million), 20% of which was dedicated to decentralized testing. Medical in vivo monitoring has, on the other hand, declined as it has met with ethical and legal barriers, and is now limited to a few applications.

Table 1-3. Possible components of a biosensor / chemical sensor characterized by selective molecular recognition and solubilization of target analytes

Selective elements

Transducers

synthetic ionophores synthetic carriers supramolecular structures, clusters solid layers: metals - metal oxides, crystals - polymers, conducting polymers organisms microorganisms plant and animal tissues cells organelles membranes, bilayers and monolayers enzymes receptors antibodies nucleic acids natural organic and inorganic molecules micelles, reversed micelles

electrochemical: - potentiometric - amperometric - conductimetric - voltammetric, polarographic - impedimetric, capacitive - piezoelectric optical: - transmission / absorbance / reflection - dispersion, interferometric - polarimetric - circular dichroism, ellipsometry - scattering - emission intensity, photon counting (luminescence)decay time calorimetric acoustic / gravimetric: - surface photo-acoustic wave - quartz microbalance

16

1 Introduction

Commission (DG XII) of the European Union [98] published an interesting report on science and technology in Europe in 1991, in which it was estimated that the total world market for sensors in 1990 was approximately 10 billion ECU (US$ 8.3 billion). Western Europe had about half the world market for sensors in engineering, whereas Japan was the leading user of sensors in robotics, and the United States was the major user of sensors for electronic applications in vehicles. European competitiveness in the hightechnology market declined in the 1980s so a financial framework program for supporting the technical potential of European industries was introduced in 1989. It included sensor technology. For four years (1989-1992), some 500 million ECU (approx. US$ 416 million) was budgeted for the whole programme. Large investments in research and development and highly qualified researchers in Europe were expected to increase competiveness. There are several reasons for the comparatively modest performance of Europe, which include: an unbalanced and fragmented distribution of human and financial resources, the lack of mobility of the workforce, little coordination of research efforts, and the lack of a large integrated home market. The thrust of financial support has been toward the mass production of sensors and also toward miniaturization. However, unlike the glucose testing market with an expected global turnover of US$2 billion (US$2 X log), only a few other applications will have a comparable sales volume [96]. Comparatively, another type of sensor, e.g., for ethanol or ammonia monitoring could also be produced on a smaller scale, supposing a frequent demand in various fields of applications, e.g., in bioprocess control, medical monitoring, and other specialized areas. In bioprocess control, voltammetric oxygen probes, pH probes and unselective redox sensors are currently commercially available. In the future, an ammonia-selectivesensor is likely to have a wide range of applications. Table 1-3 shows some possible sensor components. In view of the large number of these proposed over roughly the past 20 years, only those combinations and principles which look likely to result in effective analytical devices are listed. In the future, the design of sensor systems will involve combining those sensors with the most attractive features in order to solve a specific analytical problem. The client is unlikely to suggest the type of sensor to be used, but will be more inclined to specify the analytical parameters (detection limit, dynamic range, lifetime, etc.) the system should provide. Sensing systems must be constructed so that they are flexible and versatile enough to integrate various types of effective physical and chemical sensors working with standardized units or modules.

1.4.2 Miniaturization,Nanotechnology Miniature analytical instruments and devices have several advantages since they allow: -

on-site analysis, analysis in security areas

- extremely small amounts of substances to be rapidly analyzed, thus complying with recent trends in combinatorial chemistry, peptide synthesis, and DNA-fragment analysis

- smaller analytical devices to be produced which are more suitable for in vivo measurements since they are less likely to impair the functions and structures of living organisms


17

There are two ways in which progress is being made in miniaturizing analytical devices so as to produce more versatile and smaller instruments. First, through the development of microstructured, miniaturized systems; and secondly through the development of dedicated systems. Microstructured chips for capillary electrophoresis and gas chromatography [99. 1001 are examples of the first group (see Figure 1-4). They are especially attractive for the analysis of pico-, femto-, and attomol- quantities of peptides and DNA-fragments. In the second group belong: the ion mobility spectrometer [ 1011, hyphenated techniques [1021, and the accelerated development of chemical sensors, sensor arrays, and microsensors. A further goal of miniaturization might be to produce an instrument combining or hyphenating miniaturized single elements based on different working principles without sacrifying their versatility. These developments here look promising. The terms "mini", "micro", and "nano" are often confused. A "ministructure"means a structure in the "milli" range (dimensions of, e.g., to c 10-2 m or 10-3 to c 10-2 cm3). Structures which are 1000-fold smaller are microstructures or microsensors. Microelectrodes have tip diameters in the range of c 10 pm down to 50 nm and reach, in some cases, the nunoelectrode size. The name "microsensor"means that the size of the active sensing area is in the micro range, whereas the sensing device itself is much larger and designed so that it can be handled easily. There is a history behind the name "ultramicroelectrode" [ 1031. Ultramicroelectrodes are usually larger than microelectrodes. Currently they are in the process of being down-scaled to the nano-range for in vivo measurements and for scanning electrochemical microscopy (SECM) [ 104-1061. Nanostructures present at least one dimension in the range of to m. For comparison, the resolution of a light microscope is 10" m, implying that working with nanostructures requires special tools for visualizing the local activity. Miniaturization of an analytical device or a sensor does not have to mean making it less rugged. On the contrary, miniaturization may result in a more rugged device, such as the voltammetrically operated ultramicroelectrode. Furthermore, other specific features may be improved by miniaturization. Thus, the total information yield may be greater despite the fact that the dimensions have been reduced by several orders of magnitude. The merging of sensing elements with electronic devices for transduction and readout has led to new capabilities, but has also imposed some constraints (see below) on the sensor system. In the case of biomedical sensors, increasing the information gathering capability per unit volume is often the motivation for integrating electronics in the system. Integration also results in some very promising properties, not only because the resulting system is more versatile, but also because it allows: drifts to be corrected; fitting and calculation software to be implemented for the measurement based on nonlinear calibration functions; and interferences to be compensated by using sensing arrays. Miniaturization is particularly appropriate for sensors that improve their performance with smaller sensor and sensing layer areas, and with reduced distances from the working electrode to the reference and counter electrode. This holds for sensors based on electrokinetic techniques concerned with determining the rate of electron transfer at the working electrode which is of special interest when associated with chemical regenerating electrode reactions, and mass transport. For these electrodes, sensitivity refers to the decreasing surface area exposed to the target analyte. h the best case, mass transport is purposely restricted to diffusion in transient

18

I Introduction

Figure 1-4. The miniaturized gas chromatograph M200; left hand side: capillary column; right hand side, upper case: gas sampling chip; right hand side, lower case: conductivity detector chip (with permission [loo]) techniques, and to forced convection and diffusion in steady-state techniques [ 1031. For electrokinetic techniques, the radius r is the lateral diffusion area of amperometric and voltammetric ring or disk electrodes. Since the double-layer capacitance of the electrode cell and the total current are proportional to the surface area of the electrode -r* the cell response time and the ohmic drop both decrease with the reduced surface area, whereas the diffusion and reaction rate vary with lh2. Given this situation, voltammetric ultramicroelectrodes have the following advantages: when detecting catecholamines in stimulated brain tissue [ 1061, they enable a high scan rate and a response speed in the ms range. For the same reason, ultramicroelectrodes are often used in spectroelectrochemistry [105]. Potentiometric sensors, on the other hand, are basically affected by the size of the active area. However the size of the exposed ion-selective surface area is supposed to limit the ion-exchange current, reducing the selectivity and the sensitivity of the electrode [107]. Those parameters seem to be correlated to the stability constants and detection limits of the ligands and electrodes. Similar to the sensors discussed before, potentiometric sensors show a diffusion-limited response, where the response time increases with 8 depending on the thickness of the static Nernstian diffusion layer d at the sensor surface. The Nernstian diffusion layer decreases, not only with increasing flow or convection, but also with decreasing diameter and detection volume on the miniaturized electrode tip. A further dimension is also important in this discussion of sensors, namely, the thickness of the sensing layer. This relates to the working principle of a sensor. Miniaturization is most appropriate for sensors that are not sensitive to the thickness of the sensing layer. In optical transmission sensors, however, the optical path length is equal to the thickness of the optode membrane. In optical bulk membrane technology (see section 6.2), the optical sensing layer equilibrates with the target analyte in the sample phase. Therefore, the thickness of the sensing layer determines not only the speed of equilibration, but also the optical path length. So reducing the thickness of the sensing layer also reduces the sensitivity. As a consequence of this

1.4 Goalsfor Future Developments and Trends

19

equilibration process, the concentration of the target analyte in the sample phase is reduced by a contribution equivalent to -Ac and an uptake of +Ac by the membrane phase. This size of uptake is smaller than 1%0for membrane volumes < 10-9 L incorporating less than 10-1 mol L-' ligand in contact with an amount of analyte in the sample of more than lo4 mol referred to the whole dynamic range of the optode membrane. However, at low amounts of analyte c lo4 mol, it might be possible that the optical signal involves the consumption of the target analyte (see section 6.4). Moreover, the extraction steady-state, associated with the stability constant of the ion ligand complex, affects and modulates the detection limit and may induce a shift to very low detection limits < 10-9 m o m when operating under continuous-flowconditions. Inevitably, if this process takes place, the response in this range will be slower compared with a higher concentration range. To avoid having to use thick membranes, associated with slow equilibration, it was decided tQ investigate novel deposition techniques and optical detection technologies (see sections 6.5 and 6.6). Another way to distinguish sensors is to classify them according to how they are produced. A microsensor is a device requiring microfabrication technology. Microfabrication is used by the semiconductor (electronics) industry in the manufacture of integrated circuits (ICs). As Bergveld showed in 1970 [log], design and packaging are important in the development of electrochemical "minisensors". They are even more crucial in manufacturing micro- and nanosensors (sensors where the active sensing areas are small, but the size of the chip is still in the macroscopic range). Currently, these miniaturized electrodes, down-scaled to planar sensors cannot compete with the down-scaled microelectrodes for physiological applications (see section 5.4). An alternative is to have the chip accommodating not just one sensing field, but also related functions such as a light source, a detector, or a whole sensor array. This, plus the necessary electronics, is known as an integrated chemical sensor. For semiconductor devices, it is necessary to encapsulate the electronics, which makes it difficult for the specimen to make contact with the sensitive transducer area. This problem was solved by using a gate. The ChemFET (chemically sensitive field-effect transistor) is an excellent example of a microsensor which has suffered several developmental setbacks, owing to a lack of understanding of the basic operational principles and constraints, due to insufficient theoretical analysis of the operation [ 181. However, one of the main problems with semiconductorion-selective sensors (ion-selective field-effect transistors, ISFET) arose because it was assumed that they could be produced without a reference half-cell. Not only due to the missing reference electrode, the ISFETs showed a relevantly drifting potential which was referred to the ill defined boundary where the ion conductivity is transformed into electron conductivity. For more detail, the reader is referred to [18] and [log-1 111. Recently, some new solutions have been proposed [log, 1lo]. One recent investigation covers the fundamentals of hysteresis, long-term drift, slope, and selectivity of ISFETs [1111. Whereas the encapsulation of solid-state microsensors has been dramatically improved in recent years, the ChemFET response continues to demonstrate a significant long-term drift. This is a major obstacle in cases where a stable in situ calibration is essential, e.g., for implantable sensors. This is due partly to the fact that the reference half-cell has a reduced capacity (volume) and, also, that the sensor field responds to uncharged interfering species such as gases, e.g., carbon dioxide and oxygen. Furthermore, photochemical polymerization of the sensing layer does not allow the inclusion of the necessary amount of additives, apart from a limited selection

20

I Introduction

cartridge label

sample entry well gasket fluid channel

i-STAT Cartridge @

cartridge cover sample entry wall

Packaging, Sampling and Testing

calibrant pouch

puncture barb cartridge base air bladder

Figure 1-5. i-STAT@ cartridge incorporating electrochemical sensors and biosensors (with permission [1121 of the prepolymer for some electrodes. Tailoring the composition of the sensing layer to its application, however, is one of the main factors in determining its performance (see chapters 4, 5 and 6). Therefore, the possibilities for creating sensors incorporating novel sensing layers are rather limited. Despite these drawbacks, a whole set of analytical devices which can be used for testing near patients and in emergencies are currently available in the form of disposable sensors [112] (seeFigures 1-5 and 1-6). In the biomedical environment, the protection of the electronics is especially problematic and has limited the commercial success of ChemFETs [1111. Microelectronic components are very sensitive to temperature, humidity, pressure changes, and chemicals. Additionally, integrated devices lack modularity. The components of the sensor system which are incorporated on-chip are fixed by the mask set and must be fabricated at the same time (see Figure 1-5). Any change in the design requires an entirely new mask, and often a new process flow as well. Whenever undefined or poorly understood transduction mechanisms are employed in microsensor designs, there are bound to be development delays and fabrication problems and the reliability of the application will be reduced. One of the most urgent goals for the near future is to combine the large-scale hardware technology of physical transducers and laser optics with the "softer" approaches of sciences such


21

as chemistry and materials science, in order to find the most suitable combinations for solving specific problems. One product that involves combining miniaturization with integrated planar sensors and sensor arrays is the electronic nose, which recently came onto the market. Such transducing elements make use either of the quartz crystal microbalance (QCM) [113] or, alternatively,of various surface acoustic wave (SAW) transducers where different piezoelectric resonator materials, e.g., a quartz foil or YZ lithium niobate, is stimulated by two electrodes and works as an electromechanical transducer of oscillations with a defined frequency in theMHz range [114, 1151. Another type of sensing device for the electronic nose relies on electrochemical cells covered with a metal oxide layer [1151. The heart of the electronic nose is a more-or-less analyte-selective polymer layer cast onto the oscillator. Currently, the sensing principle is preferably based on partition equilibria of the analyte between the sample phase and polymer layer, and does not make use of known host-guest chemistry (see section 2.2 and chapter 3). The selectivity of some platforms could and should be improved. In the electronic nose, the two trends in analytical chemistry discussed previously, miniaturization and integrated design, are combined in one instrument; the electronic nose is a dedicated system making use of miniaturized sensor arrays. Similar systems are being created for solution chemistry. Frequently, nanodevices display new, unexpected properties. The role of chemists in the nano-range may seem less clear than their role in creating chemically selective tools. However, investigating a new dimension of nanoscopic phenomena has led to new physicochemical insights into chemical reactions and equilibria at the level of single molecules, and has led to insights into partitioning and interactions between single molecules. At the macroscopic level, chemical reactions and equilibria are seen to involve a majority of molecules, so that descriptions at this level are dealing with average molecular behavior. Nanotechnology allows these hypothetical mechanisms to be studied at the molecular level, so that the behavior of single molecules in different states in, say, a solution can be distinguished. For example, the permittivity and ionic strength of a contacting solution close to a surface may differ considerably from that of a bulk, and are affected by polarization phenomena [116]. The complexing sites of a polypodal ligand are not equivalent and may become saturated progressively, which means that nanoscaled sensing elements may behave differently and need to be viewed more stochastically. The availability of OH groups in different homologous pure alcohols will vary depending upon the lipophilicity of the alcohol, the free energy of hydrophobic interactions, and the density of intermolecularhydrogen bridges. When the nanoscaled sensing element is exposed to the active OH groups, the reactivity of homologous alcohols to the host molecule varies due to these effects, as well as to the extent of self-organization and the influence of electronic inductive effects. Chemical microscopy makes use of miniaturized optical devices, such as chemically selective nanofiber tips and NSOM (near-field scanning optical microscopy) fiber tips [117], as well as electrochemicaltechniques. These techniques will result in some novel physicochemical information and initiate a new area in chemistry and education which will be more adapted to chemical analysis on the micro- and nanoscale than traditional approaches. In summary, miniaturized analytical sensors and devices have great potential and are likely to have considerable impact on the development of analytical chemistry. The dream of a whole laboratory installed in a glove-box may become reality in due course.

22

I Introduction

1.4.3 In Vivo and In S i h Monitoring A rule of the thumb in life-saving says: humans can survive 3 weeks without eating, 3 days without drinking, but only 3 minutes without breathing. During a polio epidemic in 1952, two Danish anaesthetists, Bjorn Ibsen and Poul Astrup, reported on more than 100 patients artificially ventilated by volunteers squeezing oxygen bags. They noticed the high carbon dioxide concentration in the victims [118]. Astrup developed the first model of an equilibration method for measuring pH and pC02 in order to diagnose respiratory alkalosis or acidosis. Severinghaus's electrode also contributed to this work ['I 191. Polio epidemics also provided motivation for the development of the C02 and 0 2 electrodes in the United States. In 1958, Clark presented the results of continuously monitoring oxygen partial pressure and pH with sensors mounted directly in the extracorporeal blood circuit that is used for perfusion of openheart surgery patients [120]. As a consequence of the commercial development and availability of stable amplifiers and recorders, satisfactory systems for the rapid and accurate measurement of blood pH, pC02, and p02 were developed. Improvements in the electrode systems meant that intraarterial oxygen partial pressure could be monitored continuously through an implanted catheter [84]. Clark mentioned that heparinization was not necessary if the "microcatheter"was less than 3-4 feet in length. In the same paper, he describes a new design of an enzyme electrode using a double-layer membrane of Cuprophane-glucose-Oxidase-Cuprophane.At that time Clark predicted: By withdrawing blood through microcatheters,continuous recording of blood composition for many hours, even days, is possible, using only about 10cc. of blood per hr. Continued development of electrode systems may extend their usefulness to the measurement of blood ions, sugar, and urea and finally result in instruments with which analyses can be performed with a minimum of reagents and with but little delay. Another purely physical optical sensor, the pulse oximeter, measures the oxygen saturation transcutaneously, and has been applied to the monitoring of critically ill patients. The method involves a pulsed diode spectrophotometerwhich detects the internal total reflectance at multiple wavelengths [85, 121-1231. According to Severinghaus [118], Karl von Vierodt carried out the first measurements of optical density in 1870 by monitoring changes in his hand. His results were rediscovered in 1932. But it was not until the early 1970s that real progress was made by T h o Aoyagi, Tokyo, and Akio Yamanishi of the Minolta company. Pulse oximeters are now commercially available and have been used routinely for over 15 years in intensive care units (ICU) despite having many limitations, such as severe interference from HbF. However, the device is appropriate for the long-term monitoring of a constant oxygen supply and uptake, and this is how it is mostly used today. Where do we now stand? According to the US National Committee for Clinical Laboratory Standards (NCCLS, C27): blood gas...has more immediacy and potential impact on patient care than any other laboratory determination.

1.4 Goalsfor Future Developments and Trendr

23

The American Association of Clinical Chemistry (AACC) expanded upon this, clearly seeing an essential link between the blood gases and the electrolytes Na+, K+, ionized Ca2+: The measurement is essential for diagnosing and monitoring...electrolyte disorders. In 1992 some devices for evaluating pH, pC02, and pO2 based on opticalfibers were marketed by BTI, Oximetric, and Puritan Bennett. In these devices, optical fibers are introduced by catheters over an interface adapted so as to calibrate and recalibrate the sensor. For in vivo monitoring, optical methods have now replaced electrodes. Optical methods rely on the fact that oxygen quenches the luminescence of characteristicdyes and that pH changes bring about a shift in the emission spectrum. Optical pH measurements were developed by Petersen et al., who described a sensitivity (resolution) of the optical fiber sensor of 0.01 pH unit [124]. The sensors were used in blood and demonstrated in vivo in 1975 [92]. The probe did not, unfortunately, meet the in vivo biocompatibilityand reliability requirements for a one-time use of up to 72 h. In 1984 J.I. Peterson and G.G. Vurek concluded [89]: Electrode development, although of intense interest for many years, has not lived up to expectationsfor wide applicability and reliability in vivo. Fiber optic sensors are still too new to be of proven value in most applications. Long-term monitoring of electrolytes during hemodialysis is necessary since the side-effects are aggravated the longer hemodialysis continues. Continuous monitoring in an extracorporeal second circulation failed at the first attempt, owing to the instability of the calibrated setting points (see section 5.1) 1125-1281. These problems were partly solved by taking into consideration the asymmetry of the ion-selective membranes induced by blood plasma, and by varying the membrane composition. The concerted European action devoted to in vivo monitoring of blood glucose concentrations and concentrationsof several key metabolites during intensive care ended in 1996. A total of 36 European analytical centers were involved, working on a broad spectrum of projects [ 1291. Unfortunately, BIOMED 2, the new proposal, did not receive support from the European Union. In view of the length of time it has taken to develop sensors (roughly 40 years), a 3-year period for this type of project is too short. History shows the strong impact that the commercial availability of novel electronic systems and biocompatible materials may have on the realization of projects. At the same time, history also shows that the most significant progress is made when the scientists concerned are closely involved in clinical research, and are aware of see the medical problems which arise. For this reason, a concerted action on in vivo monitoring should involve the participationof medical personnel and medical centers, especially as biocompatibility problems tend to be poorly understood by purely technical scientists. In conclusion, the following points seriously restrict the viability of long-term monitoring in vivo: the sterility of the device and its aseptic handling the maintenance of the calibrated setting points, which is partly related to the biocompatibility of devices and materials - the toxicity of components - the cost-benefits of a patient having to carry an additional catheter, which is stressful -

24

I Introduction

Implanted sensors are immediately entrapped by proteins as part of a reaction in the stressed tissue compartment, with subsequent diffusional problems. This means that results in general do not correlate with determinationsin whole blood. Some companies have left the field. Others have continued [130, 1311, and yet others have shifted towards investigating noninvasive techniques [ 132, 1333. The electrochemical measurements of pH and p 0 2 are now the only "physicochemical" sensors used in biotechnology since the Severinghaus electrode is no longer used to determine the pCO2 as its response behavior is too slow. In comparison, optical sensors are likely to have an increasing impact since they show many promising features associated with the development of new dyes [134] and chromogenic ligands (see section 6.2), and with a growing market of various smallsized light sources. A new domain of analysis has recently emerged in medicine called "pointof-care testing" (POCT). POCT allows clinicians to quickly assess their patients in emergency units and on-site. POCT is practiced under the assumption "faster is better". However, rapid testing should not turn out to provide inaccurate results. Which means that all the features found in traditional instruments must be provided also in a small portable instrument based on miniaturized disposable cartridges shown in Figure 1-6 [135]. The AVL OFTI 1 calibrates itself

Figure 1-6. AVL OFTI 1 cartridge incorporating optode membranes for the analysis of pH- and blood gas (p02, 602)in whole blood. Additionally 10 calculated parameters are provided (with permission [1353)


25

and consumes typically only 80 ~1 of the specimen. Novel developments are based on experiences made with in vivo and ex vivo monitoring and have led to successful application of some of the techniques in this field to on-site determinations and front-line analysis [136]. Novel approaches are likely to affect other fields in analytical chemistry, such as environmental chemistry, toxicological studies, process monitoring, and the analysis of seawater [1371.

1.4.4 The Analytical Laboratory in the 21s' Century (Conclusions) Any perspective on the future must remain incomplete; such a perspective can only be based on a global view.

Analysis in the Centre Worldwide, a few giant companies will dominate the market for the enormously expensive and technologically highly developed hyphenated instruments such as ICP-MS, highresolution quadrupole MS sector instruments, and some N M R techniques. However most instruments wiU undergo some degree of miniaturization, and, in many cases, distribution of the specimen, sample fractionation, and pretreatment wdl need much more space than the analytical instrument itself. Space-filling robotic systems for specimen and sample distribution, literally speaking, are totally uneconomic; they are slow, space-filling, and inefficient. Either these robotic systems have to be provided with additional skills, e.g., sensors for screening, or they have to be miniaturized or replaced by more intelligent solutions. In the clinical laboratones of major hospitals, automation is particularly advanced, and routine chemical and hematological analyses are virtually centralized. Some analyzers can perform up to 36 analytical tests on plasma samples simultaneouslyand provide up to 15 0o0 analytical values within 1 h under the supervision of only a few staff. Such systems integrate ion-selective electrodes, continuously monitoring the free molality of the most frequently analyzed electrolytes. Such integrated systems are also being developed by national reference laboratories, and require capital investments of US$ 2-7 million. They will be supplied by a few global companies, with national offices taking care of servicing. Generally speaking, economic trends will lead to the growth of opportunities for economically competitive reference and consulting laboratories worldwide, and to the deporture of some smaller laboratories from the large-scale routine treating queues of specimens. The reference laboratories will run under the supervision of only a few staff. However, individuals will still be required to ensure quality, since currently no quality control system can interpret reports, manage the sources of errors, or make constructive suggestions on corrections. Reference laboratories will fulfil many functions other than merely producing results, including establishing a network of reference laboratories, for data excharige, and quality assurance worldwide. These laboratories will be completely free of daily analyticalbatch services. Under these conditions, large-scale, rapid, and safe transports of specimens submitted to the central laboratories must be organized.

26

I Introduction

Analysis in the Periphery The laboratory in the periphery is supposed to work much closer to clients. Presumably, they could provide services to the front-line analysis sites and also perform front-line analysis. At the very least, they will be responsible for adapting screening methods using dedicated systems. For analyses involving very small amounts of substances or a high risk of contamination,radiation, etc., glove-box-likeanalytical sites will be equipped with miniaturized analytical instrumentation, and with disposable and continuous monitoring sensing systems. However with on-site analysis comes the need to supervise a number of nonlaboratory personnel. In medical programmes, multiple techniques for initial trainings and subsequent follow-ups were exploited. Video presentations keep the lessons consistent. In addition, some laboratories have assigned point-ofcare coordinators. Analytical methods fulfilling special medical requirements are, increasingly, having more direct medical impact, and some analytical services will move from the central laboratory to the bedside or periphery (ICU, ECU). These methods have an immediate impact on the therapy being carried out, such as screening for acute myocardial infarction (AMI). Similar to the situation of polio epidemic in 1952, the necessary tests will be developed and made available to the medical community relying on early pioneers in point-of-care testing (POCT) which have accumulated a wealth of experience with such analyticaltechniques. In environmental technology, there is an increasing demand for continuous monitoring of landfill sites and drinking water supplies. Here, the main requirements are not necessarily selectivity and high sensitivity but rather longevity, appropriate detection of chemical classes of compounds, and the quantitation of a cut-off or limiting concentration. The evaluation of free analyte concentrations,e.g., of lead ions, in contrast to total concentrations,may be controversial, owing to a lack of consensus about legal limits, even if the free concentration is in equilibrium with the totalconcentration.Discussions about what is to be analyzed and what is to be reported will continue, and new solutions and a degree of consensus will be necessary. Consideration of the free dissolved species rather than total concentrations may lead to new ways of viewing the toxicity of chemical compounds. For on-site screening, more and more chemical sensors will be evaluated and requested. Ensuring the mobility and versatility of the analysis involves producing integrated sensing devices and cordless transmission of signals or results. The sensing element itself will be incorporated in a multidimensional and multifunctional robust modular system where it can be replaced easily and safely [136].Chemical sensing elements will either have to ensure long-term stability, extended life-times, and reversibility or, alternatively, they will be offered as cheap, low-waste, disposable elements which can still perform at a suitably high level with respect to reliability and accuracy! The state-of-the-art would currently allow production sites to monitor some highrisk effluents such as cyanide or heavy metals in situ and immediately.


27

Analysis in and during Production In biotechnology and food technology, real-time, continuous monitoring of bioprocesses saves resources, time and money. Selectivity may be less important since the detected species is known and is the predominant or limiting product; dynamic range, sensitivity, and detection limits may be more relevant parameters. The cut-off limits where metabolic processes are limited by the concentration of substrates or products are defined very precisely. In this situation, the chemical sensor is specifically indicated and has a considerable potential since the design of dedicated systems is the major strength of these applications. A large variety of sensors have actually been evaluated, to determine dissolved oxygen, carbon dioxide, inorganic cations and anions such as nitrite, neutral compounds such as alcohols, ammonia and amines, organic charged compounds, enantiomers, and enantiomeric excess (see chapter 2, 5 and 6). Those who are concerned only with the final product of a process are often unaware of the potential of dedicated systems and their contributions to process design [136].Alternatively, there is no sensor which cannot be realised by one or other of the various well-known introduced concepts, and, even an aseptic preparation or sterilization is feasible. There are no fundamental barriers to the application of chemical sensors in the future.

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[37] Behringer, Ch., Lehmann, B., Haug, J.-P., Seiler, K., Morf, W.E., Hartman, K., Simon, W., Anal. Chim. Acta, 1990,233, 41. [38] Wang, K., Seiler, K., Haug, J.-P., Lehmann, B., West, S., Hartman, K., Simon, W., Anal. Chem., 1991,63, 970. [39] Seiler, K., Wang, K., Kuratli, M., Simon, W., Anal. Chim. Acta, 1991,244, 151. [40] Spichiger, U.E., Kuratli, M., Simon, W., Proceedings of the 2nd World Congress on Biosensors, Biosensors & Bwelectronics, 1992.7, 715. [41] Spichiger, U.E., in: Scheller, F.W. et al. (eds.), Frontiers in Biosensorics, Birkhauser, Basel, 1996. [42] Btihlmann, P., Simon, W., Tetrahedron, 1993,49,7627. [43] a) Ozawa, S., Ziirich, CH: Swiss Federal Institute of Technology (ETH), 1992; PhD thesis No. 9647. b) Ozawa. S., Simon, W., in: Grattan, K.T.V., Agousti, A.T. (eds), Sensor VI Technology, Systems and Applications; Bristol: Institute of Physics Publ., Techno House, 1993, pp. 281-286. [44] a) Kuratli, M., Zurich, C H Swiss Federal Institute of Technology (ETH), 1993; PhD thesis No.10380. b) Kuratli, M., Badertscher, M., Rusterholz, B., Simon W., Anal. Chem., 1993,65,3473. c) Kuratli, M., Pretsch, E, Anal. Chem., 1994.66.85. [45] Ozawa, S., Hauser, P.C., Seiler, K., Tan, S.S.S., Mod, W.E., Simon, W., Anal. Chem.,1991.63. 640. [46] West, S., Ozawa, S., Seiler, K., Tan, S.S.S., Simon, W., Anal. Chem., 1992,64, 533. [47] Spichiger, U.E., Seiler, K., Wang, K., Suter, G., Morf, W.E., Simon, W., Proceedings of the EC04, The Hague, Netherlands, 12-13 March, 1991, Proc. SHE-lnt. Soc. Opt. Eng. 1510, 1991, pp. 118430.

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[48] Spichiger, U.E., Freiner, D., Bakker, E., Rosatzin, T., Simon, W., Sensors and Actuators B, 1993,11,263. [49] a) Gut, G., Wadenswil, CH-Zurich: Ingenieurschule, Fachbereich Lebensmitteltechnologie, 1993; Diplomarbeit. b) Wild, R., Citterio, D., Spichiger,J., Spichiger,U.E., J. Biotech., 1996,50, 37. [50] a) Spichiger, U.E., Simon, W., Bakker, E., Lerchi, M., Buhlmann, P., Haug, J.-P., Kuratli, M., Ozawa, S., West, S . , Sensors and Actuators B, 1993, 11, 1. b) Proc. Europtrode'96, Sensors and Actuators B, 1997, 38-39. [51] G8pe1, W., Hesse, J., Zemel, J.N., Sensors Vol. 2; Weinheim: VCH Verlagsgesellschaft, 1991, pp. 1-16. [52] Seijama, T. (ed.),Chemical Sensor Technology. Amsterdam: Elsevier, 1988; Vol.1, pp.1-13. [53] Oggenfuss, P., Morf, W.E., Oesch, U., Ammann, D., Pretsch, E., Simon, W., Anal. Chim. Acra, 1986, 180, 299. [54] Frant, M. S . , Analyst, 1994,119, 2293. [55] Kolthoff, LM., Saders, H.L., J. A m Soc., 1937,59,416. [56] a) Moore, C., Pressman, B.C., Biochem. Biophys. Res. Commun., 1964, 15, 562. b) Pressman B.C., Proc. Narl. Acad. Sci. USA, 1965,53, 1076. [57] Stefanac, Z., Simon, W., Chmia, 1966,20,436; Microchim J., 1967,12, 125. [58] Simon, W., Swiss Patent 479 870; 1969. [59] Frant, M.S., Ross, J.W., Science. 1970,167,987. [60] MOller, W., oral communication. [61] Pressman, P.C., Harris,E.J., Jagger, W.S., Johnson, J.H., Biochemistry, 1967,58, 1949. [62] Kilbourn, B.T., Dunitz. J.D., Pi&, L.A.R., Simon, W., J. MoL Bwl., 1967,30,559. [63] Pinkerton, M., Steinrauf, L.K., Dawkins, P., Biochem Biophys. Res. Commun., 1969,25, 512. [64] Winkler, R.,Sfructure and Bonding, 1972,10, 1. [65] Morf, W.E., Simon, W., Helv. Chim. A c t , 1971,54,2683. [66] Pedersen, C.J., J. A m Chem SOC.,1967.89.2495; ibid 7017. [67] Pedersen, C.J., Angew. Chem, 1988,100. 1053;Angew. Chem lnt. Ed Enel., 27, 1021. 1681 Lehn, J.M., Structure a d Bonding. 1973,16, 1. [69] Lehn,J.M., Graf,E., J. Am Chem.SOC.,1975,97,5022. [70] Cram, D.J., Cram, J.M., Science, 1974,183, 803. [71] Cram, D.J., Nature, 1992.356, 29. [72] Kyba, E.P.,et al., J. A m Chem Soc.,1977,99,2564. [73] Moody, G.J., Oke, R.B.,Thomas, J.D.R.,Analyst, 1979,95,910. [74] a) Eisenman, G., International Symposium on Modern Technology in Physiological Sciences; Munich, July 1971; b) Anal. Chem., 1968,40, 310. [751 Ciani, S., Eisenman, G., Szabo, G., J. Membrane Biol., 1969, I , 294. [761 Covington, A.K., in: Durst, R.A. (ed.), Ion-Selective Electrodes, Special Publication No 314; Washington, DC: National Bureau of Standards, 1969, ch. 4. [771 a) Pungor, E., Toth,K., Hung.Sci. lnsrr., 1968, 14, 15. b) Toth, K., Gavaller, I., Pungor, E., Anal. Chin Act% 1971, 57, 131. 1781 Sandblom, J., Eisenman, G., Walker, J.L., Jr., J. Phys. Chem,1967.71, 3862. [791 a) Sandblom, J., Onne, F., Membranes Vol.1; in: Eisenman, G. (ed.), New-York Marcel Dekker, 1972; b) Sandblom. J., J. Phys. Chem., 1969,73,249. [80] Buck, R.P., Anal. Chem., 1972,44,27OR. [81] Wuhrmann, H.R., Morf, W.E., Simon, W., Helv. Chim Acta, 1973,56. 1011. 1821 Morf, W.E., The principle of ion-selective electrodes rmd membrane tmnsport; Budapest: Akadkmiai Kiad6, 1981. [831 Pick, J., T6th, K., VasO, M., Pungor, E., Simon, W., in: Pungor, E., BuzPs, 1. (eds.), lon-selective Electrodes, Budapest: AkadCmiai Kiad6, 1973, pp. 245-252. [84] Clark, L.C., Lyons, C., Ann. N.Y. Acaa! Sci, 1962,102, 29. [851 Enson, Y.,Briscoe, W.A., Polanyi, M.L., Coumand, A., Appl. Physiology, 1962,17,552. [86] Bergmann, I., Nature, 1968,218, 3%. [87] Ltibbers, D.W., Opitz, N., 2 Naturforsch Teil C, 1975,30,532. [88] Ltibbers, D.W., Opitz, N., Sensors Actuators, 1983,4, 641.

30

I Introduction

[89] Peterson, J.I., Vurek, G.G., Science, 1984,224, 123. [90] Lakowicz, J.R., Szmancinski, H., Bemdt, K., in: Hansmann, D.R., Milanovich, F.P., Vurek, G.G., Walt, D.R. (eds.), Progress in Biomedical Optics, Vol. 1648, Washington: SPIE, pp. 150-163, 1992. [91] Hansmann, D.R., Milanovich, F.P., Vurek, G.G., Walt, D.R. (eds.),Proceedings of Fiber Optic Medical and Fluorescent Sensors and Applications, Vol. 1648. Bellingham, Washington: SPlE.Int. SOC. Opt. Eng..,l992. [92] Lubbers, D.W., Opitz, N., Z Natutforsch., C: Biosci. 30c, 1975,532. [93] Recommendation of the Austrian Society for Analytical Chemistry, 1st Vienna Opt(r)ode Workshop, Vienna, June 5,1989. [94] SPIE-Proceedings,ECO, 1991, The Hague, Netherlands. [95] Biosensors. Trends in Analytical Chemisfry, 9/3, V (1990). Report on “The Biosensor Market in the U S . ‘#A21339‘. [96] a) Taylor, R.F., in: Taylor, R.F., Schultz, J.S. (eds.), Chemical and Biological Sensors, Bristol: 1OP Publ. Comp., 1996, pp. 553-579. b) Kahan, J.S., Gibbs, J.N., Appl. Biochem. Biotechnol., 1985,II, 507. [97] Proceedings of the 2nd World Congress on Biosensors, Biosensors 92, Geneva, May 20-22, 1992. Oxford: Elsevier Advanced Technology, 1993. [98] Maciotti, M., Sensors and Actuators B, 1991.4, 1. [99] Harrison, D.J., Manz, A., Fan, Z., Liidi, H., Widmer, H.M., And. Chem.,1992,64, 1926. [lo03 MTI Analytical Instruments, 41762 Christy Street, Fremont, CA 94538, USA. Brechbuhler AG Analytical Instruments, CH-8952 Schlieren, Switzerland. [loll Tumer, R.B., Brokenshire, J.L., Trends in Anal. Chem.,1994,13, 275. [lo21 a) Baykut, G., Franzen, J., Trends in Anal. Chem., 1994,13, 267. b) McClennen, Arnold, N.S., Meuzelaar, HLJ., Trends in AnaL Chem.,1994.13, 286. [lo31 Andrieux, C.P., Hapiot, P., Saveant, J.-M., Chem.Rev., 1990,90,723. [lo43 Mirkin, M.V., Anal. Chern., 1996,68, 177A. [lo51 Wightman, R.M., Wipf, D.O., in: Bard, A.J. (ed.)Electroanalytical Chemistry, Vol. 16, New York: Marcel Dekker, 1988. [lo61 Stamford, J.A., Justive, J.B., Anal. Chem., 1996,68, 359A. [I071 Spichiger, U.E., Electrochimica Acta, 1997,42,3137. [lo81 Bergveld, P., IEEE Trans. Biomed Eng., 1970, BME-17, 70. [lo91 Haak,J.R., vander Val, P.D., Reinhoudt, D.N., Sensors andActuutors B, 1992,8, 211. [110] Van der Schoot. R.H., Van den Vlekkert, H.H., De Rooij, N.F., Sensors and Actuators B, 1991,4, 239. [111] see [17] and [14]. [112] 1-STAT Corporation, Kanata, Canada; distributed by Hewlett-Packard (Schweiz) AG, CH-8902 Urdorf. [113] a)Carey, W.P., Beebe, K.R., Kowalski,K.R., Anal. Chem., 1986,58, 149. b) Nakamoto, T., Fukunishi, K., Moriizumi, T., Sensors and Actuators, B1, 1990, 473. c) Henry, C., Product Review, Anal. Chem., l996,68,625A. [114] a) Ballantine, D.S., Rose, S.L., Grate, J.W., Wohltjen, H., Anal. Chem., 1986.58, 3058. b) Grate, J.W., Snow, A.W., Ballantine, D.S., Wohltjen, H., Abraham, M.H., McGill, A., Sasson, P., Anal. Chem.. 1988, 60,869. [115] various authors in: Gardner, J.W., Bartlett, P.N. (eds.), Sensors and Sensory Systems for an Electronic Nose. Dordrecht: Kluwer Academic Publisher, 1992. [116] Repphun, G., Halbritter, J., J. Vw.Sci. TechnoLA, 1995,13. 1. [I171 BaschB, T., Angav. Chem.,1994,106, 1805. [118] Severinghaus, J.W., World Congress of Anesthesiology, Washington, DC, May 26, 1988. [119] Severinghaus, J.W., in: Woolmer (ed.),Symposium on pH and Blood Gas Measurements. Little, Brown and Co, Boston, MA, 1959, pp. 126. [lu)] Clark, L.C., Jr., Kaplan, S.,Matthews, E.C., Edwards, F.K., Helmsworth, J.A., . I Thoracic . Surg., 1958, 36, 488. [I211 Kapany, N.S., Silbertrust,N.,Nature, 1964,204, 138. [122] Mendelson, Y.,Clin. Chem. 1992,38, 1601. [123] Sarnquist, F.H., Laboratory Medicine, 1988,19, 417. 11241 Peterson, J.I., Goldstein, S.R., Fitzgerald, R.V., Buckhold, D.K., Anal. Chem, 1980,SZ. 864.

References [125] [I261 [127] [128] [I291 [I301 [I311 [132] [I331 [134] [I351 [I361

[137]

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Haase, E., Schlatter, K., Spichiger, U.E., Simon, W., GITLabor-Medizin, 1992,3, 84. Haase, E., Zurich, CH: Swiss Federal Institute of Technology (ETH), 1993; PhD thesis, No.10453. Rumpf, G., Spichiger-Keller,U.E., Biihler, H., Simon, W., Analytical Sciences, 1992,8,553. Rumpf, G., Ziirich, CH: Swiss Federal Institute of Technology (ETH), 1991; PhD thesis, No. 9573. Broschure can be ordered at Dr. S.J. Alcock, Cranfield Biotechnology Centre, Cranfield University, Cranfield, Bedfordshire MK43 OAL, Fax: 01234-750907. Haller, M., Kilger, E., Briegel, J., Forst, H., Peter, K., Crit. Care Med., 1994,22, 580. Venkatesh, B., Brock, T.H.C., Hendry, S.P., Crit. CareMed, 1994.22.588. a) Wang, I., Sowa, M., Mantsch, H.H., Bittner, A,, Heise, H.M., trends in anal. chem., 1996, 15, 286. b) Heise, H.M., Marbach, R., Janatsch, G., Kruse-James, J.D., AnaL Chem., 1989,61,2009. Boyce, N., Clinical Laboratory News, 1996,22,1. a) Wolfbeis, O.S., in: Proceedings of EUROPT(R)ODE'94,Sensors and Actuators B, 1995.29, 140. b) var. authors in: Proceedings of EUROFT(R)ODE96, Sensors and Acruutors B, 1997.38-39. AVL OPTI, portable instrument, AVL Biosense Corp., Atlanta, GA. a) Spichiger, U.E., Bioworld, 1997,4, 4. b) Swiss patent application 64/97, Modulares Sensorsystem firr die Prozess-Messtechnik. c) U.E. Spichiger, Technische Rundschau, Handbuch der Automation 97/98, 1997, 32. d) Spichiger U.E.,Citterio, D., Spichiger J., in: Beckmann, D., Meister, M. (eds), Proc. 8. Heiligenstiidter Kolloquium, Heiligenstadt, 1997,200. Klimant, I., Kiihl, M., Glud, R.N., Holst, G., in: Proceedings of EUROPT(R)ODE'96, Sensors and Actuators B, 1997,38,29.

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2

Chemical and Biochemical Sensors

2.1 Classification, Specification, and Nomenclature of Chemical Sensors In chapter 1, the concept of chemical sensors was introduced (see Figures 1-1 and 1-2). A chemical sensor was defined as a device that transforms chemical information on the attributes of a specimen or a substance into an analytically useful signal. In order to transform the chemical information from the chemical and biochemical recognition process, the chemical part has to be linked to a transducer. As shown in the following chapters, many sensors make use of more than one transducing step, and these steps may consist of a chemical andor physical transformation of the recognition process. In order to justify the grouping of sensing elements described in this book, a classification according to the type of transducer is given in Table 2-1. Hence from the chemical viewpoint, a classification according to the type of recognition process may be more relevant (Table 2-2). Classification of physical sensors is based on the primary input signal, which is in most cases identical with a classification according to the measurand. Measurand is analoguous to analyte, and refers to the primary physical quantity analyzed. In general, the specified measurand is inherently different from the desired output signal. In order to convert the former quantity into the latter, a second or a third transduction principle often has to be invoked to make a sensor work. This is evident for the current state of optical sensors. These transduction principles are known as physical or chemical effects. More than 350 possible physical effects are listed in a dictionary by Schubert [l, 2a]. Lion proposed grouping the large number of possible effects according to the form of energy in which the signals are received and generated: mechanical, thermal, electrical, magnetic, radiant, or chemical [3]. It should be noted that some of the effects are reciprocal. An example is the piezoelectric effect, where mechanical stress generates an electrical charge and vice versa. Some classifications contain ambiguities. Temperature can be measured by reversible as well as irreversible probes. The displacement of an indicator in a clinical thermometer is irreversible and different from the structural change in a liquid crystal, and from the Seebeck or Peltier effects, which are based on changing electrical resistance and which are reversible. Mass can be measured by a refractive index change, by the time of flight in an electric field after ionization, and by local conductivity, or by frequency modulation of an oscillating crystal. Since radiant intensity in the infrared can be classified as a thermal or an optical effect, changes may be regarded as high-frequency electric and magnetic field effects as well as effects of the dielectric properties of matter. Hence, in some fields of application, the boundaries between different forms of energy are irrelevant. Basically, the signal conversion in transducers is unselective, a conversion of energy, and should not affect the parameters of the chemical reaction characterizing the analyte's activity. Nevertheless, the chemical sensing principle is inevitably bound to the features of the transducers. The practicality of different physical principles is very variable. Hence, in many cases the principle of the transducer is not consistent with the aims of versatility and feasability. Such

34

2 Chemical and Biochemical Sensors

Table 2-1.Classification according to the type of transducer

Electrical transducers modes: voltage current current-voltage "work function" charge transfer, resistance dielectricity Radiant or optical transducers modes: absorption, intensity

emission intensity emission and absorption scattering: phase changes polarisation and absorption

opto-thermal effect

Electrode potentiometric sensor amperometric sensor polarographic, voltammetric sensor FETs (field effect transistors) MOS (metal oxide semiconductor gas sensor) coulometric sensor, chemiresistors, ion mobility, mass spectrometry capacity sensor Optode, 10s (integrated optical sensor) transmission or absorbance in the W-,VISor IR-region of the spectrum ATR (attenuated reflection) or evanescent field sensor SPR (surface plasmon resonance) luminescence,photoemission,photon counting FOCS (fiber optic chemical sensor) e.g., Raman scattering refractive index sensor MIOS (miniaturizedintegrated optical sensor) OR (optical rotation), ellipsometry ORD (optical rotation dispersion) SPR (surface plasmon resonance) photo-acoustic effect

Thermal transducers

calorimetric sensor, pellistor

Magnetic transducers

NMR (nuclear magnetic resonance) permeability sensor mass spectrometry

Mechanical, frequency transducers

SAW (surface acoustic wave) piezoelectric oscillators,quartz balance

2.1 classification, Specification Md Nomenclature of Chemical Sensors

35

arrangements are more likely to find an application as detectors in instruments. Not all the effects have been exploited in sensing elements. Some effects are too small to be applied successfully. An attempt to enhance the effect of refractive index changes by MIRES (multiple internal reflection elements) is under investigation (see chapter 6). Finally, speed of response velocity, detection limits, and sensitivity of the different endproducts vary considerably. Depending on the application, some features of a sensor are preferred and focused on in development, whereas others are less attractive and less relevant. In environmental control, a sensor sensitive for the whole class of aromatic compounds in air or water might be more attractive than a benzene-selective sensor. Since the classification of sensors on the basis of the physical signal domains contains some ambiguities, and the domain of the chemical reaction involves an enormous variety of different types of analytes and applications,an alternative classificationsystem, based on the fundamental type of the chemical recognition process involved, may be more helpful:

Table 2-2. Classification according to the type of the recognition process involved

Sensor type

Reacting pairs

Chemical reaction recognition process

chemical sensors in the strict sense

host-guest; ligand-analyte; carrier-ion; ion, neutral species, and gas sensors

complexation association,addition, typical equilibrium reactions

oxide semiconductor sensors

inorganic metal oxide layer-reactive gases

absorption, reduction, oxidation

enzymatic sensors

active site-substratecosubstrate mediated sensing reactions active site-mediator-electrode

metabolic turnover, typical steady state,

antibody (catalytic antibody)antigen antibody-antigenic protein-hapten

affinity, association,

immunochemical sensors

receptrodes, living organs, bilayers hybndes as abzymes etc.

receptor-substrate

kinetic reactions

equilibriumreactions association, affinity, metabolic turnover

36


Various historical examples of sensor design are shown in Figure 2- 1. Sensor design type 1 shows the recognition process located in a separate layer (e.g., an enzyme) in close proximity to the physicochemical transducer (called the sensor). The recognition process is implanted in the sensing layer and is more likely to be of the bulk membrane type than the surface sensing type. The sensor is decoupled from signal processing.The chemical sensor types 2 and 3 emphasize the structural element of the host molecules and the basis of shape-fit inducing the selectivity between host and guest molecules. Hence the recognition process is characterized similarly to an affinity surface sensor. In types 2 and 3, signal processing is again decoupled from the sensing device. The sensing area is more likely a surface sensor than a bulk membrane. Sensor design type 4 is devoted to the traditional picture of the key-keyhole model. The enzymatic reaction at an active site is integrated in the biological environment (the protein bulk of the enzyme). The key (or substrate) in this particular model is coupled to a spacer to provide conformational degrees of freedom. The sensor model specified in Figure 1-2 (chapter 1) is a synthesis of well-known sensor models. The recognition reaction represents a chemical host-guest reaction incorporated in a bulk membrane, based on thermodynamic equilibrium of the reactants.

F. Scheller et al. 1989 [4] Sensor design for biosensors, affinity sensors, enzymatic sensors. ANALYWU INFORMATION

@

SENSOR

MEASURING SIGNAL

0°D2I>

0

V

SAMPLE MOLECULAR RECOGNITION

SIGNAL

Surface reaction type sensor, typical for antigen-antibody interactionsor receptrodes. Further parts are not clearly specified [5].

W. Simon et al. 1987 [6] Model for chemical bulk membrane sensors. Recognition,transduction and signal generation are coupled. All parts are clearly specified.

G. Folkers et al. 1991 [7] The key-keyhole model specified for enzymatic sensors. MATRIX SPACER

RECEPTOR

Figure 2-1.Different chemical sensor models

2. I Classification, Specification and Nomenclature of Chemical Sensors

31

Table 2-3. Classification according to the type of sensing layer

Surface active sensors:

Bulk-phase sensors: solid-state membranes and sensors

solid-state sensors

surface layer furnished with immobilized dyes (indicators), enzymes, antibodies

homogeneous: glass, single crystal, pressed cristalline body, organic and metal oxide semiconductors, metal oxide semiconducting gas sensors (MOS), heterogeneous: crystals implanted in an inert matrix (e.g., in silicone polymer) liquid membranes with a solid-state internal reference system: e.g.: semiconducting elements, gate field effect transistors (GETS), ISFETs, CHEMFETs, EN(ZYME)FETs

solvent polymeric membrane synthetic carriers sensitive for anions and cations or for ions generated at a boundary by a selective electrodes chemical reaction or by hydration. carriers: charged, neutral or classical ion exchangers optodes

multilayer membranes semipermeable coatings protecting layers

polymerized membranes

containing synthetic carriers sensitive for ions or neutral species, gases. carriers: charged, neutral or classical ion exchangers enzyme electrodes, optodes, EN(ZYME)FETs enzyme embodied electrode (EEE) biocompatible membranes, interference-preventinglayers iondiffusion barriers, coatings, gas-permeable, gas-sensitive membranes photo- and electropolymerized selective layers, selectrodes

tissues and microbial sensing adlayers

The original classification of electrodes was based on specifying the type of sensing hyer responsible for the sensing reaction. Hence, surface active sensors are generally differentiated from bulk membrane sensors since they have very different operational restrictions and interferences (see Table 2-3).

38


Many of these devices are not sensors in a strict sense since they are not thermodynamically reversible, but are more correctly classified as detectors. Typically, enzymatic sensors need a continuous supply of cosubstrate or coenzyme, whereas the analyte represents the substrate. Frequently, the product of the metabolic process is the source of a competitive inhibition of the active site (e.g., acetaldehyde with alcohol: NAD+ oxidoreductase ADH, EC 1.1.1.1, see section 2.2.7). In these cases, the reaction is limited by dissociation and diffusion of the product. Zmmunosensors work dissociation limited and are mostly not reversible in a reasonable timeframe but can, under suitable conditions, be regenerated. Even enzymatic sensors of the third generation have, under suitable conditions, to be continuously regenerated by some intelligent subsequent process, as in the case of mediated amperometric electrodes (see section 3-3). In contrast, in classical chemically selective electrodes and receptrodes, the response is modulated by the fluctuating concentration of the substrate or analyte. Surface sensors are generally exposed to several influences which are difficult to control, whereas bulk membrane sensors separate the analyte primarily from other sample components by an extraction step. The selectivity and detection limits of different sensors vary considerably, as will be discussed later.

Conclusions The lists presented focus mainly on the technical characteristics of the sensor design. Further Classificationsaccording to the type of application, the dynamic range, and the detection limit or the range of analytes dealt with may elucidate some aspects of the usefulness of chemical sensors. The number of classifications demonstrates the versatility and the broad spectrum of sensor designs and applications. Chemical sensor systems are dedicated systems tailored to restricted applications under specified conditions. Chemical sensors are often called "intelligent devices", but this is true only if they are applied in M intelligent way! Only a few of the entries in these lists will be discussed in this volume. However, most of these sensors have some physicochemical and chemical properties in common which will be treated in the following part of chapter 2 with special emphasis on biological applications in aqueous environments. Some specific examples of sensors will be given in chapters 5-7. The examples are taken from existing publications and theses, which can be referred to for more detailed descriptions (see references).

2.2

Molecular Recognition Processes for Ions and Neutral Species

2.2.1 Introduction The key to the architectureof both chemical and biochemical sensors is the recognition process of an organic or inorganic chemical component by a receptor, host molecule or reactand. This chemical component, analyte or guest, may be an ion or a neutral or uncharged molecular species. The recognition and solubilizationof a particular guest component among a plethora of

2.2 Molecular Recognition Processesfor Ions and Neutral Species

39

structurally related compounds is assumed to be the result of a combination of complementarity of the host's "cavity" shape and an exact positional, stereochemical arrangement of binding sites and/or functional groups where, as a result, partial molecular interaction energies add to the final stability of the host-guest compound. An additional factor is the partition of the species between the aqueous sample phase and a less polar phase where the recognition process occurs. In order to understand how a sensor extracts and detects an analyte successfully, and to investigate novel, similarly successful designs, it is necessary to concentrate on the mechanism of the host-guest interaction that occurs during the recognition process. With respect to the reversibility of sensing elements, noncovalent, low-energy interactions are of special interest. This section is primarily concerned with some basics and parameters of molecular recognition, comparisons between naturally occurring host-guest interactions and synthetic carriers, typical examples as well as existing structures of ionophores from the medical field. For overviews and further details, the reader is referred to [8-211. The recognition and complexation of guest molecules by biotic receptors has been studied since about 1900 when Paul Ehrlich stated "Corpora non agunt, nisi fixata", based on investigations by means of immunized animals and stained living tissues. He postulated cross reactions between molecules competing for the same binding site at the same chemoreceptor [22]. Ehrlich was not only a physician but also a well-known chemist [23]. J.N. Langley (1906) developed the model of molecular interactions between an active drug and a protein receptor [24]. In 1879, E.H. Fischer established a chair in analytical chemistry in Munich, Germany. In 1894, he postulated a stereospecific interaction between a sugar and a fermenting agent and formulated the "lock and key" notion for the interaction of an enzyme and a substrate [25]. For this work he was awarded the Nobel prize, in 1902. This hypothesis for the chemical interaction between a substrate and a biotic receptor was later known as "key-keyhole" theory, later elaborated and refined by Warburg [26], Clark [27] and Pauling [28]. A significant contribution was made by the group of Waser et al. (1957) in Zurich in workmg out the mechanisms of the activity of T-curarin and related compounds at the neuronal fiber terminal of muscle [29]. Buchi postulated a receptor model for the binding of local anesthetics, and proposed complementary molecular structures of drugs fitting the receptors [30]. His model of the receptor geometry was confirmed by the pharmacological activity profile of compounds; structure-activity relationships were explored by chemical tailoring of such compounds and studying the pharmacokinetic properties of various derivatives. These early investigations of molecular recognition led scientists to investigate the basic properties of the molecular processes observed in nature. Studies in various areas related to molecular recognition were carried out exploring, e.g., the energetics of inter- and intramolecular interactions and calculating the interaction energies by means of molecular mechanics. The design and synthesis of new molecules for specific applications are at the forefront of sensor research. In the medical field, substances have been investigated which act in specific ways as enzyme inhibitors or with DNA [31-331. The aim is to move beyond symptomatic therapy and to get to the roots of the problem, particularly in the treatment of genetic disorders. At the analytical level, attempts are being made to develop host molecules, especially for neutral guest species, such as creatinine, phenytoin, or carnitine. There will be plenty of problems in developing methods to recognize anions such as phosphate and sulfate. Many beautiful and

40


X 1 m3

A NH

2 3 4 5

NO2 NO2 S02NEt2 NO2

"'"qX

Y

n

NO2 CF3 CN NO;! NO2

1 1 1 1 2

Figure 2-2. Chromogenic cryptahemispheraplexes[37-391

promising structures for molecular recognition of cations and some neutral compounds have been described in recent years. However, only few are promising as analytical tools (see also section 2.2.3). These are mainly crown ethers [34, 351, calix[4]arene derivatives [36] and cryptates [37]such as the basic compounds for the cryptahemispherands [38] substituted by chromophores, chromoionophores in a strict sense, such as chromogenic cryptahemispheraplexes (see Figure 2-2) [39]. In analytical chemistry the solvent of the specimen and the sensing layer plays an essential role. Crown ethers have been used as masking reagents in aqueous solutions to determine electrolyte concentrations by an optical assay and by complexometric means [40]. They have been successfully implanted in solvent polymeric membranes for lithium activity assays and, less successfully, for sodium and potassium activity assays [41-44]. Apart from these developments, selectivity is mostly achieved by enzymatic tests, even for electrolytes [45-48]. Alternatively, traditional analyticalprocedures are used in order to quantify ionic species (ion chromatography,titrations, polaropphy, etc.). In the following sections 2.2.3-2.2.10, some typical examples of open-chain recognition molecules and other host-guest interactionsrelevant to analytical chemistry will be discussed. In view of the emphasis on reversible molecular interaction mechanisms throughout this volume, interaction energies will be compared and the factors influencing the potential energy will be discussed in section 2.2.2.

2.2 Molecular Recognition Processes for Ions and Neutral Species

41

2.2.2 Molecular Interactions: Tools and Calculations "Subjectedto a force, material is set into motion". Forces between atoms or molecular particles have their origin in electrical and magnetic fields and the motion of the electrons around a nucleus. According to Newton's third law, a force F exerted by an object exerts an equal but opposite force -F on that object [49]. Thus interactions between atoms, ions, and molecules are based on attractive forces and oppositely directed repulsive forces which can balance each other in thermodynamic equilibrium. Since the molecular interactions considered for biological systems are commonly referred to water as solvent, the variation of the dielectric constant is a highly relevant factor in estimates of the Gibbs free energy of interaction. Very generally, in both biotic and abiotic artificial systems, molecular interactions are based on a variety of energetically different types of interactions. For artificial as well as natural molecular recognition reactions, the equilibrium state must be reversible or at least regenerable within a reasonable time-frame. This implies that reversibility has not only a thermodynamic but also a kinetic dimension. An infinitesimalmodification of one variable of the system results in a directional change of the equilibrium state and correspondingquantum of transferred energy. To achieve reversibility, the free energy of molecular, ionic, or atomic interactions in a specific solvent has to be limited to some quantity, but also association andor dissociation kinetics must be adequate. As an example, investigations by P.M. Hofstetter made use of thioamides (N,N,N',N'-tetrabutyl-3,6-dioxaoctane-dithioamide) as carriers for heavy metals (Figure 2-3) [50].The author stipulates, that, owing to the exchange kinetics of a ligand and a metal ion as measured in variable-temperature 13CN M R experiments in organic solvents, often a transition from a cationic to an anionic electrode function is found when the free activation enthalpy exceedes the value from 46.3 kJ mole-* (e.g. for a cadmium complex in acetone) to 63.8 kJ mole-' (e.g. for a palladium complex in acetonitrile). These ion recognition reactions with relatively high association constants and high selectivity can nevertheless be reversible. As a result, covalent interactions are not usually considered as useful for artifkial reversible processes showing the highest potential energy of interaction (see Table 2-4). Nevertheless some specific chemical reactions are reversible (see sections 6.1 and 6.2). In this case, the "ligand becomes a "reactand" or "host-reactand". This is in contrast to the steady-state of enzymatic processes where covalent linking is one mode of specific, catalytic reactions (see section 2.2.7). In order to answer the question, how to design ligands and reactands, and how to influence the host-guest interactions, various parameters characterizing the atoms and atom groups have to be taken into account for estimates of the free interaction energy or potential. The interaction generally decreases with the distance r between ions, atoms and atom groups. The shell of a large chemical compound has a shielding effect. This tendency is more pronounced for weak interactive forces (van der Waals interactions). Parameters such as the charge of an ion Q, the dipole moment p, the relative dielectricconstant E ~ the , distance between molecules, atoms, and ions r, the dihedral angle describing the orientation of dipoles 0,the polarizability (temperature dependent) a,and specific factors characterizingthe type of molecules play an important role in all the interactions covering the range between covalent, electrostatic, and van der Waals interactions [51-551. All combinations of forces between ions, dipoles, and induced dipoles as well as quadrupole moments for symetric ligands, are to be considered.

42

-g


Cd2+

ETH 1062

I

Figure 2-3.Carriers for heavy metals (N,N,N',N'-tetrabutyl-3,6-dioxaoctane-dithioamide[50])

Weak interaction potentials operate mainly by their multiplicity at large binding sites (see section 2.2.9). It must be emphasized that, according to the type of molecules, very different bonding energies are calculated and reported in the literature. Free interaction energies between inorganic compounds involving halides, nitrogen, oxygen atoms, etc., are in many cases very different from interaction energies relevant for organic compounds [54]. Thus generalization is problematic. A table of internal binding energies is given in [51], estimates of maximum potential energies are given in Table 2-4. One example of calculating the standard Gibbs free energy of ion-ion interactions is given in Eq. 2-1, based on the Debye-Huckel approximation:

Considering a medium of low permittivity comparable to a solvent bulk membrane (see chapter 4), the potential energy between two monovalent ions is in the region of -60 kJ mol-1 at 298 K. (Estimations: r = distance between centres = 300 pm; E, = 8.854 x 10-l2 Cz J-l m-l; Er = 8; f = 1/41CEo; z1, z2, charge numbers = 1; e, elementary charge 1.602 x 10-19 C; N, Avogadro constant 6.022 x loz3mol-l). The standard free energy is reduced by a factor of ten in an aqueous environment. Ionic interaction potentials involving the permittivity are considerably enhanced in an apolar medium. This trends are relevant when designing the apolar environment and taking care of electroneutrality within a sensing layer. They have to be considered in estimating the dissociation constant pKa of a compound. Weak interactions were summarized as van der Waals forces, referring to the weak dispersive and attractive forces between atoms (specified as Keesom, Debye, and London forces). As a result, attractive forces are turned into repulsive forces if the electrons of two neighboring species start to interpenetrate.The overlap of the two effects means that the potential function is related to the distance between nuclei. Between apolar molecules, the London forces are responsible for nearly 100% of the interaction energy, unlike polar groups or molecules where their influence may be much smaller (25-99%).Weak interactions become more negative


43

Table 2-4. Estimates of the maximum potential energy barriers of molecular interactions (definition of symbols see text); Q i , charge of ion i; 0, torsion angle between dipole axis and ion-dipole axis; Zi, ionization potential of species i / J; a'i, polarisability volume of i / m3, a'i = a / 4 7 r ~pi, ~ ;dipole moment of i / Cm

Type of interaction

Formulation of U, parameters

Maximum potential energy U / kT mol-1

ion-ion ion-dipole ion-induced dipole van der Waals: dipole-dipole dipoleinduced dipole induced dipole-induced dipole covalent bonds

126628

hydrogen bridges

1342

with increasing polarizability and dipole moment of the molecule or groups. For a discussion of multipoles and their orientation see [ 5 3 ] .The polarizability is determined by the electric field within an atom. It can be calculated from measuring the dielectic constant induced by a polar molecule in an apolar solvent as a function of the concentration at constant temperature [54,56]. Calculations may also be based on measurements of the varying refractive index of a solution. As shown in Table 2-4, dipole-dipole interactions become less pronounced with increasing temperature in contrast to the potential energy contributionsothers than Keesom forces. In order to describe the total potential energy inherent in the weak interactions between two atoms, the linear combination of all weak interactive forces is summed (Eq. 2-2). Based on this description, isopotential curves between different atoms at a binding site can be drawn, and describe distances with the same total interaction energy at constant temperature Tlk. k , Boltzmann's constant;f = 1/4a &,. The interaction parameters c, A, and C are determined either empirically by careful adjustment to fit experimental results, or derived by fitting the potential to quantum mechanical calculations. The dipole-dipole interactions (second term) are directly related to temperature.

44


AGges= Alr12- [cf22p12p22/3kT14) + ( f ( a ' l p ~ 2 + a ' 2 p i 2 ) l r+6 )(c h ~ , a ' ~ / f i ) ]

In molecular mechanics (MM) the interactions between atoms are assumed to be pairwise additive. They are represented by simple analytical functions. The simplest functional form for the interaction potential is of the Lennard-Jones potential type, U(r), where the total potential energy of attractive and dispersion forces is summarized by two components, an attractive term showing a negative enthalpic contribution, and a repulsive term with positive sign. In the Lennard-Jones Equation (2-3), the repulsive forces are approximated by an inverse twelfth power (r-12) in the first term. The weak attractive interactions of terms 2 4 are summarized in one term, c6/r6,leading to:

u(r)=A/r12-C6/16

(2-3)

In spite of the simplicity of this potential model, MM calculations are fairly successful for geometrical predictions of small molecules. The model can be extended by an electrostatic term in order to predict ion-ligand interactions.

Hydrophobic Interactions The interaction between nonpolar molecules has been called hydrophobic since nonpolar molecules are preferentially associated with one another in the presence of water [ 5 7 ] . The validity of the term has been questioned because, for most so-called hydrophobic molecules, no real "phobia" against water has been found. Common examples of supposedly nonpolar molecules have polar as well as apolar characteristics.Traube showed that it is in fact the waterwater affinity that drives non-polar solutes out of bulk water [58]. This view of hydrophobic interactions has been supported by thermodynamic experiments. Butler [59] made the observation that the entropy of vaporization of nonpolar solutes from their aqueous solutions deviates from a rule which predicted nearly the same entropy of vaporization for all nonpolar liquids (ca. +90 J K-1 mol-l). He found that the entropy became progressively more negative with an increasing number of carbon atoms for homologous hydrocarbons in water, whereas the free energy of activation and the enthalpy increased. Frank and Evans postulated that, when a nonpolar molecule is transferred to water, it modifies the structure of water, making it more crystalline [56]. This view is now generally accepted in explaining the nature of hydrophobic interactions and has some impact on the design of sensing media (see chapter 4). The term "hydrophobic interactions" describes a heterogeneous class of atomic interactions that are very weak in nonpolar media, but become significant with high polarity of the solvent, particularly in aqueous media [55,60, 611. In the presence of water, nonpolar molecules are found preferentially associated with one another rather than with water. This behavior is called entropy-driven association (see also section 3.1). A consequence of such hydrophobic interaction is the spontaneous association of molecules forming membranes, micelles, and synthetic bilayer lipid (BL) membranes in aqueous environments or reversed micelles in apolar


45

environments. The development of sensors based on such principles continues. The theory suggests that this may be responsible for interactions between apolar parts of species in biological samples and hydrophobic surfaces (see section 4.6). These considerations have consequences for the design of the medium hosting the recognition process. In analytical chemistry, hydrophobic interactions have been introduced for molecular separation processes in creating inclusion complexes. The procedures are most commonly based on the use of various cyclodextrin derivatives, enabling enantiomer-selective recognition in liquid chromatography. Hydrophobic interactions participate in the molecular recognition process of many synthetic compounds, such as cyclophanes, macrocyclic polyethers, calixarenes, cavitands, and cryptophanes, reviewed in [62]. A further example for enantiomers was demonstrated by Cram (see section 2.2.5). An other interesting approach to a recognition process in aqueous environment has been published by Rebek et al. [63] (see section 2.2.6).

Tools Molecular recognition and the development of selective sensing elements, makes use of a set of effective tools, methods, and instruments which can be classified into six groups. These are: 1. Tools adapted to characterize and confirm the structure of synthesized compounds

2. Tools to elucidate the structure of analyte-ligand complexes 3. Tools suitable to elucidate reaction mechanisms and solvation processes 4. Devices to determine the stability constants, including the stoichiometry of analyte-ligand

complexes 5. Instruments for exploring thermodynamic parameters such as entropy and enthalpy contributions to the stability of host-guest products (see chapter 3)

6. Tools to investigate the exchange kinetics of a target compound. To answer various questions in sensor development, several methods and instruments are available. Such devices are based, e.g., on dielectric and diffraction techniques; cryoscopic methods, and vapor pressure osmometry to investigate colligative properties; calorimetric titrations, and differential scanning calorimetry for investigating thermodynamic parameters as well as several electrochemical techniques, powerful spectroscopic methods such as chiroptical methods, 'H NMR, 13CNMR, 31PNMR, IR, and mass spectroscopy which are routinely used as key techniques in molecular recognition research. N M R techniques have provided insight into enzyme structure and into the region of interaction between an enzymatic active site and a substrate at the molecular level. It has allowed to image the sequence-specific structure of noncrystalline proteins to be shown graphically [64]. Synthetic approaches in molecular

46


recognition may be improved by inspecting the coordinates of the fitting sites and are stimulated by visual inspection of the active sites of enzymes. Parameters derived from X-ray analysis have contributed considerably to improving the models as used in computational chemistry. IR and mass spectrometry, IH NMR, 13C NMR, and elemental analysis play an important role in identifying compounds after synthesis, and in studying interactions between small molecules, e.g., the position of hydrogen bridges, the association of water molecules, and for elucidating the extraction or phase transfer behavior. The development of microscopic and imaging methods (AFM, STM, SECM, NSOM) provides a new perspective which will allow further insight into the structure of various characteristics of matter, and into the interactions of molecules (see section 1.4). Scanning chemical microscopy (SECM) is developing into a new tool for investigating charge transfer processes (see also ref. [9], vol. 8).

Computational Chemistry, Molecular Modelling

The molecular geometry describes the dimensions of a molecule as defined by the intemuclear distances and angles, and relies on the electronic configuration of the groups of atoms. Computational chemistry applies mathematical techniques to predict the geometry as well as electronic, and thermodynamic properties of a chemical compound. Molecular modelling is based on the techniques of computational chemistry, but is focused on generating and imaging realistic molecular structures, and associated physicochemical properties [65-68]. Powerful workstations enable the use of modelling software to direct synthetic strategies [69]. Since the 1950s, when computers became available, enormous effort has gone into in calculating realistic molecular models. The common basis of these efforts is the fact that the Schrodinger equation describing the potential energy of a particle [70] can only be solved for a very limited number of atoms. Efforts have concentrated on investigating close approximations to the Schrodinger equation [71], describing the system of interest by simplified solutions. The common basis of the various approximation strategies consisted in dividing the Schrodinger equation into an equation describing the motion of electrons and another describing the motion of the nuclei, through the Bom-oppenheimer separation [67, 701. The Hamiltonian energy operator H(t), expresses the total kinetic energy of the nuclei and its total potential energy; the sum of both the nuclear potential energy and the electronic energy is known as the potential energy surface. On this basis, molecular mechanics or force field programs, as well as molecular dynamics software have been developed. The design of the well-known ligands described in this volume, (see section 2.2.3) was primarily based on arbitrary developments of open-chain ligands [72]. Early theoretical studies estimating free interaction energies between ions and ligands “by hand”, were based on equations similar to those listed in Table 2-4 [15, 701. The shape or spatial structure of a molecule was predicted by rules based on ligand field theory and Lewis structures [52, 731. These rules focus on the total number of single-bond electron pairs and lone electron pairs at a central atom and attribute directional character to these electron pairs. Multiple bonds are not considered. Lone pair orbitals play a key role in fixing the geometry of bonding and the shape of a molecule or a complex. Lone pair-bond pair repulsion induces distortion of bond angles and


47

bond lengths. Calculations were generally used more to explain analytical data, and to evaluate algorithms for model calculations rather than to predict them. In a next period, ab initio calculations of pair potentials were used to explain ion-ligand interactions [74,75]. Interactionenergies for a large set of complexes between alkaline, alkaline earth, and ammonium ions, and uncharged ligands were obtained by computation using ub initio SCF (self-consistentfield) molecular orbital methods [68,76]. The reliability of the calculations and their results was shown to depend heavily on the choice of basis set (e.g., STO-3G slatertype orbitals, fully optimized or experimental data sets). For ion-ligand complexes, small basis sets were shown to be generally sufficient, whereas larger basis sets are necessary for the calculations of weak interactions.Systematic evaluations of the influence of coordinating N and 0 donor groups complexing calcium in competition with magnesium ions, were based on large-scale computations by SCF-LCAO-MOtechniques [76]. Based on these experiences, strategies for searching the optimally relaxed conformation representing the global energy minimum may be developed. Several levels of approximation have been employed to approach a final solution involving the following goals: 1. To find an acceptable basic conformation. By forcefield calculations in molecular mechanics (MM) the total potential energy of a chemical structure is approximated by neglecting motions

of the nuclei. In computer modelling of molecular geometries, empirical functions combining the Lennard-Jones equation with equations describing an additive contribution by electrostatic interactions are used. The system is equilibrated in several stages to energy minimization. 2. To refme the model, the motion of atoms governed by Newtonian mechanics may be used in classical molecular dynamics methods (MD). The outcome and reliability of the results is entirely governed by the quality of the energy-minimized coordinates of the force field calculation applied previously. In the best case, the results can be quantitative. Frequently, the solution represents a local energy minimum only. Ab initio or semiempirical quantum mechanical techniques are computationallydemanding, but may provide a more accurate basis.

3. Starting from a reliable geometrical model, dynamic calculations using temperature programes (e.g., Maxwellian distribution at 300 K [77] or Simulated annealing, Sybyl3.1 [69]) allow one to approximate the structure which represents a more general global energy minimum. This is especially important for molecules composed of more than 100 atoms where the structure is complex and the probability of arriving at a structure representing a local potential energy minimum is extremely high. Geometrical models give no access to the behavior of a compound in a realistic environment. They generally refer to vacuu1?1 as the environment. However, assuming an organic medium of low permittivity as the solvent, these models can be closer to reality than models which introduce a number of independent water molecules. The preformation of a ligand characterized by polar coordinating groups in an organic apolar medium offers a favorable conformation. Therefore, the unfavorable positive contribution of the conformational energy to the free energy of interaction can frequently be overestimated for open-chain ligands. As compared to crown ether compounds, cyclodextrins, and calixarenes, the open-chain ligand shows bending and

48


rotational degrees of freedom. Investigations of torsional angles in diamide compounds have been made in view of synthetic work on magnesium-selective ligands. By contrast, in simulations of peptide conformations, explicit inclusion of water molecules in the simulation is essential. The simulation in solvent water yields structures which are much closer to the crystal structure than structures derived from in vacuo simulations [77]. Historically, the arbitrary ligand design was successful for low molecular mass ligands, and modelling software was tested by comparing the results with the experimental analytical parameters. In the design of peptide ligands, the situation is more complex; a purely arbitrary model is effectively excluded. Here, the basic software relies on the structural database derived from X-ray analysis of single crystals (Cambridge Structural Database (CSD) containing > 105 crystal structures of organic and metalloorganic compounds). The initial structure for simulations is taken from these X-ray data. The complex of adenylate kinase with its inhibitor ApsA (bis-(adenosine-5')-pentaphosphate), and one water molecule located close to the Ap5 A active site contained 2100 atoms [33]. In pharmaceutical chemistry, small drug molecules are looked for fitting the active site of enzymes. In contrast, the inspection of the active site of an enzyme may confirm sturctures for recognition of small analyte molecules to be synthesized .In a project aimed at the development of new host compounds for oxoanions, the interacting groups L-arginine, L-serine and Lhistidine of the active site of the enzyme purine nucleoside phosphorylase (PNP, EC 2.4.2.1) are considered as being the synthon of a synthetic peptide [77]. The modelling procedure aims at comparing different constitutions of ligands involving the same amino acids as active sites. Relative interaction enthalpies between HzP04, and the host molecule are modelled by computational methods using the software Sybyl (version 6.2 (1995) and 6.3 (1996), Tripos Inc., St Louis) and Amber (version 4.1 (1995), University of California, San Francisco). The force-field calculations involve energy minimization of the ligand-ion complex followed by molecular-dynamicscalculations (simulated annealing) where the position of the monovalent or divalent phosphate ion is fixed. In the Amber force-field program, point charges for individual atoms are derived from ab initio calculations of the electrostatic potential for small fragments such as single amino acid residues and can be retrieved from a database. Formal charges are assigned to phosphate and those amino acids which are expected to exist in an ionic state under physiological conditions. The modelling of electronic spectra is another task where the use of computational software is attractive (see chapter 6).

2.2.3 Molecular Recognition of Ions Electrically neutral compounds which are composed of polar coordinating sites, nonpolar alkyl chains, and cyclic moieties, where the final compound has a rather small relative molar mass (Mrc loo0 g mol-I), are known to behave as ion-complexing agents. Owing to the relatively high potential energy of dipole-ion interactions in a hydrophobic medium or membrane phase, they are capable of extracting ions from an aqueous solution and act as ionophores or ion carriers, transferring the ion complexes through such barriers by carrier translocation [78] (see also section 2.5). The principle was shown to be capable of accumulating ions by "uphill


49

transport" [79, 801. The compounds have also been utilized for transfer catalysis in organic chemistry [Sl]. Polar groups of a ligand (electric dipoles such as amide, ether, and ester groups) are able to complex the primary ion as well as interfering ions with a characteristic stoichiometry by a cavity-type site preformed in the lipophilic environment of an organic aprotic phase. There is evidence that this cavity is preformed by polar intramolecular interactionsbetween the polar sites of the ligand and by hydrophobic interactions of the ligand bulk with the membrane's apolar medium. This hypothetical model is supported by X-ray analysis of, e.g., ion-macrotetrolide complexes (see section 2.2.4) and computed models of magnesium-ligand complexes. An apolar bulky shell surrounds the coordination sphere, comparable to the hydrophobic pocket hiding the active site of an enzyme (see section 2.2.7). In contrast, ion carriers destined for complexation in the aqueous environment have to be synthetically preformed [39] (see Figure 2-4; compare inclusion complexes [82, 831, and crown compounds [841). Types of charged complexing agents (classical chelating agents) are hardly dissociated in an apolar phase, owing to the increasing electrostatic interaction potential with decreasing permittivity of the medium, or dissociation has to be imposed by adding bulky lipophilic ionic sites (see section 4.4.1). Charged ligands, such as sulfonates, are poorly soluble and, in some cases, less attractive, owing to critical kinetics. The lack of lipophilicity and bulkiness can be overcome synthetically.Two examples were presented in an optical assay for Zn2+ by Wang et al., and in potentiometry by Schaller [85,86].

Table 2-5. Thermodynamic complex formation constants Kass (kg mol-l) of macrotetrolidecation complexes in methanol or ethanol at 303 K [14,88-901. The anion is thiocyanate CNS-

Formation constants Na+

Kass l[kg mol-*] K+

Versus different ions KK+I Ktqa+

Nonactin [88,89] MeOH, VPO EtOH, VPO microcalorimetry

(2.1 *0.2) x 102 (1.8 0.2) x 103 (1.9 f0.03) x 103

(3.9 f 1.7) x 103 (4.1 f 0.8) x 104 (1.8 f 0.23) x 1 6

18.5 22.7 94.7

Monactin [88,89] MeOH, VPO EtOH, VPO

(3.3 f0.7) x 1@ (3.0f0.5) x lo3

(1.1 k0.6) x 104 (2.9 f0.7) x 104

33 9.7

0

5.2 x I@

5200

(1.2 f 1.7) x lo1

> 8 x lo3

667

Ligand

Valinomycin EtOH [9l] MeOW298K (I-) [90] potentiometry

50


Investigations of stability constants in solutions and within membranes continue, and will be discussed in sections 3.1 and 4.3. Requiring reversibility of the ion-ligand interaction, relatively weak interactions with a sufficiently high exchange rate are preferred, which corresponds to thermodynamically less stable and kinetically labile complexes. For alkaline and alkaline earth metals, exept magnesium ions, the replacement of the hydration shell by a ligand belongs to the reactions with the highest rate constants in the range of ca. 108 s-1, related to the coordination number and geometry [87]. The thermodynamic complex formation constants K , (kg mol-') for the interaction of, e.g., macrotetrolideantibiotics with Na+ and K+ have been determined by vapor pressure osmometry (VPO) at 303 K in ethanol and methanol [88, 891. They are in the range of 102-105 equivalent to -1 1 to -30 kJ mol-1 (see Table 2-5) (-AGO = 2.5 x In lo5 (K = ecAGe/Rq,see section 3.3). Thermodynamic data are given in [90]. Considerable discrepancies between stability constants for apparently identical systems have been reported, owing to the application of different experimental conditions (solvents as well as procedures [91]). Equilibrium constants differ by orders of magnitudes from 10' up to 1059 L mol-l. The last is the highest association constant ever found for a complex. It belongs to a synthetic siderand (comparable to the ferric-siderglobin complex with Kass= 1059 L mol-l) and is stable even at pH 3. The macrobicyclic tris(catecho1) (2) mimics the siderophore enterobactin (1) which is produced by microorganisms in order to collect trace amounts of Fe3+, but exhibits only an 'association constant of Kass= los2 L mo1-I (see Figure 2-4). SideropZex is an octahedral complex between the six catechol oxygen atoms of the siderand and transition metals [92]. These complexes are not reversible under normal operating conditions and exhibit an extremely low dissociation constant.

Modelsfor Complexation Considering an analyte in aqueous sample solutions, the stability of the ligand-ion complex has to provide part of the activation energy for dehydration of the ion in the membrane boundary (see section 3.1).

Hypothetical reaction mechanism: 1. Displacement of the hydration shell 2. Solvation and complexation

The rate and mechanism of substitution have been investigated by Eigen [99]. He postulated ~ which is a a push-pull dissociation mechanism, formally classified as an S N mechanism, nucleophilic first-order reaction where the hydrate shell is replaced by the coordinating sphere of the ligand. He claimed that the rate of substitution is slower the higher the charge and the smaller the ion. Therefore, the substitution rates of Mg2+- aquocomplexes are slower by 3-4 orders of magnitude than those of Ca2+ aquo complexes. This correlation is indicative of an SN1-type mechanism. In this case, the energy of the metal ion-solvent band triggers the whole substitutionprocess. Deviations from this rule, known as the Jahn-Teller effect, occur for non-


51

Figure 2-4. Preorganized donor geometry of enterobactin (1) and a synthetic siderophore analog, a cagelike Sideroplex (2) or macrobicyclic tris(catech0l) [92]

symmetric arrangements of the ligands, and correspond to the asymmetry of the complexes in d9 and d4 metal ions [loo]. Assuming a stepwisereplacement of water molecules, the energy of hydration is directly associated with the coordination number. The ligand is, for complexation of the ion, competing with the hydrating and solvent sphere. The transfer of an ion was described by the total free energy of transfer, A%, associated with the transfer of the ion from an aqueous solution into the cavity enclosed by the multidentate ligand, A G , - A G i , with AG; free energy of hydration of an ion, AG;, free energy for the transfer of an ion from a hypothetical gas phase into the cavity of the multidentate ligand [98]. The ligand-ion complex prefers a coordination number corresponding to the minimum of the free energy of hydration, which is a function of radius and charge for alkaline and alkaline earth metal ions. Energies of interaction of different alkaline and alkaline earth metal ions to hypothetically active groups of a ligand have been calculated by estimating the ion-dipole and ion-induced dipole interactions as well as contributions due to repulsion [15,7 11. The results show the increased energy of hydration for ions with a charge number of 2, and a correlation to a decreasing radius of the ions. The estimated energy of interaction of IA and IIA group ions with one water molecule are in the range of 56-314 kJ mol-l active as repulsive forces [15]. Comparison with Table 2-4 shows that the solvent of the sensing layer, as well as the whole membrane medium, must contribute considerably to the extraction of the ion (e.g., for the magnesium ion see section 5.2). In [ 151 increments of the interaction energies were given which result from changes in the dipole moment, the polarizability, and the radius of the ligand site. The data indicate that an increase of the dipole moment and polarizability of the complexing groups, as well as a decrease

52


of the radius of the cavity, increase the stability of hypothetical complexes. This effect is especially large for small and multiply charged cations and is even, amplified for anions. Hence the complexation of anions affords strong Lewis acids, such as covalently attached metal ions (tin(1V)-, mercury(I1)-, cobalt(I1)-containing ligands). Selective complexation has only been realized for chloride [93,94] and nitrite ions [95,96]. The variation of the coordination number with ionic radius has been considered for the discussion of ion packing in crystals and ionic hydration [97]. The most frequent coordination spheres of 4 (tetrahedral), 6 (octahedral), and 8 (cubic, bipyramidal) oxygen atoms correspond to radii of the ligand cavity of about 30,60, and 106 pm [15]. The natural spatial arrangement of the electron pairs in the valence shell of a central atom minimizes the electrostatic repulsions between electron pairs, and induces a natural shape of a complex between the ion and the coordinating atom groups of the ligand (see appendix 5). The shape depends on the number of single electrons and electron pairs in the valence shell. The small radius of the magnesium ion Mg2+ (57 pm) allows for a tetrahedral coordination (4 coordination sites) and an octahedral coordination (6 coordination sites) due to a radius of 72 pm. In contrast, the calcium ion Ca2+ with a ion radius of 112 pm allows for 8 coordination sites (cubic, bipyramidal). In order to prefer magnesium over calcium ions, the coordination number is decisive (see chapters 4 and 5). 2+ The radii for Be*+ is 27 pm for B q and 45 pm for B e y , whereas the lithium ion Li+ may fit exactly in the cavities of the sites which fit the magnesium ion. In this case the charge number of the ion is the discriminating factor. The radius of the cations discussed here decreases with increasing charge number. The aluminium ion, which is in the same period as the magnesium 3+ ion, has the states Aly with radius 39 pm and 54 pm for A16 . These ions are especially crucial for molecular recognition inasmuch as a high free enthalpy of hydration increases the energetic activation barrier for complexation, and complexes are more inert. Based on the concepts described in this section, a large number of ionophores for the biologically relevant alkaline earth and allcali metal ions have been designed, synthesized, and introduced in electrode and optode membranes (see Figure 2-5). In optode membranes (see chapter 6), the stability of the ion-ligand complex also has to match the p K , value of an indicator which acts a chemical first transducer. For tailoring a ligand, a good compromise of a moderately stable and labile ligand-ion complex has to be found. This can be influenced by the surrounding medium and by the shape and geometry of the ligand and the active site, depending on the physicochemical features of a host compound.

The Medium of a Sensing Layer, the Membrane Medium The solvent of a sensing layer and the polymer are not indifferent to the active components. Both can participate in the interactions and compete with the host and/or guest compound in a constructive or destructive way. In a membrane phase, the interaction free energy is influenced by the polarity of the membrane bulk and is tailored to achieve optimal properties of the sensor, such as selectivity, reversibility and, in an other context, lipophilicity. However, these interactions are only poorly understood. These aspects will be discussed later with special reference to magnesium-selectivesensors (see chapter 4)(chemical names see references).

H+

53

H+

m 1907

log= = 20.0

Li+ 2137 ETH

ti+ 14C4 dinbutam

Figure 2-5. Neutral ion carriers that are most frequently and most efficiently applied in ionselective sensors [loll (see also [102-1041, for chemical names see end of this chapter)

v o

GI*+

m 1001

log~=7.5

ca2+

ETH 5234 log, ca 20

55

56


2.2.4 Hydrogen Bonds The hydrogen bond is predominantly an electrostaticinteraction, where the hydrogen atom is not shared between two electronegative centers but remains covalently attached to its parent atom [S]. It results from the interaction of an hydrogen atom covalently linked to an electronegative atom, the donor, with the unshared electron pair of a second electronegativeatom or dipole, the acceptor. The free energy of a hydrogen bond is 4-40 kJ mol-' [52]. Hydrogen bridges are directional and, therefore, biologically very important since they promote three-dimensional structures in interactions, transport systems, etc. If higher interaction energies are involved, the metabolic steady-state and exchange of matter can be blocked. If processes with lower interaction energies are involved as the main driving forces, catabolic processes can be entropically favored under the same conditions. The Swiss scientist FreyWyssling [1051 proposed a model explaining the association between two peptide chains by covalent disulfide bonding, hydrogen bridging, ionic, and hydrophobic interactions. Pauling investigated hydrogen bonding, culminating in the presentation of the a-helix structure in 1954 [106]. The conformation of peptides is conserved by hydrogen bonds. They participate in the preformation of the ligand, e.g., of the natural antibiotics valinomycin and nigericin [8, 91, 1071111, Valinomycin is a depsipepetide, a cylic peptide consisting of a threefold repetition of L valine, D-hydroxyvaleric acid, D-valine, and L-lactic acid. Thus the molecule posesses alternating peptide and ester bonds. The ester group is predominantly planar and has no chance to promote hydrogen bonds as a donor. The torsion angle around the C-0 bond is more restricted restricted with peptide bonds. This results in relatively poor conformational freedom. The most relevant hydrogen bonds are the 1-4 and 1-5 types and are responsible for the typical shape of the ionophore. The conformation of the free ionophore depends strongly on the polarity of the solvent. Six intramolecular 1-4 type hydrogen bonds are typical for apolar solvents, whereas in solvents of medium polarity a conformation involving three hydrogen 1-4 bonds has been proposed [ 1 12, 1131. For valinomycin, X-ray studies have shown that the potassium complex is an octahedron. The polar groups are arranged around the metal ion in the centre of the molecule, whereas the nonpolar residues face the apolar medium. The six keto-oxygens participate in the complex formation, whereas the others provide the intramolecularshape of the cavity by hydrogen bonds to the amine groups of the peptide bonding (see Figure 2-6). By forming six hydrogen bonds, the conformation is changed in discrete steps. The rate constant for the K+-complex formation was determined to be 7 x 106 mol L-' s-l. The rate of complex formation for Na+-monactin is reported to be 50 times slower [108]. The conformation of the valinomycin-K+-complex,from experience with sensing devices, obviously approaches a state of minimum potential energy compared with complexes to various other ions. However, the macrotetrolides generally show negative values for the free energy of the ion transfer reaction. It was suggested that a considerable entropy increment is involved, due to the participation of solvent molecules in the transfer and complexation process. The high activation barrier must be approached by a step by step stabilization of the complexes which, finally, prevents phase transfer of the peptide to the aqueous medium.


51

The contribution of water moieties in electrostatic interactions with peptides and proteins was shown to be relevant by Kern et al. [ 1141 in molecular dynamics simulations of the interaction of the inhibitor Ap5A with adenylate kinase (AK,,). Explicit inclusion of water molecules in the model of the active site, and, most importantly, attachment of water molecules to the yphosphate group of ATP was essential to obtain an accurate model. Prelog investigated the optical activity of macrotetrolides [lo, 1151. He pointed out the remarkable fact that nonactin is optically inactive although the compound has four centers of asymmetry. It was confirmed later by X-ray analysis that the compound was found in the mesoconfiguration [1071. The conformation of valinomycin analogously shows LLDDLLDDLLDD chirality with 12 centers of asymmetry. Besides the stabilization of peptides, hydrogen bonds can be important tools in many models for molecular recognition of amines, amides, carboxylates, alcohols, glycols, and others. The number of hydrogen bonds allows an increase of the free interaction energy. For the creatinine ligand developed in our laboratory, a stability constant of lo3 was estimated. This value results in a free energy of complexation related to < 3 hydrogen bonds of AG = -RT log lo3, which is 7.44 kJ/mol. The energy of interaction involved in a single H-bridge is thus 2.48 kJ/mol. The creatinine sensor described above has a weak extraction behavior in optode membranes (sample concentration 100-1 000 mmol/L creatinine) [ 1161. Multitopic recognition could considerably enhance the association with a ligand.

K

F

Figure 2-6. Conformation of the K+complex of valinomycin (reproduced from [108, 1091); sequence of D-a-hydroxyisovalerianate, D-valine, L-lactate, and L-valine showing the monomeric constitution of the valinomycin molecule (see Figure 1-3); a) historical CPK model of the cyclododecadepsipeptide.The polar groups point toward the centre, thus building a quasicubic structure which is twisted around the cation. The nonpolar groups are situated on the periphery and prepared for ion transport in hydrophobic media; b) schematic representation of the spatial twisted conformation (reproduced from [1081)

58


2.2.5 Molecular Recognition of Enantiomers The characteristic three-dimensional structure of the binding site of an enzyme or receptor requires a perfect structural fit of substrates which are attacked by the host compound. Therefore different conformers, diastereomers, and enantiomers of biologically active molecules generally show different activity, bioavailabilty, biodegradation, and toxicity. This is generally true for biotic chiral as well as prochiral compounds, such as mediators, metabolites, substrates, coenzymes, and drugs which are characterized by sterically nonequivalent groups. This is the reason why the structural differentiation of two isomers in analytical chemistry has an enormous impact, apart from enantioselectivepreparation and synthesis of compounds. Chemical sensors have been shown to allow reagent-free structural specifications, e.g., of enantiomers. An example of a potentiometric and optical approach will be shown in the following discussion. In 1964, the cycloenantiomerismand cyclodiastereomerism of macrocycles used as ligands for the complexation of cations was recognized and discussed by Prelog [94]. The first "Pedersen Papers'' appeared in 1967 and showed the feasibility of synthesizing large cyclic polyethers (a type of crown compound) composed of cyclic ethyleneoxy units [95]. The principles of molecular recognition of chiral compounds were developed by Prelog, Lehn, Cram and others [96]. Cram demonstrated that hydrophobic interactions participate in the molecular recognition of enantiomers [97]. The simple crown compounds were found to complex ammonium and alkylammonium ions. A close examination of space-filling CPK (Corey, Pauling, Koltun) molecular models of an alkylammoniumion complexed to a 18C6-cyclic ether suggested three hydrogen bonds and three oxygen-nitrogen pairs (Figure 2-6).The ethylene units form a disk around the hydrogens of hydrophilic ammonium ions. For molecular recognition of enantiomers, the cyclic polyoxyethylene was symmetrically and asymmetrically coupled to a binaphtalyl unit. In this case, the ligand has a chirality plane and the binaphtalyl rings form a wall that extends along the sides of, and outward from, both sides of the cyclic ether. Additional hydrophobic binding sites and a stronger preformation were provided. Aryldiazonium tetrafluoroborate salts were dissolved in chloroform by 1:1 complexation to the cyclic ether. When the cavity size of the cyclic ether was decreased, complexation was not observed, Experiments were made with the two enantiomers of the a-phenylethyl- and aphenylmethyl amine salt (PEA and PMA) and the chiral cyclic ethers. The (R)-PEA rather than the @)-PEA was preferably extracted into chloroform by the (U)-ether. The excess activity of the (R)-enantiomerrelative to the (L)-enantiomer, aee(R), extracted into the organic phase, defined by:

was 67% (R)-PEA compared with 33% (L)-PEA, where % is equivalent to the activity of (R)PEA and a1 to the activity of (L)-PEA. Defined gy percentage weight, the enantiomeric excess is: % e e ( q )=- aIR R

ag+

aIs

loo%=

100% + ee

(2-5)


59

The enantiomeric excess can be explained, as expected, on the basis of the spatial orientation of the phenyl group of the analyte ion against the aromatic side-walls and the interactions of the n-systems. The experiments were repeated by implanting the ligands into ion-selective membranes of potentiometric sensors [98]. The ligand was modified by alkyl side-chains in place of the aromatic dinaphthyl groups. The chiral ionophores were denoted as (+)-0OA-l8C6 and (-)-0OA-l8C6 ((+)-(2R, 3 R, 11R, 12R)-N,N,Nf,N~Nff,Nf~N”:N”’-octaoctyl1,4,7,10,13,16-hexaoxacyclooctadecane-2,3,11,12-tetracarboxamide) and its (-)-L-enantiomer (see Figure 2-7). In 1976, Simon published the first results from studies of the development of a potentiometric sensor for 1-phenylethyl ammonium ions (PEA) based on enantioselective, electrically neutral carriers. The ligand was dissolved in a PVC bulk membrane containing 0nitrophenyloctyl ether as a plasticizer and sodium tetraphenylborate as a charge transfer catalyst. In potentiometric and ion-transport experiments, the measured selectivity of one enantiomer over the other was 8%. If the compositions of two electrode membranes differ only in the chiral form of the ionophore incorporated, the difference in the electrode potentials is a linear function of the logarithm of the enantiomeric excess of the target analyte ions in the aqueous phase. Within the membrane, the hydrophobic interactions between the phenol moiety of the plasticizer and the alkyl chains of the ligand may be weak, or the fact that the membrane medium contains water may make it a less efficient extractant than pure chloroform. Varying the solvent of the sensing layer can improve the extraction of the organic analytes and result in a more pronounced selectivity. Chiral molecules are optically active in the sense that they rotate the plane of linearly polarized light. Hence optical sensors could be attractive tools for investigating enantiomers. In 1989, an account of the basic principles of ion exchange optodes was published [99]. It led to the design and trial of a large variety of optodes for charged and neutral analytes. Cation-selective bulk membranes act as competitive ion-exchange systems, incorporating a H+-selective and an electrically neutral cation-selective ligand. By incorporating a c h i d ligand, the optically active analyte may be detected without making use of polarized light. By employing pH-sensitive dyes, the ion-complexation can be detected by a change in their absorption spectrum. Optode bulk membranes for measuring the enantiomeric excess of (+)-R-PEA and (-)&PEA have been described [96]. Enantiomer recognition was again based on the preparation of two different membranes with the chiral ionophores (+)-0OA-l8C6 and (-)-0OA-l8C6 (see Figure 2-7). The highly lipophilic H+-selective carrier, ETH 5294 (7-(diaethylamino)-3-(octadecanoylimino)-1,2-benzophenoxazine),was incorporated as a chromoionophore(Figure 2-8). The individual refractive indices or absorbance of enantiomers and the individual dispersion spectra are currently observed by circular dichroism spectroscopy (CD) or ellipsometry, both expensive and bulky instruments. Optically active ligands incorporated into sensing layers are alternative tools to quantify the excess of one enantiomerover others. Cast on the sensor pad of an integrated optical sensor, an enantioselective internal reflection element can be constructed (MIRE)[123] (see sections 6.4 and 6.5). Therefore integrated optical sensors could become useful micro-sized tools for direct quantificationof enantiomers and enantiomeric excess. On the other hand, by using MIRES where the waveguide is made from anisotropic material, miniaturized polarization detectors with enhanced sensitivity and detection limit could be con-

60


Figure 2-7. Chiral neutral carriers (+)-0OA-l8C6 and (-)-0OA-l8C6

structed. An approach with anisotropic waveguides would allow the measurement of rotation of the polarization plane of light and the construction of the first effective polarization detector for analytical instruments.

2.2.6 Molecular Interactions within the Aqueous Medium The Complexation of Nucleic Acids In view of the much stronger potential energy of ionic interactions in a medium of low permittivity, as discussed in section 2.2.2, molecular interactions in the aqueous environment must meet relatively stringent conditions. In water, single base pairing between nucleic acids is normally not observed since water is always the stronger dipole and thus interferes with polar groups. Therefore, in the intracellular space of the cytoplasm and of organelles, water molecules are less available. A water-deprived environment is available, e.g., within reversed micelles incorporated into sensing membranes containing the enzyme [124]. On the other hand, the weak van der Waals forces do not depend on the permittivity, but will dominate in an environment of high ionic strength and poor water availability (see sections 3.4 and 4.6). In an aqueous environment, the entropy contribution of small molecules, including even a relatively large aromatic n-sytem combined with strongly polar sites, is too small to provide association [1251.


61

IONOPHORE ETH 5294

1

NaTm(CF&PE 00s PVC

z

0 ta z

2 0

0- -(I?)-PEP

lx

e

8 0.5 w w

LT

(3

W

n

a

--(

S)-PEt

-'L -2

Figure 2-8. Response function of two optical enantioselectivesensing membranes based on the chiral ionophores, (+)-0OA-l8C6 and (-)-0OA-l8C6, against a solution with a molar 1:l-ratio of (R)- and (L)-phenylethylammonium ions at pH 7.0. The shift of the two response curves signifies the selectivity of the (+)-0OA-18C6-containing membrane, a, for @)-PEA or, in other words, the enantiomeric excess of @)-PEA over (L)-PEA extracted by membrane a

Therefore the key to host-guest interactions in the biotic medium are large interacting areas based on weak forces as realized in antigen-untibody complexes, or generating a water-poor environment by burying the active binding site in the protein bulk as realized in enzymes. Nevertheless, the association between the aromatic imide of a hydrophilic analogue of Kemp's triacid with aromatic amines in the aqueous phase has been demonstrated. Rebek [1251271 has repeatedly pointed out that the aromatic imides of Kemp's triacid may show catalytic functions in acyl transfer similar to those of an enzyme, which are beneath the selective recognition capabilities of templates such as nucleic acids, chiral amines, and amino acids. In some experiments, the cavity of the active site of the host molecule providing the hydrogen bonds was tailored by introducing aromatic surfaces of different sizes. For benzyl derivatives, the distance between opposing carboxyl oxygens was estimated to be 300 pm, whereas for anthracene and anthraquinonederivatives the distance between opposing carboxyl oxygens was about 850 pm. Rebek et al. found that the association constant of 9-ethyl adenine increases with increasing size of the aromatic substituent by so-called aromatic stacking even in an aqueous medium. The yield in free energy (AG)has risen to -6 kJ mol-l. The authors noticed a relationship between the hydrophobic surface area and the association constant in aqueous

62


Figure 2-9. Molecular chelation of an adenine derivative by a host based on a 2,7-naphtyldiamide substituted Kemp's triacid [125-1271

solutions. One of Rebek's conclusions was that the series of triacids can only provide a threepoint size system, with no continuous tuning of the size and distances. He wondered "if enzyme structure is, in part, nature's response to this problem". By using aliphatic substituents and aliphatic fine tuning, the advantage of the low, free confonnational energy in a rigid structure had to be sacrified. Further open questions remain, e.g., how bulky does an enzyme need to be? Short chains are not large enough to have sufficient intramolecular attachments to lock themselves into a single stable conformation. Rather, "they tend to flop from one form to another" [128]. A polypeptide chain with 30-40 residues was reported to begin to have enough internal cohesive forces to produce a dominant shape. Additional stabilization by metal ions or disulfide bridges between pairs of cysteines may be needed. An example of a natural polymeric receptor which may be cut to five units, based on polyglycane, is given in the next section.

The AT-111 Inhibitor Heparin The anticoagulant drug, heparin, is composed of sulfated glycosaminoglycanes and has a molecular mass Mrca. 16 OOO mol-l. Heparin inhibits blood coagulation by association with antithrombin III (AT-III). This complex exhibits an accelerated inhibition of blood clotting in vivo and in vim. However, it has been shown that, for a fully active heparin, a pentasaccharide is sufficient. A very potent synthetic analog of the naturally occurring fragment, containing an additional 3-0-sulfate group at the glucosamineunit 6, has been dereloped (see Figure 2-10). The pentasaccharidedomain is sufficientto activate the protease inhibitor, antithrombin III (ATIII). The activity of the pentasaccharide with an additional sulphate group is enhanced about 1.8 times more than with natural pentasaccharide, and has accelerated kinetics compared with total heparin. Synthetic pentasaccharides with a 3-0-sulfate at the glucosamine also display an anticoagulation factor Xa activity which lasts 4-5 times longer than that of the natural pentasaccharide [1291. The 6- 0-sulfate groups at units 2 and 6, the 3- 0-sulfate, and the N-sulfate group at the glucosamine of unit 4 are essential for the activiation of AT-III. The 2- 0-sulfate at iduronic acid unit 5, the 6-O-sulfate, and the N-sulfate groups at unit 6 increase the AT-III-

63


2

4

3

NHS03-X

5

OH

6

NHSO3-

Figure 2-10.Synthetic heparin, Org. 31550: 0-2-deoxy-2-(sulfoamino)-6-0-sulfo-a-D-gluc~ pyranosyl-( 1-4)-PD -glucopyranuronosyl-(1 -4)-0-2-deoxy-2-(sulfamino)-3,6-di-0-sulfo- a-Dglucopyranosyl-(1-4)-2-0-sulfo-a-L-idopyranuronosyl-( 1-4)-1 -0-methyl-2-deoxy-2-(sulfoamino)-3,6-di-0-sulfo-a-D-glucopyranoside, undecasodium salt (M,= 1830.13 g mol-1, C31H3042N52S9Nall 1301)

mediated activity, whereas the N-sulfate at unit 2 and 6- 0-sulfate at unit 4 are not essential. Replacing the sulfate with a phosphate results in a complete loss of activity. In this case, the bulkiness of the heparin decreases and controls the activity. The interactions seem to be affected by the acidity and the charge number of the monovalent anionic sites of the sulfate. The increased hydration energy of phosphate has a negative influence on the association and may dominate the positive influence of increased charge. &sed on this, the AT-111 binding sites were mapped around a molecular model of the naturally occurring heparin pentasaccharide.

2.2.7 Catalysis by Enzymes, Enzymes Mimics and Host-Reactands Enzymes are of tremendous interest in the development of chemical sensors, owing to their inherent, naturally targeted substpte specificity. Nonetheless, the specificity of enzymes, and the selectivity of artificial recognition compounds are differentiated. Characteristically for the enzymatic recognition process, an enzyme catalyzes a metabolic steady-state process and, therefore, no longer induces a simple complexation but a chemical reaction involving product generation. The enzyme specifically catalyzes a metabolically unique, and significant reaction. Hence, the "ligand" is more likely denoted "host-reactand". Therefore, the product of the metabolic turnover is, with some exceptions, unique (see sections 1.1 and 2.2.5). However, since only two classes of enzymes, the oxidases and the dehydrogenases are applied to sensing devices, the specific substrate attached is indeed unique but the products monitored are common to the whole class of sensors such as H2@ or NADH/NAD+. The reaction takes place within the confines of the enzyme-substrate complex. An enzymatic reaction is characterized by the following steady-state between the substrate S and the enzyme E, providing the enzymesubstrate complex SE,with the transition state and the product P: S+E

@ ES

2

=*,

ES*

E+P

(2-6)

The active site of an enzyme is buried in the bulk in some cases, but in some cases is more freely accessible by a substrate and not bound to an active transport. Subsequently, some error

64


rate in the enzymatic recognition process is evident by checking the substrate specificity against textbook values. Nevertheless, interfering substrates in most cases do not respond by producing an identical product or signal. On the basis of this behavior the term specijkity was coined. In analytical use, the substrate is identical with the target analyte, and the enzyme is isolated both from the natural environment and the natural metabolic process. In this context, enzymes can still act efficiently as specific catalysts for many chemical reactions by lowering the energy of the transition state of the comparable chemical reaction. However, characterizing the final biosensor, the response not only depends on the enzymatic specificity, but also on the construction of the biosensor and its operational environment. In this context, a quantitative description of the selectivity of biosensors in close analogy to chemical sensors, incorporating artificial hosts, has been made [131]. The difference between the specificity of an enzyme and the selectivity of an artificial analytical recognition process is not strict. A differentiation between "specifity" and "selectivity" was also made by Massart [132].

2.2.7.1 Nucleophilic and Electrophilic Catalysis, Interactions between Electron Donor

and Electron Acceptor Groups The structure-reactivity relationship associated with the conformation of the protein bulk of the enzyme and the conformation of the active site are part of the information needed to understand enzyme reactivity. In order to understand the process of enzymatic catalysis, many factors play a role: the chemical reaction involved, the structure of the transition state, the intermediates and products, the kinetics of the reaction steps, and the activation process involved in lowering the activation barrier. One of the most important factors in lowering the activation bamer of the transition state is the loss of entropy due to the loss of internal transition and rotation energy upon interaction between the enzyme and the substrate (see section 3.1) [133]. Depending on the internal gains and losses in internal rotation, the intramolecular reaction can be favored entropically by as much as -59 kl mol-1 at 298 K. Catalytic reactions often involve electrostatic interactions, typically in the range of -5.4 kJ mol-1 at 298 K in water with a dielectric constant cr of 78.54. It is increased by a factor of l/cr in apolar solvents or in the absence of water. Further widespread catalytic mechanisms are electrophilic catalysis by SchifS base formation, e.g., with an enzyme lysine residue, and nucleophiliccatalysis by a serine hydroxyl group. The pyridine ring in pyridoxal phosphate acts as a positive center, and stabilizesthe negative charge of the carboxylate group of any amino acid undergoing a Schiff base reaction. These reactions form the basis for racemizations and transaminations. Another catalytic process is metal ion catalysis. The metal ion acts as a Lewis acid. Lewis acids and Lewis bases can act as electron acceptors or electron donors at the active sites of enzymes. The principle is especially effective in the absence of water acting as a strong dipole. Carbonyl oxygens of an amide, an aldehyde, or an alcoholic group as substrates can coordinate to the Zn2+of the enzyme (see Figure 2-1 1).The coordination polarizes the heteroatom group of


NAD+

65

€10-

67

Figure 2-11.(a) Computer drawing of the relative position of NAD+ and ethanol (substrate) in the active center of the LADH (human liver ADH). The angles and bond lengths to the Zn2+ center are as reported by Spiro e l al. (1983) [135] during hydride transfer (drawing by T. Brodmeier); (b) Model of the hydrophobic substrate-binding pocket and the active site of ADH according to the data given in [1351 the substrate, stabilizes the intermediate, and prepares the transition of leaving groups or atoms

Consider the following example in which the recognition of ethanol by alcohol: NAD+oxidoreductase (EC. 1.1.1.1) bound to the prochiral cosubstrate NAD+/NADH is compared with the nucleophilic chemical addition of ethanol to trifluoroacetanilides. The comparison deals with the quantification of ethanol by an optode membrane, in the second case, and the enzymatic recognition of ethanol in the first case. The analogy between the natural biological mechanism of alcohol recognition and the synthetic process is striking [134-1361. In both cases, an electrophilic center interacts with the alcoholic hydroxy group inducing the oxidation of ethanol. For alcohol: NAD+-oxidoreductose,the electrophiliccenter is represented by a zinc ion. The zinc

66


ion is known to possess an extremely weak Lewis acidity, and thus has an extremely low anion binding capacity and drastically reduced polarizing properties. By coordination of the oxygen ligand atom of ethanol with the metal center, the nucleophilic reactivity of the oxygen ligand atom is decreased, i.e., the acidity of the zinc-bound alcohol group is drastically increased. This process facilitates the oxidation of the alcohol and the stereospecifichydride transfer to NAD+. The ethanol substrate complexed to the metal is mainly present in alcoholate form at a local pH which must be in the range < 7.4. The pKa of ethanol is thus decreased from 16 to values around 7 within the lipophilic cavity of the enzyme, thus burying the active site. The lipophilic channel excludes water from the active cavity of the enzyme. In optodes based on an amide of trifluoroacetylaniline,the carbonyl carbon is polarized by the fluorine atoms and the p-substituents of the anilinamide [ 1371. The carbonyl carbon is strongly electmphilicbecause of the electron-withdrawing properties of the trifluoroacetylgroup. Hence it is activated by base catalysis and a nucleophilic attack of OH- (see Figure 2-12). Within the hydrophobic membrane phase, the OH--groups are provided by methyltridodecyl ammonium hydroxide which interacts weakly with the anionic carbonyl oxygen. OH- is in thermodynamic equilibrium with the nucleophile ethanol and is quantitatively replaced by the alcohol, owing to the presence of the lipophilic ammonium cation. The function of the ammonium cation in this step is analogous to that of the coenzyme NAD+ in this case, which induces the hydride transfer from the alcohol to the coenzyme. The nucleophile carbonyl oxygen anion interacts with H+, so that the product is electrically neutral. Within the hydrophobic environment of a plasticized, polymeric, bulk membrane, the PKa of the alcohol's hydroxy group is significantly decreased. The same is true for water dissolved within the membrane medium (maximum 5 % for a membrane with a low dielectric constant of about 4). Hence the water is also in thermodynamic equilibrium with the ligand and ethanol. The water content and the selectivity.of the reactand for water has to be taken into account when the water concentration changes significantly, e.g., in calculatingthe activity of water. The activity of water was taken into account for calculations of

d-

'o\

,la+ F3C

+

MTDDAOH

R

R

~

D

n;

F3i fa

A 0+

/OH

HO

+HO-R'

'C

F3c/

OR'

MTDDAOH

Figure 2-12. Suggested mechanism of ethanol recognition by ETH 6022 trapped in a plasticized PVC bulk membrane. The interaction between the host-reactand and analyte is catalyzed by the lipophilic cation MTDDA+ and OH-. The pKa of ethanol within the membrane medium is considerably decreased


67

the alcohol concentrations in various beverages [138]. Alcohol activities, as measured by an optode, and calculationsfor a wide range of drinks (apart from spirits) showed that the results of the optode fitted well to the reference method (distillation and measurement of the refractive index) [1391.

23.7.2 Structure-Reactivity and Quantitative StructureSelectivity (QSSER) Relationships In the synthetic reactands shown in Figure 2-13, the electrophilicity of the carbonyl carbon atom of acetylaniline is dramatically increased by adding an electron-withdrawing trifluoromethyl group. The introduction of electron acceptors in para position to the trifluoroacetyl group also increase the electrophilicty of the carbonyl carbon atom. As a result, a nucleophilic attack on the carbonyl carbon atom leads to the selective addition of various nucleophilic guest molecules, such as COP, H20, and EtOH. The electronic effect of substituents in para-substituted positions within the trifluoroacetyl group of the trifluoroacetophenonereactands is predicted by the Hammett substituent constant 0 [140]. Originally, the Hammett substituent constant was obtained from the ionization of me&or para-substituted benzoic acid. A high negative substituent constant Q in the para position means a considerable electron donor effect and a decrease in the acidity constant and the pKa. By introducing substituents with different Hammett parameters, the selectivity of the reactands may be tailored. MTDDACI acts as an activator for the trifluoroacetate group, presumably by supplying hydroxyl ions in exchange for chloride when in thermodynamic equilibrium with the sample solution. In the artificial enzyme reaction based on trifluoroacetophenones,the lipophilic ammonium compound also plays the role of the coenzyme on the basis of a reversible thermodynamic equilibrium. In the gas phase, two compounds with more pronounced electronwithdrawing substituents, the p-(trifluoroacetyl) benzoate (ETH 6010) and the 4-(n dodecylsulfony1)-1-(trifluoroacetyl) benzene (ETH 6019) permit the design of a humidity sensor [1411. Reactands with weakly electronegative substituents, and thus a positive Hammett substitutent constant, allow the recognition of the strongly polarized carbonate anion in the aqueous phase by a potentiometric or optical sensor (see also section 6.2) [137, 1421. Enzymes with zinc ions as active sites are also capable of recognizing different substrates, such as alcohol, aldehyde, carbon dioxide, and the superoxide anion, depending on the participating amino acids in the neighborhood (Spiro et a1 ., 1983, Bertini et al., 1983 [1351). For human liver alcohol dehydrogenase (LADH), 8 different subunits combine to form dimers, which results in maximum of 2* combinations. The dehydrogenase activity of these dimers varies considerably. Different ethnic groups show very different levels of tolerance to alcohol, resulting in typical patterns for the enzyme dimer for each group [143]. In the optode reaction, the compounds with different substituents may be compared to isoenzymes with changing reactivity to ethanol and water.

68


REACTIVITY

OF THE ARTIFICIAL ENZYME

R:

t i t

HA&ETT SUBSTITUENT

SLOPE I

- 0.6

ETH 6019 ETH 6010 ETH 6004

- 0.5 - 0.4

ETH 6024

- 0.3

/c1fi25

ETH 6022 -a2 -0.1

-0.64

,

I

-a6 -0.4 -0.2

,

,

,

0

02

OX

, 10

-N

\

C-CH,

B ETH 6018 ETH 6011

0.6 0.8 'Og

KHP

Figure 2-13.Hammett substituent constant

d and sensitivity (slope) of the optode membrane reaction (y-axis) related to the logarithm of the equilibrium constant of hydration, log K H ~ (Ox axis), for different isologs of ETH 6022. The electron donor properties of the p-substituents increase from ETH 6019 to ETH 6011. The association of water gradually decreases with decreasing electronegativity of the substituents.The optimum sensitivity of the optode to ethanol is when the intermediate substituent constant is close to zero (chemical names see references)

2.2.7.3 The Metabolic Pathway and the Steady State For sensors based on these ligands the mechanism of reversibility is different from that of optical assays since, in the former, no back-coupling by products, such as aldehyde, occurs. In assays based on ALD, the lunetics of the enzymatic reaction is hindered by slow dissociation and back-diffusion of the products (compare Figure 2-12).The principle of the ADH reaction is: pH > 8.4 ethanol + NAD+

A Y

acetaldehyde + NADH + H+

(2-7)

ALD For the enzymatic reaction in eq. 2-7, the equilibrium constant is in the range of c lo-" mo12 L-2 (pH 7.15,298 K), varying with the origin of the enzyme. The rate-limiting step is the reduction of NAD+,and the exchange of NADH and NAD+, assuming the concentration of NAD+is no limitation. To move the equilibrium in favor of the aldehyde, a pH value of > 8.4 is needed and semicarbazide must be added continuously, to remove the generated aldehyde. The whole process is slowed down by the rather slow mass transfer to and from the relatively


69

inaccessible active site of the enzyme. The ADH sensors need a continuous supply of NAD+. This either has to be added externally or is coimmobilized and permanently regenerated in situ [144-1471. The latter procedure is made possible by the electrochemical oxidation of NADH [148], requiring potentials > 700 mV vs. Ag/AgCl as a reference electrode, although the standard potential of NAD+/NADH is -320 mV vs. Ag/AgCl [148]. This results in a stable steady state with a constant turnover rate within a relatively small dynamic range of operation. The reaction rate of the steady state is, in many cases, preferred as an analytical parameter to relate to the substrate activity. In ADH biosensors with optical transduction, the slow diffusion of products and reactants make such an approach inappropriate, which limits the reliability of this type of sensor. The homogeneous membrane reaction, a mass transfer by diffusion, is very quickly reversible and fully regenerated by pH changes. The speed of the reversible optode membrane reaction is mainly related to the thickness of the membrane and to the concentration of the guest molecule. In the dynamic range 0-40 vol% ethanol, equilibration between the diluted sample solution and the membrane takes c 30 s. Experiments with the vapor phase of a bioreuctor producing ethanol were consistent with previous results obtained using solutes [139,150].

2.2.7.4

Selectivity

The discrimination pattern of different alcohols by liver-ADH deviates from that of the optode membrane. Obviously, in artificial membranes, the basicity, as well as the molecular size of methanol, influence the reactivity, whereas the addition of propanol is sterically hindered. A detailed description and experimental evaluation of the discrimination of different alcohols as well as pH, carbonate, sugars, and acids as interferents is given in [138, 1391. The logarithmic selectivity coefficients are -1.1 for water, +0.2for methanol and butanol, -0.1 for 1-propanol, -1.1 for tert-butanol and -0.9 for isopropanol within the aqueous phase, different for the gas phase. The response time for alcohols with higher lipophilicity is much longer. A 0.01 mom bicarbonate solution increases the optical signal corresponding to 0.1% ethanol for a 10% (voYvol) ethanol solution. With a constant background of glucose, fructose, citric acid, lactic acid, and tartaric acid, no change in the absorbance was found to take place where the dynamic range of the optode was 1 5 1 2 % (vollvol) ethanol. In contrast, within the cavity of the enzyme, the coordination of the more lipophilic propanol and its interaction between NAD+ and the Zn2+ site results in a preference for propanol over methanol. However, the oxidation of propanol seems to be kinetically hindered and was reduced to a level of 10%of the ethanol activity in an assay by Syva, Palo Alto (E. Merck AG, Zurich). Structural differences in the ligands, the substituents in synthetic ligands, as well as the amino acid sequence of the enzyme, change the selectivity pattern considerably. Reversible as well as irreversible types of enzyme conversion are known from mammelian xanthine oxidase and xanthine dehydrogenase [1511, Such a conversion can provide the impulse for changes in the reactivity or selectivity of an enzyme. The xanthine oxidase type exhibits low xanthine: NAD reductase activity but high xanthine: 0 2 reductase activity. 02 is a cosubstrate and the enzyme produces considerable amounts of hydrogen peroxide and superoxide ions. In

70


contrast, the xanthine dehydrogenasetype (EC 1.1.1) has a binding site for NAD+ and catalyzes the oxidation of hypoxanthine to xanthine and to uric acid, although NAD+ is then reduced to NADH. Both enzymes are very similar in their structure as well as in their physical and enzymatic parameters. Dimeric proteins contain one FAD (flavine adenine dinucleotide), two iron sulfur centers, and one molybdopterin as cofactor and active sites. The oxidation reaction is catalyzed by the electron transfer to M o ~ The . V,,, of both enzymes can vary by 30-40%. This transformation may be the source of postischemic tissue injury [126].

Conclusions The optode membrane reaction for ethanol sensing shows very similar reaction characteristics to the enzyme reaction. Thus, the trifluoroacetophenonereactand might be considered to be an artificial enzyme, acting in an artificially lipophilized environment. However, the artificial ethanol reactand lkks any metabolic activity to transform a substrate to a product. This fact, as well as the possibility of tailoring the reactivity of the host-reactand, favors a variable analytical use according to the membrane environment and the conditions of the optical system. The mobility of the participating compounds within the artificial membrane and the accessibility of the active sites result in a thermodynamically controlled, speedy, reversible system. Other artificial reactions of this type are possible. In a project aimed at the development of new hosts for oxoanions [77],the active site of enzymes are considered as being the synthons of synthetic host-peptides (see section 2.2.2). The goal of this project is not to imitate nature, but to tailor ligands accounting for the specific environment of a sensing layer. An appropriate motto for developing artificial systems seem to be: "study nature carefully and then do it better". The introduction of metal ions as active sites in a lipophilic environment seems promising. Some schemes to mimic the activity of enzymes are available. The Schiff base reaction, for example, has not been used so far. The electrophilic substitution of carbonyl compounds has been used in alcohol, m i n e and carbonate recognition. Some other mechanisms have been investigated in OUT laboratory during the past few years, e.g., the Michael addition. Some useful analytes which appear promising for biological assays, such as carnitine, drugs, a-hydroxy butyrate, acetylacetate, and acetone in diabetics, have not yet been studied. It is likely, however, that further investigations and developments along these lines would prove fruitful.

2.2.8 Catalytic Antibodies In the 1980s, the use of catalytic antibodies was proposed to extend the range of catalytic processes provided by enzymes. One of the triumphs of this period was the enormous rate acceleration achieved for simple chemical reactions, such as hydrolysis of phenylacetate in solutions [153, 1541. In catalytic antibodies, the potential energies of the transition state of the catalyzed process and of the entropic contribution are lowered since the transition state is preformed and conserved in the active site of an antibody. The transition state is stabilized by its steric and electronic complementarity with the antigen-antibody combining site. The antibody


71

has been cultivated in immunized mice, and accumulated in hybridoma cells by linking the transition state analog hapten to a carrier protein, such as a keyhole limpet hemocyanin (KLH). A prototype potentiometric test for the hydrolysis of phenylacetate which releases hydrogen ions has been reported [155]. Other methods are described. The transition state analog of the nucleophilic attack on the phenylacetateby the hydroxide ion is a tetrahedral phosphonate group. Phenylphosphonate was coupled to the carrier protein I U H by l-ethyl-3-(3-(dimetylamino)propy1)carbidiimide)[ 1551. The antibody has been cultivated in BALB/c mice immunized with the IUH-phenyl phosphonate conjugate. Fusion was performed with Sp 2/0 myeloma cells. Five out of thirteen isolated antibodies showed a hydrolytic activity in phenylacetate. The catalytic activity katof one antibody, IgG 20G9, was found to be 1.05 (k 0.08) min-' and the Michaelis-Menten rate constant K, was 35 (+ 9) pmol/L. The dynamic range of the reversible reaction was bear over logarithmic substrate concentrations of 20-500 p m o L at pH 8.8. The detection limit was at 5 pmoVL. Antibodies are generally much more stable than enzymes. During 80 cycles of approximately 30 min each, no deterioriation was observed in a flowthrough cell.

2.2.9 Multitopic Recognition of Immunological Systems The production of antibodies is the response of a mammelian organism to an antigenic challenge. The binding of small amounts of antigen will be achieved more effectively the higher the association constant of the antigen-antibody (Ag-Ab) complex. This goal is approached by a high three-dimensional complementarity of weak binding sites and a large interacting area in an aqueous medium. Multitopic interaktions between antibodies and antigens are characterized by the avidity, introduced in order to describe the overall stabilization of the complex. In macroscopically determining the overall association or equilibrium constant of a complex, no distinctions are made between different isomeric binding sites. However, the nonlinearity of binding curves gives rise to a population of antibodies with different affiities for polyclonal antibodies. When using the term afinity strictly, a reaction between a substrate and a particular binding site in a ligand is implied. However, very frequently, the term affinity is used in the sense of the overall afinity or total afinity constant Kt,which represents the weighted affinity of

OH

Figure 2-14. Chemical constitution of biotin

72


the antibody subpopulations and is equivalent to an overall association constant. Binding (association) constants vary greatly, from lo3 L mol-1 for lectins up to I O l 5 L mol-I for the avidin- and streptavidin-biotin system, the highest association constant discovered so far in antigen-antibody interactions [156, 1571. Biochemically biotin is a vitamin and an important growth factor. Whether the high association constant depends on the efficient utilization of biotin is not yet completely established [157]. For analytical purposes, the avidin-biotin system is very widely used as a highly efficient, irreversible marker. Biotin forms a carboxyl-carrier protein (BCCP), which participates in transcarboxylation reactions [ 1581. The biotin-avidin reaction is later coupled to the bioluminescence of isoluminol, induced by acetyl-CoA carboxylase and ATP. The intramolecular forces which contribute to the stabilization of a complex are the same as those involved in the stabilization of the specific configurations of synthetic macrocycles and macromolecular hosts. Antibody affinity may be considered as the sum of attractive and repulsive interactions, mostly nonionic and noncovalent, resulting from the antibody binding area and the homologous antigenic determinant. In antibody-antigen reactions, the amino and hydroxyl groups of amino acid residues are predominantly involved. The contribution to the interaction of hydrogen bonds other than those in water molecules were assumed to be relatively small, particularly in the aqueous environment which competes with them. However, Pinkerton et al. (1969) assume that hydrogen bonds, ion-dipole and electron donor-acceptor interactions act as long-range forces which prevent selectivity [159]. The complexing area of the Fab fragment of the mouse monoclonal antibody D1.3 (globulinclass: IgG1) binding to hen egg lysozyme (HEL) is well elucidated [157]. The V H and VL fragments of the FvD1.3 fragment were obtained by cloning and expressing their genes in Escherichia coli. 16 pm2 of solvent-accessible surface area were determined by X-ray crystallography to be buried in the complex (radius of a H 2 0 molecule: 0.17 pm). The binding area involves 15-20 amino acid residues. In total, 15 hydrogen bonds, a large number of van der Waals interactions, no ion pairs, and about 50 water molecules were involved in and in close proximity to the interface, promoting contacts between the antibody and lysozyme. For analytical purposes, these types of multitopic bonds have to be addressed in order to regenerate antigen-antibody interactions. Pinkerton et al. (1969) describe the selectivity,association,and interaction by drawing heavily on information and probability theory. The equilibrium association constant is related to the temperature T (K), and thus the change in free energy for all associative reactions can be expressed by:

where Z represents overall partition functions, and AEi the free energy of molecular association when the N molecules of the species, AiL, L and Ai, are in the molecular ground state. The thermodynamic description also implies a probabilistic description. The probability of recognizing any particular analyte, Ai, is: [Ail K i

pi'

N c,,[A,,] K n

(2-9)


73

where N represents the total population of extracted molecules, A,, = Ai + A j = Ai + A j 1 + Aj2 + ...+ Aji. If the selective recognition of one particular analyte, Ai, is required and possible, then the probability:

pii

,.

N - l z . ZJ.

p.. lj +1 or < -1, the dielectric constant of the medium, as well as of the additives which catalyze charge transfer, Considerably influences the extraction process by the medium. The dielectric constant of a membrane medium influences dehydration of the ions and the creation of bulk water clusters by exothermic processes.

- The environment where the recognition process takes place (e.g., in the membrane), the additives and the catalysts greatly influence the extraction and complexing process. An optimized medium can contribute considerably to an efficient recognition process and can also induce a fine tuning of the selectivity. In a polymeric solvent membrane, the profile of the surrounding medium is given by the plasticizer which acts as a solvent and by the additives (organic, lipophilic sites). Conductivity (microelectrodes)and phase transfer resistance (surface tension) are also likely to play a role, but how is not clear. The bulk membrane constituents should not inhibit the preformation of the ligand by intermolecular interactions (see chapter 4 and section 5.1). An open-chain ligand must not exhibit a worse extraction behavior than, e.g., a crown ether, if rapid conformational changes of the ligand are possible. Interactions between the ligand and the plasticizer might be destructive. The ligand and the solvent or additives must allow an optimum preformation of the cavity and closely fit the size of the guest molecule.

- The shape (spatial structure) and geometry of a ligand are as relevant as the physicochemical features of the active site. This is clearly shown by the multitopic binding sites of antibodies and the hydrophobic transport channel of an enzyme.

- Multitopic recognition allows a step-by-step substitution of solvent molecules in the inner coordination sphere of the guest species. In each step, the desolvation energy is compensated for by the total free energy of association. A negative entropic contribution resulting from clustering of the solvent molecules (water) may contribute to desolvation. The total energy is thus conserved during the loading process and a close contact between the sites of the host and the

76


guest species should be possible, resulting in a good compromise between selective binding and energeticallybalanced conformationalchanges in the ligand.

- The association relative to the dissociation rate determines the equilibrium of a species between two phases and, thus, the uptake of the species. However, for practically relevant, reversible sensors, the useful ratio between the association and the dissociation rate is limited to a few orders of magnitude.

References [l] Schubert, J. (ed.),Physikalische Efeekre. Weinheim: Physik-Verlag, 1984. [2] a) Gtipel, W., Hesse, J., Zemel, J.N.,(eds.), Sensors. Weinheim: VCH Verlagsgesellschaft. 1989; Vol. 1, pp, 1-16; b) Vol. 2, p 2. [3] Lion, K.S., IEEE Transactions, 1969, IECI-16,2 [4] Scheller, F., Schubert, F., Pfeiffer, D., Hintsche, R., Dransfeld, I., Renneberg, R., Wollenberger, U., Riedel, K., Pavlova, M., Kiihn, M., Miiller, H.-G., Tan, P.M., Hoffmann, W., Moritz, W., Analysr, 1989,114,653. [5] Unknown author. [6] Morf, W.E., Seiler, K.,Lehmann, B., Gehrig, P., Rouilly, M., Suter, G., Rusterholz, B., Spichiger-Keller, U., Pretsch, E., Simon, W., in: Schmid, R.D., Scheller, F. (eds.), Biosensors, GBF Monographs, Vol. 13. Weinheim: VCH Verlagsgesellschaft, 1989; 321. [7] Fokers, G.. Antrittsvorlesung, Swiss Federal Institute of Technology (ETH), 1991. [8] Dietrich, B., Viout, P., h h n , J.-M. (eds.), Macrocyclic Chemistry, Weinheim: VCH Verlagsgesellschaft. 1993. 191 Atwood, J.L., Davies, J.E.D., Macnicol, D.D., Vtigtle, F. (eds.), Comprehensive Supramolecular Chemistry, Vols 1 - 10, Pergamon, Oxford: Elsevier Science Ltd., 1996. [lo] Kisakiirek,M.V., Heilbronner, E. (eds.), Highlights of Chemistry as Mirrored in Helvetica Chimica Acra, Weinheim: VCH Verlagsgesellschaft, and Basel: Verlag Helvetica Chimica Acta, 1994. [l 11 Williams, A.F., Floriani, C., Merbach, A.E. (eds.), Perspectives in Coordination Chemistry, Weinheim: VCH Verlagsgesellschaft. and Basel Verlag Helvetica Chimica Acta, 1992. 1121 Edmonds, T.E (ed.),Chemical Sensors. Glasgow: Blackie & Son, 1988; pp. 17-1 16. [13] Seiyama, T. (ed.), Chemical Sensor Technology, Vol. 2. Amsterdam: Elsevier, 1969; pp. 237-254. [14] Izatt, R.M., Christensen, J. J. (eds.), Progress in Macrocyclic Chemistry; Vol.1. New York: John Wiley & Sons, 1979. [15] Morf, W.E., Ammann, D., Bissig, R., Pretsch, E., Simon, W., in: ref. 14; pp. 1-61. 1161 hnitz, J.D., Hemmerich, P., Ibers,J.A., Jorgensen, C.K., Neilands, J.B., Reinen, D., Williams, R.J.P. (eds.), Structure and Bonding, Vol 16 et al.. Berlin: Springer-Verlag, 1973. [17] Lindoy, L.F. (ed.),The Chemistry of Macrocyclic Ligand Complexes. Cambridge: Cambridge University Press, 1989. [18] Ciba Foundation (eds.), Host-Guest Molecular Interactions: From Chemistry to Biology. Chichester: John Wiley & Sons, 1991; Ciba Foundation Symposium 158. [I91 Weber, E., Vagtle, F. (eds.), Macrocycles. Berlin: Springer-Verlag, 1992. [20] Inoue, Y., Gokel G.W. (eds.), Cation Binding by Macrocycles. New York, Basel: Marcel Dekker, Inc., 1990. [21] Patai. S . (ed.),The Chemistry of Ethers, Crown Ethers, Hydroxyl Groups, and Their Surfur Analogues. New York: John Wiley, 1980; Chapter 2. [22] a) Loewe, H. (ed.),Paul Ehrlich. Schirpfer der Chemotherapie. Stuttgart: Wissenschaftliche Verlagsgesellschaft m.b.H., 1950 p.186. b) Baumler, E.(ed.),Paul Ehrlich, Forscher f i r d a s Leben. Frankfurt: Societ;its-Verlag, 1979, pp. 36-37. [23] Ptitsch, W.R., Fischer, A., MUller, W. (eds.),Lexikon bedeutender Chemiker. Thun, Frankfurt: Verlag Harri Deutsch. 1989.

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[94] Tan, S.S.S., Hauser, P., Wang, K., Fluri, K., Seiler, K., Rusterholz, B., Suter, G., KrUttli, M., Spichiger, U.E., Simon, W., Anal. Chim Act@ 1991,255,35. [95] Stepzlnek, R., Krautler, B., Schulthess, P., Lindemann, B., Ammann., D., Simon, W., Anal. Chim. A m , 1986,182,83. [96] SchaUer, U., Bakker, E., Spichiger, U.E., Pretsch, E., Anal. Chem., 1994,66,391. [97] Pauling, L. (ed.),The Narure ofthe Chemical Bond, Ithaca NY: Cornell University Press, 1960. et al. (eds.), Structure and Bonding, Berlin: Springer[98] Simon W., Morf, W.E., Meier, P.Ch., in: Dunitz, J.D. Verlag; 1973, 113. I991 Diebler H., Eigen M., llgenfritz G., Maas G.,Winkler R., in: IUPAC, Pure and Applied Chemistry, Vol. 20. London: Butterworths; 1969, pp. 93-115. [I001 a) Reinen, D., Friebel, C., in: Dunitz, J.D. et al. (eds.), Structure and Bonding, Vol. 37, Berlin: SpringerVerlag, 1979, pp. 1-60. b) Warren, K., in: Dunitz, J.D. et al. (eds.), Structure and Bonding, Vol. 57, Berlin: Springer-Verlag. 1984, pp. 119-147. [I011 Simon, W., Spichiger, U.E., Int. Lab., 1991,8.35. [I021 Morf, W.E., Seiler, K., Lehmann, B., Gehrig, P., Rouilly, M., Suter, G., Rusterholz, B., Spichiger, U.E., Pretsch, E., Simon, W., in: Schmid, R.D., Scheller, F. (eds.), Biosensors: Application in Medicine, Environmental Protection and Process Control, GBF Monographs Vol. 13, Weinheim: VCH Verlags gesellschaft, 1989. [lo31 Dinten, O., Spichiger, U.E., et al., Anal. Chem., 1991,63,596. [I041 Kataky, R., et al., Analyst, 1991,116,135. [lo51 Frey-Wyssling, A. (ed.),Submikroskopische Morphologie des Protoplasmas und seiner Derivate. Berlin: Bumtrager, 1938; pp. 112-1 19. [lo61 Pauling, L., b r a y , R.B., Forschr. Chem. org. Natursroffe, 1954,II, 180. [lo71 Kilbourn, B.T., Dunitz, J.D., Pioda, L.A.R., Simon, W., J. Mol. Biol., 1967,30,553. [I081 Winkler, R., in: Hemmerich, P., et. a]., (eds.). Structure and Bonding, Vol. 10. Berlin: Springer-Verlag 1972, pp. 1-24. [lo91 Shemyakin, M.M., Ovchinnikov, Y.A., Ivanov, V.T.,Antonov, V.K., Vinogradova, E.I., Shkrob, A.M., Evstratov,, A.V., Laine, LA., Melnik, E.I., Ryabova, I.D., J. MembruneBiol., 1969, 1, 402. Malenkov, G.G., [110] Pinkerton, M., Steinrauf, L.K., Dawliins, P., Biochm. Biophys. Res. Commun., 1969,53,512. [ill] Umeyama, H., Morokuma, K., J. Am. Chem. Soc.,1977,99,1316. [112] Ovchinnikov, Y.A., Ivanov, V.T., Tetrahedron, 1974,30, 1871. [113] Dobler, M., lonophores and their Structures,New York Wiley, 1981. [I 141 Kern, P., Brunne, M., Folkers, G.,J. Cornput.-AidedMol. Design, 1994,8, 367. 11151 a) Prelog, V., Gerlach, H., Helv. Chim. Acta, 1964,47, 2288. b) Gerlach, H., Owtschinnikow, J.A., Preolg, V., Helv. Chim. Actta, 1964,47,2294. [116] Btihlmann, P., Swiss Federal Institute of Technology (ETH), 1993; PhD thesis Nr. 10066. [117] Spichiger U.E., in: Scheller, F.W., Schubert, F., Fedrowitz, J. (eds.), Frontiers in Biosensorics 1, Fundamental Aspects, Basel: Birkhauser Verlag, 1997; pp. 27-48. [118] Pedersen, C.J., J. A m Chem.SOC.,1967,89, 2495; ibid 7017. [I191 Holy, P., Morf, W.E., Seiler, K., Simon, W., Helv. Chim. Acta, 1990,73, 1171. [120] Cram, D.J., Cram, J.M., Science, 1974,183,803. [121] Thoma, A.P., Cimerman, Z., Fiedler, U., Bedekovic, D., Guggi, M., Jordan, P., May, K., Pretsch, E., Prelog, V., Simon, W., Chimia, 1975,29,344. [I221 Mod, W.E., Seiler, K., Lehmann, B., Behringer, Ch., Hartmann, K.,Simon, W.,Pure and Applied Chem., 1989,61,1613. [I231 Freiner, D., Spichiger, U.E.,in: Wolfbeis, O., Katzir, A. (eds.), Biochemical and Medical Sensors, Bellingham, W A S P E , Vol. 2085; pp. 124. [124] Vaillo, E., Walde, P., Spichiger, U.E., Analytical Methods and Instrumentation, 1995,2,145. [125] Rebek, J., Jr., Marshall, L., Wolak, R., Parris, K., Killoran, M., Askew, B., Nemeth, D.,Islam, N., J. Am. Chem. SOC.,1985,107,7476. 11261 Rebek, J., Jr., Askew, B., Ballester, P., Buhr, C., Jones, S., Nemeth, D., Williams, K., J. Am. Chem. Soc., 1987,109,5033.

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Rebek, J., Jr., in: Roberts, S.M., Royal Society of Chemistry, Molecular Recognition. Dorchester, GB: Henry Ling Ltd, Dorset Press, 1989; pp. 211-218. Russell, F.D., Bork, P., ScientificAmerican, 1993,10,34. Meuleman, D.G., Hobbelen, P.M.J., Van Dinther, T.G., Vogel, G.M.T., Van Boeckel, C., A.-A,, Moelker, H.C.T., Seminars in Thrombosis and Hemostasis, 1991,17, 112. 11301 a) Private communication by Organon International, Scientific Development Group, 5340 BH Oss, The Netherlands. b) Westerduin, P., Basten, J.E.M., Broekhoven, M.A., de Kimpe, V., Kuijpers, W.H.A., van Boeckel,C.A.A., Angew. Chem., 1994,108,339. a) Wang, J., Talanta, 1994,4I, 857. b) Wang, J., Chen, L., Biosensors & Bioelectronics, 1996, I I , 751. Massart, D.L., Vandeginste, B.G.M., Deming, S.N., Michotte, Y., Kaufman, L. (eds.), Chemomerrics: A Textbook. Amsterdam: Elsevier, 1988; pp. 115 ff. Fersht, A. (ed.),Eruyme Structure andMechanism. New York W.H. Freeman and Comp., 1984. Spichiger, U.E., Kuratli, M., Simon, W., Biosensors & Bioelectronics, 1992, 7,715. T.G. Spiro (ed.), Zinc enzymes, New York: John Wiley & Sons; 1983, 123. Kvassman, J., Laisson, A., Petterson, G., Em. J. Biochem., 1981, ZI4,555. Behringer, C., Lehmann, B., Haug, J.-P., Seiler, K., Morf, W.E., Hartmann, K., Simon, W., Anal. Chim. Acfa, 1990,233,41. Seiler, K., Wang, K., KuratIi, M., Simon, W., Anal. Chim. Acfa., 1991,244, 151. Wild, R., Citterio, D., Spichiger, J., Spichiger, U., J. Biotech., 1996,50,37. Hansch, L.C.A., Taft, R.W., Chem Rev., 1991,91,165. Wang, K., Seiler, K, Haug, J.P., Lehmann, B., West, S., Hartman, K., Simon, W., Anal. Chem., 1991,63, 970. Meyerhoff, M.E., Pretsch, E., Welti, D.H., Simon, W., Anal. Chem., 1987,59,144. Elghaffer, A.A., Chrostek, L. & Szmitkowski, M., J. Clin ChemClin. Biochem., 1990,28,497. Bilitewski, U., Schmid, R.D., in: ref [102],pp. 100-102. Kirstein, D., Kirstein, L., Scheller, F., in: ref. [102], pp. 47-58. Kulys, J.J., Bilitewski,U.,Schmid, R.D., in: in:ref [102], pp. 103-106. Prinzing, U., Ogbomo, I., Lehn,C., Schmidt, H.-L., Sensors and Acruutors, 1990, B1,542. Bonnichsen, R.K., Theorell, H., in: The Scandinavian Journal of Clinical & Laboratory Investigation, Vol 3. Oslo: Medisinsk Fysiologisk Forenings Forlag, 1951, pp. 58-62. 11491 Lammert, R., Ogbomo, I., Baumeister, T., Danzer, J., Kittsteiner-Eberle, R., Schmidt, H.-L., in: ref. [102], pp. 93-98. Gut, G., Diplomarbeit, Ingenieurschule WBdenswil, Zurich, Fachbereich Lebensmitteltechnologie,1993. Curti, B., Ronchi, S.,Zanetti, G. (eds.),Fluvins and Fluvoproteins 1990, Berlin: Walter de Gruyter, 1991. Lerner, R.A., Benkovic, S.J., BioEssays, 1988,9,107. Schultz P.G., Science, 1988,240,426. Blackburn, G.F., TalIey, D.B., Booth, P.M., Durfor, C.N., Martin, M.T., Napper, A.D., Rees, A.R., Anal. Chem., 1990,62,2211. Kricka, L.J. in: Fidmonds, T.E. (ed.),Chemical Sensors. Glasgow and London: 1988, pp. 3-14. Braden, B.C., Dall'Aqua, W., Eisenstein, E., et al. in: ref. [31]; pp. 225. Palmer, T., Understanding Enzymes, Chichester, West Sussex: Ellis Honnrood Ltd., 1985;pp. 233 ff. Thompson, M., Frank, M.D., Heckl, W.M., Marassi, EM., Vigmond, S.J.,in ref. 2. Steward, M.W., in: Glynn, L.E., Steward, M.W. (eds.), Immunochemistry: An Advanced Textbook. Chichester: John Wiley & Sons, 1978. Chance, B., in: Technique of Organic Chemistry, Vol. 8, part 11, New Yo&: Interscience, 1963. Eigen, M., DeMaeyer, L., in ref. 73.

References

81

Chemical Names of Ligands: ETH 1778, octadecylisonicotinate(C24H 53N02); ETH 1859, N-octadecyl- morpholine (C22H45No); TDDA , trin-dodecylamine (C36H37N); ETH 1907, 4-nonadecyl pyridine (C24H43N);ETH 1810, N,N-dicyclohexyl-N:N’diisobutyl-cis-cyclohexane-1,2,-dicarboxamide(CzaH~N202);ETH 2137, 2-butyl-2-ethylpropane-l,3-dioxybis(N,N-dicyclohexyl-acetamide)(C37H~N204);DM 14C4, 3-dodecyl-3-methyl-1,5,8,12-tetraoxacyclotetradecane (CBH~SO~); 14C4, 2,3-bis(N,N-di-n-butyl-acetamide)-1-,4,8,1l-tetraoxacyclotetradecane. ETH 2120, N,N,N:N’-tetracyclohexyl-1,2-phenylenedioxydiacetamide (C34HS2N204); ETH 227, N, N‘,N”triheptyl-N,N:N”’-~~methyl-4,4‘,4”-propy~idintns-(3-oxabutyr~de) (C 3&71N306); ETH 157, N,N‘-dibenzylN,N’-di-phenyl-l,2,-phenylenedioxydiacetamide(C36H32N204); B12C4, bis[(l2-crown-4)-methyl]-dodecylmethylmalonate (C34H ,52012); Hemisodium, (Eastman Kodak Company, 14650 New York, NY, USA) (C41H42N05);Valinomycin, (Fluka AG, CH-9470 Buchs, Switzerland) (C54HmN,@18); B15C5, bis[(l5-crown5)-2-ylmethyl]-2-dodecyl-2-methylmalonate (C38H 70014); BME 44, bis[S -(nitro-l,2-benzo-l5-crown-5)-4’-yl]-2methyl-2-dodecylmalonylamide (C&51N4018); Nonactin, (Fluka AG) (CaH ~ 0 1 2 ) ;Monactin, (C41H66OI2); V 163, (CaHsN205). ETH 6010, octyl 4-trifluoroacetyl-benzoate (Cl7H 2103F3); ETH 6011, (4-trifluoroacetyl)-phenyloctylether (C 16H2102F3); ETH 6019, l-(dodecylsulfonyl)-4-trifluoroacetylbenzene;ETH 6022, N-dodecyl-4-fluoroacetylacetamilide; ETH 6024, N,N-dioctyl-4-trifluoroacetyl-benzamide (CxH 21NOzF3); TFABB,1-butyl-4-trifluoro-acetyl-benzene(C 12H 130F3). ETH 1001, (-)-(N,N?-(R,R)-[bis( 1 1 -ethoxy-carbony1)- undecyl)]-N,N’-4,5-tetramethyl-3,6-dioxaoctane~amide (C3&#~08); ETH 129, N,N,N’,N’-tetracyclohexyl-3-oxapentanediamide (C2gHeN203); ETH 5234, N,N, dicyclohexyl-N,N’-dioctadecyl-3-oxapentanediamide. ETH 1117. N,N’-diheptyl-N,N’-dimethyl-1,4-butanediamide (C2oH 4ONzO2); ETH 2220, N,W-diheptyl-N,Wdimethyl-aspartediamide (Ca41N302); ETH 5214, N,N”-octamethyl-ene-bis( W-heptyl-W-methyl-2-methylmalon-diamide) (C32H62N404); ETH 5220, N,W-octamethyl-ene-bis(N’W-dioctyl-malon-diamide);ETH 5282, W~‘~’-imino-di-6,l-hexandiyl)tris(N-heptyl-N-methyl-m~onamide) (C45H8 4 N 6 0 6 ) .



3

Controlling Sensor Reactions

3.1

Thermodynamically Controlled Sensor Reactions: Reversibility and Thermodynamic Equilibrium

3.1.1 The Chemical Potential and the Partition Equilibrium In many cases, a purely chemical description of the sensor reaction does not help understand the sensing process. Both living organs and organisms, as well as purely chemical, artificial systems have been applied to create sensing devices. The highest available standard for an artificial sensor is its reversibility . What is basically the difference between the reversible artificial system and the continuous, regenerable response of an enzyme or an organ? For biological systems, the well-known rule that natural processes proceed by way of an increase of disorder goes against the rule that biological systems reveal an organization which can hardly be imitated by artificial systems. For comparisons of such systems, some basic thermodynamic considerations have to be made. In the biochemical and biological literature, it is common to describe biochemical or bioelectrical processes by their thermodynamics [1-4]. The two sensing systems can basically be distinguished by their thermodynamics. Thermodynamics originally dealt with the transformation of mechanical work into heat and vice versa. Thermodynamics studies the relationships between macroscopic states. Classical thermodynamics deals with thermal state changes in closed, adiabatic, homogeneous systems. For the description of closed, but not isolated, chemical systems as well as open chemical systems, heterogeneity as well as energy and mass transfer must be considered. Linear, irreversible thermodynamics is dedicated to open systems which are defined by the flow of matter and the flow of heat due to the action of forces and fluxes. The two are coupled in equations which describe a time dependent transport. For the description of enzymatic and metabolic processes in organs, the steady state is based on linear irreversible thermodynamics (see the end of this section). For analytical use in sensors, however, the kinetic description of a sensor response is often more relevant and will also be discussed. Reversibility strictly defines a thermodynamic equilibrium reaction where the analyte must not be consumed, comparable to a physical sensor (e.g., a thermometer), and the response of the sensor adapts continuously to the actual analyte activity. A typical biochemical sensor, incorporating an enzyme to achieve selectivity, operates, in contrast, in a steady state mode and involves a turnover of a substrate that might be the analyte. The chemical energy inherent in the thermodynamic equilibrium reaction is transformed into some type of work or energy, producing the typical response of the sensor. The physicochemical equilibrium reaction involves the solubility of host and guest molecules, the phasetransition of the chemical compounds, and the interaction between the host and the guest molecule. The terms host and guest are used in its largest sense for all compounds involved in reversible or regenerable sensing reactions. "A system is the part of the world in which we have a special interest" [5].

84

3 Controlling Sensor Reactions

The sensing system described here is composed of two communicating subsystems, the sample phase, mostly an aqueous phase, and the sensing phase, an organic, extracting phase with variable polarity. The two subsystems are separated by a boundary, where matter can be exchanged. The surroundings of the open, heterogeneous sensing system, to which the signal is transmitted, is generally thermostatted. A system is called "thermodynamic" if its state can be described by just a few thermal quantities [ 6 ] . The thermal equilibrium is a state described phenomenologically by the following macroscopic variables: absolute temperature, T /K; pressure, pPa; volume, V/m3, exchanged work, W/J; heat, Q 4 /J; heat capacity, C,/JK-'; and entropy, S /JK-l. The mole fraction of the ith species, xi, identifies the relative number of particles of species I in solution; ni, nj, the number of particles of I and J. I denotes the analyte compounds and J the interfering species. The entropy, S, introduces a thermal degree of freedom which is related to the temperature and the heat added reversibly to the system (dS = 6QreV/T).The thermal equilibrium is moreover characterized by state functions (in brackets: the natural variables; suffixes: arguments to be kept constant) for the internal energy U/J (V, S), the Helmholtz free energy A/J (T, V), the enthalpy HIJ (p, S) and the Gibbs free energy or free enthalpy G/J (T, p). This collection of phenomenological variables and functions is used to describe equilibrium reactions from the chemical as well as the physical point of view. Strictly, thermal equilibria do not change with time, as long as the surroundings remain unchanged. In general, thermodynamic functions in a-standardstute are identified by the superscript e. Since 1982, the standard state has been specified by a temperature 298.15 K and a pressure p o = 105 Pa (1 bar); before 1982: b= 1 atm = 1.01325 x I@ Pa). The symbol O in, e.g., the chemical potential p0, means a quantity specified at = 16 Pa (I bar) and 298.15 K where the composition of the phase is not further specified. The standard volume of one mole of gas under standard conditions is 22.4 x lo3 m3. i, j , denote chemical species, n is the amount of Imol, where N A is the Avogadro constant, 6.022 x mol-l, R is the substance, N ~ / N A absolute gas constant, 8.3143 N mot1 K-' (= J mol-' K-l) . The symbol 00, in /.Pdenotes the chemical potential for an infinitely dilute solution, which is usually assumed for modeling bulk membrane reactions. Thejrst law is the law of energy conservation, which expresses the fact that work and heat are only different forms of energy. The internal energy U is the sum of the translational, rotational, and vibrational energy of a molecule. The internal energy can increase with heat Q, absorbed at constant volume V. A system of constant volume can do work, dW. In addition to mechanical work (pv), a chemical system can perform electrochemical work, the emf. Radiation (luminesence) is treated like heat. d U = (W)v = SQ + 6W

(3-1)

This statement is very important for all analytical techniques. The increase in internal energy of the system (a chemical compound) is therefore equal to the amount of heat or energy absorbed. The absorption of irradiated spectral frequencies by a chemical compound, generates a higher level of internal energy by excitation of electronic states. Upon relaxation of the system, the absorbed energy is released, perhaps as luminescent radiation or membrane deformation but, in most cases, as heat. This means that, even in a thermostatted system, the local temperature is not necessarily constant.'

3.1 ThennodynamicallyControlled Sensor Reactions

85

Since most chemical experiments are carried out at constant pressure (atmospheric pressure) rather than constant volume, the work done by the system is not necessarily associated with zero expansion. In a closed system, the most general form of work done by a quasi-static change is:

In a perfect gas, pressure and volume are related to the number of moles of the gas and the temperature. Under these conditions the phenomenological variable defined by the internal energy and the volume at constant pressure is the enthulpy H H=U+pV=U+RTn

and

dH=d(Qb

(3-3)

The increase in enthalpy of a system is equivalent to the heat absorbed at constant pressure. In condensed phases, the internal energy U is generally equal to enthalpy H, assuming small changes in the volume by transition of n moles of a component, where n is generally >> 1. The term R T divided by the Faraday number, F (9.64846 x 104 (C mol-1 = J V-' mol-l)), and the charge number 2, of an ion denotes the slope of the ideal Nernstian response function for potentiometric measurements. This term is the basis of the electrochemical response function, and introduces the conditions on which an ideal response is based. Reversibility can be defined by different properties of the state functions and phenomenological variables. In terms of thermodynamics, a reversible process is one that can be reversed by a infinitesimal modification of one variable. For analytical use this variable is preferably the activity of the analyte. Reversibility is associated with the laws of energy conservation when a reaction proceeds. The third law stipulates the impossibility of perpetual motion. However, one aim of preparing a reversible system must be to yield maximum work and maximum information, and to avoid the production of heat, as an increase in heat, in most cases, decreases the lifetime of the chemical system. The availability of work (= exergy) depends on the existence of two connected systems, one of which is quasi-static. The dynamic system is able to exchange work, heat, or matter with this static system. According to the second law, no work is acquired in an equilibrium state. Thus the availability depends on the deviation from the equilibrium state and the maximum amount of work available. Entropy has been introduced as a convenient measure of the capacity of a system to do work. The reversibility of a process relies on the second law, the consequence of which depends on how the law is formulated. However, it stipulates the existence of irreversible processes. F. Schlogl says [ 6 ] :"For an isolated thermodynamic system a quantity exists uniquely associated with each thermal state which never decreases with time evolution." In natural processes the maximum work is never obtained. Spontaneous processes are characterized by a steadly decrease of entropy and, also, a continuous yield of information. Thus, the second law seems to go against the organization and reproduction of material. Entropy ( S ) , is a construct proposed by R. Clausius (1 860) [7] from the Greek word for "transformation".The path of the spontaneous trend in thermodynamic systems is the direction of heat flow. Thermodynamic equilibrium is characterized by maximum entropy, zero change in free energy, and maximum

86


available work. The entropy change describes the transfer, of heat at the temperature of the transfer and depends only on the initial and final state of the distribution of thermal energy: dS=-sQrev T

and

dU=TdS-RTdn

(3-4)

A thermodynamic description of a system enables a phenomenological account of macroscopic experimental observations without any information about the microstate or the chemical processes involved. A thermodynamic statistical description operates with "progressive probabilities of events after the last observation" [ 6 ] .The Boltzmann constant, k (= RINA = 1.38066x J K-l),links statistical phenomena on a molecular basis to phenomenological thermodynamics and relates the conventional units J K-' to the entropy. This relation holds for the description of diffusional processes by irreversible thermodynamics where entropy is produced by a fast exchange of matter, and is related to the probability distribution of ions or molecules. Discussions of thermodynamics are very often restricted to systems containing only one chemical component in the gas phase. How can multicomponent systems be treated, in particular those in which the chemical composition changes and those in which chemical reactions take place? Chemical reactions in which one phase is a gas phase, were exploited in environmental sensors for S02, humidity, C02,and NH3. In testing the optode membrane of the ethanol sensor in the vapor phase of a bioreactor, the principle of Le ChLelier was shown to be valid (see section 2.2.7). Within a flow-through cell with a volume of 350 pL, the absorbance measured photometrically at A = 304 nm was limited by the flow of the vapor phase through the sample cell at flow rates < 18 mL equivalent to a flow of < 15 cm2 s-'. Apart from that, chemical processes proceed in solutions, the sample and the membrane solution. The evolution of heat is of interest for calorimetric titrations, in determining equilibrium constants. The variation of the partial pressure involved in evaluating the colligative properties of a sample, especially in studying nonideal behaviour, or in determining equilibrium constants (see section 3.4). However, of major importance for artificial sensors is the exchange of matter between two homogeneous condensed phases and, in some cases, the work done. Thermodynamic functions which describe the maximum yield of work must provide useful definitions of the trend of the equilibrium in chemical processes, including those in solution. For the description of reversible chemical reactions in our two-phase system, where both phases are homogeneous, constant pressure and temperature are assumed. In this case, the work done must be different from mechanical pV work. An example is the electrical work done in electrolysis. The state function, Gibb'sfree energy G describes the type of state function which involves other types of energy transfer than mechanical pV work and heat. dG = d H - d ( T 3 = dU- d(TS ) + d@V)

(3-5)

= dU + R T dn -d(TS)

(3-6)

3.I Thermodynamically Controlled Sensor Reactions

87

Using these equations, even open systems can be described, assuming constant pressure and constant temperature. In a two-phase system, the exchange of matter is accounted for in the Gibbs-Duhem equation. For a pure analyte substance: d(TS) = d@V) + dU- dG

(3-7)

d(T S ) = d@V) + dU - pi dni

(3-8)

This extension is based on the introduction of the chemical potential pi, of the participating chemical species, I. Thus, the internal energy in an open adiabatic system changes as a function of niat constant pressure. Only small volume changes are allowed. The entropy remains unchanged in reversible adiabatic processes. By introducing:

the Gibbs-Duhem equation can be extended to describe heterogeneous systems composed of homogeneous subsystems coming to a phy sicochemical equilibrium and for several species I, participating in a chemical reaction. This equation allows one to describe the equilibration of all species participating in the chemical recognition and exchange process. The chemical potential depends on the solubility and reactivity of a chemical compound, and thus its overall distribution. The molar Gibbs free energy may be transformed to electrical work or stored as bonding energy in a so-called energy-rich compounds in biochemistry. In the following, chemical thermodynamics are applied to solutions. A solution can be solid, liquid, or gaseous. However, solutions in the liquid state are our major concern. In diffusion, the equilibration of the chemical potentials holvent and kolution , in a two-phase system is the driving force. Diffusion is associated with an increase in entropy to approach the state of highest probability. Adding a pure compound to a pure solvent generates a difference in the molar free enthalpy, the molar free energy of mixing AGm (xi denotes the mole fraction of the species I):

When no change in enthalpy occurs (AHm = 0), no interaction between solute and solvent takes place, and no change in AG, occurs as long as the temperature is constant. This type of argument explains the origin of osmotic pressure and sees it as a function of different chemical potentials on both sides of a semipermeable membrane, if one species is not allowed to permeate. Since there is only an extremely small probability that a pure solvent will have the same chemical potential as a solution, the energy difference at constant temperature is compensated for by the osmotic pressure in analytical set-ups (detailed description see [1, 61). Alternatively, in the case of flexible membranes, the osmotic pressure difference may be compensated energetically by deformation of the membrane. In this case, mechanical work is

88


involved in the restoration of the chemical potentials of two connected phases. It results in a different partial pressure of the dissolved compounds on both sides of the membrane. A thermodynamic equilibrium involves a maximum of entropy in a closed system or more usually, a minimum of molar free energy H (4 = 0,AS = 0), or a minimum of molar free enthalpy, G (AT = 0,Ap = O), in an open or heterogeneous system. In a closed, reversible system, the deviation from the equilibrium state is only moderate and the maximum possible work (W,,, = Wmm)is obtained for the equilibration. In the thermodynamic description of the equilibrium, the time variable is not discussed. In open systems, thermal equilibria do not change with time as long as the environment remains unchanged. Equilibrium thermodynamics can only provide information about the probability of a reaction or the energetic level of the equilibrium, and not about the kinetics and velocity of the process. A chemical equilibrium is related to stable chemical potentials in each of two connected systems after a sufficient time interval following a change. During the short time response usually detected with potentiometric sensors, only a transient local equilibrium is generated. In the sensor systems discussed here, the two connected systems refer to an aqueous sample phase aq, or a gas phase containing the analyte, in contact with a more or less lipophilic organic phase, mostly of high viscosity, representing the membrane m, for optical and potentiometric sensors. Typical two-phase systems are presented in Table 3-1. The complexing agents were, in most cases, implemented in thick (50-500 pm), plasticized, non-polarized,

Table 3-1. Two-phase systems of an aqueous sample phase in contact with an organic hydrophobic phase incorporating all compounds which participate in the host-guest interaction. Compare Figure 3-1 and chapters 4 , 5 and 6

Aqueous phase (aq)

Hydrophobic phase (m) (examples)

biological sample, I ca. 0.16 mol kgH20-l proteins ca. 0.070 kg L-' lipids ca. 0.005 kg L-l osmolality 0.28-0.3 osmol L-1

carrier ca. 0.03-0.007 mol kg-1 lipophilic sites ca. 0.001-0.04 mol kg-1 solvent, plasticizer ca. 65 wt% (DK 4 - 24 (70)) PVC ca. 33 wt%

seawater, I ca. 0.64 rnol kgH20-l mean:3.5 wt% salt ca. 0.47 mol L-1 NaCl 0.054 mol L-l Mg2+ 0.010 mol L-l KCI

silicone oil mediator@) enzyme

lake water, freshwater, ground water

ligand, host-reactand polymerized silicone membrane

3. I Thermodynamically Controlled Sensor Reactions

89

liquid membranes for ISE measurements or in likewise thin bulk membranes (1-4 km) for optical transduction. The chemical potential specified selectively for the species I in the presence of the species J, , :p where the phase is not specified, is directly related to the partial molar Gibbs free energy 6G,dependant on the change in the amount of substance, 6n,i of the chemical compounds I in the presence of J and can be expressed by:

(3-10) The Gibbs free energy, Go, of a system cannot be altered by a change in ni independant of 'J nj when J is participating in the equilibrium reaction. The equilibration of a system in this case is related to the restoration of the chemical potentials of all the species in two connected phases within a certain time interval after a change.

The Recognition Process in a Chemical Sensor The whole recognition process in a chemical sensor is a complex procedure consisting of the partition, xi,m/xi,aq,xj.&j,aq, xij,m/xij.aq and xijmlxij,aq of the chemical species Ivt PJand L P , LJVJ between the two phases, and the host-guest interaction resulting in an overall Gibbs free energy or chemical potential of the recognition process. The chemical potential over all components I and J is equal to the sum of the chemical potentials of all single species. For a single species I, the free enthalpy under chemical equilibrium conditions is:

.

Pi., = Piaq

(3-11) m

G; =-R T In (xi.m / X i q ) = - R Tln (ki )

(3-12)

7

where k is here the overall distribution or partition constant of I in an infinitely dilute solution under equilibrium conditions. This formulation is very generally used in considering the partition of compounds between aqueous and membrane phase related to their chemical reactivity and solubility. ki is synonymous with the lipophilicity of the compounds (see section 4.6) when only the solubility is considered. The term "chemical potential" refers to the activity ai, of a chemical target compound or the fugacity,fi, which approximate to the molal [mol kg' solvent] concentration in infinitely dilute solution. For reactive compounds, the chemical potential has a positive sign. A change in the molar free enthalpy, AGF, by introducing a compound with the activity ai, may be denoted by: 9

AG:=Gi + n i R T l n a i and

-

9

A& = p i + R T l n a i

(3-13)

with ai =A /f0 = pi / p9 for gases and vapors (p: partial pressure relative to the pressure in the standard state). Under standard equilibrium conditions:

90

3 ControllingSensor Reactions

e

Gi = - n i R Tlnai

(3-14)

e

For the standard.state at infinite dilution where 47 = 4 and a;is equal to 1, no additional assumptions are necessary to describe the thermodynamic equilibrium for solutions. A change in molar free enthalpy is always associated with an activity change. Nevertheless, the evaluation of the activity values may be very problematic (see section 3.4). Within the membrane, activities of components are generally replaced by their molal concentrations (see section 4.2). Assumptions include: -the activity coefficients of membrane components are constant or unity -the solvent activity and composition is constant, e.g., hydrated plasticizer or polymer - the ionic strength is constant - the ligand or reactand activity remains constant. Most of these assumptions are far from being fulfilled (see section 3.4 and chapter 6). Especially when making generalizations, a compromise and a general notation is needed. For aqueous systems, nonthennodynamic assumptions are made (see section 3.4). However, within the membrane neither the ionic strength nor activity coefficients are currently accessible. Therefore, for the theoretical description of membrane equilibrium reactions concentration terms, specified by square brackets [I, are used; molal concentrations should be preferred. Basically, these can be replaced by activities, an, of each of the n participating components in infinitely dilute solutions. For aqueous solutions, the activity coefficients are calculated on the basis of the Debye-Huckel and Pitzer formalism (see section 3.4). To solve the conflict in notation, an infinitely dilute membrane phase is assumed and the thermodynamic variables are used to express the generalization over different types of sensor.

The Partition of Species Between the Sample and the Organic Phase The analyte and the interfering species participate in the aqueous and the organic phase according to their chemical potentials. Following Nernst [8], the partition coeficient k is defined as the concentration ratio of a specified molecular species in a solvent pair. The terms distribution coefficient or apparent partition coeficient are reserved to describe the ratios of the distribution of total concentrations between two solvents, including ionized, complexed, and associated species [9], referred to by the term overall distribution. The relative partition of two chemical compounds in two solvents with different polarities can be denoted by the lipophilicity of the compound (equivalent to the chemical potential). The lipophilicity governs the partitioning of a molecule into the more apolar phase of an immiscible solvent pair and is quantified by different methods (see also section 4.6). (The lipophilicity can also be referred to as hydrophobicity.) A lipophilicity scale for anions and cations is given by the lyotrophic series. For cations and anions, the lyotrophic series result in the following preference of ions for the organic, apolar phase:

3.1 Thermodynamically Controlled Sensor Reactions

gases: PrNHz > MezNH

91

- EtNHz > Me3N > MeNHz > NH3

The lipophilicity of neutral compounds may be quantified by estimates of the Hansch lipophilicity, the Taft parameter, and the Henry's law constant [ 10-1 31. Experimental evaluations are provided by thin layer chromatography as well as the traditional method of extraction and partition in octanol [14, 151. The above description also applies to the partition of the free analyte and the interfering compounds, complexes and host-guest products generally. This means that the more lipophilic a compound is, the easier is the transition into the organic phase. Exchange systems without real selectivity are in some cases sufficient for a sensor response. Sensors which make use of this condition are chloride sensors, which are sensitive to the most abundant anion found in biological specimens, based on organic ammonium compounds, and calcium-selective membranes, which use phophates as ion exchangers. The performance of both systems is not, however, entirely satisfactory within the biological range. A change in this lyotrophic "Hofmeister" reactivity is typically induced by the host compound related to the specific chemical reaction. The chemical equilibrium reaction based on the partition coefficients due to solubility only is:

w

V

where R, and Xag"are ionic sites primarily soluble in the membrane and aqueous phase, respectively. They contribute to the electroneutrality of each phase. They compensate for the charges exchanged, and thus have a catalytic effect on the transfer of a charged analyte. For uncharged species where vi, vj = 0, they may be electron acceptors or donors (mediators), basic or acidic compounds, or any other reversible catalytically active compounds. Bulky lipophilic anions are generally added to the membrane phase to prevent uncontrolled exchange of anions [16, 171. Ion associations are hindered by the bulkiness of the sites and the increasing effective radius for ion interactions and pairing. Thus, bulky lipophilic anions are generally preferred as charge transfer catalysts, since the electrostatic force decrease with the radius r, as l/r6. Several such compounds are available [18,19]. Replacing [P](aq) with the activity of the analyte species ai,aq, and [Pj](aq) with the activity of the interfering species aj,ag in the aqueous phase, and introducing [P](m) and [Pj](m), the selectivity coefficient K ii, based only on the solubility of the compounds, is defined by:

92


(3-16) Within the lipophilic, solvent polymeric bulk membranes of sensors, the activity of the compounds is generally assumed to be equal to the concentration and the activity coefficient is close to unity or at least constant. General expressions, for the chemical potentials, 4Trn m and &wm,within the membrane, and within the aqueous phase, and the molar free enthalpy, AG , for the selectivity of an ion transfer under equilibrium conditions at constant pressure and temperature are:

v.aq Caq,

(3- 17) m

m

m

(3-18)

AGij=-RT(lnkj -Inki)

Determining and calculating these equilibria helps to elucidate the effects of association and solubility of differently charged or polarized species within the membrane. These equations also help to describe not only the discrimination of interfering compounds, but also the influence of the membrane medium and composition on the preference of the anaiyte. Based on the formulated partition equilibria, the selectivity coefficients of even a blank bulk membrane without ligand can be estimated and. compared with the effect of the complete analyte-selective organic phase. The consequence of this procedure is that the assumptions of infinite solution in replacing activities by concentration units have to be reconsidered. In order to take account of association processes, the mass balances have to be taken into account, as shown in the example of a primary cation I"+ and an interfering cation Jv+ which can both associate with a lipophilic anion within the membrane (m).

c-

(3-19) (3-20) Equal stoichiometry as well as equal charge is assumed for all species. The chemical potential of the associate within the apolar membrane phase can be assumed to be increased compared with the chemical potential of the dissociated ions since electrostatic repulsive forces may be at work for the charged species in the apolar medium. However, if the reactivity of the associate is lower, the ion exchange may be hindered, resulting in nontheoretical response functions. The membrane composition is stabilized if an interaction between the anionic site and, e.g., a protonated indicator occurs, this is observed for optodes generally. An exceptional membrane stability has been observed for the chloride optode. This was assumed to be due to a ligand exchange at the metal organic host compound, where the negatively charged indicator replaces the extracted analyte anion (see section 6.4.3). This assumption has been borne out by experiments not only with the chloride optode, but also with optodes involving the stabilization of the protonated chromoionophore by the lipophilic counterion [20, 211. Such

3.1 ThennodynamicallyControlled Sensor Reactions

93

mechanisms seem to operate in the stabilization of solvent liquid bulk membranes and ensure a longer life-time of the membrane by preventing immobilization of the membrane components.

3.1.2 The Recognition and Transduction Process A large variety of neutral ionophores have been developed during the past 30 years which recognize chemically ions in solvent polymeric bulk membranes [22]. The dehydration of the ion and the charge separation resulting from selective, reversible complexation by a ligand are the key features for the potential formation process at the interface, called "chemisorption of the primary ion" by E. Pungor [23]. The overall constant which quantifies the discrimination of an interfering ion against the signal induced by the primary ion is the selectivity constant Kp"', (see Figure 3-1 and section 5.2). The complexation and charge separation of the analyte rJ ion competing with interfering ions are sensed by a change in the electrical potential which counteracts the ion exchange and the charge separation. The changing potential indicates the work done by the ion exchange. However, the question, as to whether the ion or the ion-ligand complex is transferred to the organic membrane phase cannot be answered on the basis of thermodynamics. The transition of the charged species through the boundary is strongly influenced by the competition of the membrane composition. The complexity of the chemical recognition process is probably best illustrated by the Born cyclic process for recognition of an analyte I in an aqueous phase by a reactand or ligand L implemented in a membrane (see diagram in Figure 3-1) [24] (adapted version). The diagram shows an analyte or primary ion, Pi, and an interfering species JY with charge numbers vj and vj. It can be formulated in the same manner for ions, uncharged and neutral analytes. The recognition process participating between the sensing membrane and sample phase is characterized by the parameters k, denoting the partition equilibria, Ki,l and Kj.1 denoting the stability constants of the host-guest product of the species I and J assuming 1:l stoichiometry. In characterizing a specific sensor, the selectivity coefficient is reported. It represents a phenomenological, experimental variable which contains the various partial equilibria of the partition and molecular interaction process. Equilibration of the analyte and interfering species between membrane and aqueous phase:

cf

The chemical potential and the molecular interaction together act to compensate for the molar free enthalpy of hydration Ghydration, to the final, molar free energy of transfer AGtransfer,typical for the recognition process. A complete description for ions was attempted by Morf [25, 261 and Simon et al. [27]. The chemical reaction and the mass balance of the

94

3 ControIIingSensor Reactions

k r

1

t

llk

K ij.1

I vaqi + L a q + J z

Figure 3-1.Born cyclic process in terms of the partition coefficient kr, of the species I and J and the products IL and JL between membrane m, and sample phase aq, and in terms of the m equilibrium constant, 4 , of the host-guest interaction. The membrane is selective for the analyte I [8]. Only 1:l stoichiometriesare considered

complexation reaction for a cation is presented in the following equations. wual charge of the analyte, 12,and the interfering species, in the aqueous phase, and equal charge and stoichiometry of the products, I L r (m) and (m), are assumed:

c-, JT

3. I Thermodynamically Controlled Sensor Reactions

1;

+

3"; + RL- + p L + JL:

(m)

2

IL; (m) + q L + 3 ; + Rk- + :J;

95 (3-21) (3-22)

The chemical equilibrium reaction is formulated in order to allow a possible association of charged species within the membrane phase and the aqueous phase. There may be competition between the lipophilic counterions Rk-, added or caged in the polymer, and counterions X&, coextracted into the membrane. An ion association within the aqueous solution I membrane interface results in a reduction in the extracted charge and should increase the slope of a potentiometric response function. Different charge numbers of analyte and interfering species, as well as different stoichiometries of the complexes, may considerably influence the selectivity assumptions within a dynamic range, and may relate them to the ligand concentration within the membrane and the measured activity range of the primary and the interfering ions. This is especially relevant for sensing layers with a scarcely discriminating selectivity coefficient, compared with the actually measured activities (see sections 3.4 and 4.3). The overall equilibrium constant in the host-guest reaction for the analyte I, as well as for the interfering species J, ignoring nonspecific associations is: (3-23) The corresponding molar free energy of complexation is: 01

0

AGe,= AG,,

m

+ R Tln Kq

where

AG,,=-RTlnK,, 0

0

(3-24)

where AG,; = 0 under equilibrium conditions at constant temperature and pressure; p and q, are the stoichiometric numbers of the analyte-ligand complex and the complex between the ligand and interfering ions J, respectively. Ideal solutions are not a necessary condition if the activity of all the components is introduced in the mass balance. However, in order to refer to concentrations, nonthermodynamic assumptions need to be made. These assumptions can be generalized for uncharged analytes involved in a recognition process. If the stability constant can be determined, the free energy. of complexation can be calculated. Ideally, the stability of a product, and the association or stability constant of an ion ligand complex should be representative of the selectivity behavior. In the past, stability constants were frequently determined by determining the solubility of the complexes in organic solvents. Today, they are usually determined by vapor pressure osmometry (VPO), freezing point osmometry, and NMR, or calorimetric titration. Osmometric methods are complex in the case of different stoichiometries between ligand and ions; NMR is time and cost intensive. Thus the most convenient method is usually calorimetric titration. The thermodynamic quantities for a large number of ligand-cation complexes have been compiled [28]. Kauffman et al. [29] and Vogtle and Weber [30] classified the entropy (AS) and

96


the enthalpy changes (AH and AU) upon complexation into four categories according the major contributor to the changes in molar free Gibbs energy (AG). 1. A H < O , A S > O 2. AH < 0, AS < 0: enthalpy-stabilized complexes, with a minor positive or negative entropic contribution 3. AS > 0, AH < 0 4. AS > 0, AH > 0: entropy stabilized complexes, with a minor favourable or unfavourable enthalpic contribution Izatt et al. [31] showed that for 15-crown-5 and 18-crown-6 derivatives, AH and AS compensate each other, AH being the dominant quantity in determining the magnitude of log K.This effect they called the AH-AS compensation efect. Its universal validity has been tested over a vast range of thermodynamic data available for a large number of cyclic and acyclic ligands. The validity of the enthalpy-entropy compensation effect was demonstrated for a-,/3-, and y -cyclodextrins, in 1993 [32]. The inclusion complexation with naphtalenesulfonateswas exothermic and, with two exceptions, enthalpy driven (negative AH) with varying positive or negative entropy contribution (TAS) to the complex stability (negative AG). The parameters were evaluated as the slope (factor a to multiply AH) and intercept (TAS) of a least-squares fit based on the data from calorimetric titration apd iteration of the stability constant K. The entropy contribution was interpreted as deriving from the desolvation process, and seems to be a major factor governing the host-guest complexation. As long as TAS has a positive sign, the complexation can take place even in the absence of an enthalpy increase. Large slopes (a= 0.76-0.86) were interpreted as due to moderate or substantial conformational changes typical of flexible acyclic ligands (podands, cyclic crown ethers). In contrast, large intercepts (TAS = 16.0 kJ mol-l) typical of the more rigid skeleton of bicyclic cryptands, were explained as the result of extensive desolvation of both cation and ligand with small conformational changes. For the a-,p and y-cyclodextrin-naphtalenesulfonate complexes, the slope was calculated as 0.9. This was unexpected, given the rigid skeleton of the cyclodextrins (CD). This behavior, however, fits in with the proposed reorganization of the hydrogen bond network within the CD molecule upon inclusion complexation [28]. In the treatment of the thermodynamic GibbsDuhem function for complexation reactions, the chemical potential is not specified, but included in a rough summarizing calculation of the thermodynamic parameters. The results for CDs described above, are consistent with the earlier, rather surprising results of investigations into the thermodynamic parameters of interactions between various lectins (oligopeptides) and a wide variety of oligosaccharides [33]. The experimental method used relied on ultraviolet differential spectroscopy and the association constants yielded by the van't HofSplot in the temperature range 283-3 13 K [34]. The different absorbances at 290 and 3 15 nm were due to tryptophan residues present in the active site. The experimental data indicated that the interaction between the host and guest species involved very similar changes in the conformation of both. It was proposed that the reason for the linear enthalpy-entropy compensation was the weaker hydrogen bond of water to the amphiphilic surfaces compared with the stronger interaction between water molecules in the bulk water (see section 2.2 and chapter 4). Even at extended binding sites, the desolvation was combated by conformational


97

changes due to the host-guest interaction. This very common compensation pattern is likely to be a consequence of the properties of liquid water as a solvent, regardless of the solutes and the interactions studied. The selectivity coefficient of the sensor reaction under equilibrium conditions for one particular activity of the analyte (I) and the interfering species (J) is given by the ratio:

c'.

(3-25) with the molar free energy difference: m

m

m

m

m

AG,, i j =(AG,, j - AG eq I) = - R T (In K,, i- In K,, j )

(3-26)

The host-guest reaction may now be more generally considered as a chemical reaction where solubilization, complexation, and chemical reactivity contribute to the molar free transfer energy. The selectivity coefficient K F however, is an empirical quantity which describes the extraction behavior of a polymeric solvent bulk membrane and comprises the partition of an m analyte within the membrane (k ias well as the stability and association constant3;/ $. Thus the stability constant ,e.g., determined in a pure solvent is the most important factor, but is usually not sufficient for the description of the selectivity behavior of a ligand in a polymeric liquid membrane. In a sensing system at constant temperature, pressure, and mass, and with infinitesimally e small changes in volume, the standard Gibbs free energy of the chemical interaction AGR, may generally be calculated as the sum of the different contributions of the molar free standard e enthalpies according to the Born cycle, AGB, under equilibrium conditions: e e AG; = - nij AGB (products ij) + njj A% (reactants i j ) ij

(3-27)

'J

Based on this equation, the free standard enthalpy for the reactants has to exceed the free e standard enthalpy for the products (AGB (reactants ij) < 0) if the reaction is assumed to proceed spontaneously. As the membrane-based sensing elements are represented by a model e combining an extraction step with the recognition process, AG represents the sum of both contributions and can now be described in terms of the changes in the molar free energy associated with the transfer of a target species from an aqueous phase into an organic (membrane) phase involving the molecular interaction with any type of host compound. The transfer by solubilization and dehydration takes place in the boundary between the organic and the aqueous sample phase with different permittivities E r aq and E r solvent. Therefore:

AG; = AGransfer= -

g

e nij AGB (prod ij3 +

c nij A

e

6 (react ij>

(3-28)

ij

where: (3-29)

98


This formulation makes sense since some of the contributions can be estimated from parameters readily available in tables (energy of hydration, permittivity). The thermodynamic parameters reported are useful to rationalize the individual host-guest reaction in a specified solvent and the change in the stability constant or in AG for the particular guest-host-solvent complexes. The complex, with stability constant PWq,in aqueous solution, is supposed to participate ILP in the membrane and sample phase in a ratio defined by the partition coefficient k;’. The overall distribution coefficient [IUPAC], is defined by: (3-30)

where [L(m)] / kFrepresents the concentration and partition of the ligand in the membrane at the interface to the aqueous solution. By introducing the chemical potential and assuming that L and IL are mainly dissolved in the membrane medium and I in the aqueous sample, the equilibrium for a neutral ligand or reactand L, can be denoted by:

(3-31) The overall selectivity factor of a recognition process Kij ,is fully determined by the ratio of m m the overall equilibrium constants Keq / K , , of different species with the same ligand discriminating the selected analyte species I, with the equilibrium constant K Z i , from the interfering species J. Depending on the interpretation of the Born process (see earlier), the selectivity coefficient can either be defined by the transfer of the analyte-host complex (assuming, e.g., complexation in the aqueous phase Pmaq) or by the transfer of the ‘LP uncomplexed compounds described by r(l” k;, and complexation within the membrane phase

r;.Accordingly, the partition coefficients of the complexes or of the target species are

relevant. ([L(m)] / f )p expresses the artition of the host compound and its concentration in tp the aqueous phase, whereas [L(m)] expresses the concentration of the host within the membrane. In the following, both cases are formulated:

(3-32)

(3-33)


99

It is simply a question of the availability of data or of the experimental design to decide which approach is useful. Kz7 will mostly be represented by a single analyte, however, for environmental monitoring, the reactivity of a sensor with respect to a group of analytes, such as heavy metals is of interest. For the interaction of the stability constant and the partition coefficient in selectivity behavior: A reversible host-guest interaction is defined by an activation enthalpy of c 60 kJ mol-1 computed from NMR experiments (see section 3.2). Estimates of the activation energy by Eq. 3-51 result in a stability constant equivalent to j3 c 1012 at 298 K and normal pressure. In the case of the magnesium-selective membranes incorporating the carrier ETH 7025, the relative stability constant was estimated to be 104 for magnesium ions and 5 x 105 for calcium ions by potentiometric measurements with o-WOE as the solvent and 10 mol% KTpClPB relative to the carrier (see section 3.5). The free enthalpy, equivalent to a relative potentiometric stability constant of 10" is 8.3 kJ mol-1 at 297 K and atmospheric pressure (see later). By adding optimum amounts of borate (155 mol%) the extraction of magnesium ions is favored by a factor of >10 (SSM). In this case the emf values of 0.1 m o m solutions with chloride as anion are compared. This behavior is supported by the stoichiometry of the complexes, assuming 1:l complexes for Mg2+ and 1:2 complexes for Ca2+.

rq

Conclusions The free energy of transfer of an analyte, as well as that of interfering compounds, depends on a number of parameters which to some extent, can be measured by established procedures. The thermodynamic description of membrane models and interactions makes use of some phenomenological variables which can be investigated experimentally. The Gibbs free energy is a useful variable to observe the overall change in free enthalpy of a process in a closed system. However, if data for these measured variables are correlated with the composition of the participating phases, ideal solutions representing these phases have to be assumed or, for experimental assays, some nonthermodynamic assumptions have to be made (see section 3.4). This is the reason for describing the membrane parameters for infinitely dilute solutions. The interaction between host compound and analyte is one part of the extraction process which again depends on a set of parameters which can be evaluated. Examples for ions are electrostatic, dispersive, and repulsive interactions between, e.g., a cation and the ligand and the coordinating ligand sphere, the polarization of the surrounding medium by the charged complex, changes in the volume of the solvent induced by the cation and the complex, etc. The optimum coordination number, corresponding to a minimum of the free energy of hydration, is a function of ionic radius and charge. In designing a ligand these data have to be considered in the search for an optimum structure. A closed, but not isolated, system is in equilibrium when: a) its macroscopic properties remain constant with time; and b) its isolation from exchange of matter and energy with its surroundings causes no change in its properties. If a) holds but not b), the system is in a steady

100


state [35]. In most cases the system is in thermal equilibrium with the environment when working at room temperature. Thermal isolation is especially important when working in medical investigations at 310 K.

3.1.3 The Electrochemical Potential and the (Potentiometric) Sensor Response In 1987, Xie and Cammann suggested that "the response mechanism of ion-selective membrane electrodes is a very intriguing problem, which should elucidate why and how these membranes exhibit a Nernstian behavior and ion selectivity" [36-381. In 1975, Cammann focused on the electrode potential based on a theoretical description of the exchange current [39], whereas Buck, 1979, focused on the impedance model of the membrane, the boundary and the diffusion potentials [40].In 1981, Morf published an extensive report on different models of membrane transport for ion-selective electrodes and introduced a thermodynamic model [41]. On the basis of thermodynamics, the electrical potential is the work done to oppose ion exchange at the boundary of the two adjacent subsystems. The complexation, charge separation, and extraction of the analyte ion in potentiometric sensors is sensed by the change of the electrochemicalboundary potential which involves the electrical and the chemical potential. An electrochemical standard cell is defined by : Pt

I

H2(g)

I

H+(aq) 11 M+(aq)

I M(s)

(3-34)

The zero-current potential E is the difference of the electrode potential, EM,on the right side minus ERef on the left-hand side, and is identical with the potential differences, A& Aaref, of the two electrodes. Each electrode is a half-cell. The notation for a potentiometric cell, including a cation-selective bulk membrane as a part of the right half-cell is:

reference electrode

ion-selective electrode

(3-35)

For a full description of equilibrium conditions of the electrochemical cell in thermodynamic notation, the phase transitions have to be considered separately. In each phase, the chemical and electrical potential must be taken into account, since charge transfer occurs at each boundary. The electrical potential at the boundary counteracts the chemical potential change. The sum of the chemical and electrical potential is identical in each phase when the two half-cells are in equilibrium. Electrical work We is done when adding a charge to a phase with the potential @. Charge separation results in the so-called electromotoric force or emf. The work is: We=&F@ where F is the Faraday constant.

(3-36)


101

In thermodynamic terms, the molar Gibbs free energy can be identified with the yield in maximum electrical work at constant temperature and pressure, for small volume changes. The entropy production S in an electrochemical cell may be characterized as a function of the temperature change AT, the pressure change Ap, the changing chemical potential & as well as the change of the electrical potential A&

S = 6(AT, Ap, Ap, A@)

(3-37)

The change in enthalpy AH of an electrochemical system with constant T,p , and V is identified as the molar work of the reversible process Wr,=v put into the reversible system to equilibrate it.

AH = dW,v AG = dW,

(3-38) + p dV

(3-39)

A change in AG depends on the total work put into a reversible system for equilibration, minus the energy corresponding to a reversible change in volume. If no volume change occurs,

AG is equal to WE, and represents the maximum energy exchanged. With Eqs. 3-9, 3-37, and 3-40, the electrochemical potential can be related to the chemical potential and the electrical work aj, being the electrochemicalactivitiy of the species I: = y + z F @= p e + R T In ai + z F @

(3-40)

From this equation, it follows that a positive electric potential @ of one phase counteracts the uptake of a cation. For equilibration, the chemical potential of cations must decrease, assuming permselectivity. If the electric potential is negative, @ c 0, the chemical potential of cations rises at constant electrochemical potential. The region is favorable for the uptake of cations. This explains the electrophoretic separation of ions in an electric field. It is one of the fundamental principles of electrophoresis and isotachophoresis. The ion with the most prominent charge and the highest mobility is the leading ion in a defined electric field. A full thermodynamic description of the electrochemical potential of both half-cells of ionselective electrodes would be rather extensive and not useful for analytical purposes. Thus, for analytical applications, some assumptions concering thermodynamically quasi-static conditions and some nonthermodynamic assumptions (see section 3.4) are made: 1. The potential difference over the reference electrode is assumed to be constant, all boundary equilibria are assumed to be established, and the reference electrode is optimized with regard to this assumption [42]. A crucial part of the reference electrode is the liquid junction where diffusion potentials occur (see section 3.4). The composition of the calibration solution must be as close to the sample solution as possible. Under these conditions, the liquid junction potential is assumed to be constant.

102


2. The charge transfer at the membrane-sample boundary, occurs under fully reversible equilibrium conditions at constant temperature and pressure. The potential change, emf,of the permselective ion-sensitive electrode is solely induced by the selective ion transition at the membrane-sample boundary. 3. The selective ion uptake of the membrane is not competed by leaching of the same ion to the sample solution (factor influencing the detection limit). The membrane composition remains unchanged (no entropic decomposition!). 4. Nonthermodynamicassumptions (see section 3.4).

Under these conditions the description of the electrochemical reaction can be restricted to the description of the sample-membrane boundary. For further details see [37] and several theses (R. Eugster, E. Haase, G. Rumpf et al.) mentioned in the following chapters. The electrochemical standard potential for an ion-selective electrode is ideally described by the chemical standard potential p;, and the activity related contribution ai, of the analyte ion and the electric potential due to the charge transition. The neutral ligand contributes with its chemical ggtential and activity, and UL , and the complex with the chemical potential and activity h v and UIQ, of the analyte-ligand complex with the stoichiometric factor p. Complexatih is assumed to be the driving equilibrium reaction for the exchange of a species between the aqueous phase (') and the membrane phase (0) boundary. The membrane boundary potential is generated by the charged complex:

(3-41) If the ligand is a neutral one, the complex is charged and contributes, with the charge of the ion, to the electrochemical potential of the sample-membrane boundary. The equation is valid for anions and cations. For uncharged analytes, the term involving the electrical potential is zero. This representation allows an unambiguous formulation of the charge transfer and the generation of the membrane potential. The standard potentials are consistent with infinite dilution, a pressure of 100 kPa, and a temperature of 298 K. On this basis, the overall partition, the stability constant, and the selectivity factor can be formulated by the chemical and electrochemical potential (for details see [43]). In optical ion-sensing systems, the same equations can be applied. Generally, for uncharged analytes the Faraday constant F is omitted and the electrical potential is inoperative and zero. A change in volume by mass transfer is not taken into account since only extremely small volume changes are expected. This substitution of the membrane potential by the electrochemical potential is supported by the group of E. Pungor [44] who discussed the Donnan potential postulated by the theory of Teorell-Meyer-Severs (TMS model; see section 3.5). For a pure ion exchange membrane the electrochemical potential is described by the equilibrium potential between anions X+, R+,


103

and cations Iv+, of two adjacent phases, and (0), corresponding to electroneutrality conditions. However one of the cations or anions, R+, in this case, cannot permeate the boundary or, based on the partition coefficient, only in negligible amounts: (I)

Assuming that the anion R-V cannot change the phase, the change in the electrochemical potential is due to the electrical work and the phase change of the species IVY after changes of X-V. Thus the membrane potential is dominated by the chemical potential of R and is a Donnan potential.

Conclusionsf o r Sensor Technology and Sensor Development Out of these considerations, some thermodynamic assumptions on which the concept of reversible sensors is based, have to be kept in mind for future experiments and for the theoretical treatment of a reversible sensor. These assumptions are valuable for optical as well as potentiometric sensors treated in this volume. 1. The potentiometric sensor is reversible, assuming an infinite resistance of the -analytesensitive layer to charge transfer. The charge transfer may only correspond to infinitesimally small currents. Subsequently the emf (potential difference) is the equilibrium value. The charge transfer resistance for electrode membranes with a diameter of 7 mm is in the range of c lo7 a. The current raises to lo-* A if the cell potential is in the range of 1O-I V. In the reversible electrochemical reaction, the entire change in Gibbs free energy during the potentiometric cell reaction must be transformed into electrical work and ideal Nernstian behavior results. Energetic reversibility is achieved if the same amount of free energy, electrical work, is aquired from the cell reaction proceeding in one direction as is supplied to the reaction proceeding in the opposite direction. This is the basis of voltammetric and amperometric reversible electrochemicalcells. Otherwise irreversible reactions occur.

2. Since AGO = AHo - T A P , the free energy of the charge transfer is related to the temperature of the system. AGO drifts to more negative values with an increase of temperature as well as for entropically driven reactions. From the definition of AG, the system is evaluated at constant temperature, and pressure, whereas small changes of volume are taken into account.

3. Since volume changes are not considered, only infinitely small mass transfer of all participating species is allowed for if no nonthermodynamic assumptions are made.

104


4. The Gibbs free energy function is useful to describe overall thermodynamic equilibria of chemical reactions phenomenologically. On the molecular basis (temperature-controlled NMR studies), the molar enthafpy is the relevant state function. The Gibbs free energy function allows one to estimate the molar free energy of each reaction with known association or stability constant and, vice versa, to calculate the equilibrium constants from the free energy released in a temperature- and pressure-controlled system (Eq.3-12). 5. The Gibbs free energy of the recognition process for a primary ion (analyte), must be more negative than that of the discriminated species. Therefore, the selectivity coefficient may be defined by the difference in AG values as well [43]. This statement does not comment on the energetic source of the negative molar free energy change.

3.2 Thermodynamics of Nonequilibria: Diffusion and Steady-State In contrast to reversible thermodynamic processes, the nonequilibrium thermodynamic description of a process is devoted to its "dynamics". L. Onsager [45] developed the theory of processes which occur sufficiently close to equilibrium. In describing the deviation of a state from equilibrium, linear functions are applied: This is called linear thermodynamics or thermodynamics of irreversible processes. However, the thermodynamic description of states far from equilibrium is also possible using nonlinear thermodynamics. How structures organize themselves and form patterns has been the object of intensive research. In linear irreversible thermodynamics, a deviation from equilibrium can be treated as a macroscopic thermal fluctuation. Fluctuations are deviations from a mean value of a probability distribution which can be the thermal equilibrium. The statistical connection becomes directly apparent. Fluctuations of the thermal variables around a homeostatic setting point are key features of the metabolic steady-state. Pathological processes can no longer be described phenomenologically as large declinations of the physiological situation. They subsequently need to be identified by independent mathemathical and analytical approaches. The termpuctuations may build a bridge between the macroscopic deterministic theories and statistics. Alternatively, a theory of fluctuations may be a bridge between equilibrium thermodynamics and nonequilibrium thermodynamics. Fluctuations of volume, particle numbers, pressure, temperature, entropy, etc., are possible. In a closed system, a spontaneous equilibration process is associated with a state of maximum entropy. The equilibration process is the most stable state of a system. In an open system, the spontaneous structured objects are not compatible with maximum entropy. Moreover, equilibrium thermodynamics do not consider the time frame of any process and are thus not suitable for describing open, dynamic systems generally. Irreversible thermodynamics enable the exchange of entropy between an inner and an outer reference system. The magnitude of the produced entropy is a measure of the irreversibility. It is characteristic for an open system to be far from equilibrium. The entropy is never at a maximum and there is a continuous flow of energy through the system, from a source to a sink. This energy flow becomes constant over time in the steady-state. The energy which crosses the system is

3.2 Thermodynamics of Nonequilibria

105

utilized to produce the work which maintains the system far from equilibrium. In a three compartment stationary system, the entropy S2 in the intermediate system has to be smaller than the entropy in the neighboring compartments S1 and S 3 . Under these conditions, the entropy of the whole system is well below the maximum, thus ensuring that work is performed over a long period of time. This theories describe the steady-state of living organisms in contrast to the thermal equilibrium of reversible artificial systems. The entropy production in a steady-state was described by Prigogine 1945 by the theorem of minimum entropy production [46]. In contrast to thermodynamic equilibrium, the fluxes are different from zero under steady-state conditions. The conditions are limited by the invariability of all thermal variables describing the system. Assuming that the fluxes do not influence the variables, the flux of material, energy, or entropy must be compensated anyway. This is possible, e.g., by supplementationof substrates and elimination of products in a thermostatted system. This is how the metabolism of a living system is sustained. The composition and the chemical potential of the substrate regulates its affinity for some types of metabolic, enzymatic reaction. The driving forces, based on the chemical potentials, act as long as the system deviates from a general, diffusion steady-state. In a steady state, the derivation of the entropy over time vanishes: a minimum entropy is achieved. Thus, a steady-state can never be linked to a closed system. All biological system, as well as enzymatic biosensors are examples of open steady-state systems. They are characterized by constant driving forces and fluxes, of which some are far from zero (input and output fluxes), driving an intermediate flux, in contrast to the equilibrium where forces vanish and entropy is minimal [47]. However, in both systems the life-time is limited. In the artificial systems, in approximating maximum entropy, in the living system, in approaching equilibrium (death) where work is no longer done. In irreversible, linear thermodynamics it is assumed that the deviations from the equilibrium state are so small that a linear relationship between the thermal variables and their time derivatives can be posited. The fluxes J , describe the production of entropy. A flux represents the first derivative of a measurable thermal variable A, with respect to time:

d-4,

J , =-

dt

with

a, =A, -A,

0

(3-43)

where ol, means the deviation of any thermodynamic state variable A,, from the equilibrium state A:. The flux is a linear function of the driving force which is the Gibbs free energy difference, as in the case of the diffusion laws and in Donnan potential. Other examples are migration phenomena in electrophoresis or the electroosmotic flow which underlie different driving forces. Onsager has postulated the universal properties of the following equation which connects the so-called thermodynamic fluxes with the thermodynamic forces. Fluxes clearly show the differentiation of any variable with respect to time, driven by the force X,. The entropy production is related to the product of the driving force X, and the Flux J , and is simultaneously connected to the time domain. Generally these equations are called "transport equations". In contrast to reversible processes, the energy exchanged is never maximal. The diffusion equilibrium described by the chemical potentials may now be derived from the time as a diffusion steady-state. In the Gibbs-Duhem equation, the thermodynamic state

106


function for the free enthalpy G , is extended by the chemical potential (see Eqs. 3-7 and 3-8). In a closed, adiabatic system, where dU = 0 and dV = 0, the Gibbs-Duhan relation is reduced to:

The phase transfer of a compound i, with the potential pi,1, in phase 1 and, is related to an entropy production, Q = dS I dt, denoted by:

in phase 2

In Fick's law of diffusion, the differential dni I dz is the driving force for diffusion. However, when expressed in terms of linear thermodynamics, the essential force is p i ~ l T , which is a local difference in chemical potential which causes a pressure difference, where dnildt is the corresponding flux of matter. Einstein related the two quantities, the diffusion flow of matter and the gradient of matter, expressed as mole density, in the Fick diffusion coefficient D/cm2sd (for details see [48]). The coupling of charge and mass transfer in electrochemical experiments and optical sensor reactions may be described by flux equations according to linear, reversible thermodynamics, also known as "thermodynamics near equilibrium" where the time domain is taken into account. Considering electrochemicalfluxes, Cammann (1973,1975) [49] introduced charge transfer in potentiometric systems to describe the selectivitiy of an ion-selective electrode. Different efficiencies in charge transfer for different types of ions were described by the current flow densities. The current density charge (flux) at the boundary layer is initially driven by the same force, denoted by djjldz, which is the chemical potential dpfdz along the z-axis of permeation. The concentrating effect inhibits the influx and forces the efflux of the different transferred components I and J, ideally reaching equilibrium where influx and efflux have the same rate constant.

3.3 Rate-Controlled Reactions: Mediated Enzyme Reactions Thermodynamics involves the study of energy transformation in closed or open systems and descriptions of the systems by thermal variables. Time is not used as a variable in thermodynamics. In rate theories, the mechanisms of reactions and the processes involved in arriving at equilibrium are studied as time-dependent mechanisms. Thus, all chemical processes and systems can be described both thermodynamically and in accordance with rate laws, rate constants, and kinetic aspects. Steady-state conditions and enzymatic reactions are typical representatives where the mechanisms to come to partial equilibria are described by rate laws. Rate laws are further used to describe the response function of a detector or a monitoring system with respect to the geometry, volume, and flow rate of measuring cells, the speed of a chemical reaction, or the dynamics of mixing. The rate laws are fundamental in

3.3 Rate-Controlled Reaciions: Mediated Enzyme Reactions

107

describing the macroscopic life-time of sensors in terms of the Arrhenius law [5, 501 and the leaching out of membrane components by diffusion (see section 3.5). However, even for the molecular recognition of ions, the results of measuring the relative emf of different ions and of drawing a selectivity scale may be very different, owing to kinetic aspects of the ion exchange.

Rate-Controlled Reactions in Molecular Recognition When an overall reaction is the sum of several steps, the equilibrium constant is a product of all the ratios of the rate constant for the individual steps:

(3-46) where k are the rate constants for the forward reaction of the individual steps and k' for the reverse reaction [3, 51-54]. This type of description demonstrates that all the participating species contribute to the final signal, depending on their rate of uptake relative to the leaching reaction. The rate, however, for the primary species can be very different from that for the interfering species. For an activated surface, the equlibrium constants, K i and Kj, given by the rate constants for the exchange of the nj interfering species J, and the primary species I, also describe the selectivity coefficient. The general rate constants for the uptake kjo and release k'jo, the activity aj,as in the aqueous phase, and the activity in the membrane phase characterize the interfering species relative to the primary species with the rate constants ki,, k'io:

(3-47) The selectivity can now be associated with the rate constants of component J as compared with I. This notation allows reference to the analytical process. Under the condition that the equilibrium constant Ki is equal to K j , the rate constants for each reaction may nevertheless vary considerably. Assuming that ki is 102 times higher than kj, but the stability of the products JL is 100 times lower, the sensor may show a reasonable selectivity in a kinetic approach. If one or both reactions are slow, the equilibration is very slow. In this case, Nernstian behavior of an electrode is no longer observed within a reasonable measuring time (< 2 min). In this case, a kinetic influence, which is dependent on temperature and the activity of the species I and J, is observed. A kinetically limited behavior may be observed if the analyte has a markedly slower rate constant for dehydration than the discriminated species. Such kinetic effects have been observed for calcium-magnesium exchange by magnesium selective electrodes. The result is a time hysteresis of the response function. In this case the analyte is discriminated in short time measurements and the equilibration reaction shows a timedependent cyclic behavior upon activity changes. Other sources may be the different stoichiometries of two species complexed adequately.

108


In each cases where there are kinetic limitations of I or slow kinetics of J, a slow equilibration is the result. The reasons for a kinetic limitation may be slow diffusion based on hindrance of the mobility of the complex for geometric reasons, or a slow phase transition due to a charged adsorbed layer. The reason for a slow complexation may be a high free Gibbs energy of hydration and a slow solvation of the complexes. By the Arrhenius equation characterized by the pre-exponential factor A ( M - k l ) , the Gibbs free energy of second-order reactions, -AE (J mol-l), or the activation Gibbs function, -AGO. are related to the rate constant, k (M-ls-') [68]: k=Ae-

AEIR T

- e- AGOIR T

or

-

R T In k -AGO

(3-48)

-

2.47 In k -AGO

An unfavorable rate constant can be compensated for by a higher chemical potential and a higher stability constant, where the more favorable stoichiometry at low concentrations of the host compound within the membrane favors, e.g., the magnesium ion selectivity. The fact that the stoichiometry of a complex is decisive for the discrimination of the primary ion has also been shown in the case of the magnesium-selective electrode. Assuming a similar complexation constant for both species I and J, however, the species compete for binding sites if the stoichiometry of the complexes is different. The interfering species with the higher complexing stoichiometry J, is favored if the complexing sites L are abundant. Otherwise the primary ion is favored. The selectivity scale (see sections 4.2, 5.2, and 5.3) can look quite different, owing to the method of determination and the kinetics. Another relevant aspect of the rate description is the association-dissociation rate of immunological reactions (see section 2.2.9). This description demonstrates that the more binding sites involved, the lower the rate constant and the higher the activation barrier for dissociation.

Steady State Kinetics of Enzymes In section 2.2.7, some aspects of enzyme catalysis were mentioned. The equilibrium constant between an enzyme E and a substrate S can be expressed in terms of transition state theory. The equilibrium between E and S and their transition state ES* is related to the activation energy -A@ of the catalytic rate constant and to Michealis-Menten kinetics (see below). The generation of the transition state is part of the steady-state reaction, where an enzyme metabolizes a substrate and creates products of this metabolism. The steady-state normally refers to a state where the rate of formation or association is in balance with the rate of catabolism or dissociation. In enzyme kinetics the concept is applied to the concentration of intermediates in the transition state. It is during this steady-state that enzyme activities or substrate concentrations are traditionally measured. Such measurements provide a good approximation as long as the enzyme activity and substrate I product concentrations do not change considerably during a relatively short time period. Depending on the aim of an assay, either the enzyme or the substrate is in excess.

3.3 Rate-ControlledReactions: Mediated Enzyme Reactions

109

In an assay where the substrate is in excess, the enzyme activity [El, is the limiting factor for the rate of a chemical reaction measured. In an assay where the substrate concentration [Sl] is to be measured, the cosubstrate concentration [Sz], the enzyme activity [El, and in some cases the enzyme-coenzyme complex are in excess. Thus the reaction rate is limited by the substrate concentrationor activity [S 11. If the steady-state reaction is an oxidation or a reduction, it can be controlled by a heterogeneous charge transfer in an electrochemical cell with a typical applied potential. In this case, the resulting steady-state current is given by the so-called Levich equation:

w1I2v-lI6 C,b

iL = 0.62 n F A

(3-49)

where Do is the diffusion coefficient, F is the Faraday constant, n is the number of electrons exchanged, A is the electrode area, w is the rotation speed, v is the kinematic viscosity, and C ,b is the bulk concentration of the substrate. At the electrode surface the oxidation or reduction of the analyte-substrate is diffusion controlled and dependent on the shape of the concentration profile within the Nernstian diffusion layer. The best defined configuration of an amperometric electrode is the rotating disk electrode. At this electrode the shape of the diffusion layer is governed by the controlled potential perturbation of the electrode and the mass transfer by diffusion and convection. Increasing the rotational speed of the electrode increases the mass transfer and causes a thinner diffusion layer with a steeper gradient. At constant rotation speed, the concentration or activity gradient is coupled to the bulk activity or concentration of the substrate or analyte. Both the concentration and the activity are zero at the surface of the electrode. However, if the activity and concentration of a substrate are not the same in the sample bulk, the gradient will be different. However, in highly concentrated broths such as are present in a bioreactor, a considerable influence can be observed. Regardless of this theoretical difference influencing the enzyme activity, the metabolic processes of cells and enzymes are inhibited and limited by high product concentrations. According to theory, it must again be the substrate activity which is the relevant biological dimension. The selectivity of the amperometric electrode is determined by four factors: the potential applied, the mobility of the compounds (see section 3.4), the specificity of the enzyme, and the PH. An unmediated enzymatic reaction can be described by the following scheme: kl

E+S1+S2

2 I

ES1+S2

kcat.1

+ E'Si'+Pz

k-1

bt.2

2

E+P1+P2

k-cat.2

kH1

HE+S1+S2

2 I

HESl+S2

k-H1

ES1 is the enzyme substrate complex, E'S1' is the intermediate involving the transition state of the enzyme, P1 is the product of the substrate S1 transformation, whereas P2 is the product

110


of the cosubstrate, S2. For hydrolytic processes, the cosubstrate is water which is in excess in aqueous solutions and thus, does not, normally limit the process. For oxidation reactions, the cosubstrate is oxygen in most cases. Local oxygen pressure and oxygen diffusion are very decisive parameters, moreover the products H202 or OH- are known to inhibit the enzyme reaction. This is not true for a mediated reaction where considerably lower potentials can be applied and oxygen is no longer the electron acceptor. The reduced enzyme-coenzyme complex is continuously regenerated by the electrode reaction (see diagram below). The sensitivity is increased by several orders of magnitude (e.g., 10-9 mol/L) and the mass transfer and generation of products is in the range of pmoles. Thus, oxygen is no longer the limiting factor of the reaction. We call this type of electrode the third generation. For the low detection limits shown at the mediated hypoxanthine and peroxide electrode mol/L for hypoxanthine and peroxide [58-60]), the influence of the process at the counterelectrode can be neglected. The rate constants of the forward and back reaction are denoted by k l , k-1, and kH1, k-Hl, respectively, at two different pH values of the medium. This parallel reaction for a second pH can also be formulated where an inhibitor or a second substrate is involved when H is replaced by J. The transformation rate is given by kcat.1 and kcat.2 and the backcoupling effect of the product by kXat.2. The catalytic rate constant kcat, involves the transformation rate and the rate of the product being released from the enzyme and the enzyme being restored. The acidity constants KE and KESexplain the pH dependence of the enzyme reaction [%I. At sufficiently low substrate concentration [Sl] the turnover rate v increases linearly with [S]. With increasing [S], v does not increase linearly with the substrate concentration, but much more slowly. In so-called saturating activities, v tends toward a limiting value vmax.This is expressed quantitatively in the Michaelis-Menten equation, the fundamental equation of enzyme kinetics: V =

"I

KM i[Sl

where

kpat [Elo = V,,

(3-50)

The definition implies that the maximum turnover rate is defined by the catalytic activity of the enzyme kcat and the starting enzyme activity [El, when the enzyme is saturated by the substrate. In 1918, Michaelis and Menten proposed the following mass balance:

Ks E+S

kcat

ES

E+P

The first step is characterized by the dissociation constant K,, the dissociation or the reverse stability constant, the speed of the process, its reversibility, and the fact that no chemical reaction takes place except conformational changes in the enzyme. Only physicochemical forces participate in the reaction. The chemical processes then occur in a second step characterized by a first-order rate constant, kcat (the turnover number), where v is the reaction limiting turnover rate.

3.3 Rate-Controlled Reactions: Mediated Enzyme Reactions

111

(3-51) (3-52)

KM is known as the Michaelis constant and was defined by the substrate concentration at halfsaturation of the enzyme or 1/2 Vmax. In this strict sense KM is identical with the dissociation constant K s which defines the reaction rate at very low substrate concentrations close to the detection limit. In this case, the substrate concentration limits the reaction rate v denoted by: (3-53) This is the most important equation for the enzymatic analysis of substrate concentrations. Michaelis-Menten theory assumes that the enzyme-substrate complex is in thermodynamic equilibrium with the free enzyme and the free substrate activity. This is only true if k-1 >> kcat. Briggs and Haldane [56] analyzed the case in which kcat is comparable to k-1 A steady-state approximation was applied to the concentration of the enzyme substrate complex, ES: -d[ES1 - k l

dt

[El [S]

Based on this equation, the Michaelis constant was redefined and extended by the term, kcat:

KM =

kcat + k-1 kl

(3-54)

This equation can be expanded to:

(3-55) and

(3-56) Different mechanisms have been distinguished for K M > K s , K M < K s , K M = K s in the literature. For an electrode reaction, the determined K M is not only influenced by the factors mentioned in Eq.3-56, but also by the diffusion of the substrate(s) to the electrode, the stirring or rotation rate, as well as internal electrode processes, e.g., mediator diffusion, which limits kinetics of the electrode reaction. In these assays, the measured Michaelis constant is denoted as electrode KM or apparent KM or KME. The values of the first order reaction rate constants kcat lie between 1 and lo7 s-l. Theoretical investigations require techniques for mixing the enzyme and substrate rapidly as well as very rapid measuring techniques to identify concentration changes. In order to determine the rate constants of the different steps, it is necessary to resolve the rate of

1 12


approaching the steady-state. For the determination of the kinetic rate constants, several techniques are possible, e.g., the stopped-flow method, rapid luminescence quenching techniques, flash photolysis, temperature jump techniques, and NMR combined with the coalescence temperature [55]. kcat can be interpreted very differently according to how important it is to distinguish kcat.1 and kcat.2. Some authors integrate only kcat.1 in the K M value according to Briggs-Haldane, others integrate the total kcat (kcat. 1 + kcat.2). According to these differences, various cases where kcat.1 > kcat.2 0rkcat.2 > kcat.1 can be distinguished. However, kcat is called the turnover number of the enzyme reaction and is never greater than any first-order rate constant of the forward reaction. The ratio kcat IKM is called the selectivity or specificity constant [51]. This ratio is an apparent second-order rate constant, which explains how the data of the overall enzyme reaction are transformed and linearized.

Graphical Representation of Data For the graphical representation, various designs exist which transform the Michaelis-Menten equation into a linear form. The three most important transformations are: the LineweuverBurk plot, the Eadie-Hofstree plot, and the DixonLHunes- Woolf linearization, usually called simply the Hunes plor [57, 581. In the last case, which was mostly used for own data, the Lineweaver-Burk function is multiplied by the substrate concentration [ S ] :

(3-57) According to this linearization, KM lVmm is the y-value at x = 0, and 1lVmaX is the slope of the graph. The intersection point of the function with the abscissa is given by KM. This representation is used when the data points cover decades of different concentrations, but experiments are reformed with constant increments of the substrate. The y-values, [Sllv, change linearly with the added increments whereas, in the Lineweaver-Burk function, the experimental points are concentrated in the saturation region of the enzyme. The sensitive low concentration range is hardly accessible. The absolute error shows minor changes in the Hanes plot over a wide concentration range; even the relative errors show relatively small differences in contrast to other data transformations. The reverse Michealis-Menten function is called the Lineweaver-Burk function and is analogous to the linearization of a second-order reaction in a double-reciprocal form: Ilv versus 1/[S]. Each of these representations can be adapted to specific types of experiments and datasets. None is qualitatively better or worse than the others. They are only more or less suitable.

3.3 Rate-Controlled Reactions: Mediated Enzyme Reactions

Pt-cathode

113

Pt-anode 4 electrons

metal electrode

per hypoxanthine

I

mediator reduced form

mediator oxidized form

mediator reducedform

mediator oxidized form

t

peroxidase oxidized form

hydroxide Ion OH

peroxidase reduzedform

hydrogen peroxide

xanthine oxidase oxidized form

hypoxanthine

xanthine oxidase reduzedform

uric acid

H A

Figure 3-2.Flow of electrons in mediated amperometric enzyme electrodes, typical for (a) an oxidase (xanthine oxidase, E.C. 1.2.3.2) I581 and (b) a reductase (peroxidase, E.C. 1.1 1.1.7) 1591

Mediated Electrode Reactions In our studies, the hypoxanthine and peroxide concentrations were analyzed using an amperometric mediated electrode [58, 591. An excess of enzyme suspended in a silicone oil paste was incorporated into a cavity of the electrode [60].A phosphate electrode by coupling a second enzyme, a nucleoside phosphorylase, with the xanthine oxidase was developed [60]. The representation of a mediated enzyme reaction is still more complicated, for example, in determinating hypoxanthine (see Figure 3-2) where four electrons are exchanged with the anodic current per mole of hypoxanthine oxidized to uric acid. In this experiment the mediator M was an organic salt composed of TTF (tetrathiafulvalene) and TCNQ (tetracyanoquinodimethane)which change their charge upon electron transfer. The mediator continuously regenerates the FAD-iron sulfur-enzyme complex, whereas the mediator itself is regenerated by the electrode potential. Such a mediated enzymatic reaction can be described as follows:

114


kl

E+Si+Sz+M

2 7

ktrans

E S I + S ~ + M _ _ j E'Sl'+P2+M

k -1

The cosubstrate S 2 of the oxidation reaction is water. The rate constant of the mediator reaction kmed should be negligible in the optimized electrode design and under reasonable operation conditions. However, the kinetics kmed of the mediator turnover and of the electrode reaction kel determine the baseline current as a function of several electrode parameters such as applied potential, pH, type of buffer salts, stirring, or rotation rate. For further developments see [61].

3.4

Nonthermodynamic Assumptions

3.4.1 Activity Versus Concentration An analyte in a natural environment may be characterized by three fractions, at least: the activity of a component, the concentration of the free fraction, and the concentration of the bound, entrapped or complexed fraction. The latter two together contribute to the total concentration of an analyte. An analysis which discriminates between the three fractions is termed a speciation. For some applications, e.g., the analysis of a biological or environmental specimen, the question arises as to what to measure and what to report? This can be crucial when results from monitoring by sensors are compared with atomic absorption spectroscopy (AAS) in environmental analysis where there are legal cut-off limits. The biological activity of an electrolyte or a metal ion is invariably due to the activity of an analyte. An example illustrating this is furnished by the mode of reception and transmission of nerve impulses. Such a nerve impulse may induce a change in the distribution of pigment or chromophores, and subsequently a color change in the skin of some animals such as the flatfish (Pleuronectes platessa) or tree frog (Hyla arborea) [62].This mechanism is very similar to the ion-exchange mechanism of the optical bulk membranes developed in our laboratory. Discrimination between the different fractions mentioned above is essential in interpreting data. It has been the object of study and controversy since 1969 when Waugh published the first paper on the displacement of water by proteins and lipids in human serum [63]. Calibration of ion-selective electrodes for biological analyses and interpretation of data have been discussed internationally since 1975 when Mohan and Bates recommended measuring the electromotive force at 37 O C with "synthetic electrolyte mixtures simulating serum, in cells with and without liquid junction" [a]. "With and without liquid junction" refers to the fact that ion-selective bulk-membrane and glass electrodes work with a liquid junction in contrast to the lanthanum fluoride solid-state electrode which works without a liquid junction. Reports since then have focused on the activity of the analyzed components or the free analyte (ion) concentration.

3.4 NonthennodynamicAssumptions

115

In the following section, some basic theories will be mentioned. These have been described by several excellent textbooks [65-741. The terminology used to discuss electrolyte theories in some standard textbooks is unfortunately different from that recommended in clinical chemistry. However, joint recommendations have recently been made by the International Federation of Clinical Chemistry and the International Union of Pure and Applied Chemistry for both electrolyte measurements and optical spectroscopy [75,76].

Characteristics of Electrolytes and Electrolyte Solutions A true electrolyte in solution yields ions showing electrical conductivity. Solutions of strong electrolytes, such as NaCl, KCl, and MgS04, yield a high conductance even when highly diluted, whereas solutions of weak electrolytes, such as carbonates and acetates, are poor conductors. Weak and strong electrolytes are characterized by their degree of dissociation and hydration in aqueous solutions. Conductivity K and mobility u i are associated intrinsic properties of an electrolyte. K / S cm-I (= f2-I cm'), is the sum of the contribution of all ionic species i responsible for the passage of current through the solution, accomplished by the independant movement of different species. is proportional to the absolute charge number z of the ion, to the molar concentration ci / mol kg1, and the mobility, ui / cm2 V-' s-l, which is the limiting intrinsic migration velocity of an ion in an electric field of unit strength. F is the Faraday constant: K = F & I Z ~ I U ~ C with ~ I

u

Izile

--

i-

6nqr

(3-58)

The mobility of an ion decreases with increasing radius of the ion r I cm, and increasing viscosity q I g cm-1 s-1 (= poise), of the solvent. The transfer number ti for the analyte species i is the contribution made by species i divided by the total conductivity:

3-59)

The transfer number is another way to explain the selective transport and exchange of ions in the electrical circuit and segmented membrane model as well as the generation of mixed potentials. Another term which is directly related to the mobility and conductivity of an electrolyte is the mold conductivity, A / S m-1 mol-1 kg, given by K and the molal concentration of the analyte I. The equivalent conductivity is very often reported and accounts for the number of positive or negative charges ceq, equivalent to I zi 1 ci. Eq kg-I is identical with the molal normality of a solution, which is no longer supported by IUPAC.

A= ~ I c i

(3-60)

In the period after 1897, Kohlrausch showed that at low concentrations the mold conductivities of strong electrolytes obey Kohlruusch's law. The mold conductivities are

116


proportional to the square root of the molal concentrations, ~ 1 1 2 and , he confirmed that A can be expressed as the sum of contributions from individual ions. This has been called the law of independent migrution of ions:

A = A - - K ~112

(3-61)

with Am= (v+&

+ V- il,) = F (U+ + U- )

(3-62)

The coefficient K was found to depend more on the stoichiometry of an electrolyte than on other specific properties. Am denotes the molal limiting conductivity at infinite dilution of the electrolyte and 298 K. In Eq. 3-62 the molal conductivity is expressed in terms of the cation and anion mobility as well as the individual ionic conductivities, A+ and h of anions and cations. v+,v- are the stoichiometric coefficients. By Eq. 3-59 the molal conductivity of an electrolyte A is related to the conductivity at infinite dilution A:. Values for the single molal conductivity at infinite dilution, A and , :A are tabulated. The square-root relationship to the concentration has been confirmed by the dependence of the Debye-Huckel radius and the logarithmic activity coefficient on the square root of the ionic strength. Conductivity is a consequence of the dissociation factor a of an electrolyte. A solid conductor such as a silver wire can be compared to a strong electrolyte, whereas a semiconductor is likewise a weak electrolyte. Transference numbers, ionic mobilities, and mold or molar ionic conductivities are displayed in various tables for calculations, however infinite dilution of the electrolyte is assumed. These relationships constitute the theoretical background for electrophoresis, isotuchophoresis and thus form the basis for calculations of thefluid potential, ion fluxes, and ionic d i m i o n potentials.

Ideal Solutions, Real Solutions, and the Ionic Atmosphere According to Debye-Hiickel Theory

According to Raoult's law, a relationship between the composition of an ideal solution and the partial vapor pressure of the solute can be observed experimentally. In ideal solutions, the solute as well as the solvent obey Ruoult's law which introduces the mole fraction x to describe the proportionality to the partial vapor pressure. According to Henry's law, a link to real solutions has been made in introducing a proportionality constant. In Henry's law, the vapor pressure of the solute I is still proportional to the mole fraction, however the proportionality constant Ki is an empirical constant, which can be evaluated for ideally dilute solutions (-) in accord with the free enthalpy of mixing (see Eq. 3-9). The law has been extended to describe the behavior of real solutions. If the solute 1 obeys Henry's law, the partial vapor pressure of the solute pi is given by Kj xi (see also Eqs. 3-80 to 3-83). The chemical potential of I in a solution depends on the chemical potential of the pure solute A*,its partial vapor pressure pi*,and the molal fraction of i in a solvent xi. In Eq. 3-62,

3.4

NowhemdynamicAssumptions

117

a new standard state pf' involving the parameters of the pure compounds p: and pi* has been formulated.

The standard state fi0involving Ki has been defined, and the chemical potential pi has been formulated for real solutions. It characterizes such phenomena as the behavior of 0 2 dissolved in aqueous biological fluids. At very low concentrations, the solute I obeys Henry's law and the activity of the dissolved analyte ai can be determined by measuring its partial vapor pressurepi. For real solutions, the mole fraction Xj has been replaced by the analyte activity ai:

pi =pf' + R T In ai

(3-65)

The nonideal behavior is accounted for by the mean activity coeficient yh derived from the proportionality constant Ki. An electrolyte solution outwardly seems to be uncharged. Within the electrolyte solution, the positively and negatively charged ions move randomly in all directions, depending on their thermal energy. In the neighborhood of cations, anions are more likely to be found than other cations, and vice versa. This means that, a slight surplus of oppositely charged ions appears in a symmetrical sphere around a central ion. This space charge domain has been termed "ionic sphere" by Debye and Huckel. The charge density in the ionic atmosphere is distributed according to the Maxwell-Boltzmann distribution law. The electrostatic forces operating between the ions act over much larger distances than the van der Waalsforces (see section 2.2.2). A region of deviation from electroneutrality extends to very small distances from the ion, characterized by the Debye length LD, or Debye-Hiickel radius m. It is again influenced by the permittivity of the surrounding medium relative to the permittivity in vacuum &&. LD =

4

E ~ RE T/2pF21 ~

= r D = 4 E r & kT/2e2N~pl

(3-66)

F, R , k, e, and NA have their usual meanings; I denotes the ionic strength; p the mass concentration. The Debye length denotes the distance from the core of an ion where the electrostatic forces to counter ions just compensate each other and the net charge is zero. The Debye length extends with decreasing ionic strength (see also sections 4.2 and 4.5). The spherical shell shields the charge of the central ion from interactions with counter ions. This shell decreases the chemical potential p as well as the electrostaticCoulombpotential @ of this ion. The difference in the chemical potential Ap is defined by: Ap = R T In y+

(3-67)

The activity coefficient y+ is an important quantity when describing equilibrium conditions for real solutions in a quantitative way. The Debye-Hiickel limiting law makes use of an approximation analogous to the ideal gas laws. Its derivation assumes that ions are point charges and that the ionic atmosphere is thus

118

3 Conrrolling Sensor Reactions

distributed over the distance r = 0 to r = 0 3 , where r~ is the Debye length LD.The electrostatic potential decreases with (Ur) e-r’m. For large values of a,the shielded potential comes very close to the Coulomb potential. This shielded potential is termed Debye-Hiickel potential 0, and may be calculated for any distance r with respect to the radius of the ionic shell Q: (3-68) The Debye-Hiickel potential decreases more rapidly with higher relative permittivity E~ of the solvent. This means that the potential around a central ion in a plasticizer with = 4-22 of the membrane environment is shielded less closely than in an aqueous solution where q = 80.37 (20 OC),and the radius of interaction increases. within a sovent polymeric membrane. Subsequently the radius of interaction can be influenced by the solvent and the ionic strength of the environment (see sections 4.2 and 4.6).

3.4.2 Ionic Strength and Estimates of Activity Coefficients The electrostatic interaction between ions increases with their ionic charge and with decreasing ion radius (see Appendix 4). The first influence, the ionic charge, has been quantitatively expressed by Lewis in terms of the ionic strength I: 2

2

2

2

I = 112 (z 1 c1 + z 2 c2 + 2 3 c3 + . . . . + z, c,)

(3-69)

where z1,z2, z3, ....z,, are the charge numbers of the individual types of ions and cl, c2, c3, ... c, are the individual concentrations of each ion. Here, the ionic strength is defined in terms of the concentration of the solution, whatever this means (see section 3.4.3). It is often used as a dimensionless parameter divided by the unit molality or unit molarity . For dilute electrolyte solutions, the following empirical relationship holds: -log y*- I 1’2

and

log y* = - I Z+ z I A -Jr

(3-70)

For alkali and alkaline-earth salts, the formalism proposed by Debye and Hiickel is traditionally used to obtain a fair approximation of the mean activity coefficient for an ion and its counter-ion [77, 781. The product, 1 z+ z I, signifies the absolute product valencies. The terms A and B are constants, related to the temperature T, the Avogadro constant NA,the permittivities .qand 6, and the Boltzman constant k. e is the elementary charge:

A=

e3 lnlO (47~&)3/2k3J2

1

(3-71) (3-72)

3.4 Nonthermodynamic Assumptions

119

The approximation further allows for the radius of an ion by introducing parameter, a. a and C are constants which fit the theoretical relationship to measured values of y+. They have been computed by Citterio for molar (A, B,) and molal (Am, B,) quantities at various temperatures (see section 3.4.3) [79]. log y+ =

I z+z M 1+Ba$

+c I

(3-73)

The activity coefficient of a single ion, which is not measurable per se, is given by a convention proposed by Debye and Huckel, and by Bates et al. [79-811.

ze

log y+ = I - I log y*

z

and

z

log y - = I- I logy* z+

(3-74)

*

Hence, the activity coefficient for a single cation can be approximated by y + = y Z+/Z. It is then y+ = yk2 for a divalent cation. For an anion the single ion activity coefficient is given by y - = y *Z-lZ+ and for a divalent anion by y - = y ,112. The values of single ion activity coefficients for various ions are given in Appendix 2. The Debye-Huckel approximation is based on a simplified model using a solution with a strong electrolyte where the ions are not hydrated. The ions are only involved in electrostatic interactions. Further attempts have been made to find approximations which can deal with hydrated ions and interactions in mixed electrolyte solutions. According to Stokes and Robinson, the true molality mo of the solution of an electrolyte is different from the molality m due to hydration, Within the hydration sphere of an ion, the water molecules are fixed and are not available as solvent. They assumed that the chemical potential of the solvent is not affected by solvation and that the solvation number h is independent of the concentration. They corrected the molality m by the solvation number h the number of coordinated water molecules per ion where 55.51 is the molality of water: mo

55.51 m m --55.51 - hm- 1-0.018

(3-75)

hm

The logarithmic mean molal activity coefficient after integration between 0 and m,where v is the stoichiometric coefficient, is: lnoyk=ln y + + ( h / v ) l n a ~ 2 ~ + l n ( 1 - 0 . 0 1 8 h m )

(3-76)

This term acts as a correction factor in the Debye-Hiickel limiting law which deals with parameters in molal activities (A,,,, B,) and the osmolality,th = (-ln U H ~ O ) I M H ~commonly O, used as a parameter in clinical chemistry, and represented by (for details see [82]): In y k = -

1 +Bma$

+ (h / V )

MH~OIn [l - 0.018 (h - v) m]

(3-77)

120


For Stokes-Robinson estimations of the single ion activity coefficients, no hydration of the anion is assumed hcl- = 0. The values for h are given in tables. The Stokes-Robinson approximation of the activity coefficient uses the osmotic coefficient @ as an experimental parameter for I > 1 mol k g l . Differences between estimated results and the Debye-Hiickel approximation are presented for physiological solutions in Figure 3-3.However one drawback of the Stokes-Robinson approximation is that an experimental parameter is involved and, secondly, that no temperature correction is available for the hydration parameter. The DebyeHuckel equation is thus generally preferred. Both approximations are devoted to single electrolyte solutions and do not consider interactions between ions. Sigaard-Andersen, Thode, and Fogh-Andersen presented an equation for mixed electrolytes derived from the Stokes-Robinson approximation. The new approximation sums all the species present in the solution in a third term. In y k = -

InlOl~lAmJj + (h l V ) l+BmaJj

where

h=v+h++v-h-

and

MH~O In [I

v=v++v-

- 0.018 ?(hi

-lhi]

(3-78) (3-79)

This formulation does not appear to have a clear thermodynamic basis. Generally the ionic character of the parameter a is not specified. Debye-Huckel calculations of activity coefficients are based on long-range Coulombic forces between the charged species within pure electrolyte solutions. Thus acceptable results for diluted solutions containing ions with low charge number such as monovalent ions can be obtained. Little attention has been paid to the fact that short-range forces between ions, not taken into account by the Debye-Huckel model, cannot be neglected at higher concentrations and especially in case of ions which show strong electrostatic attraction effects, such as ion pairing. A further problem is the handling of mixed electrolyte solutions which the DebyeHuckel model does not cope with. An improved model including ionic short-range interactions as well as mixed electrolyte solutions is therefore desirable. The most recent investigations have been made by adapting two different approximations given by Reilly and Wood and by Pitzer for biological fluids [83, 841. Both approaches can cope with mixed electrolytes and optimally approximate clinical data. Characteristically, both approximations are made by introducing a term to take account of interactions between ion pairs. In the Reilly and Wood equations, the interaction term is evaluated by means of experimental values for the osmotic coefficient. The approach of Pitzer establishes a well-defined link between the activity as a macroscopic thermodynamic property and a detailed microscopic theory of electrolyte solutions based on statistical mechanics. Using a virial equation, which can semiempirically be fitted according to easily measurable thermodynamic properties (e.g.. the osmotic pressure of an electrolyte solution), a set of parameters can be determined for each pure electrolyte that also allow a sound treatment of mixed electrolyte solutions [81, 821. Consideration of further mixing parameters can be necessary in special cases and is often essential for ionic strengths I > 0.01 molL and multiply charged species. They can mostly be obtained by considering simple cases of mixtures and exploiting similarities between certain ions. Interactions between neutral compounds and ions within the solution are basically included in the Pitzer equations,


121

by considering the osmolality of solutions. They can be neglected in many cases, however, as well as short-range forces between ions carrying charges of the same sign. Pitzer gives two equations, one for cations and one for anions, to calculate single ion activities in mixed electrolyte solutions. The activity factors according to Pitzer and Debye-Hiickel are in good agreement for monovalent ions, surprisingly. In contrast, there is a considerable difference for divalent ions [79]. The computing program used comes from the WATSTORE Program Office, US Geological Survey, 437 National Center, Reston, VA 22092. Copies of the code based on the equations were developed by Plummer et al. (US Geological Survey, Water-Resources Investigations Report 88-4153) and are available at US Geological Survey, Books and Open File Reports Section, Federal Center, Bldg. 810, P.O. Box 25425, Denver, CO 80225.

Conclusions Figure 3-3 clearly shows that variation in the single ion activity coefficient depends, above all, on the ionic strength of the solution and deviates much more for divalent ions than for monovalent ones. For monovalent ions, the estimations following Pitzer deviate from those following Debye-Huckel by c +0.27% over the whole range examined. For divalent ions, this relative deviation is in the range of < +2.6%. The differences are much more relevant for divalent ions which are present in concentrations of the free ions c 1.5 mmoIL The Pitzer estimations seem to be the best approximations for mixed electrolyte solutions so far, since they take account of interactions between ions. The parameters have been tabulated (not entirely for 310 K) and profoundly described and investigated. They have also been supported by Covington [85].

3.4.3 Activity and Concentration of an Electrolyte: IFCC / IUPAC Definitions For nonideal solutions, a standard state must be defined where the chemical potential pi is e equal to the standard chemical potential pi and close to the chemical potential of an ideal solution p; for an infinitely dilute electrolyte at 298 K and lo5 Pa. The standard state is defined by XA, YA, and ' y j approaching 1 and xi approaching zero. For nonideal solutions, the mole fraction xi is replaced by the molal activity ai. For ideal solutions: (3-80) Thus for real solutions the relative activity is: ai

e t (4-

4)

1~

r~

(3-81)

122


a) For the monovalent sodium (Na+) and potassium (K+) ions

b) For the divalent calcium (Ca2+)and magnesium (Mg2+)ions

Figure 3-3.Graphical presentation of calculated values of the molal single ion activity coefficients for physiological cations in mixed aqueous solutions relative to an increasing molal concentration of sodium chloride. The activity coefficients were estimated according to Pitzer (Pit), to the Debye-Huckel formalism (DH), to Sigaard Andersen (SA) and StokesRobinson (SR). The estimates base on a common physiological background of 0.5 mmol kg-' Mg2+, 1.25 mmol kg-1 Ca2+ and 4.5 mmol k g l K+. The x-axis mimics a variable ionic strength and water concentration represented in this case by the variable molal sodium concentration.

3.4 NonthennodynarnicAssumptions

123

If the chemical potential pi of an analyte ion I is equal to the standard chemical potential 48 then the analyte activity ai is equal to 1 if a is defined to be 1 under standard conditions. The difference between the ideal chemical potential of an electrolyte and its real chemical potential is given by the difference between the logarithmic activity ai and the logarithmic mole fraction

7

Xi.

pi - y.00= R T lnai - R T In xi = R T ln-ai 1

(3-82)

Xi

The ratio, ai /xi, is another definition of the activity coefficient ('yid.It quantifies the deviation of the activity relative to the mole fraction of the real solution from 1. This is consistent with Eqs. 3-63 to 3-65 and 3-67. 'yik

(3-83)

ailxi = pilKi

Ideally, this coefficient should take into account the various possible interactions between ions, as shown in the previous section. Various assumptions for the estimation of xk can be made, resulting in different values for 'yi+ At this point, the notation in practical use deviates from the notation employed in fundamental physical chemistry. In clinical chemistry, analytical parameters are referred to the volume of the native specimen. In a joint document of the International Federation of Clinical Chemistry and the International Union of Pure and Applied Chemistry, different notations were recommended to distinguish between terms related to volume and those related to mass. Molarity or number of species n per volume of solution V is termed substance concentration, ci = ni1V I mol L-l, and the mass m per volume ratio of the solution is termed mass Table 3-2.Notations supported by IFCC and IUPAC

Active molality (Relative) mold activity (dimensionless) Mold activity coefficient Concentrational activity coefficient Molality

[mol kg-'1 iFip = 1 mol k g 1

[mol kg-' solvent] [mol kg-1 solvent]

of the solute I Substance concentration, molarity Active (substance) concentration Concentrational relative activity

[mol L-'specimen] [mol L-'specimen] ?? = 1 m o l ~ - l

Mass concentration Molar mass

[kg L-'I [kg mol-l]

124


concentration pi = mi/V / kg L-I [75, 761. The molality mi is equal to number of species I per mass of solvent, nilmA, (mol kg-l). The molarity Ci can be transformed into molality via the mass concentration of water, PA* I kg L-l, where A and I are solvent and solute, respectively:

Unlike the relative molal activity, the activity defined by the mole fraction has units. The variables ai and are dependent on temperature T, pressurep, and active molalitykl, ii22... ~3 is dimensionless and never negative. Equation 3-84 in terms of molality is:

n

(3-85) Since clinical chemists are accustomed to working with molar units, it is important to distinguish between the molar activity coefficient yi and the molal activity coefficient yi. The molal activity coefficient can be estimated by the relation: (3-86) and vice versa. pi and PA* are identified with kg L-I.This coefficient is dimensionless from the physical point of view although, it is objectively not dimensionless since the volume of solution is related to the volume of pure solvent. In protein-containing solutions where the proteins exhibit a large volume fraction, the ratio pi /PA* has the dimensions L L-' yi_+and yi+ are not identical.

3.4.4 The Osmotic Coefficient When the concentration of molecules in water exceeds the limit of mol/L, the decrease in water vapor pressure does not correspond to the ideal value calculated from concentrations. Electrostatic and dipole interactions are operative between ions and molecules in solution (see section 2.2). Hence, the measurement of the solvent activity can be helpful to explore the number of particles in a solution as an indicator for ion association and for host-guest complexation. The following example for the very different behavior of a glucose solution and a solution of sodium chloride illustrates the differences in the osmotic effects of a charged and a neutral ialyte. For nonelectrolyte solutions especially, the nonideal behavior is allowed for by the osmotic coefficient. Generally, it is convenient to express the solvent chemical potential in terms of the experimental osmotic coeficient @. In clinical chemistry, osmolality is chosen as the analytical parameter. It is a convenient quantity corresponding to the water activity of a sample. The mean reference osmolality of blood is 0.290 f 0.01 mosm kg-1, which refers to the osmotically active number of moles kg-' solvent (= 290 mosm kg-'). This osmolality is

3.4 Nonthermodymmic Assumptions

125

represented artificially in the following two solutions, well-known as isotonic NaCl solution and isotonic glucose solution. Isotonic solutions are defined by a freezing point depression of 0.558 K, identical to the freezing point of blood. This freezing point can be calibrated by a solution of 9.463 g NaCl per kg solvent (water) or by weighing 53.312 g glucose per kg solvent. -

9.463 g NaCl per kg water = 0.1619 rnol per kg water ( M , 58.443 g mol-l), according to Eq. 3-69 the ionic strength of this solution in molal units is I = 1/2 (12 x 0.1619 + l 2 x 0.1619) = 0.1619 and the number of particles is 0.32328 mol kg-* water, resulting in an osmolality of 0.300 osmol k g l . Thus the osmotic coefficient is 0.9264.

- 53.312 g glucose per kg water = 0.2959 rnol per kg water (M, 180.16 g mol-I), the number of particles is 0.2959 mol per kg water resulting in an osmolality of 0.300 osmol kg-1. Thus the osmotic coefficient is 1.0138.

As can be seen from the isotonic composition of the two solutions, the osmotic coefficient is not in agreement with the number of particles or ionic strength. Since glucose is not present in ionic form, glucose behaves differently from NaCl. Glucose raises the activity of water, the osmotic pressure, and the chemical potential. This is due to the entropic effect of the hydrophilic glucose molecules which break down the lattice of liquid water in the solution. This is the opposite effect to that of large number of hydrophobic components. For practical use, the osmotic coefficient replaces the mole fraction scale to express the difference between the ideal chemical potential of the solvent PA* and the real one PA. The osmotic coefficient Q, for a strong electrolyte is defined by: (3-87) M A is the molar mass of the solvent, v_+= V+ + V- are the stoichiometric coefficients, mi the stoichiometric molality of the solution [mol kg-11. aA is the activity of the solvent. If associations or ion-pairing can be neglected, v_+mi = v+m+ + v-m- is valid. Since the activity of water can be related to the vapor pressure, it can be measured by comparing the real vapor pressure of the solution P A with the ideal vapor pressure of the pure solvent: PA* a A = P A I P A *

(3-88)

It follows that:

(3-89) or: din mi MA = In (PA /PA*)

(3-90)

0 can be evaluated by vapor pressure osmometry (VPO). The Gibbs-Duhem equation now includes the osmotic coefficient as an experimentally accessible parameter, in addition to thermodynamic quantities:

126


In clinical chemistry, osmolality 2 is measured as an indicator of the activity of water: rh = (-

In aH20)/ M H ~ O

(3-92)

The molar stoichiometric activity coefficient, L i of the electrolyte I in solution A can be calculated on the basis of vapor pressure osmometry (VPO) or freezing point depression osmometry. In VPO, the vapor pressure of a solution of I in A allows the activity of the solvent to be 0 0 0 calculated, since fiA aIA,prA,is the vapor pressure for an ideal solution under standard conditions. Experimental values for the vapor pressure ~ I Aare corrected for 298 K and 1.OOO bar (p = 760 mmHg = 101.6 @a). VPO measures the changing chemical potential of the solvent at different mole ratios.

-

(3-93) where the mole fraction activity coefficient of a pure solvent ( y x , ~ ) "is 1 and the chemical potential of the pure solvent is that of the ideal solution, PA* = p1~"K:p).The mole fraction can be replaced by any other quantity which is used in osmometry calibration, usually molality. In the case where associations and ion pairing have to be taken into account, the chemical potential is written in molal units mihe:

pi = &e + v R T In ( v k n milme)

(3-94)

The molality scale stoichiometric activity coeficient yi of the electrolyte I with charge V+ in solvent A is calculated by introducing a term a for the fraction of ions that do not associate to form ion pairs with:

Ti a ' +

[I - ((1-a) (v+/v-) 1 V-'Vy*

(3-95)

On the basis of Eq.3-93 and the definition of the osmotic coefficient, the osmotic behavior of different solutions can be analyzed and interpreted. One of the drawbacks of osmometry in analyzing ion complexation, however, has been the fact, that different stoichiometries of a host-guest interaction are extremely difficult to distinguish. Table 3-3 shows that the components listed below and accounted for in calculations cover the essential osmotic and electrochemically active components. 0.5%~ethanol concentration in blood is given for comparison. The relatively low ethanol content obviously exhibits a strong osmotic activity in low concentrations. The range of the physiological osmolality varies between 280 and 300 mosmol kg-*. The upper limit agrees with a freezing point depression of 0.56 K represented by a physiological NaCl solution of 9.463 mmol kg-1 water (see above).

127


Table 3-3. Main osmotic active components [mmol kg'] in human blood plasma water and in [mmol L-'1 in human blood plasma volume Mean mmolal concentration

Electrochemical activity (mmolal)

Mean mmosmolal osmotic activity (0)

277 (0.923) as NaCl

(D.H.; k,Y-1

Sodium ions

150

111.5 (0.743)

Potassium ions

4.3

3.1 (0.726)

Chloride ions

113

84.2 (0.745)

Bicarbonate ions

27

19.3 (0.713)

Glucose

6

6.08 (1.013)

Urea

6

6.0 (1.009)

Ethanol (0.5%~)

10

10

Total:

306.3 mmol kg-* without ethanol

218.1 mmol kg-1 without ethanol

289 mosmol kg-I

psemm= 1.026

298.5 mmol L-I

212.6 mmol L-l

281.7 mosmol L-l

3.4.5 Calibration, Standardization, and Comparisons with Definitive or Reference Procedures Ion-selective electrodes used in specimens such as whole blood, undiluted plasma, or serum respond to the electrochemical activity of the ion. At the high ionic'strengths of I = 0.16 moVL encountered in these biological samples, the molal concentration can no longer be substituted for molal ion activities. The molal concentration of the ion I, mi, may be converted to the active molality m"i by multiplying by the single ion activity coefficient n.

-

mi=min

with

x#l

(3-96)

By definition, the active molality is related to the relative activity ui by dividing m"i by the unit molality rZp [1 mol kg-'1: ui = r Z j I

(dimensionless)

(3-97)

128


Concomitantly, the molal free ion concentration mi differs from the molal total concentration of the ion mi,tot by the association of the ions; I, with both organic and inorganic ligands, anions and cations (Lj), and their molal concentrations mLj. The degree of complexation is an important factor in the chemical speciation of an analyte ion. In general, the complexed fraction increases with the charge number of the ions and the pH. It is denoted by the association constant, KaS: (3-98)

In analytical laboratories, systems which determine substance concentrations in mole such as atomic absorption spectroscopy (AAS) and flame atomic emission spectroscopy (FAES) compete with potentiometric electrodes which determine relative ion activities within the undiluted specimen and in diluted samples. Considering the basic theories on dissociation of electrolytes, ion activities, and the osmotic coefficient discussed above, it is obvious that method comparisons are very problematic. In an attempt to achieve the same results for both types of procedures in diluted specimens, the International Federation of Clinical Chemistry has proposed the following equations for computing and reporting results for sodium and potassium ions. This attempt includes the possibility of converting the results of ISE assays in the specimen directly to FAES / AAS and vice versa. The system relies on an adjustment factor by which the measured relative activity and the active substance concentration of the analyte ion I is related to the total substance concentration, ci,tot. The system is based on the assumption of a standard plasma specimen defined as having a mass concentration of water in plasma of 0.93 kgL, a bicarbonate concentration of 24 mmolk, and pH 7.4. For sodium ions, the complexed fraction ($=1Kass;j CL,) is assumed to be 2%. Based on these assumptions, the total substance concentration of the ion I may be converted to the total molality of the analyte ion by dividing by the mass concentration of plasma water, Lspecimen-l

PHZOP:

(3-99) in the following full equation, the total substance concentration of I in [mol Lplasma-'] is related to the relative activity of an ion measured by ISEs: (3-100)

Although the system is based on molal units by definition (IUPAC and IFCC), the results are greatly influenced by the temperature since the slope of the ISE response function increases with rising temperature, and sample and reagents are dispensed volumetrically. Routinely, all measurements are made at 37 OC. Equation 3-100 allows a rough estimation of a mean conversion factor. However, if this factor were generally valid for variable sample compositions, the mass concentration of water has to be measured, the activity coefficient for each ion has to be estimated from the ionic strength of a sample, and the equilibrium constants of the most relevant complexes have to be known. A large experimentd set-up attempted to achieve an estimate of the deviations of single specimens from the mean assumptions.

3.4 NonthermodynamicAssumptions

129

To estimate the mass concentration of water in plasma, a volume displacement effect by proteins and lipids has to be taken into account. Therefore, the total concentration of lipids and proteins is integrated into the equation for the calculation of the mass concentration of water in standard plasma specimens. The compensation factor for the mean specific volume of proteins is assumed to be 0.73 L kg-' and 1.03 L kg-* for lipids. The specific partial volume of proteins corresponds to the specific volume of albumin. Globulins exhibit partial volumes between 0.739 for gammaglobulins (IgG) and 0.70 L kg-' for some smaller globulin fractions [86].

PH,OP = Q,OP P H 2 0 c r )

(3- 102)

The term 0.991 represents the difference of 1 L plasma minus the volume of dry ash or salts in plasma. To calculate the mass concentration of water in kg per Lplasma, the volume/volume fraction, r ~ , o ; p ,has to be multiplied by the mass concentration of water p~ O(T) at 298 or 310 2 K. This contribution is negligible, however, compared with the uncertainties of the plasma protein and lipid concentrations and the specific volumes for single samples. The mean mass concentration of water in plasma amounts to 0.93 kg L-'. On the basis of these equations, the bias between total concentrations of electrolytes as analyzed by atomic absorption spectroscopy (AAS) or flame emission spectroscopy (FAES) and potentiometric measurements in the specimen directly have been calculated for different concentrations of proteins and lipids [87]. The mean physiological set point of the total concentration of sodium ions in plasma (FAES, ISE indirect, 37 OC) is 139 mmol L-I [88]. Under physiological conditions, this concentration is equivalent to 135.5 mmol kg-I plasma, assuming a mean mass concentration of plasma of 1.026 kg L-1. In plasma, 1L plasma contains 0.93 L water when the mean protein Concentration is 0.073 kg L-' and total lipids amount to 0.006 kg L-l [86].The mean lipid fractions triglyceride and cholesterol are 0.0017 and 0.0021 molL [87]. Since potentiometric electrodes analyze the active molality of ions in individual specimens directly, the ion concentration in the water volume has to be taken into account. This is equivalent to 149.5 mmol NaCl per L plasma water volume at 310 K or 150 mmol NaCl kg' in the water fraction at 298 K (m,o, 2 9 8 = ~ 997.043 kg m-3, ~H,o,3 1 0 = ~ 993.326 kg m-3). A theoretically predicted positive bias of 7.5 % for direct potentiometry (ISEs) (total ion concentration in the plasma water volume, 310 K) vs. indirect assay (total ion concentration in the whole plasma sample volume) is generally accepted for normal situations and is compensated by calibration. For calibration of ISEs in terms of molar concentrations, the single ion activity coefficients and the ionic strength of aqueous solutions are calculated. Assuming a mean ionic strength for the individual specimens and mean single ion activity coefficients, the measured molal ion activities (emf) are transformed into molal concentrationunits. Molar and molal concentrations are not differentiated routinely. The water concentration of individual specimens is not considered, regarded as a constant when comparing the resultsyielded from ISE measurements with results derived from the analysis of molar ion concentrations. The calibration process is shown schematically in Figure 3-4. The problematic steps are indicated by question marks.

130


Active molality, mi mol kg-'

Activity coefficient, ionic strength, water concentration

aqueous standard

parameters calculable from weight and composition of aqueous calibrators

Y33 1, PH

Aqueous standard

+

Jr ??

Human standard

J

human standard

??

??

Human specimen

2 I

??

individual human specimen

parameter constant for different standards ? complexed fraction ? water concentration ?

individual parameters ? complexed fraction ? water concentration ?

Figure 3-4. The calibration of active molality units as measured by ISEs in molar concentrations. Comparisons between active molality and molar concentration values regarding the influence of the water concentration. Question marks indicate the accuracy of assumed conditions for calibration

Experiments The variation in the interindividual water concentration and activity coefficient of ions has been determined and calculated for a reference group of "healthy" volunteers, at the University Hospital Zurich and the ETH, and different groups of patients: patients before and after hemodialysis and patients from the intensive care unit (ICU)(number of volunteers and patients: n = 80) [79,89]. The following analytical parameters were measured: Total concentration of potassium and sodium were determined by ISEs in each individual diluted specimen. The concentrations of chloride, total protein, albumin, triglyceride, phosphatide, cholesterol, glucose, and urea were analyzed photometrically in the diluted plasma on a Hitachi 747 automated analyzer. The active molalities of sodium, potassium, magnesium, and calcium ions as well as the pH were analyzed by ISEs in undiluted plasma (Analyzer AVL-988, Biomedical Instruments, A-8020 Graz). Glucose and urea concentration served to control the osmolality, the hematocrit (relative cell volume in whole blood) was

3.4 Nonthemdynamic Assumptions

131

measured to refer to whole blood. The results of all analytes were controlled by a quality control program and by aqueous standards. The statistical analysis attempted to answer the following questions: a) How reliable is the transformation of active molalities as measured by ion-selective electrodes (ISEs) into molar ion concentrations as recommended by the IFCC's Working Group on pH, blood gas and electolytes for sodium and potassium ions? b) Can one assume a mean ionic strength and a mean constant activity coefficient for single ions to calibrate ISEs and calculate molar total ion concentrations? c) Can the ratio between the substance concentration of an electrolyte and the active molality serve to monitor the water concentration of a specimen? Question a) was answered by quantifying the correlation between the water concentration and the difference between measured molal activity and molar total ion concentration for each individual sample. Question b) was answered by the significance of the interindividual variance of the parameters within and between groups. The set of analytical parameters which led to the most efficient discrimination of the group of volunteers and the patient groups, was looked for. The results are part of an upcoming paper. The water concentration on the one hand and the difference in active molality and molar concentration of magnesium ions on the other contributed most to this discrimination [88]. The molar and molal individual activity coefficients were estimated, depending on the individual ionic strength of each specimen at 310 K. The sum of the free electrolyte concentrations and the water concentration were taken into account. The mean mold ionic strength of "healthy" volunteers (n = 36) accounted for 0.161 f 1.4 (k 1 SD) mol kg-1 in plasma water.

Table 3-4. Mold single ion activity coefficients in human plasma of healthy volunteers (n = 36) calculated from experimental results (see text) according to Debye-Huckel and Pitzer [79]

Parameter

Na+

K+

c1-

Ca2+

Mg2+

Pitzer mean 1SD

0.743 0.001

0.726 0.001

0.745 0.001

0.334 0.001

0.343 0.001

Debye-Huckel mean 1 SD

0.742 0.001

0.728

0.742 0.001

0.325 0.001

0.336 0.001

0.001

132


The variation of the molal single ion activity coefficients for Na+, K+, C1- was < 0.1%, but 0.28% and 0.26% for Ca2+and Mg2+,respectively, according to the Debye-Huckel estimates. In fact there was no variation between different individuals (1 SD = 0.001 throughout) (see Table 3-4). According to Pitzer, the molal activity coefficients for Na+, K+ and C1- showed identical variation c 0.1% and 0.25% and 0.23% for Ca2+ and Mg2+, respectively. The molal single ion activity coefficients were found to be extremly constant, even before and after hemodialysis. In such cases, where the biological activity of electrolytes is especially relevant, the assumption of a mean activity coefficient is valid, and can be calibrated in contrast to the molar parameters. In a project devoted to the experimental investigation of the mean activity coefficients for "healthy" persons and its variation the results shown in Table 3-4 were found [88].Table 3-4 vividly demonstrates the problems of calibration of the potentiometric response function by aqueous solutions and of the calculation of ion concentrations in human plasma samples. On the basis of the limitations presented in the previous sections, it is possible to estimate the single ion activity coefficients in aqueous solutions. This estimates give reasonable activity values to calibrate a potentiometric sensor by aqueous solutions. Table 3-4 shows that the interindividual ionic strength and the single ion activity coefficients are surprisingly constant for volunteers. This is true even for patients before and after hemodialysis. However, it does not allow one to calculate the molar single ion concentrations from the measured activities of unknown samples. For the groups of subjects studied, a significant correlation between the water conqentration and the difference in sodium active molality and molar concentration was shown. Hence, the comparison between total molar concentration and single ion active molality of sodium ions allows one to calculate the water concentration of each sample in the cases studied here. Conversely, for potassium and the divalent ions, the relationships were shown to be much more complex.

Conclusions The ion-selective electrodes directly offer an observable value for the biologically relevant parameter: the mold ion activity in the aqueous phase of the genuine biological specimen. This yields new information for elements such as magnesium and calcium, which are 30-50% associated to different anions, For alkaline and alkaline earth cations, the Debye-Hiickel formula allows a fair approximation of the mean single ion activity coefficient xk, as measured for an ion and its counter-ion in an aqueous calibration solution. As shown in an earlier section, the approximations for real solutions and the philosophy in the calibration procedure have varied considerably at different times. The favored approximation must be that which can provide a high accuracy for the estimate of the true single ion activity coefficients in plasma or whole blood to calculate molal ion concentrations on the basis of measured ion activities. The argument for this procedure is that activities cannot be interpreted and adjusted in a medical treatment. The approximation which provides the highest accuracy for estimations of single ion activities in the biological specimen is considered to be the Pitzer approximation. Molal single ion activity coefficients for individual human plasma water samples with molal ionic strength

3.4 Nonrhermodynamic Assumptions

133

I = 0.161 mol kg-' were estimated using the Debye-Huckel formalism and the Pitzer approximation at 37 OC. They are given in Table 3-4 and Appendix 2. However, the experiments, which are to be published, showed that the water and molar sodium concentration (osmolality) discriminates between different classes of patients and "healthy" volunteers. In theses cases, the adjustment of single ion activities to measured ion concentrations on the basis of fixed factors is useless and dangerous, since wrong information is yielded. This must be considered for all cases involving large changes of the water concentration due to hyper- and hypoproteinemia, -lipidemia, hyperhydration, or changes of the ionic strength due to a loss of electrolytes. In these cases, the outstanding information content of the molal single ion activity (helpful in biological measurements) is lost or biased through computing and interpreting total ion concentrations based on wrong assumptions. In general, the ionic strength and the molal single ion activity coefficients are surprisingly constant and strongly balanced by the steady-state of the electrolytes. In the cases reported above, the molal ion concentrations can be calculated based on mean molal single ion activity coefficients. Honest comparisons between these ion concentrations or the measured ion activities and the measured total electrolyte molarity in plasma can provide extremely helpful information on the state of the water balance. In contrast to single electrolyte activities, molar electrolyte concentrations cannot provide any information on the electrolyte balance. Unfortunately no standard reference material is at present available for the ion activity assay. However it could be prepared on the basis of the symmetric assembly of the potentiometric cell reported in section 5.2 The evaluation of standard specimens providing assigned values for ion activities should be possible in a symmetric cell arrangement, and may be considered in the future. Calibration of the electrode is usually required. A calibration-free assay was undertaken in a completely symmetric cell arrangement by Rumpf et al. (see section 5.2). The calibration solution should match the mean sample composition as closely as possible. Addition of albumin to the calibration standard does not guarantee high accuracy, owing to a shift in the assay standard potential which differs for plasma, serum, and albumin. Reports on comparisons of clinical analyzers show that interinstrumental deviations may be considerable. Recommendations for calibration and standardizationby the IFCC Committee on Electrolytes and Blood Gases are in preparation. Electrolyte total concentrations are usually evaluated in samples diluted by using an ionic strength and pH buffer in the so-called indirect method. Since the ionic background is standardized in this case, calibration and calculation of the active ion concentration using the Debye-Huckel formalism is possible. Differences between indirect ISE assays and FAES or AAS are marked, amounting to about 3 4 % higher results for ISEs. These differences are probably related to the volumetric dilution and the volume displacement, which is caused by macromolecules even in diluted samples, as discussed above. Electrodes measure the activity of an electrolyte in the aqueous phase. This value is correct if no artifacts and interferents have to be taken into account. In section 5.2, the implications of this are explored by using an absolutely symmetric arrangement of the electrode cell. Discussions of what should be measured and reported still continue, owing to the extremely high quality requirements for most analytes in medical analysis and taking care of the correct interpretation of the results.

134


3.4.6 The Liquid Junction Potential under Physiological Conditions The liquid junction potential is generated between the salt bridge, the so-called liquid junction, of the reference electrode and the specimen by diffusion of ions and is a diffusion potential. The theoretical description is based on the irreversible linear thermodynamics of open systems (see section 3.2). A diffusion potential is, in general, described in terms of a flux Ji of the participating species I and its mobilities ui along a time axis. However, the flux of the ions has been described as a function of a concentration gradient dci(x)/&, and a potential gradient d@ (x)/&, along the x-axis, according to the Nemst-Planck equations [90].

(3-103)

0, symbolizes the sample side of the diffusion layer d the side of the salt bridge. Accordingly, the thermodynamic notation is: dPi

Ji = - U i R T gradient Ci - zi ui ci ( x ) F gradient @ = - U'c'-

'dx

(3-104)

According to Hendersson, the Nemst-Planck equation has been integrated assuming a linear concentration profile along x for all ions within the diffusion layer [91,92]. This leads to the Hendersson approximation where the diffusion potential ED can be calculated according to:

The first term in Eq. 3-105 describes the concentration gradient due to difference in the concentration of cations Acm related to the difference of the concentration of anions Acx over all species present in the aqueous solutions and the salt bridge Z. The second term describes the potential gradient due to different concentrations of anions and cations in the aqueous solution relative to the salt bridge. Calculations for different calibration solutions were made, the salt bridge was either a 3 m o m KC1 solution or a 1 m o m KC1 solution. In biological assays, the sample volume is as small as necessary (0.1-0.5 mL). Thus the reference and the ion-selective electrode are close together. Nevertheless the liquid junction potential is the more stable the higher the concentration of the salt bridge. The 1 mol/L salt bridge is a good compromise regarding diffusion of KC1 to the selective membranes. A further objective is to choose a salt bridge with high mobilities of the ions. Thus the diffusion layer is at the sample side of the salt bridge and the long-term deterioriation of the reference electrode is slowed down. Since the biological specimen is ususally a mixture with a high ratio of low-mobility ions, especially anions, the gradient within the diffusion layer is steep and nicely confined. The influence of deposits at the surface of the salt bridge is further inhibited by the free-flow, free-diffusion type of reference electrode which is generally used in

3.4 Nonthemdynamic Assumptions

135

our laboratory, especially for protein containing solutions [93]. Other approaches have tried to work without a liquid junction [94] or with salt bridges at physiological concentrations [95]. For ions, the mobility and the conductivity Ai of an ion are consistent. The mobility u characterizes the velocity of penetration through a medium under the influence of any gradient or physical field, whereas the electrolytic mobility is given by the product of the molar charge number z i k F and the mobility ui. The diffusion coefficient Dj is related by the mobility uj by:

(3-106) since the first term of the Nernst-Planck equation (Eq.3-103) comes from Fick's diffusion law. The units of the absolute mobility are [cm2 s-1 J-1 moll. The absolute mobilities of cations are in the range of 376 x for H+ to 80 x 10-lO for K+ and 29.0 x 1O-l0cm2 s-1 J1 mol for Mg2+ [79]. The mobility of anions are in the same range. KC1 with very similar for K+ and 81.1 x for C1-) result in so-called absolute mobilities of the ions (80 x equitrunsferent solutions. The mobilities of an uncharged compound within the organic membrane layer are higher. In 1988, Armstrong [96] reported relatively higher mobilities for a neutral calcium ligand (us = 124 x c d s-l J-' mol compared with the values above). These estimates are valid for infinitely dilute solutions. According to [67b] the dissusion coefficients and subsequently the mobilities are reduced by about 2.5% for NaCl going from 10-3 to 10-2 m o w at 298 K.

Experiments The liquid junction potential changes when different calibration solutions are used. In the analysis of magnesium activities in plasma and serum, the response function emf= f(1ogui) is calibrated for ion concentrations from 0.35 to 0.75 mmoyL Mg2+.An ion background of 1.25 mmol/L, CaC12, 140 mmol/L NaCl, 4.0 mmoVL KC1 was generally used as a physiological background ( I = 0.149). In this case, the emf of the potentiometric cell is raised by the pure chloride ion background by +0.577 mV, owing to a liquid junction potential of +1.039 mV and +1.041 mV for 0.35 mmol/L and 0.75 mmol/L Mg2+ solutions, respectively. The bridge electrolyte is generally composed of a 1 m o m KCl solution, a good compromise for physiological measurements. The mobility of the organic anions in the biological fluid can be adequately dealt with by replacing 40 mmoYL chloride by acetate. In this case the liquid junction potential drops to 4 . 4 6 1 and 4 . 4 6 4 mV for the solutions mentioned above. This can be demonstrated by emf measurements in different solutions. In calculations of the liquid junction potential, molar concentrations are used. This is reasonable, since the activity coefficients cancel out in the first term of the Hendersson approximation. In the second term, the activity coefficient of the 1 m o m bridge electrolyte is negligible for equivalent electrolytes of the bridge solution compared with the large difference in the concentration of bridge and sample solution. The activity coefficient of the 1 moVL bridge electrolyte cannot be estimated correctly.

136


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4 The Artificial Analyte-Selective Membrane Limitations, Technological Precautions and Developments

4.1 Introduction Traditionally, the term "membrane" is used to characterize selective polymeric sensor membranes attached to transducers. In view of the present state of knowledge about biological membranes, and the likely future reinvestigation of artificial membranes, some questions have to be asked: Is this term correct? How did this term come to be used instead of the term "layer"? What are the main features distinguishing membranes from layers? The Latin expression membmm means a thin skin [l]. In biology, the meaning of the word "membrane" is very different from its technical meaning. In biology, a membrane is defined as a "phase that acts as a barrier to the flow of matter or heat" [2]. In the technical sense, a membrane is defined as a "circular platelet which is fixed at the borders and transduces e.g. vibrations" [11. The two definitions are nearly identical if the term "vibrations"is replaced by the term "matter". However, in the second definition, the bamer function or selectivity is not explicitly mentioned. Semipermeable membranes play an important role both in technology and in living organisms. In most cases, the membrane acts as a selective barrier controlling the uptake and passage of organic and inorganic ions, and small, neutral molecules. Three modes of exchange of matter across biological membranes are recognized: passive, facilitated and active transport. Technically, membranes are used in separation processes such as filtration and dialysis. The basic principles involved in a passive transport process is diffusion-controlled separation along the concentration gradient which is also described by a permeability factor equivalent to Hofmeister behavior (see section 3.1). The permeability factor is determined by the typical physicochemical characteristics of the permeating and the retained species relative to the membrane features (solubility, diffusion rate, flow dynamics) and, in addition, by size exclusion. By contrast, an active transport can be induced, e.g., in voltage-driven migration. In this case, the diffusion-drivenprocess following the concentration gradient is converted into an active mass transport against this gradient, which consumes energy. Alternatively, the facilitated transport is linked to specific carriers or transporters which interact selectively with a target compound, but which still facilitate a net flux "downhill"energetically. Biological membranes have a wide variety of functions as a result of these passive, facilitated and active transport abilities. The active transport of biological membranes is considered in the next section as a first step in classifying technical analyte-selective membranes and sensing layers.

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4.2

4 The Artificial Anulyte-Selective Membrune

Types of Membranes and Membrane Models

4.2.1 The Biological Membrane In 1895, Overton described a correlation between the rate at which various small molecules penetrate plant cells and their partition coefficients between oil and water, leading him to speculate on the lipid nature of those membranes [3]. It had taken over 80 years since the inception of cell theory in 1839 to discover the basic structure of biological membranes [4]. Since then, an enormous amount of work has been devoted to exploring the nature of biological membranes. Hence the molecular structures, dynamics, biochemistry and functions of many types of membranes are well understood today [5]. It is now clear that the lipid bilayer forms the structural framework of virtually all biomembranes. However, there are many chemically distinct lipids, and, in addition, extrinsic (peripheral) and intrinsic (integral) membrane proteins, which contribute to 2040%of the mass, and provide the functional diversity of membranes. Even if schematic drawings show a rigid membrane structure, it must be kept in mind that all biological structures are dynamic. The rate and motional degrees of freedom are important in considering biological functions. As a consequence, the biological membrane phase has to be seen as a liquid where the structural components are not fixed in position, but exhibit a wide range of motions representing 20 orders of magnitude in terms of frequency from -CH2vibrations observed in the IR- and Raman spectra to the transbilayer flip-flop of lipids in the range of 10-3 to 10-6 s-1 [5]. From examining the structure of the bilayers, it can be seen that biological membranes must be heterogeneous, axially structured and asymmetric. The thickness is approximately in the range of 4.5 f 1.4 nm [ 5 ] . In contrast to the cell membrane, the cell wall is the outside boundary of the cell which is exposed to an external medium. The thickness is in the range of 10 nm and protection is functionally more important than permeability. The cell wall is tangentially layered and rigid. The wide variety of membranes in living organisms has led to them having a range of functions, such as protection, receptor-mediated selective mass transfer, voltage-mediated selective mass transfer, signal transduction, and passive and active transports. These distinguish different membranes from each other, and are fundamentally important for specifying different cell compartments: "It can be truly said of living cells, that by their membranes ye shall know them" [6].A membrane such as the membrane of the erythrocytes, which is frequently referred to as a model membrane, is normally composed of 40-50% w/w lipids and 5040% w/w proteins [5,7]. The membrane composition of erythrocytes is visualized graphically in Figure 55 and is compared with the composition of human blood plasma (the composition is given in Table 4-4). The rather different compositions of human whole blood and blood serum are relevant when considering their biocompatibility with artificial membranes. Biological membranes are perfectly organized bilayers incorporating specific proteins as carriers, pores, channels, receptors and antigenic structures involved in selective mass transport and communication. At this point, it may be helpful to classify a few of a membrane's general mechanisms which are at work in nature and to explain some of the related terms. For example, mass transport is peptide- and protein-mediated. There are two different structures and mechanisms involved in mass transport: mass transport through channeEs (or pores) and by transporters [5, 81. In the first case, the two major groups of channels consist of voltage-

4.2 Types of Membranes and Membrane Models

141

regulated and chemically regulated channels. Voltage-regulatedchannels are the ones involved in ion exchange, such as the Na+/K+-antiport,whereas chemically regulated channels are receptorbased and respond to specific chemical agents, such as hormones and neurotransmitters, as well as drugs and toxic agents. Transporters can be subdivided into passive transporters working along a diffusion gradient (e.g. erythrocyte glucose transporter), and active transporters/carriers coupled to an exothermic process (e.g. cytochrome c oxidase, Na+/K+-ATPase,H+/K+-ATPase, Caz+-ATPase).The selectivetransport of a target compound is associated with a conformational change in the structure of the transporter or ion channel protein.

Active Transport of Ions Through Voltage-RegulatedChannels As the name suggests, voltage-regulated channels are involved in the active transport of ions through the biological membrane. The basic driving force of communication along the nerve fibers, arises from the polarization voltage of the membrane due to a gradient in the sodium, CN~+ and , potassium concentration, CK+, between the extra-, (ext), and intracellular, (int), space (CNa+ext/Na+int = typically 12.7;CK+int/K+ext= typically 23, e.g. for erythrocytes). In order to stabilize.this gradient and the related electrochemical potential difference of 80-100 mV, the Na+/K+-pumpis linked to the p r o m motoricforce, which provides the energy for the active mass transport and sodium exclusion from the cytoplasm (see below). In the cytoplasm, the negatively charged sites of anions are mainly compensated for by potassium and magnesium. The voltage generated by the so-called Na+/K+-pump can be calculated from the ratio between the sodium activity inside (aj,jn) and outside (qOut)the membrane, as mentioned above. According to the Nernst equation, AG is given by (see chapters 3 and 5) [9]:

Since potassium-sodiumion exchange is in competition with proton-sodium exchange, it is the sodium gradient that primarily determines the membrane voltage. The electrochemicalpotential difference, AD ,of 0.08-0.1 V is equivalent to a molar Gibbs free energy, AG, of +7.7 to +9.65 W equivalent-' which has to be provided by an exoergonic process (see Eq.3-40, 3-41). The system, which provides the energy for the following three endergonic processes, namely the proton motoric force, the phosphorylation of ADP and finally the Na+/K+-pump,is the respiratory chain located in the mitochondria. Three unlike complexes of enzymes are coupled in the respiratory chain involving the following redox pairs (standard potential, A P vs. NHE, pH 7,298 K A P 'N (pH 7) = At" (NHE,pH 0) -0.413 / V): redox mediator: NAD+/NADH ubiquinonehbiquinone-H2 (coenzyme Q (NADH reductase) cytochrome c (Fe3+/Fe2+) 02/02-

Ozm20

rn -0.320 V +0.110 v -0.300 to +0.550 V +0.280 V +0.820 V

142

4 The Artijicial Analyre-SelectiveMembrane

The terminal reduction of oxygen is irreversible and is thus the driving force for the steady state. The transfer of a total of four electrons along the respiratory chain for the reduction of oxygen is an exergonic process and provides a free energy of -220 W mol-'. The intermediate peroxide ion, 02-is toxic. Therefore, what the exact mechanism involved in the proton- and electron-gradientreally is has been the subject of discussions for years. The generation of a FeIV+ intermediate of cytochrome c upon complexation of the peroxide ion (02-) has been proposed [11I. The mediator or coenzyme coupling the transport of electrons to the respiratory chain is nicotine adenine dinucleotide (NAD+/NADH)(see section 3.3 and chapter 8) which intializes the electron transfer. Two electrons are released per NADH molecule, along with the hydride transfer from NADH to a substrate. The net reaction can be described by the following steady state which involves energy storage in a hydrogen ion gradient over the inner mitochondria membrane [9]:

The so-called proton motoric force is generated by an active transport mechanism of hydrogen ions linked to the respiratory chain. The transport mechanism consumes +21.76 kJImol. Part of the free energy of the respiratory chain, A%+, is stored within a permanent potential difference over the inner mitochondria membrane of A Y = 0.14 V and the chemical potential of the transient pH difference ApH. The two contribute to a difference in the electrochemical potential, A ~ H which + is equivalent to 0.184.2 V in a normal metabolic steadystate: AGHt = A&+=

F A Y - 2.3 R T ApH

(4-3)

The proton motoric force stored in the gradient of hydrogen ions is described by Afi H+I F = A Y-2.3 R T I F ApH

(4-4)

The depolarizationpotential difference(gain in energy) over a nerve membrane expends only 0.08 to 0.1 V. In addition, chemical energy is consumed for the oxidative phosphorylation of ADP to ATP, which is also an endergonic reaction, and consumes +30.5 kJ mol-I. The chemical energy stored in ATP drives the Na+/K+-pump. The transfer of information, e.g. along nerve fibers, is switched by guest I receptor interactions at the muscle-endplateof nerves, and transmitted by mass transfer of ions along the nerve fiber membrane associated with breakdown and depolarization of the membrane potential (state associated with maximum entropy). Another system facilitating ion transpod for the exchange of ions through membranes was intensively discussed in the 1980s. The most famous model for the channel mechanism is the gramicidin channel found in bacteria membranes [12]. Gramicidin, inserted in a lipophilic bilayer, increases the ion permeability of the membrane. The transport mechanism was investigated by Grell et al. [13]. Facilitated, passive transport was discussed along with the channel-gated model.


(3

143

f!

Figure 4-1. Schematic diagram of the mechanism involved in facilitated ion transport. Carrier model (a) vs. channel model (b) (according to Grell et al. [13]). The model refers to the natural bilayer membranes with polar sites versus the aqueous medium and less polar chains inside

This model led to two alternative mechanisms being proposed for ion transport through artificial ion-selective membranes, especially by valinomycin and macrotetrolides (see section 1.5 and chapter 3). The biological bilayer was frequently imitated and used for in vitro transport studies. The lipid bilayers (BLM) have a lifetime of only a week in an artificial environment [14,151. Bilayer membranes which mimic living membrane functions have not yet been produced although considerable effort has been devoted to this project. It is an open question to what extent mass transport is really connected tightly to the structure.

Conclusion Biological membranes are liquids with a bilayered structure and various functions. The active transport of target compounds through biological membranes has been discussed. The next section looks at mass transfer by passive transporters. The biological membrane serves as a barrier enabling the transfer of matter and information to be controlled, e.g., by controlling pH and electrolyte activities, by raising a dual signal, by being excited or relaxed, and by saying "yes" or "no". A biological membrane never acts as a "meter", but is more like a switch. The characteristics of biomembranes differ fundamentally from any metric membrane in that both sides have to be active in nature. For artificial membranes, one side of the metric membrane must remain entirely invariant, regardless of the sample composition and any kind of change, whereas the other must respond to the target analyte alone. Biomimetric membranes do not exist in nature [16]! The more, artificial biomimetic membranes, even artificial bilayers, can serve to create metric systems for analytical use [17]. They are supposed to be able to extract ions, biological substrates, and target analytes by a

144

4 The Art$cial Analyte-Selective Membrane

"facilitateduptake" and will be discussed in the following part of this chapter. Many of the basic questions are the same for the different types of sensing layers which are all coupled to transducers and rely on general aspects of a selectiveexchange of matter with a stationary phase, the membrane. Other characteristics are typical only of electrochemical membranes or only of optical sensing layers. These factors are discussed further in chapters 5 and 6 . In the next section, basic models of the structure of membranes, the uptake and transport of matter through membranes are described, with reference also to energetic aspects.

4.2.2 Artificial Membranes The natural as well as artificial homogenous and heterogenous membranes are increasingly important in science and technology. Artificial membranes are classified as homogeneous and heterogeneous, symmetric and asymmetric layers, and involve heterogeneous bilayers, asymmetric solid contact membranes, porous polymers such as sol-gel materials, homogeneous solvent polymeric membranes as well as many hybrides. Artificial bilayer membranes have developed into an efficient tool for incorporating receptors and studying natural transport processes, e.g., through ion channels [ 18, 191. Investigations have been made in order to evaluate the relationship between structure - on a molecular scale - and properties. The use of homogeneous membranes in technology is advantageous because they offer a simple, durable, rugged technique for various applications. Analyte-selective membranes and ion-selective membranes, particularly, offer plenty of possibilities for extraction and transport studies in varying the extraction and transport properties of the membrane and in influencing the recognition process as well by the membrane medium. In 1906, the report of Cremer [20] on a soft glass, which showed a transmembrane potential if solutions of different pH were separated by the glass, may be said to be the starting point of ion-selective membranes as part of ion-selective electrodes. Since then, an enormous development in artificial analyte-selective membranes has been made. In the 1960s,a number of theoretical attempts to describe the transport through membranes, both biological and artificial ones, began. Subsequently, the theoretical description of the membrane potential and its generation had been the object of a great deal of discussionsand many papers. Adsorption-based sensors, where the host compounds are immobilized on a surface, were described by adsorption isotherms [21, 223. To rule out the problems with adsorption and nonthermodynamic behavior of surface sensors, the main element of the chemical sensors presented here is a homogeneous solvent polymeric bulk membrane used to prepare analyteselective layers attached to optical and electrochemical transducers in order to prepare so-called analyte-selectiveoptodes and electrodes. In a first approach all active components are mobile and, analogously to biomembranes, a high degree of translational freedom is admitted. In a second step it will be shown that immobilization of active components is feasible under certain conditions (see section 4.6). The borderline characteristics of these membranes are selectivity, reversibility or the ability to regenerate the signal, lifetime, stability of the signal, and response Characteristicsrelying on the use of membranes and their composition which are discussed in this chapter.


145

In the following section, the three most important membrane models discussed earlier will be presented. As far as the generation of the potentiometricsignal is discussed, the models concern electrochemical layers generally and potentiometric membranes especially. A fourth model presents an asymmetric sensor arrangement where a homogeneous membrane attached to a solid support, e.g., an optical waveguide is discussed. Most features are generally valid and can also be extrapolated to polymeric layers applied to conductive, amperometric, surface acoustic wave (SAW) and other sensors dealing with analyte-sensitivelayers.

Models Explaining the Functionul Structure of the Homogeneous Artificial Membrane and the Transport of the Analyte Membrane models have to cope with several features such as symmetry, chemical homogeneity, but functional segmentation, and electroneutrality of the membrane phase, selectivity and mixed responses, stability of the signal, and mobility of membrane components. The following models were introduced to explain the functional structure of ion-selective membranes, the transport of ions through membranes, the formation of the membrane potential, and, to some extent, the deviations from ideal behavior of an electrode. Although the models and theories have been created specifically for ion-exchange membranes which incorporate charged carriers, theories were extrapolated to ion-selective electrodes incorporating neutral carriers. The segmented membrane model'and the model for the asymmetric arrangement have a very general impact for various types of symmetric and asymmetric chemical sensors apart from explaining the membrane potential.

The Multilayer Model: The Segmented Membrane Model The segmented model was introduced in 1935/1936 by Sollner [23], Teorell [24], and Meyer and Sievers [25] and developed in the following years by some classic contributions. For the history of further developments see [26]. The two boundary phases of the membrane and the interior are treated separately. The two phase boundaries are treated as being permselective and polarizable, and the potentials are treated as Donnan potentials [27] whereas the interior transmembrane potential is treated as a diffusion potential. The interior potential contributes to the total membrane potential if the mobilities of the charged species within the membrane are different. The assumptions for this model are: 1. Implies selectivity of the membrane phase (see section 4.3): Each phase boundary must be perfectly permselective, so that the thermodynamic equilibrium potential at the interface can be expressed in terms of a Donnan potential

146


2. Implies mobility of the participating components (see section 4.6): The participating components are mobile. The mobilities of all species within the membrane are invariant and the chemical potentials in the bulk of the membrane do not vary with space and time 3. Implies thermodynamic equilibrium between membrane phase and specimen (see chapter 3): A thermodynamic equilibrium involving the partition of all participating components between membrane and sample phase, and the association of the free analyte with the free ligand at the membrane-sample boundary is established. Sample and membrane are involved in the equilibration process. Pressure and temperature gradients do not exist 4. This point is decisive for potentiometric membranes: The system is in ner zero-current steady-state 5. The membrane is homogeneous 6. The system is symmetric as far as a solvent, or the same solvent may be used on both sides of the membrane 7. The solvent flow across the membrane is negligible 8. Implies constant activity coefficients within the membrane phase: Within the membrane, the local activity coefficients are the same or at least constant for all ions/components, or the individual activity coefficientsare the same or invariant for all cations and for all anions

On the basis of thermodynamic equilibration, the segmented model can provide a general model for homogeneous membranes. The model does not differentiate between apolar and polar membrane media. Symmetry can go as far as identical solutions on both sides in order to study technically induced deviations from zero potential (see section 5.2). For asymmetric arrangements the model would be more complex. In accord with the thermodynamic laws, the segmented model explains the generation of a stable boundary potential if only small amounts of ions are exchanged (e.g., < lo-" mol s-1, so-called currentless transport, A E m = 0.1 V, membrane resistance > 105 Q) and the boundary process usually dominates the generation of the potential. In this case, the internal composition of the membrane and the diffusion potential do not change considerably. The model does not take account of the time factor and the exchange rates. Nevertheless, the exchange rate for the primary ion at the phase boundary must be far higher than for any interfering ion in reaching a permselectivethermodynamic equilibrium with the host-guest complex. A technique to evaluate the real-time response of the electrode membrane was established by Pungor et al. [28]. If a diffusion potential inside the membrane occurs, the relation between the mass transport and the generated electrochemical potential gradient, as the driving force for the diffusion of ions inside the membrane, has to be examined. This can be relevant if ions of different charge, greatly different mobilities, and different stoichiometries from the ligand compete in the recognition or extraction process, and if their activities in the sample phase relative to the internal electrolyte vary considerably. In this case, a contribution of the internal diffusion potential cannot be excluded and is observed in the form of a long-term drift due to a reconditioning of the membrane bulk and a higher detection limit (see section 5-4). The membrane behavior can be analyzed by modeling the transport processes through the segmented membrane by the NernstPlanck equation, Eyring's absolute rate theory [29] or the laws of irreversible thermodynamics (see section 3.2). By the Nernst-Planck ion-flux equations [30], the local thermodynamic properties of the membrane are functions of fluxes in the z-direction within the membrane


147

(compare the asymmetric model). The analysis leads to a set of differential equations that can be solved for any given set of boundary conditions. This approach is largely due to Mod [3 11. The model is limited by the requirement for detailed knowledge about the structure and/or thermodynamic properties of the membrane, and is thus not suitable for heterogeneous membranes. Irreversible thermodynamics avoids the limitations of the Nemst-Planck model by a phenomenological description of the membrane-solute-solvent system [32]. The NernstPlanck model has been applied in modeling gradients of the free ligand distribution in. magnesium-selective membranes [33]. A perfect thermodynamic description of the boundary, considering the electrochemical potential on each side of a boundary, is also given by Pungor et al. [34]. EMF

REFERENCE ELECTRODE

REFERENCE ELECTRODE

SPECIMEN

Figure 4-2. Schematic representation of the membrane electrode assembly. Theoretically, the membrane potential EM is the sum of the two Donnan potentials located at the interfaces x = 0 and x = d, and the diffusion potential which arises in the bulk of the membrane (see also section 4.2 and Figure 4-6). In analytical use, the Donnan potential at x = 0 must be the sole variable and correlate to the changing activity of the target analyte. ai. analyte activity; aj, activity of the interfering ion; UL, activity of the ligand within the membrane; cl.tot, weighed ligand concentration; CR,concentrationof the charged lipophilic sites

148

4 The Artificial Analyte-Selective Membrane

The segmented membrane model requires an exact description of the permselectivity of the membrane. Methods to establish the selectivity coefficient have been given by IUPAC [35] (see section 4.3). Occasionally kinetic parameters have been used for the description of the selectivity (see section 3.3 and [36,371). The main drawback of the segmented membrane model for theoretical studies was tthe need for information on mobilities and activity coefficients within the membrane. A single publication [38] reports mobilities within the membrane. This information was used to model the free ligand distribution within the membrane by Eugster [33]. Various types of ion-selective systems, especially asymmetric and heterogeneous systems (bilayers and ion-selective solid contact and semiconducting sensors), cannot be treated directly by the segmented membrane theory. In addition, the model cannot model nonideal, non-Nernstian behavior with reasonable effort. Nevertheless, it is frequently used to model the general behavior of solvent polymeric bulk membranes and electrodes.

The Mixed Potential Approach In order to look for a theory, that not only explains nonideal electrode behavior, but also ion exchange through biological membranes, the mixed potential approach was considered. It refers to linear irreversible thermodynamics (see section 3.2) and involves also faradaic contributions to the potential, such as the single ion exchange current and its transfer coefficient. The model was introduced by Buck and elaborated by Cammann [36,38]. It refers to studies on biological membranes by Ciani, Eisenman et al. [39]. In 1970, Lauger and Stark [40] refuted the model which supposed that key chemical reactions were at equilibrium and that the rate-limiting step was always diffusion of the complexes across the membrane interior, based on current-voltage characteristics of the ion exchange. Both authors introduced a single barrier model and appropriate rate constants describing the ion exchange currents, stipulating that the model is of sufficient generality to account for most observations on steady-state membrane properties. In this model, the polarization process of the sample-membrane boundary is described by that contribution to the potential which arises from the typical partial ion current induced by the selective ion exchange, and, therefore, by charge transfer and charge transfer kinetics. The physicochemical theory of the selectivity behavior has been based on the determination of different ion exchange current densities. Thus, partial currents are accepted as relevant parameters to explain the ion transfer and selectivity of the boundary, whereas the thermodynamic models are based on zero current and, therefore, infinite resistance. The model is derived from the Butler-Volmer equation for a reversibly polarizable electrode [41]. The ion-selective electrode boundary is treated as being identical with the metallelectrolyte solution interface, with particular concern for the kinetics of the interfacial reactions and their effect on Nernstian behavior. An ideal slope in mixed aqueous solutions and an effective discrimination of ions is associated with quick, reversible charge transfer kinetics of the primary ion. Similar to the biomembrane model, a quick ion exchange is related to high exchange current density and is equivalent to a rapidly polarizing and depolarizing boundary. The phase boundaxy kinetics are described by exchange current densities which create an overpotential as a directed


149

driving force for discriminating interfering ions. The selectivity coefficient depends on the ratio of the charge transfer kinetics between the primary and the interfering ion assuming parallel ion transfer. In the Evans diagram [37], the interfacial potential difference is plotted against the current density of those partial current voltage curves which add up to zero net current flow at the mixed potential point. The current-voltage curve for an ideal potentiometric sensor shows a steep slope nearly parallel to the current axis. All ion transfer reactions involved react with different overpotentials to establish the steady-state. By addition of lipophilic anionic sites into cation-selectiveelectrode membranes, the anion exchange and a negative contribution of anions to the membrane potential driven by the positive overpotentialof the cation-selective extraction process is inhibited (see section 4.4.5). The same is true for anion-selective electrode membranes, when adding lipophilic cations. Thus, mixed potentials in this case are mainly attributed to the exchange of counterions [41]. The nonthermodynamicdescription is specifically appropriateto characterize asymmetric assemblies [42-43], coated wire electrodes [MI, blocked electrodes [45], selectrodes [46], ISFET [47], and steady-state situations [48] in general. Current-voltage curves explain some of the observed phenomena by referring the electrochemicalpotential and the selectivity to the ion-exchange rate.

The Electrical Circuit Model The electrical circuit model is a consequenceof the mixed potential model, treating overpotential, polarization, and depolarization of the boundary, and the membrane internal diffusion potential as time-resolved processes [42, 45, 49, 501. In contradiction to the segmented model, the membrane behavior in the electrical circuit, model is modeled by a closed electrical circuit and the response behavior of an electrode is explained by different time constants of overlapping processes. The dependence of the response, e.g., the admittance, of a dielectric sample on frequency induced by, e.g., an alternating field is known as dispersion.Since different processes are investigated by frequency-dependent analysis in dielectric spectroscopy, the model is primarily a time-resolved presentation of those processes. Such processes are reorientation and

Csfl SAMPLE

BOUNDARV

s IS€-MEMBRANE

c912 INTERNAL BUJNDARY

Figure 4-3.Equivalent circuit of an ion-selectiveelectrode [36,48]. R1, resistance of the sample solution; Rpt, phase transfer resistance; Rw, Warburg impedance (no traditional symbol exists); R , ,membrane resistance; Cd, double-layer boundary capacitance; Cg geometric capacitance of the membrane; 1, 2, aqueous solution adjacent to both boundaries of the membrane; in the symmetric arrangement the electrolyte solutions 1 and 2 are identical, the analyte exepted

150

4 The Artificial Anulyte-Selective Membrane

relaxation of mobile dipoles in an alternating electric field as well as “charge hopping“ as a function of inertia and viscous damping. In modeling the ion-selective half-cell, the membrane interior and the two boundaries are differentiated. The boundaries 1 and 2, and the membrane phase m have been viewed by their double-layer capacitance and simulated by a capacitor C with a resistance in parallel R , which represents the corresponding charge transfer resistance. At each boundary, the membrane resistance is in series with a so-called Warburg impedance, R, also denoted C , or Z,, which comprises resistive and capacitive parts and stands for diffusional control. In some models the Warburg impedance is included into the equivalent circuit of the boundary, in others distinguished as the impedance of the boundary electrolyte. The whole circuit is in series with the IR drop due to the bulk resistance of the electrolyte solution. The factor RC has the dimensions of time and is identical to the time constant z of a specific process. The impedance function relates output voltage to perturbing input current. Several ways of viewing the output exist, e.g., the Nyquist or Cole-Cole plots which are not identical in detail [51, 521. In the Nyquist complex plane plot, the real ZR and the imaginary part -ZI of the complex impedance are plotted on the x- and y-axes. The Nyquist plot is parametric in frequency w.The plot represents a semicircle with intercepts on the real axis at infinite (maximum) frequency ( w = ”) and at zero frequency (o= 0). The maxiumum occurs at ZR = R/2 where Z 1 = R / 2 a n d a = 1. In simulating the resistance and capacitance of the compartments, the different contributions can be quantified by approximatingthe experimentalimpedance-frequency plots by a theoretical function in an iterative procedure. The variables identify processes within the membrane and at the boundary, and visualize characteristics such as the a.c. resistance of the membrane, which is associated with the mobility of the charged species. Fortunately for thick ISE membranes ( d > 100 pm), the corresponding time constants do not often overlap. This means that the RC products of some processes involving coupled resistance and capacitance can be separated [45]. Time constants in order of increasing magnitude are scaled, starting from bulk resistance and geometric capacitance, to the Warburg diffusion of charge carriers and complexed species. Ion transfer characteristics of the boundary can be derived from impedance measurements in the low frequency range ( l e 3to 1 Hz).The Warburg impedance is observed only at the lowest frequencies available with high-performance instruments. This impedance is caused by concentration polarization of charged species within the boundary at simultaneous current

s Figure 4-4. Simplified equivalent circuit of a ion-selective membrane half-cell at high frequencies (103 to 106 Hz; sinusoidal voltage: 20-50 mV; Cg pF cm-2)

-


1s1

through the membrane. This case is of special interest in observing Donnan potentials of the membrane or adsorption processes at the boundary (components of the biological matrix). The electrical circuit illustrates the electric heterogeneity of the potentiometric cell. In measuring the impedance of the cell at variable electric frequencies, simplified equivalentcircuits result, and the various factors can be studied separately. At high frequencies, e.g., the resistance of the boundary approximates zero and the membrane circuit can be simplified to that shown in Figure 4-4. The results of impedance measurements depend on the bulk permittivity of the membrane. Hence, the membrane permittivity can be measured by an appropriate experimental design. The transfer coefficients of ionic species can be derived from the d.c. resistance relative to the a.c. resistance.

Model for the Equilibration Process of Homogeneous Asymmetric Optical Membranes Based on Fick's DifSusion Laws A variety of analyte-selective bulk membranes for use in optodes have been developed. They combine effectively with various optical transducers and detection techniques with mass sensitive, conductive, or capacitive sensors. The common feature of such assemblies is asymmetry since one boundary of the analyte-selective membrane is contacted to a mostly solid support and the other is in contact with a liquid or gaseous sample phase. Although the working principles of these set-ups are different, the basic principle is a diffusion-limited reversible exchange of target compounds at the membrane boundary. The viscosity of the membrane governs the diffusion rate and, therefore, the response time and equilibration kinetics of the sensor whereas the thickness of the layer governs primarily the equilibration time. The reversible facilitated carrier-inducedtransport of the target analyte increases the rate of exchange, lowers the detection limits,and, in addition, attenuates nonspecific background effects, such as the influence of humidity. In accord with the analytical requirements, some specificationsof solvent polymeric layers can be predicted from the measurement of a so-called overall difsuon coeficient of species involved in the recognition and extraction process of the membrane phase. The ATR approach is an attractive technique for such investigations [53].An ATR crystal (sapphire with n589 nm = 1.77) was coated with a Ca2+-selective optode membrane and implemented into a flow-cell, allowing for very efficient contact between membrane and aqueous solution and very efficient exchange of the aqueous solution (see Figure 4-5). The optode reaction is based on the following mass balance of the ion exchange (see section 5.2):

(4-5)

152


The overall "diffusion coefficient of the spectral change" was calculated from the change in the ATR absorbance induced by a change in calcium activity in the aqueous phase between C, and C i . The spectral change is displayed as a time-dependent response curve at the fixed wavelength of 660 nm, the maximum absorbance A(t) of the protonated chromoionophore with absorption coefficient &k,CH&]. The basic assumptions for the model describing a purely diffusion-based response behavior of a homogeneous membrane faed to a solid support are the following: 2+

1. The time constant of the complexation between ligand (L(m)) and analyte (Cq,,,)) is much higher than that of the diffusion 2+ 2, The ratio of the complexed analyte relative to the free fraction (CaLr(m) /Ca(,)) within the membrane is high

(a) solution inlet and outlet

membrane

a) View from top, showing the sample inlet at four positions and the outlet of he sample. Seven positions are marked with solid lines where the thickness of the membrane is determined interferometri-

4 Y Figure 4-5. Graph of the ATR-flow through cell

lightbeam

b) View from the side. The membrane is mounted only on the upper side of the waveguide. The sealing rubber ring defines the working area and the geometry of the active membrane area


153

3. The overall diffusion coefficient D of the protonated indicator (CH& reflects the diffusion behavior of the analyte-ligand complex within the membrane. D is the same in each membrane segment, the membrane being isotropic 4. Only the sample-membrane boundary contributes to the complexation and decomplexation reaction. The reactivity of the membrane-solid phase boundary can be neglected. 5. Solely the diffusion-gradientalong the x-axis normal to the membrane surface and along the thickness d is relevant 6. The diffusion process is reflected and inversed in sign at the solid phase boundary. The flux across this boundary is zero 7. The ionic strength of the sample (aq), the single ion activity coefficients, and the composition of the membrane phase (m) do not change during an experiment

An uncontrolled uptake of counterions is prevented by adding lipophilic counterions (2R&). The reader is referred to section 4.4.5and chapters 5 and 6 for more details. Diffusion of the analyte is observed through a plane membrane of thickness d, with a sample boundary at x = d and the waveguide boundary at x = 0. At time t = to, the system is in a steadystate and the active molality of the analyte in the entire membrane phase (0 < x < d ) is a = a,. Under the assumptions made above, Fick's laws of diffusion lead to the following solution [54], where c stands for concentration, and B for the absorbance coefficient:

c- co 4 ' (-17 -D(2n+1) ~-l-;Z n = O 2n + 1exP 412 ci- co 00

2 2 'IC

t

cos

(2n + 1) 7c x 21

(4-6)

If concentration is proportional to absorbance:

A = Co 0 4 log(e) - B 4 log(e) ( Co-Ci)

In conclusion, the time-dependent change in absorbance can be fitted perfectly by the equations presented here, which are derived from Fick's laws. An overall diffusion coefficient D (as measured by ATR) accounts for the spectral change due to protonation and deprotonation of the indicator as a consequence of the diffusion of all components which participate in the equilibrium reaction and in the ion-exchange process between aqueous sample phase and the membrane. This means that the ion exchange of such solvent polymeric membranes is diffusion controlled. The overall diffusion coefficients and the response times of the exchange reactions in either direction (see Eq. 4-5) have been determined [53]. As noticed in earlier experiments, the

154


response time of the release of calcium and uptake of hydrogen ions was significantly slower than the uptake of calcium and release of hydrogen ions. This effect may be explained by different association and dissociation rates of the complexes or by different lipophilicity and mobilities of the ions and complexes in the two phases. The model is called the difSusion of spectral change. The model served to describe and interpret the kinetics of the equilibration process. Under thermodynamic equilibrium conditions the model of the homogeneous membrane is based on the description and calculation of the mass balances as described in section 3.1 and chapter 6.

Conclusions Assuming a reversible recognition process and the reversible equilibration of a target analyte and of interfering compounds with a sensing layer, equilibriumconditions are primarily represented by mass and energy balances in a thermodynamic model as described in section 3.1, and chapters 5 and 6. Nevertheless, many effects of the response behavior of a selective sensor cannot be described and elucidated on this basis and need to be modelled by different theories such as Ficks laws, or the Butler-Volmer equation. Phenomena such as steady-state behavior, kinetic effects, diffusion processes, and charge transfer at the sample-membrane boundary and within the membranes are investigated by analytical methods such as cyclic voltammetry, impedance analysis, ATR- and dielectric spectroscopy. The models presented here aim at extending the thermodynamic description; models were reviewed briefly. The reader is referred to the literatke for more details. Very relevant differencesbetween artificial and biomembranesare obvious from the different structure of bilayers and homogeneous polymeric bulk membranes. Basic differences are also seen in that artificial membranes are able to induce an active transport of target compounds through membranes, whereas traditional analyte-selective membranes make use of a facilitated uptake by carriers. The solvent flow across the membrane is assumed to be negligible, whereas water easily penetrates the phospholipid bilayer of a biomembrane with a rate constant of about 106 s-1[5]. Therefore ion uptake and transport of biomembranes is less bound to dehydration and solvation of ions. This means that, besides the type of the carrier, the whole composition of artificial membranes decisively contributes to the uptake of analyte compounds. These factors will be discussed at the end of this chapter. Nevertheless some models, specifically the electric circuit model, can indeed serve to describe the polarization and depolarization steady-state of both artificial as well as natural membranes. As a conclusion, the design of chemical sensors on the basis of lipid-like mono- and bilayers must follow rules which are different from those of polymeric bulk membranes. It is not possible to account for all the parameters which exert an influence on the recognition and transport process by one equation or one membrane model. Thus, all four models as well as a number of different equations must often be applied to explain some of the phenomena observed. In applying these models, the approach is usually to explain deviations of analyteselective membrane behavior from ideal behavior, especially in contact with biological specimens, and to find good compromises in preparing useful electrode membranes.

4.3 The Selectiviry CoefJicient

4.3

155

The Selectivity Coefficient

The ability of a chemical sensor or sensing layer to extract the analyte or a class of analytes selectively and to discriminate interfering species, which respond with the same type of signal, is called "selectivity" and specified by the selectivity coefficient for potentiometric, $Pt for optical, and K""' for amperometric sensors (for nomenclature see [55, 561, see also section rl 1.2). A selectivity coefficient of 0.01 means that a background species is disciminated by a factor of 100 and that the background species contributes 1% to the analyte signal if both analyte and background species are present at the same activity. The definition of the selectivity coefficient, at least, is clear and generally agreed. Ideally, the association or stability constant of an analyte-ligand or host-guest complex should be representative for the selectivity behavior (see also section 3.1). In this case, the association constants as determined by the methods mentioned in section 3.1 should be representative for the value of the selectivity coefficients of a sensor against interfering species. The selectivity coefficient however, is more an empirical than a theoretical quantity which describes the overall extraction behavior of the sensing element, such as a solvent polymeric bulk membrane. It comprises the solubility or partition of the analyte between sample and membrane phase ki as well as the stability or association constant h. of the host-guest reaction compared with the same properties of the interfering compounds. Thus, the association constant as determined in a pure solvent is the most important factor, but usually not sufficient for the description of the selectivity behavior of a host compound in any type of sensing layer. The mechanism of permselectivity based on a thermodynamicmodel is discussed by Morf [31 (pp. 274 fo] (see also section 3.1). The selectivity coefficient is supposed to show three main characteristics:

qt

1. It is a correction-factor and should fit a real response function to the theoretical response of the respective sensor; 2. It is evaluated on a sound theoretical basis for pure and mixed solutions and can subsequently be transferred to fit the response function of any specific real application; 3. It is used to characterize and compare various types of sensing layers and sensors. Therefore, a simple, internationally accepted reference method must be defined which allows comparison of selectivity coefficients within each class of chemical sensors

In view of these theoretical and applied aspects, an analytical method has to cope with requirements which appear incompatible. Several methods have been discussed along the three main streams mentioned above.

IUPAC-Recommended Analytical Methods Analytical methods generally compare the signal intensity due to the most relevant interfering compounds to the response generated by the analyte. Two different methods for the determination of the selectivity coefficient are traditionally recommended by IUPAC, the

156


separate solution method (SSM) and the fixed interference method (FIM) [35] which aim at quantifying the selectivity of ion-selective electrodes generally. Meanwhile, with the growing number of different types of sensors, these methods have been widely applied, and their validity has been discussed intensively [62-681. Pure 0.1 m o m aqueous solutions are used in SSM for both the analyte ( U A ) and the interfering species (ag).The selectivity coefficient is calculated from the difference in the signal intensity, e.g., the potential difference (E2 - El ) due to identical activities of both the target and the interfering species. Equation 4-8 is derived from the Nemstian response function relating the potentiometric signal due to the activity of ion A to that of ion B. The slope or sensitivity is assumed to be related to the charge number of the species:

The signal intensities, e.g., the potential values obtained, are plotted against the activity of the target analyte. The very popular graphic selectivity patterns are typical products of this data treatment (see Figure 4-7 and section 5.1). Problems arise, however, from a purely mathematical inconsistency when treating the primary ion as the interfering ion and vice versa. Owing to the dependency of the selectivity coefficient from the charge number of ions A and B, the KfYt has a significantly different value while just a change in the sign is expected. This problem is currently analyzed based on the characteristics of the magnesium-selective electrode 1681. In mM, a fixed background of an interfering compound is used and the activity of the analyte species is varied. The selectivity coefficient is calculated from the ion activities at the detection limit, which is the point of intersection of the analyte response function and that of the interfering ion, below the detection limit [35]:

The detection limit is commonly evaluated graphically. An algorithm based on nonlinear regression analysis is proposed [57]. Referring to the IUPAC papers, the selectivity coefficients of optical [58, 591 and amperometric sensors [60]are defined in a similar way for pure and mixed solutions. The IUPAC recommendation (Nernstian response) is based on a thermodynamic model associated with an estimate of single ion activity coefficients and ion activities in pure or mixed solutions (see section 3.4). The influence of the variable liquid junction potential of the reference electrode with changing composition of the electrolyte solutions is obscured by a shift of the cell potential (see sections 3.4 and 5.1). The liquid junction potential must be taken into account when evaluatingthe cell potential. The segmented membrane model is useful for distinguishing the equilibrium conditions at the boundary phases from those in the bulk of the membrane. The boundary is assumed to equlibrate much more rapidly (between 6 s and 2 min) than the bulk. According to Fick‘s diffusion equations, the equilibration of a membrane of thickness 200 pm takes about 2.8 h, assuming a mean diffusion coefficient for the species within the membrane bulk [61] of lo-* an2 s-1. Nevertheless, other factors in the equilibration process, e.g., the release of mobile ions

4.3 The Selectivity Coejicienr

157

from the bulk and from the inner electrolyte which are not considered by basic membrane models, may be cited. In view of a nonsymmetric electrode arrangement (see section 5.2), a correct theoretical treatment of electrodes and selectivity coefficients is relatively delicate, since different effects may contribute to the emf which influence the value of selectivity coefficient and the detection limit. Therefore, some assumptions have to be made in order to describe the potentiometric cell, the thermodynamic conditions of the boundary [62], or the sensing layer (see section 4.2). The selectivity coefficient has been the subject of discussion for many years [62-661. The selectivity coefficient as determined by IUPAC recommendations was treated as a constant and intended for use in the semiempirical extended Nikolsky-Eisenman formalism (see section 5.1) which is the general basis for modeling the response function of an ion-selective electrode in a mixed solution. Nonetheless, discrepancies between the coefficients derived from traditional IUPAC recommendations [64a] and those determined in real samples prevented their direct application. Currently, the SSM selectivity factor is primarily used as a weighting parameter, equivalent to the stability constant and the partition coefficient, in order to compare membmie preparations. At least, the experimental conditions are simple and relatively clear as far as the composition of test solutions and equilibriumconditions are concerned. Therefore, SSM may be treated as a reference method to validate sensing layers and sensing devices in the future. For this use, predictions of required selectivity coefsicients have to be made under the same conditions as the measurements, which in addition raises the question whether the method used for estimating required selectivity coefficients is correct.

Comprehensive Description of the Boundary Potential In answering the question of how to treat selectivity coefficients for mixed potentials based on a general thermodynamic model, a main concern was to take account of the charge numbers of analyte and interfering ions adequateIy. A comprehensive description for various types of potentiometric bulk membrane electrodes was presented by Bakker et al. [67] and is consistent with Matched Potential Method (MPM) described in [a]. The authors present a selectivity coefficient k?' to be included in the response function due to activity changes of the primary ion 1/ in a mixed electrolyte solution wherej respects the activity of the sum of interfering ions, a J. The sel selectivity coefficient k.. involves the emprirical Nikolsky coefficient for mixed solutions as ZJ well as a contribution by the charge number and activity of the primary ion in pure solutions of

qt

I: (4-10) Derived from the thermodynamic description of the boundary equilibrium, the Nikolsky coefficient is now modified by the power of the charge number ratio. In the simplest case the response function, based on the assumption that pure solutions of the primary and interfering ions show identical standard potentials and an ideal slope of the response function, is then described by:

158

4 The Artificial Analyte-SelectiveMembrane

(4-11) This equation is only valid in the activity range of I where the activity of other ions induces

< 10% inaccuracy. For all the other cases, the equation describing the emf response is much more complex. The calculation of the required selectivity coefficient involves the activities of both primary and interfering ions in mixed solutions (IJ), and now the allowable error p i due to insufficient selectivity of an ion-selective electrode to the power of the charge number ratio. The required selectivity coefficient is predicted by: (4-12)

Table 4-1. Effect of selectivity coefficients calculated from SSM (procedure 11) and SAM (procedure I) on the resulting accuracy of determinations of the magnesium ion activity in solutions with physiological background composition (q@+, 0.36-0.60 mmoUL; cca2+, 1.101.5 mmol/L; C N ~ + ,120-150 mmol/L; CK+, 3.0-6.0 mmoYL) (see text). Seven different membrane compositions were compared (I-VII). Compositions: ligand ETH 7025 4.1-35 pmolal; anionic sites (KTpClPB) 1.55 moYmol ligand; 2.2-2.5 mmolal o-NPOE; 360 p.g/g PVC; (see Appendix 8 and [62]) molality is referred to the total membrane mass

ah

Membrane

l o g a b according to procedure 11 (SSM)

1% according to procedure I (SAM)

error [%I using log according to procedure n2

error [%] using log according to procedure I2

I

-0.80

II

-0.90

111

-1

Iv

-0.90

V

-1.05 -1.20 -1 -40

-0.35 -0.50 -0.35 -0.35 -0.80 -0.75 4.60

10.6 7.2 12.1 11.1 3.2 5.1 8.9

2.0 2.0 3.2 3.O 1.6 2.0 2.8

VI

w

.oo

@b

log KPSgCaaccording to procedure I is the most sensible value of log K$Lca resulting when performing procedure I with a certain membrane. The resulting error is calculated as the average deviation of experimental values evaluated according to the transformed Nikolsky equation iterated with different selectivity coefficients, using the emf values of procedure I, from the assigned magnesium activity of the test solutions

4.3 The Selectivity Coeficient

159

Based on Eq. 4-12, required selectivity coefficients of l@ in order to discriminate sodium vs. magnesium ions were calculated. This contradicts experimental values which show no detectable interference with membranes exhibiting SSM coefficients'of c 10"O (see also Table 4-1). Required selectivity coefficients for ions of equal charge number are not affected. Validating these equations in the future will show its usefulness. In this volume, selectivity coefficients according to IUPAC recommendations (1976) and SSM-based measurements will be referred to throughout. SSM-based values are applied as standard values specifically for the comparison of membranes and host-guest chemistry (see Appendix 9).

Alternative Methods Applied to Mixed Solutions When implementing analyte-selective layers into an instrument, scientists have to face the situation that selectivity coefficientsare not conserved. Necessarily, selectivity correction factors are evaluated for each dedicated system specifically. Nevertheless, in applied research it is recommended to work as close to reality as possible. In this sense the mixed potential method (MPM) was proposed [63, 641 and evaluated by Zhang et al. [68]. Another approach was inspired by the collaboration in the European Electrolyte and Blood Gas Division of AACC/IFCC (American Association for Clinical Chemistryhtemational Federation of Clinical Chemistry) and is discussed below [65].

S A M (SpecificApplied Method) In S A M , mixed standard or calibration solutions are used where the activities of analyte and interfering species cover the whole range of natural variations. The selectivity coefficient is evaluated by an iterative procedure looking for the best fit of the experimental values to the theoretical response curve according to the NikolskylEisenmm formalism. Both methods are reported in more detail in Appendix 8. SSM and S A M were evaluated for medical use of the magnesium-selectiveelectrode over the range of 6 x lo4 to 3.6 x 10-4M CMg2t (see Table 4-1). The results in Table 4-1 show that the selectivity coefficients resulting from SSM may be totally misleading and induce a considerable error when used for calculations of activities from emf values according to the Nikolsky-Eisenman equation. Even a considerably lower but true selectivity coefficient is shown to result in a higher reliabilty of the assay, if the activity of the interfering ion is adequately taken into account.

Critical Considerationsand Comments Validity of selectivity coefficients and their measurements: The procedures discussed here provide no absolute information on selectivity coefficients in accord with stability constants or

160

4 The Artijicial Analyte-SelectiveMembrane

distribution coefficients, although relative changes of the selectivity pattern can be distinguished. Necessarily, the analytical conditions need to be defined concisely, the results need a statistical validation and also the maesurements of a blank is recommended. Crucial are, e.g., the order of pure solutions exposed to the sensor in SSM and the time of changing solutions. Both can be referred to reorganization of the membrane-boundary composition in context with the significantly different composition of the electrolyte solutions in contact with both membrne boundaries, which rises dramatic emf changes, especially for highly discriminated species. In addition, the ions involved in SSM measurements show different exchange kinetics (see section 3.2). Further critical assumptions are: conservation of the selectivity coefficients over time, extrapolating the selectivity behavior over a broad dynamic range, and ruggedness of the selectivitybehavior under changing analytical conditions.

Required Selectivity Coeficient and Allowable Analytical Errors A lack in the selectivity of a chemical sensor causes two different types of error: first, inaccurucy, which is traced back to the composition of the calibrating solution relative to the measured sample, and, second, imprecision which can be avoided by multiplying sensor setups and using sensor arrays. The inaccuracy, also indicated by a shift in the response function, is avoided if the sensor is calibrated with a mean expected activity of the interfering compound. The remaining imprecision due to insufficient selectivity is caused by variations of the activity of interfering species around the calibrated setting point. This contribution can be avoided by chemometric correction of the analyte signal based on measurements of the activity of interfering species, if possible. However, each of the sensors in a sensor array needs a high quality of performance. According to the laws of propagation of errors, the variance of each sensor adds to the total error of the -YFor a reliable medical interpretation of the results for the primary analyte species, the allowable analytical error is defined by the biological variation of the analyte (see Appendices 4 and 9) assuming that no inaccuracy is involved in the analytical process. These rules have been applied to calculation of the required selectivity coefficients for ion selective assays. As a first priority, the required selectivity coefficient was calculated based on the biological variation (cv a S 0.5 CVb) or maximum of 1%as a second priority:

and according to

a.4-12 for ions of different charge [67]:

kr' (required) = (0.5 C V ~ ) ' ~ ' ~(a1 (IJ) / { U J (IJ) )z"zJ)

(4-14)

4.4 The Membrane Composition and the Membrane Medium

1 61

where CVb is the biological coefficient of variation (see Appendix 4). Unfortunately, biological variations, based on extensive studies by Fraser [69], are known only for total electrolyte concentrations, not taking molal ion activities into account. The required selectivity coefficients for a large physiological range of ion concentrations are presented in Appendix 9 based on the intraindividual CVb.intra. For longitudinal studies all calculations are based on Eq. 4-13 and ate consistent with SSM measurements (for alternatives see [57,68]). The tabulated limits involve values for dilute samples (1+19) and undiluted specimen as well as values incorporating a mean calibrated background, and assays without such a background correction. The limits for diluted samples and ions with different charge are not valid for optodes (see chapter 6). In optical sensors, the charge is not primarily relevant for estimations of the required selectivity coefficients [59]. The term z&j can assumed to be 1. However, the practical selectivity of the membrane depends on the pH of the sample solution. Estimates of the selectivity coefficient are based on the response function. The tabulated values are extremes, since, statistically, a difference of > 0.5 x 2.8 sa (= 1.4 sa for one partner) might be significant to discriminate two neighbouring values (see section 7.3 and Appendix 12). In comparing the errors made with and without correction for interfering background species, it can be shown that the calibration of the background allows an increased gain in information. The errors due to insufficient selectivity can be considerably decreased. More details on the determinationand interpretation of selectivity data are given in [59,70-721.

4.4 The Membrane Composition and the Membrane Medium A large variety of different sensing layers, the core of every chemical sensor, have been developed, exhibiting considerably different features. Solvent polymeric bulk membranes are one class of such layers, which typically consist of 33 wt% polymer (e.g., polyvinylchloride (PVC)), 64 wt% plasticizer, 1-5 wt% host compound (carrier, ion-selective ionophore) and additives (e.g., anionic or cationic lipophilic sites, catalysts). The introduction of high molecular poly(vinylch1oride) (PVC) as a matrix for the preparation of membranes for ion-selective electrodes corresponds to a milestone in membrane technology for chemical sensors [73, 741. This step encouraged transferring the achievements of polymer chemistry to membrane technology and studying the effects of many plasticizers known from industrial PVC processing. However, more generally the final design of analyte-selective membranes is related to their application and depends critically on the required performance and features of the sensor. A series of critical parameters determine the properties of the membrane and limit the application of the final sensor. Examples of these are:

-

-

-

- the concentration of carriers and the molar ratio of additives (charged sites) relative to the analyte-selective carrier and relative to the chromoionophore for optodes (see sections 4.4.5 and 4.4.6)

162


-

the lipophilicity of the incorporated compounds and the life-time of the membranes, immobilization of components (see section 4.6)

-

the permeability for and solubility of water within the sensing layer, the hydrophilicity, wettability, and adsorptive properties of the surface (see section 4.4.3)

- the permittivity of the plasticizer and the membrane medium with regard to the association of charged compounds, and the mobility and reactivity of host molecules (see section 4.4.1); influence of donor/acceptor effects and solvatochromic shifts in optical membranes (see section 4.4.2)

- the structural characteristics of the plasticizer and the carrier or indicator in view of the mobility of the ligands and the interaction between plasticizer and ligand (see section 4.4.1) -

the solubilizationproperties of the membrane medium or plasticizer preventingcrystallization and exudation (see section 4.4.1) of the components; transparency of the membrane is required for some optical assays

Some of the experimental setups, e.g., the measurement of the permittivity of membranes, have been investigated [75]. The reader is referred to the following references for details: The determination of the lipophilicity is presented in [61,76]. Initial attempts at determination of the dielectric constants of membranes are reported in [75, 771. Further experiments are in progress [68b]. The molar ratio of anionic sites relative to the ionophore influencing the selectivity is reported in [78]. The influence of ionic sites on the performance of charged carrierbased ion-selective electrodes (ISEs) has been investigated [79-821. The immobilization of carrier, chromoionophore, and anionic sites, and the technique of molecular imprinting have been reported, especially for optode membranes, by Rosatzin and Mosbach [83-851. These investigations have brought to light the transport conditions of artificial membranes. The complex behavior of analyte-selective membranes must be extended to aspects of viscosity and surface tension in the future. In addition, viscosity and surface tension are supposed to be parameters which contribute to the membrane function, particularly in view of interactions between the surface and the biological sample, or of attaching a layer to a membrane support (optical waveguide).

4.4.1 The Influence of the Permittivity and of Plasticizers The factor cr was formerly called the relative dielectic constant. It is measured by comparing the capacitance of a cell of unit dimensions filled with the sample relative to the capacitance of the same cell containing a vacuum (C,,= 8.854 x C2 J-l m-l Er = F m-l, E,, = 8.854 x UG).But, since the dielectic constant is not a constant (e.g., the material exhibits dielectric dispersion), it is more properly referred to as the peminivity [86]. 9


163

To explain the mechanisms of the interaction between plasticizer and polymer, several theories had been proposed [87-891. At that time, little effort was made to adjust the properties of the plasticizers to the requirements of the recognition process. Morf et al. postulated the impact of the dielectric constant of the membrane on the selectivity constant ( F q 4-16 and section 4.4). Therefore, plasticizers with relatively high permittivity, e.g., o-WOE (cr = 23.9 f 0.3 [77]) were introduced to enhance the preference for divalent over monovalent cations of the same radius [75, 90, 911 (for acronyms and chemical IUPAC names of plasticizers see (Appendix 7). The observations were based on very few data, although, related to ion-selective electrode membranes, they confirm a general iule for the solubility of species with different charge numbers and different free energy of hydration in polar solvents. Any selective recognition process may be favored in controlling the extraction process by an intelligent choice of the composition of the surrounding media. Hence, in genereal, the dissociation of charged components and their activity coefficients within the membrane are governed by the polarity of the bulk membrane medium. This is important in view of the assumptions that are made for modeling the membrane processes. The Debye lenghth r D is dependent on the relative permittivity Er of the solvent and increases with increasing permittivity, Q decreases concomitantly with the ionic strength I, and increases with the temperature T /K according to the Debye-Huckel equation in section 3.4. For example, the Debye radius of a strong 1:l electrolyte such as NaCl in an aqueous solution with E r = 78.5 and I = 0.01 is in the range of 3 nm. It decreases to 949 pm in the same solution with I = 0.1 and E = 78.5 , and to 214 pm with I = 0.1 and E = 4 (298K). The activity coefficient, of salt solutions with different permittivities may be estimated by substituting r D in the following equation [62]:

+,

(4- 15) or by using the Debye-Huckel formalism given in section 3.4. A considerable change of the ionic strength for different conditions can be estimated, assuming p = 0.997, equal to water at T = 298 K, an ionic strength, I = 0.1, and monovalent ions with z = 1 the activity coefficient, y f is 0.770 for KCl. For a permittivity of the same solution and E = 4 the ionic ( ~ ~ =078.54). , strength will be extremely low and the activity coefficient tends toward 1. However, if the ionic strength is fixed by anionic sites which are sterically prevented from association, the ionic strength of a membrane can be in the range of I = 0.02-0.04 under electroneutrality conditions and the activity coefficient can be unexpectedly low. A rough estimation of the mean activity coefficient of a monovalent salt, dissolved in different media, shows the impact of the permittivity on the assumption of constant ion activity within the membrane in optical and potentiometric assays. Interactions between ions have not been considered in basic models so far (compare section 3.2). Experiments with reversed micelles, where AOT (sodium bis(2-ethyl hexyl) sulfosuccinate) is the main component of the heterogeneous micellar membrane, showed that ion-pairing greatly influences the distribution of all charged compounds [93,941. According to Morf et al., EQ. 4-16 was used to estimate the effect of the permittivity related to the charge number and radius of the participating ions for the permselective extraction of magnesium ions [ 3 1,70,77,951:

164

4 The Artijicial Analyte-Selective Membrane

(4- 16)

where selectivity coefficient [(mol L-l)-*] Avogadro constant (6.022 x 1023mol L-l) dielectric constant of the membrane [A2 s4 m-3 kg-'] elementary charge (1.602 x l ~ C)- ~ ~ charge number of Na+ (dimensionless) charge number of Mg2+(dimensionless) radius of the Na+-ligand complex [m] radius of the Mg2+-ligand complex [m] gas constant (8.314 J K-' mol-I) absolute temperature [K] Where there is a preference for Mg2+ over Ca2+, the dependence on the permittivity of the membrane can be derived on the basis of the Born equation [31,95] (see also section 3.1): (4-17)

KE~' Er EO

selectivity coefficient [mol-11 = relative dielectric constant of the membrane (dimensionless) = electrical field constant (8.854 x A2 s4 m-3 kg-1) =

Equations 4-16 and 4-17 suggest an increase in the discrimination of larger ion-ligand complexes as E, increases. Since Ca2+ tends to form more voluminous ion-ligand complexes than Mg2+, owing to its higher complex stoichiometry and its larger ionic radius, plasticizers with high permittivities should improve the preference for Mg2+ over Ca2+. For example, an increase in E, from 4 to 18 theoretically induces a change in the selectivity coefficient Alog -1.32 for r c , =~ 1.9 nm and r ~ = 1.5 g nm ~ (total volume assumption). Plasticizers need to hlfil the four principal criteria mentioned already: high lipophilicity, solubility in the polymeric membrane (no crystallization),no exudation (one-phase system) and support of the ligand in the selectivity behavior of the resulting membrane. On the other hand, optimization of the selectivities should be achieved for each application. Dinten and Oesch et al. [61,83,97-991 described the lipophilicity of a plasticizer as a critical parameter which may limit the life-time of a sensor by leaching from the membrane into the surrounding media. Therefore, it was undertaken to prepare plasticizers and ionophores of high lipophilicity [75, 1001 (see Appendix 6), the hydrophilicity and vapor pressure being exeemly low. For magnesium-selective membranes, the effect of the permittivity of the membrane phase showed a more complex behavior and gave evidence that other factors of the membrane composition play a role. In liquid membranes of high polarity (with o-NPOE derivatives as

Kgg*=

4.4

The Membrane Composition and the Membrane Medium

I65

plasticizers), the extraction and exchange of doubly charged ions such as Mg2+ and Ca2+ was facilitated and monovalent ions thus were rejected. However, Mg*+, exhibiting a higher free energy of hydration than Ca2+,was significantly favored over Ca2+ with increasing lipophilicity of the plasticizer (log P n c (ETH 220) = 15 k 0.1 (see Appendix 6) in addition to the effect of lipophilic anions [33, 78, 1021. Although, for isologs of the same basic structure, a high lipophilicity decreases its permittivity. Further experimentsare in progress [57,68]. Subsequently a strategy was proposed to optimize all four requirements mentioned above. The synthesis of different compounds was described (see Appendix 7). Structural elements such as branched alkyl chains, aromatic rings, and bulky adamantyl-groups may increase lipophilicity without loss of solubility and mobility (see Appendices 6 and 11). Substitution by several polar or polarizable groups may enhance the polarity of the plasticizer molecule. The introduction of alkyl residues with halogen atoms (R,HrX> or several functional groups with favourable dipole moments occasionally lead to compounds with melting points above room temperature (see Appendix 6). Mixing of different plasticizers can result in good compromises. For comparison of the influence of different plasticizers, a standard membrane containing the relatively weakly Mg2+-selectivecarrier ETH 7025 (see section 5.1) was used. A total of 55 plasticizers, based on a large variety of structural elements, were investigated (see Appendices 6 and 7). The acitve membranes incorporating the target ligand are compared with a ligand-free blank membrane of identical composition.The influence of plasticizers on the membrane properties was studied for optical as well as potentiometric chemical sensors. In magnesium-selective electrodes, the chemical and structural properties of the plasticizer were decisive for a high discriminhtion of monovalent and calcium ions and for the homogeneity of the membrane. Owing to the high sensitivity of the magnesium-selective ligands to their

Table 4-2. Dipole moments p of some selected compounds [loll. Values are given in Debye units (1 Debye = 3.33 10-30 Cm) (compare Appendices 6 and 7)

Compound

Dipole moment p [D]

3,CDinitrodie

8.9 7.1 7.O 6.0 5.6 5.2 5.0 4.8

N,N-Dimethyl-p-nitroaniline 3,4Dinitrophenol 2-Methoxy-4-nitrophenol N,N-Dimethyl-p-toluenesulfonamide Methyl p-toluenesulfonate Methyl phenyl sulfone o-Nitroanisole

Commercially available

Plasticizer ETH Nr. or acronym

4332 4358 4315 8032 8028

O-NPOE'

166

4 The Ariijicial Analyre-SelectiveMembrane

environment, the magnesium-selective electrode was used as a test electrode. Based on wide experience with the ligand ETH 7025 and 155 mol% anionic sites (KTpClPB) relative to the ligand in o-NPOE and PVC, this composition was chosen as the reference membrane composition. Alternative membrane compositions were decided relative to this reference membrane electrode. An overview collecting the results is given in [75]. Some results of these investigations are summarized in the following notes. The constitutions of the most useful plasticizers are shown in Figure 4-6. 1. The plasticizer ETH 5373 effects maximum discrimination of alkali and calcium ions, but exudes from the membrane owing to its high lipophilicity (log PTLC= 13.5 f 0.5) and solubility problems in the mixture with PVC. Introducing polar or polarizable groups in the alkyl chain of the o-nitrophenylether-type plasticizers prevents these plasticizers from exuding, but they all induce somewhat worse selectivities than analogs without such groups. In the future it must be paid attention that only a minimum of polar or polarizable groups in the side chain are introduced which are necessary to avoid exudation. The more numerous such groups are, the

2-Nitrophenyloctylether o-NPOE

a N O a a N O a 0

2-Nitrophenylpentadecylether

0 -NPP D E

0

2-Nitrophenyldihydrophytylether E TH

U 0

N

5373

0 'I \

U

ETH 8045

Figure 4-6. Constitution of some of the most relevant plasticizers used in magnesium-selective electrode membranes. For a complete set, characteristics, and synthesis of the plasticizers see Appendices 6 and 7


167

more the discrimination of interfering ions decreases. Neither by optimizing plasticizers of the reference membrane, e.g., ETH 8045, nor by using mixtures of ETH 5373 with o-NPOE, can selectivity coefficients for calcium below log K E L a = -1.25 be obtained, which is necessary for realistic long-term monitoring. However, the selectivity coefficient may be improved to log KK& = -1.5 with the plasticizer ETH 5373 (see Figure 4-6). Results from membranes incorporating the more effective ligand ETH 3832 are shown in Figure 4-7. It is noteworthy, that the side chain of the plasticizer ETH 5373 is the dihydrated derivative of the natural phytyl side chain of chlorophyll a and b, and contributes there to the high lipid solubility of chlorophyll. In membrane type C (Figure 4-6, third column from left) incorporating the plasticizer ETH 5373, 155 mol% anionic sites (KTpCiPB) relative to the ligand, and PVC, the highest selectivity coefficients were observed, sofar. Nevertheless, membrane type C shows unreliable performance, owing to exuding of the plasticizer. With respect to these criteria membrane types E and F were preferred for studies in real samples. 2. In contrast to alcohols and esters, o-nitrophenyl ethers show impressive selectivities for Mg2+ over Ca2+, Na+, and K+. The reference membrane with ETH 5373 as a solvent, for example, exhibits a remarkable discrimination for calcium (log K = -1.5). A further improvement of the selectivity coefficientscan be achieved by increasing the length of the alkyl chains, which at the same time increases the lipophilicity. This holds not only for the plasticizer, but also for the ligand, e.g., alkylation of ETH 3832 in position 10 (1,3,5-tris-(lO-methyl-7,9dioxo-6,1O-diazaheptadecyl)-benzene)[102al.

Kica

Conclusions, Further Working Hypotheses, and Statements The following hypotheses and statements have been proposed to account for the main effects observed, so far: 1. Plasticizers may compete with the carrier. Therefore, they should not contain competing

functional groups which may act as competitive coordination sites. Plasticizers with long alkyl chains are able to separate the polymer chains. That is why they are thought to be excellent plasticizers, but on the other hand the small interaction with the polymer chain is responsible for their tendency to exude. For that reason the use of polymers with less intermolecular interaction and the substitution of the alkyl chains of the plasticizer by polar or polarizable groups is proposed. However, the substitution of PVC by other polymers, e.g., polystyrene-butadiene (PSB), leads to other restrictions, such as an increase of the membrane resistance by a factor of 10 or more. In further work, o-nitrophenylether derivatives substituted by alkyl chains containing polar or polarizable groups (e.g., phenyl groups, multiple bonds, halogens) to prevent exudation were developed. 2. Since a correlation of the selectivity behavior and the dielectric constant of the membrane was postulated (Eqs. 4-16 and 4-17), and since the dielectric constant of a plasticizer corresponds approximatly to the square of its dipole moment, plasticizers based on the compounds shown in Figure 4-6 and Appendices 6 and 7 were synthesized. They were expected

168

4 The Artijicial Analyte-Selective Membrane

log

Pot KMg j

1

0

-1

-

-H -H -H -ca -Ca

-Ca

-Sr

-Ca

-Sr

-2

-H -ca

-Sr

-3

-Sr -Sr

-Sr

-

4

-4

-5

-LiNa 02%

m3832.

0-NPOE,

wc

1% N3832.

ETH 500. DNPOE, PVC

1% EM3832 ETH 5373: PVC

1% EM3832. O-NPPM.

wc

1% N3832. ETH 8045.

wc

1% N3832. E l H 500. ETH 8045. PVC

Figure 4-7. Selectivity pattern of magnesium-selective membranes based on the ligand ETH 3832 (% in the column's legend, wt% relative to the membrane mass) with different plasticizers determined by the SSM method. The SSM conditions are standardized for screening at 3 10 K in a 10 min time interval. From left to right: membranes type A to F with varying composition. For synonyms and chemical names of the plasticizers, see Appendices 6 and 7 and Figure 4-6. ETH 500, tetradodecylammoniumtetrakis(4-chloropheny1)borate; all membranes contain 155 mol% potassium tetrakis(4chlorophenyl)borate (KTpCPB)

to show higher dielectric constants than 0-WOE. Therefore membranes prepared from those plasticizers should show increasing selectivity coefficients. The results show that the lipophilic 3,411itrophenyletherderivative ETH 4358 and the sulfonamide ETH 8032 (Appendix 6), which are supposed to exhibit relative dielectric constants in the range of 50 and 30, reduce the preference of Mg2+ over Ca2+,Na+, and K+ [75]. Hence such a simple correlation could not be confirmed. If even higher dipole moments are sought for, molecules with the features of an amphoteric ion (e.g., o-benzbetaine, dipole moment p = 13.2) may be used. As a matter of course, substitution of the benzene ring is always possible in order to increase the dipole moment [ 1031.


169

Remembering even the small selectivity loss when changing from o-NPOE to Chloroparaffin or Mesamoll, one has to question the validity of Eqs. 4-16 and 4-17. 3. Three reasons for the deviation of experimental results from theory should be kept in mind. First, the permittivity of the membrane must not exactly correspond to the permittivity of the plasticizer, because molecular interaction in the membrane phase and ion-pairing [la, 1051. The latter effect, however, does not seem to occur in membranes of high permittivity. Second, it might be that enthalpy effects caused by structural differences of the plasticizer dominate the effects expressed by Eqs. 4-16 and 4-17. In addition, entropy effects may add to the deviation from a rudimentary theory (see section 4.4.3). Third, the only polar membrane solvents used in earlier contributions were nitrophenyl ether compounds, whereas the apolar plasticizers always contain other functional groups with potential coordination sites which might compete with the carrier. Therefore, it cannot be excluded that the dependence of the selectivity coefficient on the dielectric constant of the membrane, as published by other workers [31, 77, 951, was actually caused by the influence of the competing functional groups of the plasticizer used. Nevertheless, Eq. 4-16 was introduced to explain the facilitated dehydration and generation of the ion-camer complex by a high permittivity of the membrane phase, and thus makes sense in this respect.

4.4.2 The Effect of Electron Pair Donor (EPD) and Acceptor (EPA). Properties of Solvents. Solubilization Properties of the Membrane I

Quite a list of different compounds are available as solvents for chemically selective layers. In respect of the environment of the host-guest chemistry, the term "solvent" comprises not only the plasticizer, but also the polymer and, occasionally, some additives. Plasticizers have been modified synthetically according to the required features (see Appendices 6 and 7). The classification of solvents in terms of specific solute/solvent interactions may prove very useful in this context [ 1061. The fundamental distinction between protic and aprotic solvents, allows a differentiation based on the ability of forming or breaking hydrogen bonds (HBD: hydrogen bond donor; HBA: hydrogen bond acceptor). Plasticizers may be regarded as aprotic solvents with varying polarity. The polarity is characterized by the relative dielectric constant or permittivity E ~Polar . and upolur uprotic solvents are characterized by an arbitrary cut-off value ~ ~ variety l ~ of. polar aprotic plasticizers with different at 0 > Er,apolar < 15 c ~ ~ ,A large lipophilicity had been synthesized as reported in the previous section. The influence of the lipophilicity of plasticizers with high dielectric constant on the selectivity of the magnesiumselective electrode was investigated and shown to be fundamentally important [71, 75,771. The arbitrary choice of a borderline permittivity at E~ = 15 is experimentallyuseful as ion association occurs in the lower range, and free solvated ions are generally no longer observed there, whereas the dipolar aprotic solvents show an extraordinary specific ion solvation. This gives one explanation for the increasing discrimination of monovalent ions relative to magnesium ions by polar solvents where the solvent facilitates solvation and extraction of the magnesium species. Protic solvents are particularly good anion solvators, owing to their hydrogen binding ability. This feature is comparable to the high stabilization of the lipophilic anions in optode membranes by the charged protonated chromoionophoreand electrostaticinteractions.

170

4 The ArtiJicial Analyte-Selective Membrane

To further evaluate the influence of the solvent on the mobility of the membrane components and on the energy barrier necessary for a conformational change of the ligand, electron donor and electron acceptor properties of the participating compounds have to be considered. Interactions between polar chemical groups are much more pronounced in the organic phase if water is more or less absent. Several methods have been proposed to determine the water content within the membrane [log-1 101. No quantitative values have been published, although the water concentration may be relevant. Water was supposed to be organized in clusters if a sufficiently lipophilic environment is created (see section 4.4.3). Assuming no interaction with water, an EPD molecule (electron pair donor) with an occupied molecular orbital of sufficiently high energy in the presence of a sufficiently low unoccupied orbital of an EPA molecule (electron pair acceptor) is a condition for an interaction. EPD-EPA interactions can be utilized for transduction processes, however they may be observed to cause interferences as well, by increasing the conformational energy barrier, inhibiting the recognition process, and decreasing the mobility of the components. %electron pair donors are represented by aromatic compounds, such as the p-nitrophenylether derivatives and the phenyl boronic acids. The p- nitrophenylether derivatives are n-electron pair donors whereas the acceptor property of the boron nucleus of phenylboronate is probably not effective, owing to the shielding effect of the phenyl groups. Further examples for n-EPD are ethers, amines, carboxamides, nitriles, ketones, esters, and N-, and P-oxides which are partly used as plasticizers or ligands, the PVC being a o-donor. So far no electron pair acceptors are currently involved in the membrane composition. Only with a cation as the analyte, is an electron acceptor introduced into the system. If this analyte has a soft character and acts as a Lewis acid (magnesium, aluminium, lithium, transition metal ions) interactions with all this components have to be taken into account to optimize the membrane composition. For a donicity scale see [106]. However the donor properties of the o-NPOE might enhance the negativity of the active coordinating sites, e.g., by participation in deprotonation of an indicator (see chapter 6). Thermodynamic analysis, reaction rates, and spectroscopic evaluations of the membranes (impedance spectroscopy and chemical shifts of NMR signals) may be helpful in elucidating these interactions.

4.4.3 Influence of the Aqueous Sample Environment One of several methods for the evaluation of association constants, is extraction of the analyte into a phase of opposite polarity. To obtain a rough estimate of the increased solubility of an analyte in the presence of the ligand, the ligand has been dissolved in, e.g., methylenechlorideor deuterated chloroform. The extraction of the analyte by complexation is observed by different spectroscopic methods [111-1 141. In the case of creatinine recognition, the solubility increased by a factor of about 200, even in a pure plasticizer medium @OS and others) [114]. Solubility broke down after conditioning the membrane in aqueous solution. Various explanations have been put forward. One reason might be that the influence of water suppresses the extraction of creatinine. The plasticized PVC membranes contain water in two forms: dissolved in the plasticizer and aggregated in clusters (- 0.016 pm diameter) where it crystallizes very easily between 0 and -15 OC [log, 115, 1161. This situation was elucidated by using a spatial imaging


171

photometer (SIP), impedance measurements, and by variable temperature IH NMR and 2H NMR studies. The NMR shifts of water were shown to be a function of the concentration of anionic sites (potassium tetraphenyl borate, KBPh4) added to a membrane which was plastified with dioctyladipate, DOA. Our own studies with a membraneless amperometric xanthine electrode showed that water permeates even in silicone oil, if insufficiently shielded charges (dodecyltrimethylammonium bromide, DTA) are present [ 1171. A silicone oil layer incorporating DTA, xanthine oxidase, and mediators disintegrated immediately, owing to water uptake. The magnesium ion has been called a "structure-breaking" ion, in contrast to calcium ions. The activation energy for selfdiffusion of the species H20(~~0) and H20(@2+) was evaluated experimentally in aqueous solutions of 4.6 molal MgCl2 [118]. The theoretical description of the diffusion of water molecules in conjunction with neutron inelastic scattering diffusion, showed the structure-breaking properties of the magnesium ion. A higher activation barrier for diffusion of water molecules in water, as compared with water in magnesium salt solution was shown. The diffusion of water in magnesium chloride solution is facilitated with an reversed behavior at > 338 K. The activation energy for the self-diffusionof water from the inner coordination sphere of an ion has been determined. Mobilities and temperature coefficients were introduced to achieve a more correct approach [1 181. This extension will not be presented here. The sign of the difference:

depends on the conditions at a given temperature. A negative AG shows a structure-breaking effect and means that water molecules prefer to diffuse from the coordination sphere of the magnesium ion than to diffuse from the water lattice. This correlates with a lower enthalpy of the magnesium ion at infinite dilution as compared with calcium and monovalent ions, and an entropy-driven dehydration of Mgz+ and may be an important effect within the lipophilic membrane. The criterion &/ r, square root (charge number/radius), was used to classify ions in structure-promoting and structure-breaking ions. For the magnesium ion, this criterion shows that the ion must be surrounded by an ice structure of varying extent. Eigen based his suggestions on the low rate constant of 105 s-l of water exchange from the inner coordination sphere (see Appendix 5 ) which was interpreted as Mg2+ being more structure-ordering than calcium ions [I 191. The 170NMR absorption studies, which involved the aqueous solutions of Mg2+, yielded exchange times for HzO molecules between the hydration shell and the solvent (CDCl3) of c lo4 s [120]. The free energy of exchange explicitely depends on the nature of the ion, the nature of the environment and the concentration, temperature aside. Under different conditions an ion can change its nature from a structure-breaking to a structure-promoting ion, e.g., the magnesium ion at 65 OC. A clear distinction has to be made' to selectivity data under equilibrium conditions. These data are in the kinetic domain and do not fit the aforementioned selectivity scales; nevertheless, they show a trend. For further explanations some additional facts on the action of water in a lipophilic environment are imperative. X-ray structure experiments elucidating the structure of the associate formed between lectin IV and a tetrasaccharide, showed a simultaneous decrease in both the standard enthalpy and the standard entropy, upon association [121]. Decreases are

172

4 The ArtiJicialAnalyte-Selective Membrane

largest when hydroxyl groups at the periphery of the active combining site are in contact with water. The binding reactions involve very similar changes in the conformation of both the ligand (carbohydrate) and the host (lectin). It is therefore proposed that the enthalpy-entropy compensation arises because water molecules bonded to the amphophilic surfaces are more mobile and exhibit a higher entropy than water molecules in the bulk water. It was concluded that the enthalpy-entropy compensation pattern is very common and a consequence of the specific properties of liquid water as a solvent. These facts suggest that water associates and clusters even more easily in a lipophilic membrane medium which again facilitates dehydration and preformation of the active cavity by entropy and enthalpy changes upon complexation of the ion and water clustering. The conformation energy in this case is fully compensated by the water clustering and the entropy change. Interaction energies measured and estimated in pure solvents may be overestimated.

4.4.4 The Influence of the Surface Tension The thermodynamic description given in section 3.1 does not deal with the influence of the surface tension at the membrane boundary. Although it may have a considerabe influence on the transfer of the analyte, it has not been considered as phenonomenological term to have more influence than a molecular one. Nevertheless, the surface tension must be part of the thermodynamic description of the boundazy between sample and membrane phase. The surface area itself is not a thermodynamic variable as there is no energy of direct interaction within the surface. However, real liquids have the tendency to minimize or maximize their surface area. Hence, the free energy of an actual system is related to its surface area A. The derivative, dGOldA describes the surface tension, y. By means of the surface tension, the free energy of the interface, AGC, can be described as related to the area and the chemical potential, pi, of all species i, participating in the boundary reaction, where n is the amount of substance in mol [122]:

If one of the two fluids in contact at the membrane surface has a high surface tension, then there will be a low wettability and a positive contribution to the free energy of transfer. High surface tension is similar to high molar enthalpy of hydration in counteracting the analyte transition. The surface tension was not regarded as an important factor in characterizing the sensor response. This may change, regarding adsorption isotherms at the membrane boundary in contact with the biological specimen. Also, in considering the adhesion of a membrane on a multiple internal reflection element (MIRE) or on any optical waveguide, the surface tension is measured and controlled (see chapter 6).


I13

4.4.5 The Effect of Lipophilic Ionic Sites Originally, neutral-carrier-based liquid membrane electrodes with incorporated anionic sites, e.g., tetraphenylborate ions, were introduced in order to reduce interference by lipid-soluble sample anions and to create permselectivity of potentiometric membranes [79, 1251. In recent years it has been shown, however, that the addition of ionic sites is very decisive in cases where the ligand has a critical dissociation constant depending on the permittivity of the membrane medium [78, 126, 1271. The papers cited here shed light on the question whether a carrier is charged or not; it has allowed determination of the deficit in counterions in an ion-selective membrane approach and to explain nontheoretical response functions. Subsequently, the work has enabled to receive a theoretical electrode response function based on careful evaluation of the membrane composition and the related response characteristics. This will prevent misinterpretation of mixed potentials, especially necessary in view of the development of peptide-like ligands for anions [1281. The presence of mobile cation-exchangesites in cation-selectivemembranes based on neutral carriers has also proved beneficial in many other respects. The additive lowers the electrical membrane resistance as well as the activation barrier for the cation-exchange reaction at the membraneholution interface, reduces the time response after an activity step, and gives rise to significant changes in selectivity [129, 1301.

Anionic Sites The concentration of anionic membrane components affects the ion selectivity, primarily, by controlling the concentration of exchangeable cations and, in addition, by influencing the concentration of free carriers available for complexation of cations. A theoretical analysis of the selectivity-modifying influence of charged components in neutral-carrier-based membrane electrodes is presented in [78,79, 122, 1331. The theoretical model may be used to evaluate the optimum composition of neutral carrier membranes, yielding the highest possible carrierinduced selectivity for the respective primary ion [33]. The basic assumptions as well as the derivation of a general formula for the calculation of optimum anionic sitekarrier ratios has been described [78]. The results show that these optimum ratios are only a function of ion charges and ion/ligand complex stoichiometries, but are virtually independent of ionic distribution coefficientsand complex stability constants. The specific interactions between lipophilic anions and complexed cations in the membrane phase were not taken into account. This contribution is not evident in the case of tetraphenylborateanions because the negative charge is shielded to a t large extent by the phenyl groups. Selectivity factors of membrane electrodes that contain a given amount of neutral carrier (ETH 5282 [134], 6,6-dibenzyl-14-crown-4 [135, 1361 or ETH 2220 [ 1371) and varying amounts of the additive potassium tetrakis(p-chloropheny1)borate (KTpClPB), were determined by the separate solution method (see section 4.3). The theoretical treatment as well as the experimental results clearly show that the selectivity characteristics of certain electrodes can be improved to a large extent by the optimization of the KTpClPBlcarrier

174

4 The Art$icial Analyte-Selective Membrane

Table 4-3. Optimum amounts of charged sites trapped in ion-selective membranes based on neutral carriers. The values are given as molar ratios, CR/Q,$,t, relative to the ligand [78]

1 2 3 1 2 3 1

2 2 2 1

1 1 1

2 3 4 1 2 3 2

1.41 0.77 0.54 1.62 0.73 0.46 0.7 1

ratio. In addition, the experimental data provide information on ionnigand complex stoichiometries [78, 1381, which might be useful for the design of new ionophores. In [1331, the treatment considered a liquid membrane based on electrically neutral carrier ligands L (total concentration C L , ~ Jwhich form complexes of the type ILzi (given stoichiometry 1:p;stability constant p ~with, the ~ primary ion Izi and complexes of Pthe type JL? with an interfering ion J z In ~ addition, the membrane contains a certain amount of anionic sites R(Concentration CR). The aim of the analysis was to provide information on the optimum amount of anionic sites in the membrane (expressed in mol% relative to the ligand) that guarantees the lowest selectivity coefficient for interferingrelative to primary ions when separate solutions of two ions are compared. The quantity ai is the sensed activity of primary ions in the sample solution, ~ ( 0 is) the concentration of the same species (uncomplexed primary ion) in the membrane surface and ki is the ionic distribution coefficient. A completely analogous relationship can be used for the emf response to an interfering ion J"jin a separate solution. We now focus on the quantity ci(O), the concentration of the primary ion within the membrane at the sample interface, which is determined by two processes. First, the total amount of cationic species (partly or mainly in the complexed form) is fixed by the amount of anionic sites trapped in the membrane. Second, the amount of free cations is controlled by the complexation equilibria and depends on the concentration of uncomplexed carrier. This consideration led directly to a distinctionbetween two limiting cases which are described below. In limiting case (a) there is an excess of carrier in the membrane surface (concentration c~(0)), which results in a nearly complete complexation of primary ions. Hence, the amount of freecations is very small and the correspondingemf value is relatively high. In limiting case (b) the carrier concentration is too low for an adequate complexation of cations. Accordingly, the amount of free cations is much higher and the emf value comparatively low. In view of a high ion selectivity accordingto the separate solution measuring procedure, it is a prerequisite that limiting case (a) is fulfilled for the primary ion whereas limiting case (b) should apply for any interfering ion. This guarantees a sufficiently high discrimination in the emf response between primary and interfering ions.

qt


175

In order to get the optimum selectivity, the maximum of the emf difference, EI - EJ, has to be determined with respect to cR/a,tot :

(4-20)

&rt

According to the model described stepwise changes of are expected for CR -> cL,toti’q where cj(0) drastically increases (decrease of q y t ) and for CR -> c ~ , ~ ~where t Z ~ci(0) . suddenly increases (increase of K r t ) . For membrane systems with ideal selectivity the following relation must therefore hold (see the examples shown in Table 4-3):

It becomes obvious that selectivitiescan be optimized only by adjusting the sitekarrier ratio if the primary ion has either a higher charge and/or if it is complexed by fewer ligands than the interfering ion. Thirdly, it should be mentioned that exactly the same optimum amounts would be found for cationic sites in anion-selectivemembranes based on neutral carriers.

Example of Further Investigations Reversible host-guest interactions were observed to be consistent with an activation enthalpy of < 60 kJ mol-1 estimated from NMR experiments (see sections 2.2.2 and 3.2). Estimations of the activation energy by FQ. 3-48 result in a stability constant equivalent to PI c 3 x lOl0 at 298 K and normal pressure. In the case of the magnesium-selective membranes incorporating the carrier ETH 7025, the stability constant was estimated to be lo4 for magnesium ions and 5 x lo5 for calcium ions by potentiometric measurements with o-NPOE as solvent and 10 mol% KTpClPB relative to the carrier. By adding optimum amounts of borate (155 mol%), the extraction of magnesium ions is favored by a factor of > 10 (SSM). In this case, the emf values of 0.1 m o m solutions, both of Ca2+ and Mg2+, with chloride as anion are compared. This behavior is supported by the stoichiometry of the complexes, assuming 1:1 complexes for Mg2+ and 1:2 complexes for Ca2+. Nevertheless, for both ions, complexes‘with higher stoichiometry are observed [33].

176


4.4.6 The Effect of the Ligand Concentration The successful simulation of the behavior of a magnesium-selective membrane based on the ligand ETH 7025 (see Appendices 10, 11) has been attributed to different stoichiometries of the calcium-ligand relative to the magnesium-ligand complexes [33]. In this case, the thermodynamic equilibrium reaction at the two boundaries is not symmetric. This fact calls for an isolated theoretical treatment of only one boundary in a first step, which takes the free ligand activity into account, assuming a constant ion activity of the inner electrolyte. In the emf function the free ligand activity does not cancel out as commonly assumed in the Nikolsky-Eisenman approximation (see section 5.2). Introducing the free ligand activity into the Nikolsky-Eisenman function results in a close agreement between the theoretical model and the experimental results. The increase of the relation a ~ ~ /(ac,(') l ) in the sample solution is always associated with a decrease of aL(0) (for symbols see section 4.2, Figure 4-2 "segmented membrane model"). As a further consequence, the investigation of the concentration profile for the free ligand has yielded a distribution model which is consistent with the long-term response properties of the membrane. We therefore conclude that the traditional Nikolsky-type emf function may be used only for activity evaluations applying the virtual selectivity coefficient evaluated, e.g., by S A M (see section 4.4) where the change of the free ligand activity is compensated by the change of the calcium activity: (4-22) where UMgC)

4-J) QL(O)

KE~'

= = = =

magnesium activity in the sample solution calcium activity in the sample solution activity of the carrier at the membrane surface selectivity constant

The assumptionsfor the mathematical modeling are:

1. The concentration of anionic sites is constant all over the membrane. The anionic sites are completely trapped within the membrane and are free to move. 2. In the membrane the activity coefficients of all ions and ion-ligand complexes of the same charge are the same. The activity coefficients are invariable over the range of sample ion activitiestested. 3. The activity of neutral molecules (e.g., the carrier) is equal to their concentration. The membrane is an infinitely dilute solution. 4. The carrier S is uncharged (of the neutral carrier type) and its total concentration qtot is supposed to be constant throughout the membrane The interfacial potential has been described by two relations, namely the electroneutrality condition and the validity of the thermodynamic equilibriumfor the extraction and complexation of each cation. The overall distribution coefficient of the ion-ligand complex K L , between ~ ~ the sample and the interface (0) was modeled as well as the distribution coefficient ki and the (I)

4.4 The Membrane Composition and the Membrcrne Mediiuii

177

stability constant P L , of ~ ~the ion-carrier complex. It is seen at once that Eq. 4-22 differs from the conventional Nikolsky equation in the free amount of ligand which is not kept constant.

Conclusions 1. Calculations on the basis of Eq. 4-22 show that there exists an optimum total amount of for which the amount of free carrier is independent of the sample carrier c~,tot,optimum(0) solution and therefore eq. 4-22 reduces to the Nikolsky equation. If cL,tot(0)> c~,tot,op~mum(0) the emf response takes a sickle form and tends toward too low values, as shown in Figure 4-8, whereas for cL,tot(0) < q,tot,optimum(O) the opposite holds. 2. The selectivity for the primary ion over the interfering ion depends on the amount of free pot.se1 carrier. For our magnesium membrane for instance, the selectivity term K MgCa is -1.12 for %,(') > a ~ ~ ( ' It) . must be emphasized that the selectivity term is not constant unless cL,tot(0) = q,tot,optimum(0).

The ligand concentration was increased in many cases to increase the reservoir of ligand and to decrease the membrane resistance. However, a high ligand concentration is counterproductive in this case. In a further step we calculated the concentration profiles of all species in the membrane in a steady-state as a function of the sample solution so as to investigate whether the initial assumptions, that the potential of the inner membrane boundary and the diffusion potential over the membrane remained constant, were justified. This corresponds to the determination of the membrane composition in the zero-current steady-state. In contrast to the model suggested in Figure 4-8 for the carrier L and the anionic sites R- only the average concentration in the membrane (which is known from the membrane preparation), but not their concentration profiles, are given in advance. Therefore the following assumptions were used according to the segmented membrane model: 1. There is a rapidly established electrochemicalequilibrium at the interfaces at x = 0 and x = d, whereas the slow kinetics in the membrane cause a diffusion potential between x = 0 and x=d 2. The activities of all species in the membrane are equal to their concentrations. The membrane is thus consistent with an infinitely dilute solution. 3. The concentration profiles of all cationic species in the membrane are linear.

The description of the steady-statewas applied to the Mg2+-selectiveelectrode with Mg2+ for Izi and Ca2+ for Jzjas well as the assumptionsp i = 1 and q = 2. The graphical model in Figure 4-8 is based on 12 equations involving the equilibria at the interfaces, the mass balances, and the flux equations used to describe the steady-state.

178


EMF

Pot

log K

rmv3

1 'lo ETH 702

8060MEMBRANE : 0.3wt01. ETH 7025 0.4wtVo ETH 7025

4020-

lDWtX ETH 7025 155 molola KTpClPB 55.0 Wt% O-NPOE 30wtX ETH 500 PVC

0-20

-

IDEAL NERNSTIAN SLOPE

-40I

I

I

I

I

I

I

I

I

I

Figure 4-8. Emf response to solutions with a varying amount of magnesium chloride and a constant active molality of calcium (0.434 mmolkg) calculated on the basis of Eq. 3-73, assumptions and constants given in the text. Four cases are differentiated: 0,CL,tot(0) = 0.01 16 M > CL,tot optimum(0) (1 wt%); 0,CL,tot(O) = 0.0046 m o h g = CL,tot optimum(0) (0.4 wt%); 0, Q t o t ( 0 )= 0.0035 molkg < CL,totoptimum(0) (0.3 wt%); 0,CL,tot(0)= 0.007 molkg, practical useful concentration (0.6 wt%). The calculated values are compared with the Nikolsky-type emf response (----)

Model a) with a low content of anionic sites corresponds to the classical valinomycin-based membrane with 1 wt% carrier, which, owing to impurities of the membrane materials (PVC) contains anionic sites up to 5 mol% relative to the ligand [1391. Compared with the low number of cations which are fixed by the electroneutrality condition, such membranes exhibit a large excess of carrier, a multiple of the amount necessary for complete complexation. As expected, the carrier concentration profile does not change significantly when changing from MgCl2 to CaC12 solutions. The deviation from the Nikolsky equation which considers m(x),the internal boundary potential, and the diffusion potential, is smaller than 0.1 mV and therefore negligible. A totally different situation is met for a membrane with high or even optimized amount of anionic sites as shown in Figure 4-9 b. This is the typical situation for a magnesium-selective membrane with 155 mol% borate (KTpClPB). The decrease of the activity of the free carrier which occurs when changing the sample solution from MgC12 to CaC12 causes an extinctive diffusion of the carrier from x = d, the inner membrane boundary, to x = 0, the sample-contacted boundary of the membrane. The subsequent change of the uniform distribution of the anionic sites is c 2% and corresponds to a diffusion potential of c 0.5 mV. This is in agreement with the

4.5 Response Behavior, Sensifivity, und Derecliorz Limit

179

0.008 .

0.006

'

I."

xld

Figure 49. Carrier concentration profile for a Mg2+-selectivemembrane based on ETH 7025 at a zero-current steady-state and 0.1 molL MgCl2 as inner reference electrolyte. The ligand concentration is assumed to be equivalent to the activity a&) and is given as a function of log UM&) /Q(') of the sample solution. x, position over the membrane profile a) for a membrane with 5 mol% (relative to the ligand) anionic sites, b) for a membrane with 155 mol% anionic sites see Appendix 8

assumption of a homogeneous distribution of the ion-ligand complexes. The assumption that the diffusion potential ED is constant is thereforejustified. The changing distribution of the free ligand should cause an emf increase of 15 mV which is observed as a long-term drift during an equilibration period of about 4-7 h. After a sample change, the quick response of the boundary at d = 0 dominates the slow membrane kinetics and determines the interfacial potential. In practice these potential changes can be measured changing from 0.1 m o m MgC12 to 0.1 m o m CaC12 and vice versa. The extent of the quantitative emf change is associated with the mobility of the free ligand. The emf change increases with increasing mobility. In this case, the ligand mobility exceeds the cation mobility by a factor of four, The process produces a maximum overpotential of 5 mV and is fully reversible. As a very general conclusion, the optimization of the site-carrier ratio and the membrane composition as a whole is of practical importance for the accuracy of potentiometric evaluations.

4.5

Response Behavior, Sensitivity, and Detection Limit

Assuming an exponential response function limited by diffusion through the Nernstian stagnant layer or any boundary, a generally valid description is of the type: a ( t ) = a ( t o ) {I -exp(-t/T,)}

(4-23)

180

4 The ArtiJicial Analyte-Selective Membrane

where a (t ) is the analyte activity at any time t , and a (r,) is the analyte activity when initializing the activity change at t = 0. The time constant, T,, is theoretically claimed to represent 63% of maximum response. For example, the ideal potential difference, Aemf, of 59.16 mV at 298 K is expected for 1 decade difference in the sensitivity of the primary ion versus the activity of an interferingion (Alogag = I), T, is equal to 37.3 mV. 3 Tx correspond to the 95%equilibration. This rule can be misleading if a new organization of the whole membrane bulk is involved. The response behavior of an electrochemical or optical cell is a limiting factor in many biological and medical applications. If the analyte concentration is close to the detection limit, and, therefore, the boundary extraction process is associated with a low exchange density of the analyte (< mg L-1 or < ppm), the response time can extend over an hour, e.g., for thin optode membranes ( d < 4 pm). In this case, the sample phase is deprived of the analyte and the kinetics of the extraction process overlap with the redistribution of the analyte. The situation is still more complex in a continuous flow system. The overall response behavior of a sensor may be affected by the rate and time constants of as many as five different processes (see also section 4.2, diffusion model, segmented membrane model).

1. The diffusion of the analyte from the sample bulk solution to the electrode surface boundary after a step change in the sample activity and the analyte diffusion through the stagnant Nemstian layer at the sample-sensor surface. These processes rely on the hydrodynamics of the measuring cell. 2. The rate of the analyte transfer reaction across the membrandsample interface, the boundary at position 0 (see section 4.2, segmented membrane model). 3. The diffusion processes within the membrane bulk, 0 to d , and the time constant of the steady-state within the membrane bulk. 4. The equilibration of the internal interface of the sensor d versus the transducer (the internal electrolyte,the solid state contact or the branch circuit). 5. The time constant of a complex process at the sensor surface related to adsorption and interaction between the membrane surface and the biological matrix. This is a mixed timeconstant, which is the result of adsorption isotherms and the subsequent continuously changing Donnan potential. In preventing adsorption, this time constant is negligible.

In addition, the time constants of the reference system (the liquid junction for ISEs [I401 see section 3.3), the monitoring system [141, 1421 and the time constant of the life-ime of the sensor could be specified. Different methods have been used to investigate the electrode response time. Impedance measurements revealed primarily the quantitative influence of the resistance of the membrane bulk and the capacitance of the interface [143-1451 (compare section 4.2, electrical circuit model) and of diffusional processes at the membrane surface. Other methods (cyclic voltammetry), have been applied [31,49] to study the ISE response behavior. Response time studies by the wall-jet procedure, make it possible to distinguish between processes within the stagnant layer at the membrane/sample interface and diffusional processes taking place within the boundary and within the membrane bulk [34,146].

4.5 Response Behavior, Sensitivity, und Detection Liini:

18 1

Important aims in characterizing ion-selective electrodes are the definition of practical response times [28, 31, 147, 1481 the evaluation of the rate-limiting step [149], the theoretical description of the experimental response curves, and the influence of the neutral carrier membrane composition on the response behavior [28, 150-1551. The response time studies mainly used the segmented membrane model. The response of the boundary reaction was differentiated from the response period of the membrane equilibration process by two different response functions. Early models were revisited by Buck [156]. The relationship between the selectivity coefficients and the exchange kinetics as well as the thermodynamic parameters was treated theoretically for ISEs, ion-selective field effect transistors (ISFETs), and coated wire electrodes (CWEs) [1571. A useful summary concerning the response behavior of ion-selective solvent polymeric membranes is given in [ 1581. This paper is focused on the change in response behavior upon immobilizing a pH-selective carrier. Further papers are devoted to the response characteristics of solid state electrodes, related to adsorption isothenns also [159-1621. Many of the theories involving response characteristicsof electrodes go back on observations made with glass electrodes [165] and on studies of polarization phenomena at an interface of two immiscible electrolyte solutions.

Characterisation of the Hydrodynamics at the Electrode SurJace The experimental setup is particularly focused here. In many systems the reaction rate is limited by the steady-state mass transfer of the analyte from the bulk solution to the sensing boundary. In the theory of the Nernstian diffusion layer, a stagnant layer of thickness 6 adjacent to the sensor surface is assumed. In ISEs, the analyte consumption at the boundary is not really relevant, being very small (< 5 x 10-l2 mol s-l at an emf of 50 mV and a membrane resistance of 105 n).The sample-membrane boundary equilibrates with the analyte activity in the aqueous bulk and is sensitive to the stepwise activity changes. The speed of the response to the variable activity depends on the thickness of the stagnant layer 6. For a thin layer planar sensor surface with length L, and width W, or radius R, and for a disk electrode, assuming laminar flow with the flow Vaq I cm s-* of the sample solution, the thickness of the Nernstian layer 6 is given by Eq.4-18 [61,77, 1641:

-

(4-24)

For laminar flow through a tubular system, 6 is approximated by: (4-25)

A flow-through system is involved in most of the experiments. The diffusion coefficient of an analyte in an aqueous environment at infinite dilution is denoted by D i.aq and is in the range of 5 x 10-6 cm2 s-1 for ions as well as for uncharged species with low molecular mass [ 1641. The length of the zone of a planar surface where the membrane is exposed to the sample is 0.1

182

4 The Artificial Analyre-Selective Membrane

cm in our optical standard cell. Vaq, the flow of the sample is typically 1.27 cm s-l; the radius R is typically 0.05 cm. V, is the kinematic viscosity [cm2 s-11. The thickness of the Nernstian boundary layer can be estimated for dilute aqueous solutions. It is in the range of 30 pm for the typical tubular laminar-flow system. The Nernstian boundary layer can increase to 100 pm, depending on the flow rate. For serum with a flow of 18 ml h-l in a tube with a radius of 0.5 mm as described previously it rises up to 627 pm [61]. The kinematic viscosity for aqueous solutions is in the range of 0.90 mm2 s-l. However, for biological fluids it is much increased, and is for serum 1.05-1.24 mm2 s-l, and for whole blood 2.91 f 0.56 mm2 s-l (95%-range) [165]. The dynamic viscosity of whole blood is directly related to the hematocrit which is the volume of blood cells (erythrocytes) relative to the total volume. The viscosity shows a pseudoplastic behavior ([163]). Owing to the increased viscosity and the pseudoplastic behavior the time constant of the system increases with decreasing flow.

4.6 Lifetime, Lipophilicity, and Immobilization The Long-Term Stability of the Electrode and the Lipophilicity of the Electrode Components The lipophilicity 10gPTLC of membrane components, as determined by thin layer chromatography, is of utmost relevance for the life-time of liquid membrane sensors [61, 77, 97,98, 1001. Since blood serum and whole blood are much more lipophilic as compared with a purely aqueous solution, they are much more efficient extractants for membrane components. The life-time decreases exponentially by a factor of 1 for direct measurements. Hence, much higher lipophilicities of host molecules and additives are required when membranes have to be contacted with these media. The required lipophilicity logPTLC for neutral carriers incorporated in ion-selective liquid membranes with a thickness of approximetaly 200 pm and a minimum life-time of 720 h of contact to whole blood or plasma is > 11.3. For plasticizers the required logPmc is > 14.3 (for more detailed information see [61,97,98]). For thin optical membranes of about 2 pm thickness, the requirements are even more restrictive. A lipophilicity, logPmc, of the ligand > 20 is required for continuous operation of the sensor over more than 720 h in plasma or whole blood [61]. In diluted biological samples and aqueous solutions the limiting life-time is equivalent to a lipophilicity of about 10. Covalent binding of membrane components to increase the life-time of these sensors can be used in only a few cases. Most surprisingly, the lifetime of ISEs running in automated clinical laboratories with plasma samples for 24 h, is at least 3 months. OW2e5

Immobilization of components Basically the immobilization of membrane components is contradictory to the models concerned with bulky electrode membranes.

4.7 Interaciions by the Biological Mairix and Precautions

183

1. Immobilization of ionophores. Several attempts to immobilize ionophores in order to increase the life-time of sensing membranes have been reported. The potassium-selective ionophore 4'aminobenzo-15-crown-5 was coupled to carboxy PVC by means of a carbodiimide mediated reaction [166]. The polymer was used for the preparation of an ion-selective membrane with 2nitrophenyloctylether (66 wt%) as a plasticizer and potassium tetrakis(chloropheny1)borate(0.04 wt%) as anionic sites. The electrode showed a slope of the response function of 56 mVldecade which was preferred to a membrane incorporating a mobile carrier with PVC or PVC-COOH as a polymer matrix. The detection limit was decreased compared with conventional electrodes; the selectivity and the life-time were enhanced. An approach in our laboratory with a lithiumselective ligand was not successful [84]. 2. Immobilization of chromoionophores (indicators) for thin (< 3 vm) optode membranes. The immobilization of indicators such as nile blue was successful if a spacer alkyl chain was used for coupling of the indicator to PVC-COOH. The response rate was slower, but the life-time was enhanced [76,84]. 3. Immobilization of lipophilic sites [83, 841. For the immobilization of anionic sites 2,6dinonylnaphtalene-4-sulfonicacid (DNNS) and a polystyrol copolymer with immobilized sulfonic acid groups was applied. In liquid membranes the sulfonic acid group is dissociated, in contrast to the carboxyl group. The features of electrodes which incorporate highly selective carriers are very similar to those of membranes incorporating mobile sites, with the exception of a decreased selectivity and response time in a membrane medium of low dielectic properties. Interactions with the indicator result in an additional hypsochromic peak of the protonated species in the spectrum. The sensitivity is slightly decreased. The selectivity of poorly selective membranes (Mg2+)is almost completely lost.

4.7

Interactions with the Biological Matrix and Precautions

4.7.1 Biocompatibility Biocompatibility has many meanings, which can be summarized as compatible with biological metabolism, or compatible with life (see section 5.2) [167]. Many equate "biocompatible" with "nontoxic". In a toxicological study by the Institute of Toxicology of the ETH, the calcium-, potassium- and sodium-selectiveelectrode of ETH were considered to be nontoxic. The biological environment may be "toxic" for the sensor. In this case, unreliable results may be dangerous in medical applications. In these situations biocompatibility is not achieved. Basically, the uncontrolled onset of coagulation processes has been considered the most important factor impairing the surface of sensing elements. It has been observed in many cases that the sensing device becomes wrapped in a network of fibrin when implanted in tissue or deposited in a vessel for some time. It is known that negatively charged surfaces activate coagulation. In general, a layer of proteins is rapidly adsorbed on artificial surfaces; subsequently this film triggers the hemostatic

184


system and generates thrombogenicity. In vitro studies of coagulability often use purified proteins to investigate the adsorption behavior of specific proteins, particularly proteins involved in the coagulation process. However, it has been shown that the adsorption of factor XI, for example, is significantly influenced by other proteins. Therefore, it was concluded that relevant data about protein adsorption and biocompatibility of materials can be obtained only with complex media such as serum, plasma, and whole blood. In several studies, the influence of foreign material on the coagulability of blood was studied for various applications, such as hemodialysis and transplant surgery. A sensor dedicated to in vivo studies has to be treated as a transplant. In my opinion there are three different mechanisms to be considered: -the simple adsorption of biological material - the activation of the intrinsic coagulation process - the rejection of foreign material by immunological reactions Nonetheless, in all three cases, contact with the surface exposed to the biological tissue or blood, containing proteins, carbohydrates, and lipids, is a prerequisite. The interactions may be greatly influenced by such factors as the flow velocity, the polarity of a surface, the surface tension, and by additives to the bloodstream, such as heparin. In hemodialysis, high activities of heparin are added to the ex vivo blood circulation to prevent coagulation within the artifical circulation and the filters. The materials of the dialysis filters and tubes have been investigated, paying particular attention to the activation of the hemostatic system. The observation that an alien device becomes wrapped in a network of fibrin is considered as an in vivo protective mechanism. Another protective mechanism is high blood flow in capillary vessels which prevents localized concentration of precursers of the clotting system and removes activated material. A further control is provided by enzymes such as plasmin, which acts as a protease. Plasmin degrades fibrin and inactivates the clotting factors VIII and V. The fourth category of regulators involves protease inhibitors such as antithrombin 111, which inactivate the coagulation enzymes. On the basis of this knowledge, the coating of alien materials by endothelial tissue has been proposed. However, this approach is not applicable to the surface of a chemical sensor. The question arises what type of chemical structure or material is needed to mimic these protective functions of endothelial tissue? What is an endothelialized surface, chemically? Adsorption of proteins and adhesion of blood cells has been called "fate determining". In the last few years, some attempts have been made to find the sources of deviations between ion activities measured by electrodes and true values, or values received from a central laboratory [168, 1691. Microscopically, adsorption of biological material can be observed. By atomic force microscopy (AFM)it was concluded that the surface of the polymeric liquid membrane really is a liquid solution. The AFM cantilever force of 10-l2 kP was too heavy to scan the membrane. The plasticizer and dissolved compounds (charged anionic sites) may be responsible for most of the interactions. The adsorbed layers were not further specified in these initial investigations. Studies were primarily focused on the development of a procedure to characterize, localize, and quantify the effects of the interactions at the sensor surface and on preventing the deposition of

4.7 Interactions by the Biological Mairk and Precautions

185

biological material (see section 5.2). It is well known that hydrophilic surfaces are more or less resistant to protein adsorption, and adsorbed species can easily be washed off. The application of hydrogels for solid sensing layers has been proposed. A highly polar sensing layer, however, often hinders extraction by tailored lipophilic carriers. Thus, polar dialysis membranes based, for example, on cellulose acetate (CuprophanR) have been used as protective layers to cover the sensor. Such a layer induces slow diffusion as well as a diffusion potential in the case of potentiometric sensors and leeds to a considerably reduced response rate. In our own studies we observed, in agreement with Mannhalter [ 1671, that results obtained with pure compounds, such as typical protein fractions or lipids, deviate considerably from results obtained with true serum, heparinized plasma, or whole blood. Drifts and variations of the potentiometric signal induced by the absorbed layer were influenced by several factors, e.g., the nature, composition, and pH of the specimen, the exposure time, the type of pretreatement or interval treatement of the artificial surface, and last but not least the temperature of the system. Adsorption isotherms show that the first adsorption of a molecule evokes an avalanche. The most plausible mechanism is adapted from chromatography, and is discussed in the following section.

4.7.2 Possible Mechanisms of Protein Adsorption The theory of protein retention in chromatography combines the effect of ionic strength and charge density for oppositely charged surfaces [170]. The interplay of Coulombic and van der Waals forces can be described by combining the electrostatic theory with a first approximation of the Lifshitz treatment of van der Waals interactions [171]. It can be shown that a minimum free energy is achieved (maximum interaction or retention) at a certain distance from the stationary phase. This situation is exactly comparable to the positively charged surface of a cation-selective sensing membrane (the stationary phase) and a protein-containing biological sample with changing ionic strength. The interaction is denoted by AGIA,, the free energy change per unit surface area of the stationary phase when the protein-containing surface is approached from infinity to a distance L. The van der Waals interaction, AGpvdWIAp,is decsribed by:

A G p v d I~A,, = - H I 1 2 L~

(4-26)

where H is the Hamaker constant which is related to the dielectric dispersion, E,,E~, of the intervening medium between the two surfaces. The electrostatic interaction AGes related to the ionic strength I is given by the expression:

(4-27)

186

4 The Art@cial Analyte-Selective Membrane

with the reciprocal Debye length K = F (21 ) 1/2 / (GE, R T )lI2 in units of D-l. The combined free energy, AGr, of both effects is described by:

(4-28) Plots of the equilibrium of the two forces (isoforce plots) according to Eq. 4-28 relate the Gibbs free energy per unit surface area to the distance between the two planes at different ionic J in plot A. The surface charge density opof the proteins of -0.03 strength. H is set to 3 x c m-2 is proportional to 5.3 x 10-18 m2 or 5.3 nm2 surface area of one protein unit equivalent to 1 C. The surface charge density of the stationary phase a, = 0.16 C m-2 is higher. Within a distance < 0.2 nm, the van der Waals interactions tend toward minus infinity for solutions with ionic strength > 1.O mom. This is independent of the surface charge in the range covered in this experiment. At a distance of 1.6 nm, the free energy has a minimum for a I = 0.1 mom solution, thus the retention data reach a maximum. At shorter distances, the surfaces repel each other. The Gibbs free energy of interaction is increased with an increase in charge density of the protein at an ionic strength between 0.1 to 0.5 moVL. With an increase of the charge density of the stationary phase (+. opposite charge) an energy barrier in close proximity to the surface, < 0.2 nm, builds up for high ionic strength. This distance of maximum free enthalpy is dependent on the ionic strength and decreases with increasing ionic strength (see also section 3.4).Thus, a dilute solution can demonstrateincreased interaction at distances of 1-3 nm. At an ionic strength 2 1.0 mom the gain in energy is dominated by the van der Waals interaction, whereas the electrostatic repulsion as well as the electrostatic interaction are attenuated. The decreasing entropy fully offsets the electrostatic interactionsin this case. The conclusion is that the interaction of a charged surface with proteins or other charged species is driven by different forces. The Gibbs free energy depends strongly on the composition, ionic strength, and dielectic constant of the solution, and shows a minimum at a defined distance of approach. For solutions with ionic strength of 0.1-0.5 m o m the electrostatic interactions are responsible for the adhesion of charged species (e.g., proteins) approaching a distance of 0.5 to ca. 3 nm. Close to the surface, > 0.2 nm, van der Waals interactions are responsible for adsorption, especially for ionic strengths > 0.5 m o m . However, the ionic strength in proximity to the surface may change considerably since the solution in the gap may be comprimised by the loss in entropy. This conclusions are consistent with the observation of decreased interactions for highly concentrated thrombocyte solutions. The strongly polar surface of a membrane is supposed to exert no van der Waals interactions, in contrast to many other more or less lipophilic sample components. With reference to the strong van der Waals interactions close to the surface, it is evident that these interactions can be avoided by structural means as well as by introducing polar functional groups. An OH group has a molecular length given by the van der Waals radii and

4.7 Interactions by the Biological Matrix and Precautions

187

'1

Figure 4-10. Plots according to Eq. 4-28; Gibbs free energy per unit area vs. distance between the negatively charged biological surface (see text) and a positively charged stationary surface. Ionic strength, I = 0.1 moYL; 0, = 0.16 C m-2; 4 = -0.03 C m-2; H = 3 x 1W2*J (see text)

the distance between the nuclei (355 pm) [172]. At a surface exposing OH groups with high density, no van der Waals interactions occur. In complete analogy to natural membranes, the dominating apolar interactions close to the surface are inhibited. The length of a methyl group is in the range of 350 pm and attenuates planar multitopic interactions. In contrast to the van der Waals attraction, the long-range coulombic interactions cannot be inhibited by structural means, and may be mainly responsible for first contacts, long-range adhesion, and drifting surface potentials. Such potentials may be described by a Doman Potential which changes continuously during a saturation process. This conclusion is consistent with the observation that an ionselective membrane exhibiting a high permselectivity and a high exchange current for the analyte ion is generally less affected by nonspecific interferencesdue to proteins, heparin, etc., since the charge transfer due to the analyte ion is a higher fraction relative to the diffusion and nonspecific Donnan potentials. These aspects provide a new starting point for theoretical evaluations of the behavior of artificial surfaces with biological components.

188


4.7.3 Influence of Thrombocyteson PVC Solvent Polymeric Membranes The thrombus formation process involves a platelet receptor, a glycoprotein Ib, a plasma cofactor called the von Willebrand factor, and collagen. Thrombogenicityof surfaces is strongly connected to the adhesion of platelets, see section 5.2.

4.7.4 The Donnan Potential The Donnan equilibrium or Donnan effect is named after F.G. Donnan (1870-1956) [27]. The Donnan equilibrium describes the equilibrium distribution of ions in electrolyte solutions on both sides a,p of a semipermeablemembrane with respect to a polyelectrolyte PZ- which is not permeable. In a less strict sense, semipermeability means permeable for the solvent as well as for some of the ionic species I+ and X- but not for the species PZ-. Under equilibrium conditions, the chemical potential of the compound IX is the same on both sides of the membrane:

The electroneutralitycondition is expressed by: (4-30)

Based on these assumptions, the ion activities on both sides of the membrane can be calculated by quantitative analysis of one of the activities or concentrations: For electroneutralityreasons, the sum of the charges on both sides of the membrane must be equilibrated. The result is a different activity and concentration of species I+ and PZ- on both sides of the membrane, and thus a partial pressure of the solvent over the membrane, the osmotic pressure n: a P z= R T { ( c apz- + a I+ + a ar)- ( a P + ax))

(4-31)

The Donnan potential due to proteins overlaps with the potential generated at the membrane boundary and contributes, presumably, to a membrane internal diffusion potential. Taking the many unknown parameters in the biological fluid into account, a full description of the effects is hardly possible. However, the potential difference due to the charge density of albumin, which exhibits the lowest PI, in a layer of 1 nm thickness close to the surface can be roughly estimated as follows. Proteins, nucleic acids, carbonic and dicarbonic acids, amino acids, lipoproteins, and glycoproteins are charged compounds present in biological fluids, and can participate in a Donnan diffusion potential. For direct measurements pH 7.4 is the decisive average biological pH. The most abundant fraction of proteins in normal blood plasma is albumin with 40-52 g


189

L-I (total plasma protein: 61-78 g L-I) [173] with a molar mass of 66 x 103 g mol-I and a PI of 4.9 [165, 1741. A loss of albumin or an impaired synthesis results in a serious imbalance of the intravascular oncotic pressure, the osmotic pressure due to the Donnan potential induced by proteins, mainly. A low albumin level is manifested clinically by the development of peripheral edema. Also, albumin serves as a mobile depository of amino acids from the liver, where it is synthesized. A third function ascribed to albumin is a general transport function as a nonspecific carrier protein in most cases. Many organic and inorganic ligands (drugs, free fatty acids, free slightly soluble ions, Mg2+,Ca2+,transition and trace metal ions, slightly soluble metabolites such as bilirubin) are complexed or even covalently bound to different regions of the protein moiety. Albumin consists of 585 amino acids arranged in nine loops. Of the 35 cysteine residues, 34 form intramolecular disulfide bonds and 1 is free. Upon storage for several days, albumin forms dimers covalently linked through the free cysteine moiety. Elevated levels of serum albumin occur on dehydration and, artificially, on prolonged application of a tourniquet for venipuncture. This is the source of a very important preanalytical error. About 8% of circulating albumin become gycosylated in healthy individuals, nonenzymatically,whereas 25% becomes glycosylated during hyperglycemia, in analogy with glycosylated hemoglobin. The half-life of circulating albumin is about 17 days [174]. From Table 4-2 it is obvious that all proteins which contribute considerably to the total protein fraction in blood plasma, primarily the albumin fraction, exhibit isoelectric points lower than 7.4, and thus represent a more or less negatively charged bulky background of the specimen. The proteins, for example, have to be considered as polyelectrolytes which contribute

Table 4-4. Physicochemical data and mass concentration of proteins in human plasma [ 165, 1471

Protein fraction name

albumin clotting protein: fibrinogen y - globulins Ig G IgM a1 - antitrypsin (a1 - globulin) a1 - glycoprotein Orosomucoid

x I@ g mol-1

Specific volume Isoelectric point PI c m 3 g-1

Mass concentration g L-1

66.5

0.733

4.9

40-52

34 1

0.723

5.5

2.045

38-150 900-935

0.739 0.724

5.8-7.3

7.2-23 0.6-2.8

50

0.728

4.0

2.6

44

0.675

2.7

0.55-1.4

Molar mass

190

4 The Art$cbl Analyte-Selective Membrane

most importantly to the osmotic/oncotic diffusion equilibrium over a semipermeable membrane. If the sensor is contacted with the biological specimen, it is exposed to a layer of macromolecular bulk opposed to the boundary of the membrane, including the electrolyte solution. The membrane boundary and the macromolecular layer are semipermeable and a Donnan diffusion potential between the two layers can develop. The second abundant fraction of plasma proteins is the very heterogeneous fraction of the plasma globulins (M,(54-850) x 1 8 g mol-I), which contributes, together with fibrinogen with 1 4 g L-1 ( M , 340 x 1 8 g mol-I), to a maximum of 78 g L-' proteins for an average person. Considerations in the following part are based on assuming a sodium-selective polymeric solvent membrane electrode in contact with human blood plasma. The mean molal ionic strength of plasma is I = 0.16 mol kg-1 and the molal sodium and chloride concentration are each assumed to be 0.15 molL each. The albumin concentration is assumed to amount to 50 g L-' plasma. According to the dissociation equilibrium below, only 0.32% of albumin is neutral or charge compensated.

PZ-I pH = 7.4 = PI + log -

(4-32)

PI

(4-33) mol L-I or 0.443 molecular units L-1 amino 50 g L-' albumin is equivalent to 0.75 acids in plasma, which are up to 99.68% negatively charged. In a critical layer of 1 nm thickness, a charge density opof 0.44 x 0.9968 x 96'846 C x 10-6 m-2 nm-I = 0.0425 C m-2 nm-I is effective, which is nearly identical with the assumptions made by Horvath et al. [170]. The charge density in the same 1 nm layer for the electrolytes with respect to a mean activity coefficient for sodium and chloride o , l of 0.75 is equivalent to 0.225 x x 96846 C m-2 nm-1 = 0.02179 C m-2 nm-1. The steady-state Donnan potential is approximated by the charge distribution, e.g., due to albumin, given by [175, 1761. The steady-state potential sensed at the electrode surface for 1 nm thickness of the adjacent layer can be approximately 1.32 mV or 3 mV per 2.3 nm thickness, assumed for a protein monolayer (see 4-21):

a= R T/F2.301 log(1 -

( ~ p / ~)) d

a= 59.16 log (1 - 1.95) = -1.32 mV / nm

(4-34) (4-35)

This potential is negative, as observed in most experiments described in section 5.2. The measured drifts and so-called asymmetry potentials, investigated by the symmetric cell assembly in section 5.2, vary between 0 and 13 mV. However, the range is usually 1-3 mV.


19 1

Conclusions The model developed for chromatography provides resonable explanations for the phenomena observed when ion-selective membranes are contacted with human plasma specimens. An effect additional to albumin by other compounds is expected; a layer of 1 nm is standard. Considering diffusion phenomena, the thickness of this layer involved in an ion exchange may be considerably increased. The diffusion potential and the charge density at the surface are continuously changing as long as the adsorbed layer is building up. This explains the continuous drift of the electrode. After some hours, saturation is observed, the asymmetric membrane potential no longer affects the results of the electrode if the electrode is recalibrated. As a last effect, the layer is peeled off occasionally, preferably in a flow-through system, and the electrode starts drifting again. It must be emphasized that commercial instruments involve a continuous automatic recalibration and differential evaluations referred to the calibrating solution. A different situation is met in in vivo monitoring where recalibration is not possible. With this application in view, the experimentsof section 5.2 were planned.

4.7.5 The Influence of Anticoagulants The Effect of Heparin Figure 4-1 1 presents the emf changes of a magnesium-selective electrode based on the ligand ETH 3832 due to added heparin as measured in a symmetric cell arrangement [177] (see section 5.2). The theoretical slope of the magnesium-selective membrane based on ETH 3832 was measured by varying the magnesium activity within one sample half-cell relative to the second half-cell which was filled with a physiological electrolyte containing 0.1 mol kg-1 MgC12 (ligand see Appendices 8 and 10). The electric asymmetry of the membrane was taken into account. Changing to a solution containing 5 U ml-l. heparin in 0.14 mol kg-' NaCl and 4 mmol kg-1 KC1, a significant emf-drop by -42.5 mV was noticed, owing to the lack of magnesium ions and the selectivity of the electrode versus sodium and potassium. Adding 2U ml-l heparin, resulted in an additional emf-drop of 17.07 mV opposite to the physiological solution containing 0.001 mol kg-1 MgC12 where the addition of 2 U ml -l heparin resulted only in an emf-drop of 0.15 mV. At higher heparin activities, the electrode shows a nearaly linear negative emf response to the increasing activity of heparin. The effect is due to the strongly dissociated negatively charged sulfate groups of the polymeric carbohydrate, and is explained by the negative D O M potential ~ exhibited by heparin at the membrane surface (if the effect were due to a change in the liquid potential, it would have the opposite sign) (for heparin structure compare section 2-2-6). An uptake of heparin is rather unlikely, owing to the high membrane concentration in lipophilic anions. An uptake would be combined with an exchange of lipophilic anions. These investigations support the statement that the species with the highest mass transfer and/or transfer rate dominates the emf of the potentiometric cell. The high selectivity of this electrode for magnesium ions prevents from a

192

4 The Arrificiul Anulyte-Selective Membrane

0

0.7 0.85

1p

1.15

ma,

EMF

Cmvl -50-

-5361

-5979 -59.06

-6Qo4

-60.32

-60-

-m-80 -90 -

0.001 M MgCI2 0.140 M NaCl 0.004M KCI

EMF-RESPONSE VERSUS HEPARIN IN ELECTROLYTE SOLUTIONS WITH AND WITHOUT MAGNESIUM IONS.

---

SLOPE (5-50 U/ml): -1430 mV

-120 L

0

0.140M NaCl 0.004M KCI

I

1

I

I

5

7

14

50

“4

Figure 4-11. Influence of heparin, an AT III activator, in physiological aqueous solutions on the emf response of a magnesium-selective membrane incorporating ETH 3832 as carrier. The effect of heparin activities between 5 and 50 U d - l , common activities for anticoagulated whole blood (lower x-axis), in magnesium-freeand physiological solutions was investigated. Upper xaxis, logarithmic scale of the heparin activity; y-axis, measured emf of the assay in mV. For comments see text, membrane compositions see Appendix 8

decisive response to interferents such as heparin. If an active ion transfer dominates the electrical field changes at the membrane surface, the effect of heparin added to a solution containing 10-3 mol L-’ Mg2+ is very small. Heparin adsorption or uptake is irreversible over > 16 h, however. After conditioning the membrane to a constant heparin activity between 5 and 50 U ml-I in whole blood, the heparin has no additional short-time effect on the membrane potential. The assay of heparinated whole blood is proposed. Most interestingly Meyerhoff et. al. [178, 1791 applied electrochemical sensors to the quantification of heparin. A polymeric membrane doped with the quarternary ammonium salt t r i d o d e c y l m e t h y l a i u m chloride, a typical Hofmeister electrode, was reported to provide optimum anion response toward macromolecular heparin. The membranes contain PVC or a poly(vinyl)/poly(acetate) copolymer and DOS (dioctylsebacate) as plasticizer. It can even be shown that heparin is transported through the membrane in electrodialysis experiments by applying fluorescently labeled heparin [179]. The collected data pointed to the fact that the potentiometric response of polymeric films to heparin was dependent on the specific structure and the concentration of the dopant quaternary ammonium ligand in very complex way. The membrane composition was a further relevant factor. The data agree with a report by Harrison [180], who observed a decrease of the membrane resistance by uptake of lipophilic ions by a polymeric membrane in human whole blood.

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However no such effects were observed with membranes incorporating lipophilic sites and a neutral selective carrier which exhibits a high permselective transfer rate for the analyte ion. Most likely, the potential of ion-selective electrodes being used for montoring organic ions is not yet fully exploited.

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Moritz, W., Miiller, L., Analyst 1991,116,589. Alegret, S., Florido, A., Analyst 1991,116,473. Rechnitz, G.A., Kugler, G.C., Anal. Chem., 1967,39,1683. Cussler, E.L. (ed.), DifJusion, Mass transfer in fluid systems. Cambridge, NY: Cambridge University Press, 1988. Ciba-Geigy AG (ed.), Wissenschaftliche Tabellen, Vol. Physikalische Chemie, Blut, Humangenetik, Stoffwechsel von Xenobiotica, Basle, Switzerland: Ciba-Geigy AG, 1979, pp. 69-70. Daunert, S., Bachas, L.G., Anal. Chem., 1990,62,1428. Mannhalter, Ch., Sensors and Actuators B, Haase, E., Untersuchung der Wechselwirkungen zwischen ionenselektiven Fliissigmembranen und Messgut im Hinblick auf die kontinuierliche Erfassung von Kaionen im Vollblut, Zurich, Switzerland: Swiss Federal Institute of Technology, 1993; PhD thesis No. 10 453. Haase, E.A., Spichiger, U.E., Schlatter, K.J., Hermann, R., Miiller, M., Simon, W., GIT, LaborMedizin, 1992, 3, 84. Stahlberg, J., Jonsson, B., Horvath, C., Anal. Chem., 1992,64,31 18. Israelachvili, J. (ed.), Intermolecular & Surface Forces. London: Academic Press, 1992. Webster, B. (ed.), Chemical Bonding Theory, Oxford, London: Blackwell Scientific Publications, 1990. Spichiger, U.E.,A Self-Consistent Set of Reference Values, Zurich: Swiss Federal Institute of Technology (ETH), PhD thesis No 8830,1989. Henry, J.B. (ed.), Clinical Diagnosis& Management by Laboratory Merhods, Philadelphia et al.: W, B. Saunders Comp., 18th edition, 1991. Adam, G., Lituger, P., Stark, G. (eds.), Physikalische Chemie, Berlin: Springer-Verlag, 1977. Van Holde, K.E. (ed.),Physical Biochemistry,Englewoods Cliffs, NJ: Prentice-Hall Inc., 1985. Spichiger, U.E.,Wild, R., in: Porta, S., Zirm, B., Karpf, H. (eds.), Magnesium. Graz: Leykam Buchverlagsges., 1994. Ma, S.-C., Yang, V.C., Fu, B., Meyerhoff, M.E., Anal. Chem., 1993,65,2078. Ma, S., Meyerhoff, M.E., Yang, V.C., AmL Chem., 1992,64,694. Harrison, D.J., J. Electroanal. Chem., 1990,278,193.


5 Potentiometric Chemical Sensors and Biological Applications

This chapter deals with various principles of sensors, which were investigated by the own team between 1989 and 1996. The optical and potentiometric sensors are based on thermodynamic reversible chemical recognition processes as discussed in section 3.1. Nonthermodynamic assumptions (see section 3.4) are involved in the definition of the potentiometric cell, the membrane composition, and the evaluation of free analyte concentration. The chemical recognition process is coupled to an electrochemical or optical transducing element. These chemical sensors, in a strict sense, work in a thermodynamically reversible way. The selectivity is based on size and shape recognition of the analyte by the complexing host compound. However, for optical sensors, the thermodynamic reversibility and the chemical transducing process are strictly related to the activity of a second, indicator ion. For amperometric sensors are biosensors, the analytes are redox-active compounds. As described in sections 1.1, 2.2.6, 3.1, and 3.3, these sensors incorporate a biochemical recognition element, an enzyme in this case. The amperometric sensing reaction follows steady-state kinetics. The rate-determining step of the overall electrolytic process is controlled by the experimental conditions. Ideally, the sensor's response current should depend on the turnover rate of the substrate, according to section 3.3. The study of biosensors has been prompted by a strong practical interest, with clear applications in sight. Biosensors can be realized immediately, and were seen as a basis for long-term studies of more sophisticated sensors with increased life-times. They provide appropriate models for artificial chemical recognition of analytes (see section 2.2.6). Surprisingly the practical detection limit is around 10-6 mol L-1,in the best case mol L-l for all these sensors. It can be lower in optical sensors under special conditions. The dynamic response range can cover up to eight decades of ion activity in potentiometric sensors. It is generally lower in optical and amperomelric sensors.

5.1 Principles of Ion-Selective Electrodes The Electric Potential Difference and the Electromotive Force In an electrochemical cell, the direction-sensitive quantitity AG is related to a directioninsensitive variable IE I. This is a source of confusion with regard to sign conventions [l]. A thermodynamic quantity called the electromotive force (emf) of the cell can be defined [2, 31. Each electrochemical cell reaction relies on a schematic cell arrangement. By IUPAC convention, the reference electrode is the left-hand electrode. The emf, also usually denoted by E, is the limiting value of the electric potential difference for net zero current through the

200


potentiometric cell, all local charge transfer equilibria and chemical equilibria being established. The emf of the cell reaction therefore corresponds to the electrostatic potential of the right-hand electrode minus the left-hand electrode. That means that cation transfer is associated with a positive emf whereas anion transfer results in a negative emf (see Figure 5-l% b). Under standard conditions (standard or normal hydrogen reference electrode, SHE, NHE wherep(H2) = p e = 1 6 Pa, ak(HC1) = 1, and T = 298.15 K), a working electrode such as an ion-selective electrode, an anode or a cathode, are connected to a standard reference electrode such as a calomel electrode (Hg I Hg2C12 I sat'd KC1). The calomel electrode (HCI I Hg2C12 I Hg) exhibits a standard potential E of +268.2 mV at 298.15 K, associated with the transfer of two electrons referred to NHE. When saturated KC1 replaces the strongly acid conditions of the internal electrode solution (Hg I Hg2C12 I sat'd KCl), the reference emf shifts to 241.5 mV [3]. Comparably, the silverhilver chloride electrode (HCl I AgCl I Ag) exerts a standard potential of E e of +222.17 mV at 298.15 K vs. NHE [I]. Forpe = 101325 Pa (1 atm) the standard potential increases by +O.17 mV. Ion-selective potentiometric cells and electrodes are discussed on the basis of the various models presented in section 4.1 [4-81. The reader is referred to these references for a more comprehensive presentation of the principles.

Ion-Selective Electrodes, Potentiometric Sensors Ion-selective electrodes (ISEs) are chemical sensors for ions as analytes where the transduction is potentiometric (Figure 1-2 in chapter 1) [9]. A conventional ISE half-cell consists of a bulk membrane in charge of the recognition process of the analyte, an internal filling solution (electrolyte), and an internal (inner) reference electrode (chlorinated silver wire). The potential difference across the ion-selective membrane depends on the active molality and molal activity (or, less precisely, on the molal free ion concentration) of a particular analyte ion in any specimen (see section 3.4, Table 3-2). The complexation of the analyte ion by the ligand results in a charge separation at the boundary of the specimen-membrane interface. The chemical potential due to the extraction of the analyte and interfering ions is compensated by the electrical work measured and identified as the emf (see end of section 3.1). The internal diffusion potential of the membrane is assumed to be invariant since the diffusion coefficients of the extracted and generated species are assumed to be constant, and changes in the diffusion potential are about 300 times slower than the boundary processes (see sections 4.2.2,4.5 and 4.6). In an assembly where an external reference electrode (reference half-cell) is connected to the ISE half-cell in the specimen, the cell emf is supposed to represent the changes in the potential difference across the membrane, all other boundary potentials being invariant. The cell emf, therefore, provides information on the analyte's active molalityfib and molal activity a i in the specimen. If considerations are restricted to permselective membranes for the analyte ion I, with charge z i , and interfering ions J, with charge zj, the description of the emf function of a potentiometric cell is ideally assumed to be consistent with the classical NikolskyEisenman equation [lo, 111, at least for identically charged ions (see Eq. 5-1 and section 4.3):

5.1 Principles of Ion-Selective Electrodes

RT zi F

'

-In ai = s = 2.303

zi F

Tlog a;= 59.16 Izi log

4

[mV, 298 .16K]

20 1

(5-2)

In Eqs. 5-1 and 5-2, s is the slope of the electrode function and EP is a characteristic constant potential difference between the two electrodes, the standard potential of the cell. The standard potential depends primarily on the characteristics of the two electrodes, one of which is the reference electrode, including the liquid junction potential (see section 3.4.6), and on the temperature (independent of sample solution) assuming that no uncontrolled Donnan potentials occur at the membrane surface (see section 4.7); R is the gas constant (8.314 J K-l mol-l); T the absolute temperature; F the Faraday equivalent (9.6487 x 104 C mol-l); zi. zj are the charge numbers of the primary ion I, and the interfering ions J, respectively (in units of the proton charge); aj, aj are the molal activities of the prim ion I, and the interfering ion J, respectively, in the sample solution (dimensionless); K ii is the selectivity coefficient, a measure of the preference of the chemical sensor for the interferin ion J, relative to the analyte ion I. For an ideally permselective membrane electrode, all Kii values are infinitely small and approximate zero. Although the selectivity coefficient is dimensionless (like the is commonly referred to molarity (or more correctly, molality), if the two molal activity), ions I and J carry different charge numbers (mol L-l)l--Zi/zj or (mol kgl)l-ziW. The latter term, involving the charge numbers of the primary and interfering ion in the exponent of the selectivity coefficient is currently under discussion (see section 4.3). Derived from the Nernst equation, the slope of an electrode function must generally depend on the charge number of the target species involved in the ion-exchange. Therefore the molal activity term of the interfering ion aj is subject to the power of zilzj, which results when the Nernst equation describing the emf of the interfering ion is subtracted from the equation describing the primary ion. SSM calculations according to IUPAC (see section 4.3) are based is on equation 5-3a in order to calculate the selectivity coefficient. In equation 5-3a, log K divided by the charge number zj. From purely mathematical reasons, the calculated activity coefficients deviate from each other if the emf values of the primary ion are introduced as interfering ions and vice versa. Since the selectivity coefficient is a correction factor for a different slope, and an additional emf-contribution involved in E;, in the case of a mixed response function for the primary ion owing to the molal activity of interfering ions it is not evident why KT' is subjected to a power term. Therefore equation 5-3b is proposed, at least for SSM calculations. Based on equation 5-3b experimental and calculated selectivity coefficients are completely consistent. Experimental results and calculations are discussed and compared in [121.

P Y

bt

c'

rt

(5-3a)

(5-3b)

202

5 Porentiometric Chemical Sensors and Biological Applications

EMf [mv

EMF(25%)= E.,+- 59.16 rnV log[a, +,f, K~,zl'zl]

t

2,

Jc /

'

DETECTION LIMIT

\A

ANION INTERFERENCE

n,\ ANION INTERFERENCE

/:I

lit DETECTION LIMIT

-

\

log a*''

-

log

al

Figure 5-1. Response function of a potentiometric ion-selective electrode referring to the ideal slope s of 59.16 mV per decade of activity change (Aai) for a monovalent ion (zi = 1). The upper limit of the dynamic range is set by: a) the anion breakthrough for a cation-selective electrode, the lower limit by the cation interference: b) the cation breakthrough for an anionselective electrode, the lower limit by the anion interference

Reversibility implies that the entire change in the Gibbs free energy during the cell reaction is transformed into electrical work, and that no processes occur other than the thermodynamic equilibration of the extraction and complexing reaction within the membrane, dependent on the active molality of free ions in the sample solution. The dynamic range of most ion-selective electrodes covers about five decades in units of active molality (mol kg-* solvent) or free ion concentration (mol L-l). The lower limit is considerably influenced by ions released from the half-cells, including the ion-selective membrane. In the case of calcium-selectivemicroelectrodes, the lower detection limit has been shown to be shifted down to lW9 molL by adequately buffering the sample solution (see section 5.4). Ion-buffering of the internal electrolyte solution may offer an adequate alternative.

The Standard Electrode Potential and the Liquid Junction Potential The standard electrode potential, E;, corresponds to the intercept of the linear response function of the electrode, and should be constant, whereas the emf change is a function of the

203

5.2 The Symmetric Potentiometric Cell

logari$m,pf the active molality of ions at the boundary of the ion-selective membrane (Aemf = f(1og q l a i ) ; see model in section 4.2). The standard electrode potential, E j , represents a sum parameter for a voltage shift of the emf by various contributions 'which are not immediately related to the active molality of the primary ion I or the interfering ion J.

E; = ERef +EJ + Eel + Eas

(5-4)

EJ is the liquid junction diffusion potential generated between the inner electrolyte of the reference electrode and the sample solution following the bridge electrolyte. By appropriate choice of the bridge electrolyte, it is often sufficiently independent of the sample composition (see later in this chapter, as well as section 3.4.6 and [13]). For biological samples, four different contributions to the standard potential, $,can be observed: the contribution of the internal standard potential of the reference electrode ERefi the diffusion potential over the liquid junction EJ, generated between the sample solution and the reference electrode, a potential difference (electrical asymmetry) of the ion-selective membrane after preparation and conditioning, Eel,, and a sample- induced asymmetry of the membrane Eas. For direct measurements in human blood samples, the adsorption of sample components at the membrane surface creates a drift associated with the affinity of the membrane for lipids as well as proteins [14-151. Three of these effects can be controlled with the symmetric assembly of the potentiometric cell given in section 5.2 (see also section 4.6). On the basis of the principles given so far, many different types of ion-selective electrodes as well as various applications were presented and discussed between 1979 and 1992 [16, 171. The following sections deal with specific developments in ion-selective electrodes apart from those published in [4-9, 16, 171.

5.2 The Symmetric Potentiometric Cell The emf of the potentiometric cell is related to theion activity ai at the sample-membrane boundary (0) relative to the mold activity of the analyte at the inner electrolyte-membrane boundary (1) of the electrode half-cell (compare section 4.2, segmented membrane model). Assuming that the analyte ion activity of the two solutions contacting the membrane is equal, the emf of the potentiometric cell should be zero, if there are no further contributions to the emf. This condition may be controlled by an entirely symmetric arrangement of the potentiometric cell as expressed by the following notation: Reference electrode EJ1 .. Hg I Hg2C12 I KCl (as, sat.) i bridge electrolyte :: sample or reference solution I membrane I

EJ2

Indicator electrode

reference solution i i bridge electrolyte i KC1 (aq, sat.) I HgzC12 I Hg where E J ~EJ2 , are liquid junction potentials.

(5-5)

204


In English, the terms "potential" and "potential difference" are not clearly distinguished. The term potential is used, even to refer to the potential difference between two interfaces.

"AbInitio" Active Molalities of Electrolytes Two entirely equivalent calomel reference electrodes (SCE) are connected and enclose the ionselective membrane symmetrically. According to the definition, the left-hand half-cell is the reference electrode and the riiht-hand electrode is the indicator electrode. The two liquid junction potentials are equal as long as both solutions have equal composition. On changing the composition of the reference or sample solution, the liquid junction potential can be calculated (see section 3.4.6). If the same electrolyte solution is pipetted into both half-cells, an emf of zero should result, assuming electrical symmetry of the homogeneous membrane, and compensation of the potentials of two identical reference electrodes [18, 191. "Electrical symmetry" denotes a state described by the compensation of the Ohmic resistance on both boundaries of the electrode membrane, compensation of the ion currents associated with the ion exchange, compensation of the boundary potentials, and compensation of the liquid junction potentials. The electrochemical potential is identical for all species on both sides of the interfacing ISE membrane. Therefore, there is no need to consider an ion gradient over the membrane. The emf of the cell indicating an electrolyte activity ratio of 1 on both sides of the selective membrane is zero under these conditions (log 1 = 0; E = : 0):

(5-7)

To check the response of the electrically symmetric cell to varying ion activities, the molal activity of the analyte ion, a j ( S ) , in the sample half-cell is vaned, whereas the molal activity in the reference half-cell, ai(r), is kept constant. The theoretical molal activity ai and active molality & of the analyte ion are estimated from the known concentrations and ionic strength of the aqueous reference solutions, based on the Debye-Hiickel formalism (see sections 3.4.1 and 3.4.2), whereas the experimental relative molal activity and active molality equivalent to lOemf/s are calculated from the experimental emf values, assuming an ideal slope s of 59.16 mVldec (298.16 K) for monovalent ions. The results are strongly related to the temperature for thermodynamic reasons. The slope of the ISE response function increases with increasing temperature. Routinely, all measurements are made at 310 K, where the slope is corrected to 61.54 mV for monovalent and 30.77 mV for divalent ions. The slope ai(r)expof the first order linear regression function of ads), y-axis, on lWmfIs, xaxis, is equal to the calculated molal activity ai(r) of the reference solution. Ideally the slope ui(r)exp should be identical with the theoretical molal activity of the target ion of the internal standard solution at emf = 0 and 10emfIs= 1 (see Figures 5-3a and b).


205

Relatively large symmetric cells, requiring about 5 ml specimen were used in our laboratory [ 181. For practical reasons, attempts were made at miniaturization of the symmetric cell arrangement. The result is shown in Figure 5-2. The miniaturized symmetric potentiometric cell is constructed with two heparinized hematocrit capillaries as sample channels. The two capillaries are arranged face to face in a polycarbonate holder. They are separated from each other on the ISE membrane, which is inserted in the center of the potentiometric cell by a mobile support. The liquid junction is composed of two chromatographic capillaries with an inner diameter of 50 or 75 pm. Those connect the sample with the standard calomel reference electrode (SCE) or an ArgenthalR reference electrode [ 181. The sample volume consumed is 50-100 pl.

5.2.1 The Asymmetry of the ISE Membrane and Reference Electrodes Solvent polymeric membranes based on PVC and a plasticizer are not inherently symmetric after preparation. Even after 24-48 h conditioning by bathing the membranes within a solution of the analyte, 0.1 m o m solutions of the target analyte in most cases, an asymmetry may still be observed. The allowable asymmetry of a conditioned membrane was arbitrarily limited to 60 pV, the allowable error of the reference system for biological measurements (compare Appendix 4).

Figure 5-2. Prototype of a miniaturized symmetric potentiometric cell configuration. The sample channel has an inner diameter of < 1 mm, and is composed of two heparinized hematocrit capillaries, which contact the membrane (see text)

206


In contact with human blood plasma, a membrane potential is induced which contributes to the analyte-specific emf. The extent of the sample-induced membrane asymmetry depends on the composition of the membrane and should be checked in a symmetric cell configuration for different applications. Electrically symmetric membranes and membranes which are indifferent to short-time (20 min) contacts to the biological matrix can be prepared, if the composition of the membrane is specifically taken care of. In this case a reliable calibration is possible and even an ‘lab initio” determination of molal electrolyte activities is achieved, so that calibration-free electrodes may be realized [ 18-19]. Recently the preparation of standard reference samples for ion activity assays has been proposed.

Results of “AbInitio ” Measurements To a first approximation, it is assumed that the potential of the reference electrode including the liquid junction potential, ERef + EJ, is constant for both reference electrodes, that the liquid junction potential EJ of both half-cells is compensated, and that AEJ arising from the varying molality of the target ion and the sample composition is negligibly small. Changes are minimized by using concentrated equitransferent electrolyte solutions: 1moYL KC1 or LiCl solutions or the respective nitrates represent a fairly good compromise for biological measurements. Under these conditions, the results shown in Figure 5-3a-d were registered. These assumptions were shown to be reasonably consistent when analyzing aqueous solutions, as shown in Figure 5-3a, b for sodium- and potassium-selective membranes based on hemisodium (Kodak)and valinomycin respectively. The plasticizers were carefully selected in order to optimize the ISE membrane for its indifference with biological specimens. For the potassium-selective cell, the theoretically calculated active molality of 3.13 mmoYkg K+ at lWmf I s = 1.0 (on the x-axis) is comparable to an experimental value of the slope ai(r)exp equivalent to an active molality of 3.14 mmollkg K+ based on first-order linear regression analysis. For the sodium-selective cell, the theoretically calculated active molality of 104.5 mmovkg is comparable to an experimental value of ai(r)exp= 104.1. The standard deviations (ISD) were 0.06 mmovkg for potassium (n = 20) and 1.2 mmoYkg for sodium (n = 60) in terms of active molality. To estimate the theoretical active molality of K+ and Na+ for human serum specimens, total concentrations were measured by flame atomic emission spectroscopy (FAES). The active molality of Na+ and K+ of each specimen was estimated, accounting for the overall ionic strength based on FAES results, a small fraction of complexed ions (about 5% [15b]) and a theoretical mean volume replacement of water by proteins and lipids of 7% (see section 3.4.6 and Appendix 3). Surprisingly the results differed considerably for serum samples. Whereas the potassium-selective assay still showed theoretical behavior, the correlation between theoretical and experimental active molality in the sodium-selective approach showed a significant deviation of 2.9 mmovkg (107.4-104.5 mmoYkg) from the theoretical behavior, along with a significantly increased SD of 4.0 mmoYkg. Remarkably, the active molality of Naf calculated from FAES results decreased with increasing active molality as measured by

207


calc. active rnolality, I%,(S)-,~

calc. active rnolality, E,(S)=,~

id

K* aqueous solution ligand: valinomycin

Na+aqueous solution ligand: hemisodium

150

100

f 50

s,, b n

srx = 0.06I mobkg" b = 3.14 n = 20

(a) 0

0.5

1.0

1.5

0

1.56

3.13

4.69

2.0 lo""^ 6.25 mmol kg-'

experimental active molality.(lSE),

6,(r)-

= 1.2 rno1.kg.l = 0.99262 = 60

(b)

0 0

0

0.5 52.3

1.o 104.5

1.5 156.8

mmol kg"

experimental active molality (ISE), r%,(r)ew

Figure 5-3a, b. Plots of the calculated active molality of aqueous K+- and Na+-solutions (yaxis) vs. the experimental ab initio activity, loemfIs, on the upper scale of the x-axis and ai(r) x f i i lOeds in 10-3 mol k g l (see Table 3-2) on the lower scale. s ~denotes . ~ the overall residual active molality on the y-axis. Aqueous solutions of physiological composition with a background of 0.625 mmol L-l MgC12, 1.1 mmol L-l CaC12, 4.25 mmol L-l KC1 and 140 mmol L-l NaCl, respectively, were used throughout [l8, 191. a) K+-measurementswith an ionselective membrane consisting of valinomycin, BBPA as plasticizer (see Appendix 9), and PVC as the polymer matrix; y-axis, K+-active molalities calculated for 2.75, 3.25, 4.25, 5.0, and 5.75 mmol L-1 solutions ( y ~=+ 0.728), b) Na+-measurements with an ion-selective membrane consisting of hemisodium, BBPA as plasticizer, and PVC as the polymer matrix; yaxis, Na+-active molalities calculated for 100, 120, 140, 160, and 180 mmol L-l solutions (ma+= 0.742)

208

5 Potenriometric Chemical Sensors and Biological Applications

active molality, G,(s)-~,from FAES exp K' in serum ligand: valinomycin

active molality, Si(s)*,, from FAES exp.

I

Na' in serum ligand: hernisodium

150

100

50 sY.. = 0.08 mol b = 3.15 n = 15

sI., = 4.0 mol.kg" b = 1.0278 n = 10

0

0

0.5

1.0 3.13

1.5 4.69

2.0

10'"""

1.56 6.25 mmol kg" experimental active molalii (ISE), fii(r)ew

0

0

I

I

I

0.5

1 .o

1.5

lo'*'

52.3 104.5 156.8 mmol kg" experimental active molalii (ISE), 6i(r)em

0

Figure 5-3c, d. Ion-selective measurements in plasma samples. The active molality was calculated on the basis of total concentration values obtained by independently performed flame atomic absorption spectrophotometry determinations. A mean mass concentration of water, p~,o;p,of 930 g L-' (according to section 3 . 4 3 , a mean activity coefficient according to Debye-Huckel theory, and a mean ionic strength I = 0.16 mol kg-' were assumed [18, 191. c) K+-measurements in plasma samples with the same membrane as in a); y-axis, calculated active molality of K+ assuming a mean activity coefficient of YK+= 0.728, d) Na+measurements in plasma samples with the same membrane as in b); y-axis, calculated active molality of Na+ assuming a mean activity coefficient of ma+= 0.742

5.2 The Symmetric Potentiorncrric Cell

209

ISE concentrations, which means that the electrode results exceed those obtained and calculated from FAES with increasing sodium concentrations.The only plausible explanation for this effect is that the influence of the water concentration or replacement by proteins and lipids has not been adequately accounted for. If high sodium concentrations correlate with dehydration for the majority of patients or specimen, the water replacement factor of 0.07 is underestimated, and the estimates of the active molality of true specimens are too low. For all other ions, different mechanisms obtain. This hypothesis was strongly supported by further investigations [201. Comparing the results shown in Figure 5-3a-c, a major influence from the liquid junction potential of the reference electrodes can be excluded. This was also shown by correcting the liquid junction potentials on both sides [18]. In Table 5-1, further evidence is given for a negligible error by serum samples in contact with the free-flow, free-diffusion calomel reference electrodes. The potential of a SC-reference electrode was reported to be strongly influenced by the biological sample: (1) due to deposits at the liquid junction, (2) due to an additional Donnan potential arising from the protein content of the specimen [21].The study of these hypotheses is tricky since any real specimen will produce a membrane or boundary potential simultaneously, and working with pure bovine serum albumin (BSA) solution is not representative. From our own experience, the electrochemical effects in BSA solutions differ considerably from those in plasma, serum, or whole blood, owing to the completely different protein and lipid composition (see section 4.7). Owing to the PI of albumin of 4.9, albumin is up to 99% negativeli charged at pH 7.4, and induces a Donnan potential very different from that of plasma or whole blood. The localized negative charges are neutralized by cations, which results in a different distribution of cations and, additionally, of water. In order to gain more detailed information on the behavior of the free-flow, free-diffusion calomel reference electrodes, the potential differences of eight pairs of free-flow, freediffusion reference electrodes were measured on the basis of the electrically symmetric configuration of the potentiometric cell; first, by immersing both electrodes in the same physiological reference electrolyte solution Second, the measurements in reference electrolyte solution were repeated after immersing one electrode of the pair into a human plasma or serum specimen for one hour The whole period of contact of one electrode with the specimen was up to 86 h (number of repetitions n multiplied by 1 h see Table 5-1). The electrodes were operated with a flux around 1 pl/h ( E R .free-flow) ~ as well as by applying a total pressure of 1.2 bar which results in a flux of about 5 jNh E R . ~The . results are shown in Table 5-1. Clearly, an asymmetry potential due to deposition of proteins can be tested by these experiments. Surprisingly, the variation of the potential differences decreased after contact with the biological sample. This behavior is well-known from polymer surfaces, e.g., the vaporization cells of AAS or AES instruments, which must be conditioned by protein solutions before analyzing biological specimens in order to provide a homogeneous wettability of the surface, and a decreasing surface tension of such materials. The contact to the biological specimen increased the reproducibility of the reference potential and the electrical symmetry in aqueous electrolyte solution significantly (statistical F-

r.

gU.

2 10


Table 5-1.Relative potential AER of pairs of SC reference electrodes with a free-flow, freediffusion liquid junction [ 131, measured in an aqueous physiological electrolyte solution at room temperature before and after immersing them for 1 h in human pool plasma. For abbreviations, see text

Flux

Number of repetitions n

Mean potential difference YlmV

Confidence interval, 2SD of mean f 2 sy 1 mV

1plkl 1 pl h-1

82

-0.01

86

+0.003

f 0.020 f 0.009

AE =; :

5 pl h-1

39

-0.02

AEE

5 pl k1

42

4.01

Notation of the electrode pair

AE AE

:Om

f 0.038 f0.015

test). This effect may be typical for the free-flow reference electrode. The mean electrical asymmetry of the pair of reference electrodes was in no case significantly different from zero. AER was in all cases between 0 and f 60 pV. An increased flux, however, is the source of additional uncertainty of the emf. (The results are based on statistical analysis of variances.) Under routine conditions, the ideal behavior of ISEs is usually not attained for different reasons, one of which is that the liquid junction potential does in fact change considerably, owing to the different ion background of calibrating solutions (chlorides as anion background) compared with real samples. An emf shift up to 2-8% of the analyte's active molality may be observed. Using such calibrators, the electrode function must be corrected by calculating MJ due to the different ion background based on the Henderson equation (see Eq. 3-105) by using appropriate software to take account of the active molality of the ion background (see [13]). Payne [21], proposed an isotonic potassium chloride bridge electrolyte. However, this type of liquid junction potential becomes sensitive to the variable composition of consecutive specimens in continuous flow analysis.

Conclusions The electrically symmetric cell allows one to evaluate the various sources of error, and to determine the active molality of electrolytes in reference and standard specimens. Based on the electrically symmetric cell, the net asymmetry of membranes, and the asymmetry due to

5.2 The Symmetric Poientionzelric Cell

21 1

absorption phenomena (see section 4.7) can be distinguished, and the induced voltage shift can be quantified. Based on this technique, the potentiometric cell and the membrane composition are optimized for minimum interaction with the biological specimen. These are the basic conditions to define a potentiometric cell for measuring the active molality of primary standards, and to approach calibration-freeassays.

5.2.2 Analysis During Hernodialysis In automated electrolyte analyzers, the electrical asymmetry of the membrane is taken into account, and compensated by the calibration procedure. Measuring techniques recommended by the EWGSE (European Working Group on Sensors and Electrodes) seek to compensate or eliminate asymmetries responsible for inaccuracies by continuous recalibration of the electrodes [22]. However, a contribution of the biological matrix to the membrane potential is disastrous for in vivo monitoring where recalibration is not possible. Continuous direct monitoring of electrolytes in whole blood is of growing interest. In many cases, e.g., in heart surgery or hemodialysis [14], intervention can be more direct and immediate [23]. The period of time that the patient is exposed to hemodialysis can often be considerably restricted by electrolyte monitoring. Hence, secondary effects, such as cramps, headache, sickness, waterloss, and others can be relieved or inhibited. The initial experience with direct monitoring on the basis of ion-selective electrode membranes implanted in PVC tubes was not very encouraging. The ISE results could not be interpreted since they did not accord with data determined in the central laboratory of the university hospital. Two different problems arose from these early measurements: First, the deviation between total molar electrolyte concentration and the active molality, as indicated by the electrode response, was anticipated; second, the deviations bet\;leen the results provided by the two methods could not be fully explained by the aforementioned effects. Obviously, technical problems (artifacts) were involved (see hemodialysis patients [20]).

Localizing and Quantifying Artifacts In order to localize and quantify the artifacts, the symmetric arrangement proved very useful. It was possible to control the membrane potential in the native state after preparation, after conditioning, and after different periods of contact with the bio1ogic.d matrix. We resorted to simulations of the membrane behavior during continuous monitoring. Quantitation errors were partly explained by emf drifts due to inadvertant interactions between the biological matrix and the membrane surface. The emf was stabilized after several hours of contact, and resulted in a final emf shift of 0.3-5 mV for a large number of membranes and specimens, depending strongly on the composition of the ion-selective membrane compare section 4.7. The observed asymmetry even reached 14 mV within 60 min contact with pool plasma. The aim was to eliminate or, at least to reduce, these interactions (see Figure 5-4a, b).

2 12


Preventing Artifacts

Different technologies were employed. On the one hand, modified membrane matrices were studied. Membranes were modified: (1) by changing the ligand and plasticizer quality: (2) by changing the polymer. ISE membranes based on hydroxy-poly(viny1chloride), where about 14 mol% of C1 atoms are replaced by OH groups, were investigated for comparisons, as proposed earlier [24]. Three different methods for synthesis of the hydroxy-PVC by hydrolyzing a poly(viny1 chloride)/poly(vinyl acetate) copolymer were used. The most stable product was achieved by basic hydrolysis in methanol at 263 K (ETH 3528) (see Appendix 8). On the other hand, polymers for preparation of biocompatible materials are well known, and are used as surgical materials (see also section 4.7). The copolymer (poly[(R)-3hydroxybutyratel(R)-3-hydroxyvalerate]) as well as three different qualities of the medical grade polyurethane, Tekoflex (Thermomedics Inc., Woburn, MA), based on a prepolymer of 4,4'-diisocyanato-dicyclohexylmethaneand poly(oxytetramethy1ene ether)glycol, were evaluated as coating [15] and bulk membrane materials [15, 251. The investigations demonstrated that PVC can be replaced as membrane polymer without considerable loss in selectivity and sensitivity in the case of sodium-selective membranes with ETH 2120 as a carrier (unpublished results). Unfortunately, this is not generally valid and, in addition, an optimized membrane composition has to be evaluated and characterized for each new electrode. Therefore, for more general use, a coating technique was developed that allowed one to prepare ISE membranes with strongly reduced asymmetry and emf drift on the basis of biocompatible polymers as coating material (see Appendix 8). An example where a worst-case sodium-selective membrane is coated with Tekoflex EG-85A is shown in Figure 5-4. Na+selective PVC membranes containing the ionophore N,N,N,M,-tetracyclohexyl-1,2phenylenedioxydiacetamide (ETH2120) and the plasticizer bis( l-butylpenty1)adipate (BBPA) were investigated as the worst case membrane to take interactions with the biological matrix into account. Heparinized plasma was chosen for worst case investigations in view of the specimen type. Using the coating technique, the sample-induced emf shift could be reduced to < 0.25 mV. For coating of the PVC membranes, bis-cyclohexyl-polyurethanes(Tekoflex EG-85A) as well as the biocopolymer (poly[(R)-3-hydroxybutyrate/(R)-3-hydroxyvalerate]) were used. When using a spin-on device for the manual coating technique, we had to cope with poorly reproducible thickness of the coated layer. Successfully coated membranes were achieved more or less by chance. However successful the coating with "biopolymers" appears, the slope and selectivity of coated membranes may be slightly changed and decreased. At least for sodium-selectiveISEs, the use of OH-PVC looked like being as successful in preventing the adsorption of biological components. However, in this case, the toxicity of HC1 residues, epoxide, and toxic secondary oxidation products might be a problem. The results of the potentiometric assay were checked by AFM (atomic force microscopy) and SEM (scanning electron microscopy) and by scanning IR-ATR spectra methods orthogonal to potentiometric measurements [ 151. The microscopic pictures agree with the results of potentiometric measurements in that the asymmetry and drift were caused by

2 13


t

-"I -4

-45

Ez

O5

T t

0

- 0.5

-'

-1.5 -2

t

1

Figure 5-4. Comparison between the electrical asymmetry of the cell potential as measured for coated and uncoated Na+-selective membranes before and after contact with a heparinized human pool plasma. The potentials were measured in a step-by-step procedure within about 3 h (30 min between measurements, represented on the x-axis). Each asymmetry voltage is denoted by E and subscripts: R, reference electrode; m, membrane. 1, starting the test series with aqueous physiological solutions: E R ~asymmetry , potential of the pair of reference electrodes in contact with the same electrolyte solution; El, potential of the conditioned membrane contacted by an identical activity of sodium ions on both sides of the membrane; Em = E I - E R ~calculated , membrane-induced asymmetry potential. E R ~asymmetry , potential of the reference electrode in an aqueous physiological electrolyte before contact with pool plasma, and E R ~immediately , after contact to pool plasma in electrolyte; E R ~repetition , after evaluating the membrane asymmetry. Ep, electrical asymmetry emf due to plasma contact of

214


one half-cell (not specified in this graph, see [12]);E2, plasma-induced asymmetry potential of ~ the the membrane (for most cation-selective membranes negative); E A (E2-Em-(E~3-E~2)), asymmetry of the ion-selective membrane induced by the human pool plasma, a) PVC solvent polymeric Na+-selective membrane, b) the same membrane type as in a) coated with Tekoflex 85A (for coating procedure see Appendix 8)

adsorption of compounds at the membrane surface. The adsorption process reaches saturation after a few hours. However, the adsorbed layer can break off suddenly and cause a new emfoffset [26].

5.2.3 How About Human Whole Blood? In order to shift the experimental conditions closer to the situation in whole blood, the response of a worst case sodium-selective membrane (ETH 2120,BBPA,PVC) was studied against a human blood plasma enriched in thrombocytes (3 x l O I 3 cells L-*) [15]. Surprisingly, the preparation exhibited a cleaning effect on the membrane surface, which was improved by scanning in the electron microscope. In order to explain those results, the chemistry of the erythrocyte membrane, which was assumed to exhibit a composition similar to thrombocytes, was compared with the composition of human blood plasma (see Figure 5-5). Since blood cells occupy a volume fraction of about 45% of human blood, the measurement of plasma looks like an unnatural stress for polymeric surfaces. The cleaning effect was explained by the high overall surface of bilayered cell membranes and the high content of surfactants (e.g., phospholipids and cholesterol) which solubilize proteins and/or lipids, and prevent deposition at the polymeric surface. The effect could be compared to endothelial protection of surfaces to increase the biocompatibility (section 4.7).At least, these results imply a considerable body of evidence that the worst case was really studied, and quantitation errors should not be worse when compared whole blood. Further investigations on the mass concentration of water and the molal activity of electrolytes before and after hemodialysis will provide insights into the problems involved in comparing the results of different methods. It will further elucidate the role of sodiumselective measurements in establishing the state of hydration of patients. A population of "healthy" volunteers is involved in these studies as a control group [27]. Comparison to gather more information on the nature and mechanism of the adsorption process needs to be done in future with anion-selective membranes. The asymmetry is predicted to be less pronounced, and the sign should be inverted by contact with positively charged peptides.

5.3 The Magnesium-Selective Electrode

215

Conclusions In potentiometric sensors the molal activity of charged analytes is directly accessible over several orders of magnitude of sample activity. Selective carriers are available for many electrolytes, especially cations, whereas anion recognition has been less investigated. The theoretical background of the electrode response and membrane function has been studied by many excellent researchers during the last three decades (chapter 2, [15, 161). Our own theoretical investigations have covered some aspects of to the development of the magnesium electrode and their application in biological specimens. Adsorption of components of the biological matrix at the surface of the solvent polymeric bulk membrane has been shown to cause a considerable drift and membrane assymetry. Albumin is assumed to contribute considerably to these inaccuracies. Means to prevent these artifacts have been evaluated and recommended. The symmetric cell assembly is a suitable device to analyze reference material, and to provide values for the active molality of electrolytes. However, the procedure commonly used to calculate sample molar concentrations, and the lack of expertise in interpreting values result in considerableuncertainties in interpretation of results (see [20]).

5.3 The Magnesium-Selective Electrode Ion-selective electrodes based on solvent polymeric membranes, and facilitated extraction by neutral carriers were described by Stefanac and Simon in 1966 [28]. I n 1972, potassiumselective solvent polymeric membrane electrodes based on valinomycin found their first application in a commercial analyzer (STAT-ION, Technicon Tarrytown, New York / Photovolt Corp., Indianapolis, Indiana, see section 1.3). The interaction of neutral macrotetrolide antibiotics as well as synthetic carriers with alkali and alkaline earth metal ions in free solution was demonstrated by vapor pressure osmometry (VPO) [29]. Neutral ligands for most of the biologically relevant ions have been developed since, but not for the magnesium ion [9]. Thus, the magnesium ion was called the "forgotten ion" [30]. However, the search for magnesium-selective carriers started about 20 years ago [31], but only in 1990 did it result in successful measurements in the extracellular space (see section 1.3 and Appendix 1) [32, 331. In 1996, "recommendations for measuring and reporting ionized magnesium in undiluted serum, plasma or whole blood" were published [34]. The recommendations stipulate "A discrepancy between total magnesium by ISE and conventional (e.g., photometric) methods would indicate a salt or water disturbance or an abnormal binding of magnesium in plasma. Total magnesium by ISE would be the more relevant quantity, being proportional to the Mg*+ activity." The terminology used in clinical chemistry has to be appreciated. The fascinating history [35] of the continuing search for magnesium-selective carriers is unparalleled, partly because of the special characteristics of the magnesium ion.

2 16


PLASMA MASS CONCENTRATION

TOTAL PROTEINS ALBUMIN

H GLOBULINS FIBRINOGEN TOTAL LIPIDS PHOSPHOLIPIDS CHOLESTEROL

TRIGLYCERIMS

0 OTHER LPlDS

ERYTHROCYTE-MEMBRANE MASS CONCENTRATION

TOTAL PROTEINS TOTAL LIPIDS PHOSPHOLIPIDS CHOLESTEROL OTHER LIPIDS

Figure 5-5. Histogram of the ratio of the most abundant protein and lipid fractions in (a) an average human blood plasma relative to (b) the average composition of the most abundant fractions of the erythrocyte membrane in mass per 100 ml plasma and mass per 100 g dry mass of erythrocytes


217

5.3.1 Characteristics of the Magnesium Ion The thermodynamic stability of the complexes formed by different types of ion are to some degree independent of the ligand structure, but follow more general rules based on the position of an element in the periodic table. A clear separation or grouping of ions into 'hard' (class A) and lsoft' (class B) ions can be demonstrated by plotting chargehadim d r versus second ionization energy for divalent ions. The polarizability of an ion determines the reactivity of class B cations with thiolate (RS2-), sulfide (S2-), and selenide (Se2-), whereas class A cations coordinate preferably with halides and oxygen donors. For class A cations, the order of binding by anions is F > C1- > B r > I- and 02-> S2-. For cass B cations, this order is reversed. Binding of class B cations shows a stronger covalent character. The strongly electropositive s1 and s2 metals tend to form essentially ionic derivatives, with the exception of lithium and beryllium, which tend to polymerize. A joint feature of these two ions, as well as of magnesium and aluminum ions, is the tendency to form organometallic compounds. These ions show some Lewis acidity, which enables them to coordinate with electron pair donors preferably halides, nitrogen, and oxygen compounds. The ionic character of the magnesium atom in a C-Mg bond of an organometallic compound versus the carbanion amounts to about 34%, calculated from the difference in the electronegativity of both atoms [36-40],66% of the bonding energy is covalent in character. The Lewis acidity increases from group I to group I11 elements of the same period, and is even more pronounced for aluminum than for magnesium ions. To account for these considerations, a relatively weak Lewis acidity can be attributed to the magnesium ion, and this has a controlling influence, especially within the hydrophobic environment of the sensing membrane (for further details see Appendix 5). The Lewis acidity is more or less favored by the composition of the membrane, the lipophilicity and polarity of the solvent, and the activity of polarized coordinating groups.

5.3.2 Analytical Techniques Total Molar ConcentrationAssays The standard reference technique for the analysis of total magnesium concentrations is atomic absorption spectroscopy (AAS) [41, 421. The sample is diluted with acid lanthanum chloride solution to facilitate atomization of the magnesium salts. The method is used both for the determination of total magnesium concentrations in plasma and serum and for determinations of the hemolyzed erythrocyte fraction. Total magnesium concentrations have been analyzed in erythrocytes by the so-called indirect method, where the magnesium concentration is quantified in whole blood and plasma, or in whole blood and the erythrocyte fraction [43,44]. In both cases, the hematocrit, the volume of the erythrocyte fraction in whole blood, has to be taken into account, and the plasma encapsulated in the erythrocyte fraction must be compensated for. Photometric assays in the transmission mode use complexometric methods with, e.g., CalmagitG (3-hydroxy-4-[(2-hydroxy-5-methylphenyl)azo]-l-naphtalinesulfonic acid) as

218


ligand. Calcium ions are masked by EGTA (ethylene bis(oxiethy1ene nitri1o)-tetraacetic acid) up to a concentration of 3.8 mmoyL. Application of the arsenazo method for a magnesiumselective assay is possible only in the absence of, or after selectively chelating, the calcium ions [45, 461. Plenty of other chelating agents have been proposed (magon dye, xylidyl blue, titan yellow, chlorophosphonazo 111). DMSO was added to reduce the interference from protein. A luminescent assay on the basis of 2-hydroxy-1-naphthaldehydesalicyloylhydrazone has been proposed [47]. Alternatively, in situ analysis can be carried out by X-ray fluorescence [48]. Investigations were started in Switzerland in 1991 with tissue from the tongue [49]. The technique delivers an intensity and frequency pattern of the reflected X-ray radiation, corresponding to the relative concentrations of the different elements in the tissue. The influence of complexing is still largely unknown, owing to the lack of reliable reference methods for intracellular measurements. Fluorescent chelating agents as well as 31PNMR and 25Mg NMR spectroscopy have proved reliable reference methods for intracellular determination of magnesum activity or concentration. Mn2+ is usually introduced as a colored spectroscopic probe, replacing Mg2+. However it has a higher affinity for N atoms than calcium or magnesium ions. For further information associated with the distribution of the magnesium ion and its complexes, especially clinical parameters, see ref. [50,51].

Fluorescence Indicators and Intracellular Evaluations The evaluation of the role of Mg2+ as a regulator of cell function has been hampered by the lack of suitable methods for continuous monitoring of the free cytosolic Mg2+ [36]. This limitation is particulary apparent in comparison with cytosolic Ca2+, which is readily monitored by the fluorescent indicators developed by Tsien and co-workers [52]. A fluorinated, magnesium-selective chelating indicator was developed by Raju, Murphy, and coworkers [5 31. This indicator, FURAPTRA (2- [2-( 5-carboxy)oxazole]-5- hydroxy-6aminobenzofuran-N,N, 0-triaceticacid tetraacetoxymethylester) is hydrolyzed upon passing the cell membrane, and exhibits a characteristic excitation shift on complexation of Mg2+. Dissociation constants K = 1.5 mmoVL and K F = 53 pmol/L for C$+ at pH 7.05 with HEPES (N-2-hydroxyethyl piperazine-N’-2-ethanesulfonicacid) as pH buffer was reported, although this has been reevaluated and revised several times since [54]. Calcium ions are preferred by the fluorescent dye [53]. FURAPTRA generates 1:1 complexes with magnesium and with calcium ions. Even the stoichiometry of the ion-carrier complexes cannot support the discrimination of calcium ions. The intracellular calcium activity is a factor of > 500 lower than the magnesium ion activity, however. The intracellular magnesium activity measured in hepatocytes was 0.59 f 0.04 mmol/L (n = 5). Calculations were made assuming that the intensity of the fluorescence emission relative to the magnesium activity and the dissociation constant can be calibrated in vitro The leakage from cytoplasm to other intracellular compartments and the consumption of Mg2+ by the chelating indicator was discussed. Values for the analyte consumption can be computed with aid of the stability constant, and can be compared with microelectrode values.

Eg

.

5.3 The Magnesium-SeleciiveElectrode

2 19

OCH2COOH

HOOC

(mag-fura-2) (C18H15N2011) CALMAGlTE (C19H1405N2)

Figure 5-6. Chelating agents applied in magnesium-selective assays (for chemical names and further details see text)

Some atomic nuclei of natural isotopes in the ground state behave as a small magnetic dipole. NMR can be used for any molecule containing atomic nuclei with nonzero magnetic dipole moments, e.g., 'H,3H,13C, lSN,19F, 29Si, and 31Pwith spin quantum number r n ~ ,with I = 1/2, as well as atomic nuclei with nonzero spin quantum numbers, such as llB,170, or diamagnetic metals such as ll'Cd, l99Hg, and others. Isotopes with a low natural abundance, e.g., 15Nand 170, are normally undetectable by NMR. Each nucleus with nonzero spin has a magnetic moment pz , which is proportional to the spin quantum numberrnI, the gyromagnetic ratio y, and the Planck constant 4 = h /2n.Since y cannot be calculated reliably, it is treated as an empirical factor. In a static magnetic field B,, the orientations of the nuclei have different

220


energies. If a sample is exposed to a frequency v,, the nuclei come into resonance when the irradiated frequency satisfies the resonance conditions. This energy is called the Larmor frequency O. w = V , B,

and

hVo =

yh B,

(5-8)

This Larmor frequency is, e.g., 80.96 MHz at 4.7 Tesla for the 31Pnucleus (200 mHz for 'H N M R and 50.29 MHz for 13C NMR under the same conditions). Nuclear magnetic moments interact with the local magnetic field, which normally differs from the applied field. The additional field is identified by the shielding constant 0 . Since the Larmor frequency of an atomic nucleus is different in different environments the so-called chemical sh$t 6 of the resonance frequency can be used for analytical purposes to probe the environment of the nucleus of an isotope. The sample is placed in a static magnetic field B, and subjected to irradition by one or several radiofrequency rf fields B1, B2. The chemical shift is referred to a reference standard, which is commonly tetramethylsilane (Si(CH3)4. TMS) for proton NMR. Chemical shifts are reported on the 6 scale which is defined by:

v - vo s= 7 106 V

(5-9)

where fl is the resonance frequency of the standard. Magnets used in 'H NMR are operated with magnetic flux densities of 1.41-14.09 Tesla, which correspond to frequencies, \p of 60600 MHz for the reference standard. For work with biopolymers B, is typically 11.74 Tesla, and the Larmor frequency of the proton is VO = 500 MHz (1 Tesla = lo4 Gauss). 3lP N M R was proposed for analytical use where a second nucleus, e.g., H+ or Mg2+ interacts with the PO nuclei [36, 55-57]. It was first proposed for in vivo, intracellular pH measurements (H2POT vs. HI-'($); second, to provide information on the metabolism and equilibration of phosphorylated compounds such as ATP, ADP, AMP, and creatine phosphate; and third, to locate polynucleotides and investigate their structure, conformation, and function. The sensitivity of the 31PNMR signal is only 6.6% that of the 'H hydrogen signal, but 31Pis the only natural isotope of phosphorus (100% occurrence). The N M R technique has also been used to estimate the free magnesium ion activity in vivo, based on the determination of the association constant of Mg2+ and phosphate ions. Typically, the NMR signal is the inverse of the potentiometric signal. However, association constants increase with increasing local ionic strength. This effect is difficult to be estimated. In 1978, Gupta [55] presented 31PNMR spectra showing the the resonances, chemical shifts, and coupling constants of the a-,p- and yP atomic nuclei of ATP in human whole blood (Figure 5-7). On saturation of ATP with Mg ions, the resonances of all nuclei shift downfield (310 K, pH 7.2, I = 0.15) (Figure 5-7a and d). The shift for the p-P nucleus amounts to about 100 Hz. The chemical shift and the change in the coupling constants, Jap and Jh,are directly dependent on the ratio of total ATP to free ATP. The dissociation constants for the different adenosine phosphates were calculated; that of MgATP was determined to be KO = 0.038 f 0.004 mmol/L,. The association constant is the inverse value (26.3 mmoYL-l). The chemical shift and coupling constants were studied for oxygenated and deoxygenated blood. A correlation


~

2

0

0

H

Z

22 1

l

Figure 5-7. 31P NMR spectra showing the resonances of the a-, and y-P nuclei of intracellular ATP in human whole blood with appropriate controls. All experiments were done at 310 K. a) samples contdned 4 mmoYL ATP, 10 mmoVL Mg2+, 0.02 mol/L bis-tris buffer pH 7.2, and 0.15 mol/L KCl; b) and c) intracellular signals: b) oxygenated blood; c) deoxygenated blood; d) as a) without Mg2+ [(with permission from [55])

between the concentration of Mg-phosphate complexes, of glycerate-2,3-phosphate, and the degree of Hb oxygenation was expected and reported.The free magnesium concentration was determined to be 0.25 0.07 mmol/L for aerobic cells and 0.67 f 0.65 mmolL for anaerobic cells. The difference between anaerobic and aerobic cells has never been studied and reproduced with magnesium-selective electrodes. It would be worth repeating these studies with microeIectrodes. Mg2+ contains 10% of the isotope 25Mg2+,with nuclear spin moment I = 5/2. Hence, the magnesium ion can be determined by 25Mg NMR spectroscopy. The technique is especially valuable for discriminationbetween intra- and extracellular magnesium availability. The discrimination of magnesium from calcium ions under physiological extracellular conditions turned out to be a tricky problem, although differences between the two ions are obvious. These differences are in the affinity for coordinating atoms of ligands, as described earlier, in the size of the coordination sphere, the coordination number, and the geometry of the complexes. The free energy of hydration of calcium ions is more positive than that of magnesium ions ( dGhydr.Ca = -1650 kl mol-1).

222


5.3.3 Natural Carriers In aqueous media, the stability of complexes with charged,chelators of calcium ions exceeds that of magnesium ions, with few exceptions [58, 591. Related to its high surface charge density and its high free energy of hydration, the magnesium ion is preferably complexed by anions with high charge density, e.g., ATP", oxalic acid, or malonic acid. The magnesium ion coordinates with an Mg-0 distance of 200-212 pm to octahedral complexes. The central field of the small magnesium ion is supposed to dominate the coordination sphere, in contrast to ions with a larger radius where outer coordination spheres are relevant. There is a noticeable, though weak, tendency of small cations to bind to nitrogen donors, which makes it possible to design small-cavity ligands based on nitrogen as active sites. Such a ligand is the chlorine ring of chlorophyll (see Appendix 5).

Complexation to Chlorophyll The Mg2+ is encapsulated in the chlorine ring (see Figure 5-8a). The complexation is catalyzed by a MgZ+-chelatase (a dioxogenase) and ATP a as coenzyme or cosubstrate. The magnesium ion is fixed by a two-step reaction where ATP is the selective reversible ligand 1. The second step, in which the chlorine ring is probably ligand 2, is irreversible. The Mg2+ is symmetrically positioned in the chlorine plane with a 205 pm distance to the pyrrole nitrogens. Two of them, oppositely positioned, are secondary amines and are deprotonated. Because of the misfit of Mg2+ to the cavity of the chlorine ring, the ion lies 30 pm out of plane, resulting in a nearly ideal trigonal bipyramidal geometry with an imidazole-N from the protein moiety positioned axially. The axial distance is 210 pm. Mg2+is irreversibly encapsulated by the protein moiety and the hydrophobic phytyl substituent. Only by hydrolysis of the phytol unit (C20H370H) is the enzymatic release of Mg2+ initiated. The calcium activity in the cytosol is c 10-6 mol/L, whereas the magnesium activity is in the range of 10-3 mom. Chlorophyll is tuned to energy transfer induced by the absorption of photons [60-621. The magnesium ion typically does not interfere with the electron-conducting function. This is in contrast to redox metals which would interfere and cause a pH-dependent electron transfer, as observed in oyxgen saturation of hemoglobin. The protein moiety has a controlling effect on the ground and the excited states of the chlorine complex, allowing for minor changes in the bond lengths of the coordination sites. The mechanism relies on adjusting the planarity of the complex and on altering the state of solvation by the protein side chain. A comparison with the artificial "electron wires" created for chemical sensors has been made [63]. The competition in this case is no longer from calcium, but from transition metal cations such as zinc. Transition metals are inactivated by different mechanisms: by complexation to sulfur and nitrogencontaining ligands which are mainly buried in enzyme cavities; by changing the oxidation state; by sustaining a low activity within the cell (pumping mechanism); and by sequestration. The extent to which magnesium ions compete with amines and organic ammonium compounds is an interesting question. Tam and Williams explored the competition between Mg2+ and polyamines with homologous dicarbonic acids, and demonstrated that the

223

5.3 The Magnesium-Selective Electrode Chlorophylla

H2C=CH

Chlorophyll b

2.05

A

+

A

(lx-'2.1

H

I

OCH,

0 I

R,

CH,-R

3

9

(Protein)

,CH3

R, = -CH~-CH=C-CH~-(CH,-CH,-CH-CH~~--CH,-CH,-CH

(a>

'CH,

1

-

*/

0

D-Alanin:

0

--0-CH, -OR

H,N+

(b)

'

OH

Figure 5-8. Natural Mg2+ chelating ligands: a) The Mg2+-chlorophyll complex [62]); b) Teichoic acid [67]

magnesium ion is preferred if the anionic ligand has a high local charge densitiy, e.g., from oxalate to malonate and o-phthalic acid [64]. If the anionic charged sites are dispersed and well fitted by the structure of the polyamine, protonated polyamines are preferred as counterions. Fundamental investigations have been made on Mg2+and Ca2+complexation by phosphate, phospholipids, and especially serine phosphate [64, 651. Gresh [65] reported calculated free energies of inter- and intramolecular interactions of 1 1 different conformers of serine phosphate with Mg2+ and Ca2+. The intermolecular interaction energies were consistently larger for Mg2+,owing to the smaller radius and the closer approach to the ligand.

224


Owing to the slow exchange rate (see Appendix 5), magnesium cannot act as a fast trigger ion competing with calcium ions. Generally, magnesium is active in the intracellular space under partial exclusion of calcium and other divalent cations. There is no agreement concerning the mechanism of the ion pumping to maintain the calcium-magnesium gradient.

Teichoic Acid A structure-conserving mechanism has been demonstrated for teichoic acid (Figure 5-8b) in the hydrophobic medium of membranes of bacteria [66, 671. Teichoic acid, a polymer of 2530 glycerol phosphate residues, is linked over two glycosyl units. In the side chains, D-alanyl is substituted by an ester bond to the glycerol. Teichoic acid is also linked to a phosphatidylglycolipid or peptidoglycan by a phosphodiester moiety. The polyanionic character results in an affinity for partially dehydrated divalent cations with a weak preference for magnesium ions. The activity of Mg2+ within the membrane has been shown to rise to a maximum 15 x lW3 mo1L The low affinity of teichoic acid for, e.g., Ca2+ has been ascribed to the D-alanine unit which is supposed to be a controlling element of the Mg2+-gradient.The amount of alanine ester units in teichoic acid decreases with increasing concentration of NaCl in the culture medium. The group led by J. Baddiley have suggested a protecting mechanism for the complexation of divalent cations such as Ca2+. A fairly wide range of structural and constitutional variations in the teichoic acids exist. From investigations of the function of teichoic acid in gram-positive bacterial walls and membranes, it had been concluded that the highly cross-linked structure plays a major role in the physical strength of the wall by a sol-gel process. It was further suggested that the teichoic acid serves to transport divalent cations through hydrophobic membranes without any solvation in a "ping-pong" process. The polymers have been shown to be major antigens with either group or type specific reactions towards antisera and with an influence on enzyme synthesis within membranes. As a comparison, the uncharged p -hydroxybutanoate and khydroxyvalerate polymers, which were investigated as possible ion carriers, showed no extraction properties for cations and anions in our experiments.

Complexation to Polyphosphates As a counterion for anions such as A n 4 - , Mg2+ does not inhibit fast reactions, owing to the minor stability of the complexes. Generally the stability is c 1@in biologically relevant complexes. The magnesium is a catalytic species for slow enzyme reactions. It catalyzes reactions with participation of ATP-ases, e.g., in creatine phosphorylation, it activates tyrosine kinase in rus proteins, enolase, and glutamine synthetase. The impairment of biopterin synthesis in Alzheimer's disease was postulated to occur at the second stage of B& synthesis, with a defect in the action of the magnesium-requiring enzyme, pyruvoyl tetrahydrobiopterin

5.3 The Magnesium-SelectiveElectrode

225

synthetase [68]. Very high binding constants up to 108 L/mol have been observed in systems where the magnesium ion has a structure-conservating function rather than a high turnover rate. The rigidity of the coordination sphere prevents distortion of the complex structure, e.g., in the ATP-synthetase of thylakoids (chloroplast membranes) and mitochondria, and in the ATPases of muscle cells. Mg2+ is never used to assist amide or peptide hydrolysis and synthesis, e.g., by peptidases, proteinases, and urease. Coordinated to ATP the Mg2+ is attached to the p- and yunit, protecting the ATP from hydrolysis. On the enzyme surface, this protection is removed by movement of Mg2+ to the aand P-phosphate. The catalytic activity of the metal ions in an enzyme is based on structure fixation and a resulting entropy minimum of the reactants. In a metalloenzyme cavity, a ternary complex is created by the substrate, the second reactant, mostly a coenzyme (ATP in this case), and the active site. The degree of freedoms for translation and rotation of the reactants is minimized by preforming the conformation with the highest probability of interaction by the enzyme bulk enclosing the hydrophobic cavity (compare ADH). The theory of the "entatic state" proposes preformation of the transition state in the enzyme cavity. In this context, the magnesium ion decreases the entropy of the triphosphate chain of ATP, now fixed in the optimum conformation for interaction with the substrate and the active site of the enzyme. The dehydration and translation of the metal ion, e.g., into the hydrophobic medium of a membrane or an enzyme cavity is facilitated due to the high charge density of the polyphosphates. Remember that even DNA is highly anionic by the bridging phosphate. Mg2+is the ideally exchangeable cation for a (catalytic) fixation to the phosphate moiety of these compounds. The mobility of the magnesium ion along phosphates created the idea of "magnesiumdependent biomechanical devices" [52]. The principle, however, is known to be effective even in the polymerase chain reaction, and must not be underestimated. Even the transcription and translation of the genetic code is magnesium ion catalyzed. In biological compartments, the hydrated cations mentioned above must be in a fast exchange with protein anions and lowmass organic anions (compare ATP). Despite all these important functions and relationships, the medical impact of the analysis of magnesium turnover is not established. This is partly due to the insufficient quality and reliability of the analytical procedures (see chapter 7, Appendix 12) and partly due to the fact that the magnesium ion has no toxic effects. However, it is well known that the magnesium ion level decreases, e.g., in cis-platinate therapy. What happens on application of calcium antagonists? The magnesium ion activity has been shown to have important impact on subjective wellness.

5.3.4 Synthetic Carriers One of the primary goals of carrier development is to obtain selectivity over a relevant scale of background ions in a specific application (for historical background see [35]). (No sensor is universally suitable !). The required logarithmic selectivity coefficient for a magnesium selective assay in human blood and serum samples is presented in Table 5-2. An allowable

226


error of 1% is assumed for calculations [13, 691. The requirements for discrimination of calcium ions are less stringent for the intracellular space (see section 5.4, [70]). The scope of this section is to demonstrate the usefulness of combined efforts involving intuition, computer modeling, membrane technology, and systematic chemical and analytical research, taking as an example the development of magnesium-selective carriers (see Figure 5-1 1). Owing to the exceptionally high surface charge density of the magnesium ion, water of hydration is not easily displaced (see Appendix 5 ) . With a free energy of hydration of -1 857.7 kJ mol-l, the Mgz+-hydrate is stabilized by 207.7 kJ mol-l compared to the Ca2+-hydrate. However, in contrast to the hydrated ions of alkaline metals, the entropy of hydration of the alkaline earth metals is a negative sign, which means that solvation is entropically favored. In particular the activity of an ionic transfer catalyst such as sodium tetrakis(4ch1orophenyl)borate must have a much more pronounced effect on the extraction kinetics of magnesium ions, in response to the high surface charge density, than on the kinetics of calcium or alkaline ions. Nevertheless, because of the higher free energy of hydration and a comparably higher activation barrier, the complexation and equilibration of a magnesium-selective membrane with magnesium ions must be slower than the equilibration with calcium ions. These effects were observed during SSM measurements and are critical when strongly discriminated electrolytes are evaluated in series. On the selectivity scale, the emf of the magnesium ion is not fully regained after contact with calcium ions in due time. However on the molecular scale, these effects are much reduced, the ion exchange involving a current of < 1@A, equivalent to an exchange of c l&'3 charge equivalents s-1 and a difference in < lo-' Js, equivalent to Aemf < 10-3 V. In this case, the rate constants differ by a factor < 2. Overall, the free energy of hydration has to be compensated by the free energy of solvation as well as complexation. The enthalpy of solvation is accessible to an appropriate choice of membrane components and phase transfer catalysis. In an organic medium, such like the artificial membrane environment, the PKa of acids is increased by 2-4 orders of magnitude. Thus, for most organic acids the negatively charged carboxylate is not available for complexation. However, the stability of ion-dipole interactions is increased in the absence of water. Highly interactive groups include atoms which act as electron pair donors (EPD), e.g., oxygen and nitrogen atoms. Owing to the exceptionally high charge density, the magnesium ion has a strongly polarizing effect which may be mainly responsible for the reversible coordination to N-centers and amides. Comparabl ,the required selectivity coefficients published by Bakker [12] are (see section 7 = -2.3, log ot = -2.9 and log ot = -5.9 (neglecting any ion 4.3): log background calibration).

GgCa

GgK

GgNa

Complexation to Antibiotics and Peptides

rt

Cyclo(Lpro-~Leu-)~ was shown to induce a prominent selectivity for Mg2+ over Li+, Na+, and K+(K = 400, 200, 10 respectively), while the selectivity over Ca2+ was poor. Alternatively,


227

Table 5-2. Required logarithmic selectivity coefficients (SSM, IUPAC) for magnesium ion detection in plasma, assuming an allowable analytical error, cv,, of 1.O% at the lower level of a physiological magnesium active molality, U M ~ Z +of , 0.12 mmol/kg (free molar magnesium ion concentration: 0.34 mmol/L, I = 0.160 mol kg-', 37 OC) and with respect to calibration without and with a physiological ion background (Ac, assumed variation of the background ion molar concentration around the mean physiological setting point). Calculations are based on the traditional Nemstian algorithm (see section 4.3) [70] = 0.12 = 0.40 uca2+ 3.0 a ~ + = a ~ ~= +110.0 UMg2+

Measured ion

mmolkg mmolkg mmoVkg mmolkg

(ionconcentration (ion concentration (ionconcentration (ion concentration

=

0.34 1.20 = 4.0 = 150.0 =

Interfering ions Required log coefficient Without background calibration

Magnesium

mmol/L) mmolL) mmol/L) mmolL)

Pot

Selectivity log Kij With background calibration

Calcium

-2.63 -2.57

(1.51 mmoVL) la (1.32 mmoUL) lb

-1.94 (Ack0.31 m o V L ) -1.53 (AckO.12 mmol/L)

Potassium

-1.22 -1.02

(6.0 IIUIIOVL) (4.8 mmoVL)

-0.96 (Ac f 2.0 mmoVL) -0.51 (Ac f 0.80 mmoyL)

Sodium

4 . 1 2 (170 mmoVL) -4.02 (150 mmoVL)

-3.45 -2.89

(Ac f 20 mmol/L) (Ac f 6.0 mmolL) 2a

0. Miiller-Plathe, in: H. Greiling, A.M. Gressner (eds.), Lehrbuch der Klinischen Chemie und Puthobiochemie, Stuttgart, 1989: Schattauer, pp. 380-385. la upper reference value for blood from the umbilical cord. lb upper reference value for adults.

U.E. Spichiger, PhD thesis ETH Nr. 8830. Upper reference values for male and female blood donors in m o l d concentration. 2a relative to the lower reference limit of 144 mmolal activity.

with cyclo(~Pro-oLeu-)~ (see Figure 5-10 (4)) and cyclo(.cPro-oLeu-LPro-LLeu-LPro-.cLeuoPro-Leu-LPro-LLeu-) the logarithmic selectivity coefficient over calcium ions was < -2 while the required selectivity over monovalent ions was lost [71]. Furthermore, the ligands had relatively poor lipophilicity. The influence of the concentration of anionic sites (KTpCIPB, potassium-tetrakis-(4-chlorophenyl)-borate) within the membrane on the selectivity scale of these carriers was tested.

228


\N / H

A 23 187 (C29H3406N3)

Figure 5-9. Constitution of the carboxylic polyether antibiotic A23187

In 1979 N. Otake and M. Mitani [72] reported a monocarboxylic polyether, antibiotic-6061, to be magnesium ion selective. The ionophore was observed to display preferential extraction of Mg2+ over Ca2+ and Ba2+ from an aqueous into an organic phase. However, no such selectivities were detected potentiometrically when the antibiotic was incorporated in solvent polymeric membranes [73]. Subsequently even cyclolactames, which showed some preference for were evaluated [74]. Another natural carboxylic polyether antibiotic, A23 187, whose chemical constitution is shown in Figure 5-9, is generally used for Mgz+-transport studies in electrophysiology [75,76]. There was excellent discrimination of all monovalent ions against magnesium ions in a fiber optical probe [77]. The logarithmic selectivity coefficient over calcium, however, was -0.4 in the environment of a liquid PVC membrane containing 71 wt% dibutyl sebacate as a plasticizer. These results were in contrast to others who reported selectivity sequences of Ba2+ > Ca2+> Mg2+ [78].

w+,

Noncyclic Synthetic Ligands Di- and tri-oxaalkane diamides have investigated for some years as possible synthetic neutral ligands for alkaline earth cations. The N,N-di[( 1l-ethoxycarbonyl)undecyl]-N,iV',4,5tetramethyl-3,6-dioxaoctaneamide, ETH 1001 (Figure 5-10 (1)) has been reported, as the selective recognition molecule in an "improved calcium ion-selective electrode based on a neutral carrier" [79]. Success with this type of compound as a host for calcium gave rise to ab initio calculations of interactions between small host molecules and calcium as well as magnesium ions.


229

Model Calculations Based on an electrostatic model, initial calculations of the interaction of different ions with water of hydration in the gas phase were made and related to the dipole moment and polarizability of the coordinating functional groups, the thickness of the ligand shell, and the radius and charge of the ion. Ligands which incorporate coordinating groups with high dipole moments were predicted to show a preference for Mg2+.For example, 3-oxapentane diamides were supposed to form a 1:2 complex to the magnesium ion by hexadentate coordination of the cation in an octahedral coordination sphere. Nevertheless, the formation of the highly lipophilic Ca2+-ligand complex with 1:3 stoichiometry was suggested as the origin of the preference for calcium ions [80]. Interactions of Ca2+and Mg2+ with ionophores were studied by using a pair-potential model based on ab initio SCF (self-consistent field) computations. Pair potentials for model complexes with N,N-dimethylacetamide, N,N-dimethylbutyramide, and malonamide were obtained. The interaction energies for 271 different complexes with amides were fitted by a least-squares procedure [81]. Maximum free energy was calculated for the planar conformation of malonamides in contrast to N,N-dimethyl acetamide, N,N-dimethyl butyramide and the 4 5 O twisted conformation of malonamide. The optimal Mg2+-0 distance of 187 pm and Mg2+-O-C angle of 135O were evaluated, compared with a Ca2+-0 distance of 225 pm for the malondiamide complex [82]. The maximum free energy of interaction between Mg2+ and the malondiamide unit of -675 kJ mol-1 was computed, compared with -483 kJ mol-1 for Ca2+.

Membranes with Lipophilic Di- and Triamides as Ionophores Incorporating Cation Exchanger Sites The Mg2+-selective carrier ETH 1117 (see Figure 5-10 (3)) was used as a test compound for evaluating the changing selectivities of poorly selective carriers related to varying concentrations of KTpClPB (potassium tetrakisb-chloropheny1)-borate) added to the membrane bulk (see also section 4.4.5; selectivity data refer to SSM measurements, section 4.3 and Appendix 11). It was confirmed theoretically and experimentally confirmed that an optimum composition of the membranes with respect to the borate/ ionophore ratio exists, comparing ions with different valencies. For divalent cations and complexes with 1:2 stoichiometry (iodigand) an optimum molar ratio of additive to carrier of about 70 mol% was evaluated [83]. In a next step, electrically neutral lipophilic bipodale and tripodale carriers based on succinic and malonic acid diamides were systematically screened for their ability to distinguish alkaline earth metal ions and Mg2+ specifically from alkali metal ions [84]. According to model calculations indicated that preference for Mg2+ was achieved by an octahedral coordination of the cation with the 0 atoms present in highly dipolar ligand groups. The interaction of the ionophore N,N-diheptyl-N,N'-dimethyl-succinamide (ETH 1117 (3)) with Mg2+ was corroborated by 13C NMR in CDCh,. The solubility of Mg(SCN)2 in the

230

5 Porentiometric Chemical Sensors and Biological Applications

3

5

ETH1117

ETH 1224

Figure 5-10. Some of the most relevant compounds tested for their discrimination of physiologic background ions against magnesium ions. (1) N,"-di[( 1 I-ethoxycarbonyl) undecyl]-NJV',4,5-tetramethyl-3,6-dioxaoctanediamide; (2) dibenzoylmethane; (3) N,Mdiheptyl-N,N-dimethyl-succinamide(ETH 1 117); (4) cyclo(~Pro-~Leu-)5; (5) 1,13-bis-[4'-(3"phenyl-1",3"-dioxopropyl)-phenyl]-tridecane (ETH 1224); ( 6 ) N,M-diheptyl-NJV"'dimethy1aspartamide (ETH 2220); (7) N~-octamethylenebis(ZV-heptyl-N-methyl-malonamide (ETH 4030); (8) N~'-octamethylenebis(N-heptyl-N'-methyl-malonamide) (ETH 52 14); (9) (N&~'-imino-di-6,1-hexanediyl)tris(N-heptyl-N-methyl-malonamide) (ETH 5282); ( 10) (M,M'&"-imino-di-8,1-octanediyl)tris(N-heptyl-N-methyl-malonmide)(ETH 7025)

23 I

-N '

4

6

9

ETH5282

n=6

10 ETH7025 n = 8 11 ETH7052

n=lO

ETH2220

232

5 Potentiomeiric Chemical Sensors and Biological Applicaiions

presence of the ligand indicated a 2:3 stoichiometry (Mg2+ : ligand). The spectral data however indicated at least one further stoichiometry. The ligand preferred Ca2+ over Mg2+ by a factor of 20, but rejected Na+ with respect to Mg2+ by a factor of 100, and K+ by a factor of 10. The ionophore was suggested to have sufficient selectivity for intrucellulur Mg2+ measurements. The PVC liquid membranes were prepared with o-nitrophenyl octyl ether (oNPOE) and 50 mol% potassium tetrakisb-chloropheny1)borate (KTpClPB) relative to the ligand. With the physiological intracellular ion background, the detection limit was at 10" molL free Mg2+concentration. Microelectrodes had been realized [85]. Out of the class of diamide carriers, a highly Mg2+ over Ca2+ selective carrier was presented: the N,N'-diheptyl-N,N'-dimethyl-aspartamide(ETH 2220 Figure 5-10 (6)) which rejects Na+ and K+ by factors of 400 and 200, and Ca2+by a factor of 300 [86]. Unfortunately, there was severe interference by hydrogen ions, which limited the application to hydrogen ion buffered solutions at pH values 8-9 (see also Appendix 11). Homologs of N-methyl-N-heptyl-malonic and succinic acid diamide bridged by methylene moieties were synthesized in order to prepare bipodale carriers. They were incorporated in membranes with 70 mol% lipophilic borate KTpClPB relative to the ligand. ETH 4030 (Figure 5-10 (7)) exhibited the highest rejection of Na+ and K+, at about equal selectivity for Mg2+ and Ca2+ [14b, 871. Through the choice of the plasticizer, the selectivity was tuned to a large extent. Chloropdfin was optimal in respect of equal selectivity for Mg2+ and Ca2+and high discrimination of Na+ and K+, prepared for a water hardness assay. Unfortunately the sensor concept proved unavailing, of the hardness could not be computed, owing to the unknown proportion of one ion to the other in water and the different activity coefficients [88]. The logarithmic selectivity factors for sodium and potassium ions were up to -3.8 and -3.7, respectively. A new synthetic neutral carrier N,N"-octamethylenebis(N-heptyl-N-methyl)malonamide (ETH 5214, Figure 5- 10 (8)) in o-WOE for intracellular magnesium activity measurements has been reported [70] (see also Appendix 11). ETH 5282 (Figure 5-10 (9)) (N~~'-imino-di-6,l-hexanediyl)tris(~-heptyl-~-me~ylmalonamide) was the first tripodale ligand based on malondiamide subunits. This ligand was dissolved in plasticized PVC membranes and initially evaluated by realistic serum measurements [32]. The calcium activity present at physiological concentrations still interfered, but could be corrected for by chemometric calculations. The logarithmic selectivity coefficient against calcium was -0.8. The selectivity over the monovalent ions in o-NPOE with 150 mol% lipophilic borate relative to the ionophore was just sufficient. This membrane composition was regarded as a reference for further evaluations. Simultaneously the SSM procedure was standardized for improved comparability of the results. The ionophore was assumed to complex in a 1:1 stoichiometry with respect to the selectivity-enhancing ligandhorate ratio. Unfortunately the Mg2+-ligand complex could not be crystallize for X-ray structural studies (see also Appendix 10). The tripodale ionophore ETH 7025 (Figure 5-10 (10)) (N',N",N"-imino-di-8,1octanediyl)tris(N-heptyl-N-methyl-malonamide)was reported in connection with measurements in human serum samples [33, 891 (see section 5.3.4). The lipophilicity was increased by two units compared with ETH 5214, the logarithmic selectivity coefficient over

5.3 The Magnesiwn-SelectiveElectrode

233

calcium was improved to almost -1 .O, accompanied by an improved selectivity over monovalent ions. The flexibility of the selectivity scale associated with the composition of the bulk membrane allowed the preparation of two microelectrodes based on ETH 7025, one for intracellular and one for extracellular use [89]. The optimization of critical parameters of the magnesium-selective liquid membrane were reported subsequently. Supported by highly lipophilic plasticizers, the selectivity over calcium and the monovalent ions could be improved to a logarithmic selectivity coefficient of 15 over Li+ and Na+, -3.5 over K+ and, -1.5 over Ca2+ [14b, 901. The selectivitiy of the electrodes is strongly related to the composition of the membrane and ligand concentration in different magnesium / calcium activity ranges (see section 4.3). These facts gave rise to a new membrane model [91] as well as to a special evaluation procedure for a realistic selectivity and slope of the emf response function within the relevant dynamic range [90]. Unfortunately, the highest discrimination of the background ions was only available by applying highly lipophilic plasticizers (see section 4.4.1).However, the plasticizer exuded from these membranes. Homologs of the ligand ETH 7025, with the diamide units bridged by 6-12 methylene, groups showed a maximum selectivity for magnesium ions with 8 to 10 methylene groups. This result was supposed to be due to the necessary conformational energies for complexation and relaxation of the alkyl chains around the coordinating sites. Simultaneously, various core compounds to which diamide moieties are linked have been studied, as well as various modifications of the nitrogen substituents. A more lipophilic homolog of ETH 7025 named ETH 5405, with a dodecyl subunit replacing the heptyl subunit, was also tested and showed no loss in selectivity (see Appendix 11). The magnesium-selective ligand ETH 3832, synthesized by H. Li, showed sufficient discrimination of all background ions in measurements in blood serum, plasma, and whole blood [92]. The selectivity coefficients reported in the previous section are again slightly improved (see Figure 4-7, section 4.4), without the use of membranes which exude plasticizer. On the basis of this ligand, the calcium activity has an influence of only < 1.6%(coefficient of variation) on measured magnesium activities within the physiological, interindividual range of variation. These data were confirmed by measurements in real specimens according to the procedure proposed by Maas et al. [22]. No interference by sodium or potassium ions was observed [92] which contradicts the predictions by Bakker (see section 4.3). As a plasticizer ETH 8045 was and is still successfully applied [92-941. The characterization of the electrode was referred to 37 O C . The influence of pH and heparinate on magnesium activity determinations were evaluated. Inspired by the encouraging results of Suzuki [95], both ligands ETH 7025 and 3832 were further modified by adamantyl substituents which introduce a relatively high lipophilicity while occupying a minimum space (see Appendix 11: ETH 4375 and 7160). The adamantyl substituents force the discrimination of monovalent ions. The ligand ETHT 5506 shows a currently unrivalled selectivity pattern for the discrimination of calcium ions, accompanied by a sufficient rejection of alkaline earth metal ions. Unfortunately, the synthesis is very time consuming and entails high production costs [96]. A project involving a synthetic approach for ETHT 5506 is aimed at reducing these costs [97]. A successful alternative is proposed in

234


Table 5-3. Slope and selectivity coefficients (SSM) of magnesium-selective membranes based on the ligands ETHT 5506 [96,981, ETH 3832 [92], K22B5 [loo], ETH 5220 [97,99] and P. diketone [IOS], SD 5 & 0.1 (n = 6)

M 5506 M3832' M 5506 K22B5 3 MK22B54 ETH 5220 p-diketone 6

*

29.63 29.40 29.92 f0.21 29.39 f 0.11 29.98 60

-1.9 -1.5 -1.8 -2.5 -2.3 -0.19 -2.2

-3.8 4.4 -4. I -3.2 -2.7 -3.0 -2.7

-3.3 -3.4 -2.9 -1.5 -1.1 -2.15 -1.9

-2.9 -2.6

-4.2 -3.9

+0.4 -0.7

-3 .O

-3.8

-0.7

-1.9

+1.47

Membrane composition: 1.8 mg ligand, 117 mg ETH 8045 (90 mg for M3832), 56 mg PVC, 1.40 mg KTpClPB (see text); own results: n = 4-5, cv < 2.7%. see [93,94], membrane composition as l, plasticizer o-WOE. see [I001 (o-WOE; PVC; 100 mol% KTpClPB). see [93], own measurements with own membranes (o-NPOE PVC; 100 mol% KTpClPB). see [104, 1061 and Appendix 11. see [lo51 operated at pH 10 (12 wt% ionophore, 60 ~% dibenzylether, 1 wt% KTpCIPB, 27 wt% PVC) and Figure 5-10.

Appendix 8 [98]. A membrane prepared with ETH 8045 as plasticizer, PVC, and 155 mol% KTpClPB relative to the ligand induces a selectivity pattern which satisfies the required specifications for measurements in whole blood, serum, and plasma (see Table 5-3). (For further details see section 5.3.4). For Li-heparinate, frequently used as anticoagulant in heparinated tubes, a logarithmic selectivity coefficient of +0.2 is required (see Appendix 8). The selectivity pattern of M 5506 reacts very sensitively to changes in the membrane composition, however it is more robust to varying borate concentrations, compared with M 3832 and membranes containing ETH 7025. Based on the previous series of ligands, an explanation of the selectivity pattern was sought. The bidentate "monomers" as well as various core compounds were studied systematically (see Figure 5-11, see also [99]). The ligand ETHT 5506 incorporated into the membrane medium mentioned above must provide a thermodynamically optimum preconformation since any structural changes destroy the magnesium-selectivity. The total number of magnesium-selective carriers prepared over more than 20 years and evaluated in potentiometric electrodes was estimated to be close to 200 compounds. Between

5.3 The Magnesium-Selective Elecrrode

-

lipophilic amide terminus

235

--core

bridge

recognition site

yf5 (ETH 5506); A, B, C, = CH2; X, Y, Z = 0 ; y€6 (ETH 5507);A, B, C,X, Y,Z = 0 yf7;A, B, C, = CH2; X, Y, Z = S yf8;A, B, C, = 0 ; X, Y,Z = S

Figure 5-11.Structural modifications of ETHT 5506

1989 and 1992, at least 44 compounds were systematically synthesized and tested (for some of them see Appendix 1l), by a combinatorial chemistry-like approach. The analytical methods used for characterizing the compounds were standardized, and two reference membranes were defined, a blank membrane (without ligand) and a standard composition (see Appendix 8).

Developments by Other Researchers Six papers presenting magnesium-selective compounds were published, treating comparable techniques [77, 100-1061. From the selectivity data collected in Table 5-3 it emerges that discrimination sufficient of both calcium and monovalent ions is very critical (see Table 5-2). One device is based on the carrier ETH 5220 [97, 991 which just sufficiently discriminates the monovalent ions, taking the calcium activity into account in the calibration procedure (see Table 5-3). Nevertheless, calcium and magnesium are detected with the same sensitivity. The calcium activity is represented mathematically as the point of intersection of the time dependent response functions of the two electrolytes. Other groups engaged in ionophore synthesis are exploring further concepts [loo, 1051. In both cases, the ionophore is strongly discriminating for calcium ions, but the discrimination of sodium is insufficient. In [ 1051, the working pH is 10. This confirms that there is some competition of the magnesium ion with hydrogen ions, as noticed in our own experiments. The approaches adopted so far do not comply with the requirements specified for the determination of electrolytes in biological samples. Reviews published in 1991-1992 cite only one of these approaches [107-1091.

236

5 Potentiomerric Chemical Sensors and Biological Applications

Conclusions Many examples presented in Appendix 11 show that the selectivity of the ligands is associated with the presence of one secondary amine in the diamide moiety. Based on IR-investigations, preformation of the ligand associated with a resonance structure stabilized by intramolecular hydrogen bridging was shown [99]. In this case, the magnesium ion has to displace the hydrogen ion for complexation. The case of ETH 2220 demonstrates that Mg2+ dominates the potentiometric response if a basic hydrogen acceptor group is adjacent to the diamide moiety. Under these circumstances, no hydrogen bridge is formed, or displacement of the hydrogen is highly facilitated, and the carbonyl group is easily accessible for coordination of the Mg2+. It was shown by 13C N M R that the conformations of the amides about the C-N bond are not identical for adamantyl- and heptyl-substituted amides. The tertiary amide carbonyls exhibit only a single signal for the adamantyl-substituted ionophores, in contrast to those of ETH 7025 and ETH? 5506 where the carbonyl moieties of the tertiary amides exhibit a split 13C NMR peak at 233 K [96, 991. The bulky substituents must force the tertiary amide groups into a single conformation which is more favorable for coordination of Mg2+. These results are consistent with modeling calculations where various conformations of the "monomers" were involved (for a more comprehensive discussion see [1 lo]). The molar borate:ligand ratio indicates the stoichiometry of the ion-ligand complex, which is 1:l for the tripodale ligands discussed here. For novel ligands, where the stoichiometry is not known exactly, the optimum borate:ligand ratio is titrated by preparing membranes with different ratios [ 1 lo]. In strongly apolar media, the magnesium ion has an enforced B-character, increased softness, and higher Lewis acidity (see section 5.3.1). The stronger Lewis acidity facilitates complexation to electron donor groups. Concomitantly, the clustering of water molecules in the highly lipophilic media is facilitated by a positive entropic contribution through dehydration of the magnesium ion. On the other hand, a compromise between high lipophilicity and polarity of the medium enhances the solvation of Mg2+. The available lipophilicity is restricted by the solubility of the ligand in the plasticizer, the solubility of the plasticizer itself, and the compatibility with the PVC matrix. Or incorporating the o-nitrophenyl pentadecyl ether as well as higher isologs, the membranes exude the solvated ligand within tiny drops at the surface of the membrane (confirmed spectroscopically). To account for on these phenomena, the lipophilic van der Waals interactions have to be

n

K2265

Figure 5-12. Alternative magnesium-selective ligand (for selectivity data see Table 5-3)


231

considered. Stereochemical fits between apolar sites may be inhibited by branched alkyl chains, by introducing hexyl and adamantyl groups as substituents, as well as aromatic rings substituted by halides for a simultaneously high lipophilicity (see also Appendix 7).

5.3.5 Applications In 1990, the first results derived from human serum at the thermal setting point of 3 10.15 K were published [33, 88, 1041. Spichiger et al. [33], evaluated the magnesium activity at 37 O C by an alternating measurement of serum sample and calibration solution in accord the recommendations of the Working Group on Selective Electrodes of the International Federation of Clinical Chemistry [22] (see Appendix 8). The ion concentration was evaluated with reference to an intermediate measurement of the activity of the calibration solution. The repeatability of these evaluations was 1.6 % for a mean free Mg2+ concentration of 0.57 mmol kg-1 serum water or 0.185 mmol kg-' in terms of active molality. The complexed fraction / Lemm) to the total Mg2+ concentration in serum (AAS, total contributed 24% (kgsemm concentration in serum pool: 0.75 mmol L-l). A complexed fraction of 0.45 as published traditionally may be too high, even if the serum total volume is corrected for its water concentration. In a bovine serum pool, the free Mg2+ concentration measured by the magnesium-selective electrode based on ETH 7025 accounted for 0.68 mmol k g ' f 1.6 %cv corrected for pH 7.4 (37 OC). The activity coefficients reported in Appendices 2 and 4 were taken into account. The degree of complexation was 30% [33]. Unfortunately the magnesium activity and concentration in the ultrafiltrate were not measured correctly. These data were more or less confirmed by using a more selective electrode, based on the ionophore ETH 3832 [92] (see Table 5-4). In the last two years, an alternative, practically relevant procedure for the determination of the selectivity coefficients within the physiological range ( S A M )with respect to an interfering ion background has been evaluated experimentally for magnesium-selective electrodes (see section 4.3 and Appendix 8). Table 5-4 collects data presented between 1990 and 1997 by several groups which for different types of ionophores, electrodes, and instruments. The results presented in Table 5-4 provide rather comparable information on mean concentrations of free and total magnesium ions in a reference specimen. In spite of the large number of convincing results and the high repeatability of measurements, the comparability of the instruments remains a problem, especially for a real specimen in the pathologic range [114]. Apart from these justified complaints, for a non-electrochemist the significant factors are hard to evaluate [115]. Very frequently the errors induced by the testing procedure (change in ionic strength, active molality of background ions, both in the complexed fraction and in the liquid junction potential) are larger than the real errors of the instruments. In a critical validation of the performance of instruments, as presented in Table 5-4, a high repeatability may, simply indicate a low sensitivity of the electrodes.

238

5 Poieniiomeiric Chemical Sensors and Biological Applications

Table 5-4. Selection of results of magnesium-selective measurements on human reference specimens by different electrodes and instruments

ISE-type

ETH 3832 ~921

ETH 5220 / MicrolyteR [1041 in [113]

Specimen (repetitions)

serum pool pH 7.6 ( n = 5-6) pH corrected (7.4) ultrafiltrate (n = 3) e.g., seronorm (human) pH 7.26 (n = 3) seronorm, instrument 1 seronorm, instrument 3 serononn, instrument 3

AVL 988-4 healthy adults pool serum pH 7.47 [45, 1121 ultrafiltrate pH 7.5 in [1131 human plasma (n = 20, within run) human whole blood (n = 20, within run)

Alma et al. human plasma, heparin Nova SP8 (n = 10) [1131 ( n = 74) human serum (n = 10) ultrafiltrate serum pH 7.8-7.9 (n = 10) whole blood (n = 10)

Free Mg2+ mmol (kgH,O)-'

Total Mg2+lAAS mmol

Mg2+-fraction

(LspecirneJ-l

(kgH,O)-'

0.63 f 0.001 0.678

0.977 f 0.009 0.694 f 0.004

0.69 (pH 7.4)

0.557 f 0.3 0.581 f 0.006 0.565 f 0.002 0.541 f 0.002

0.79

0.705

0.57 f 0.03 0.533 0.495

0.877 0.77 0.60

0.65 0.69 0.83

0.60 f 0.04 0.56 f0.06

0.89 f0.05 0.78 f 0.08

0.67 0.72

0.61 f 0.03 0.47 f 0.01 0.62 f 0.04

0.84 f0.04

0.73

0.60 f0.05

0.78

Lspecimen

0.584 f 0.004 0.587 f 0.005

p H Buffering and pH Correction References [45, 92, 106, 111-1 141 provide a broad information base from which to decide on the influence of pH variation, buffer composition, freeze and thaw effects, transition metals and additives such as anticoagulants, on the results of free magnesium concentrations.


239

Complexation of magnesium ions by HEPES (N-2-hydroxyethyl piperazine-N-2-ethanesulfonic acid) as a buffer component was studied and found of less significance than for calcium assays. The sample pH together with an equation to adjust the magnesium activity to pH 7.4 have been reported [92, 1061. The molar Mg2+activity can be transformed to pH 7.4 by the following equation: log &!Mg2+ (PH 7.4) = (log aMg2+ (PHX)) - (4.99 (7.4 - pHX)/s)

(5-8)

where s is the slope of the electrode function within the range of the measured Mg2+ activity [84]. The constant 4.99 is a mean linear correction factor, determined for the linear range of pH-dependent variation of the magnesium molality between pH 7.17 and 7.6. The factor 4.99/s is multiplied by the deviation of the experimental pH from 7.4. The procedure and the notation follow the recommendation by IFCC for pH-correction of ionized calcium concentrations [22d]. The factor is based on five measurements with five different electrodes incorporating ETH 3832 (see Table 5-3) and is, therefore, subject to a high degree of uncertainty (SD k 26%).

Interferences: Heparin, Oligo(siloxanes), TransitionMetals, Organic Anions Quantitative data on the effect of heparin, were aquired in a symmetric potentiometric cell, as reported in detail in sections 4.7 and 5.2 [ l l l ] . Further results were reported on the influence and discrimination of heparin, transition metals, organic ions, and the storage of samples [45, 96, 11, 112, 1131. The influence of (o1igo)siloxanes used as lubricants in blood tubes for anaerobic sampling, was found to be significant [93]. In addition, the effect of abnormally high thiocyanate concentrations has been discussed [1141.

5.3.6 Stop-Flow Analysis, the Continuous Flow System The following studies were made with the carrier ETH 3832. In order to avoid problems with the adsorption of biological matrix components and the equilibration period of the whole membrane in a static system, a thermostatted flow-through system made of polysulfone was constructed (see Figure 5- 13). A standardized measurement procedure was used and delivered highly reproducible results. In a stop-flow procedure, sampling times of 20 s for aqueous calibrators and 10 s for plasma were fixed. Data acquisition was made over 2 min under static conditions (stop-flow). Emf data for the last 18 s, corresponding to 6 acquisitions every third second (n = 6) were averaged. The system was operated continuously at 310.15 K. The emf data of samples were referred to the assigned values of the aqueous calibrators which were measured in an alternating pattern. For more details see [92a]. The flow-through system can operate up to four membranes simultaneously.

240


In order to evaluate the selectivity coefficient within this system and the error due to the calcium ion interference, a membrane containing 2.5 wt% carrier ETH 3832 and 155 mol% KTpClPB was introduced into the flow-through system (for details see Appendix 8). The calcium activity was calibrated corresponding to a calcium ion background of 1.2 x 10-3 mom. The calcium ion concentration was varied between 1 .O and 1.4 x lW3 mol/L relative to an invariable magnesium ion background concentrations of 0.8 x (VIM, see also section 4.3 and Appendix 8, procedure 111). The selectivity versus sodium and potassium ions was tested in the same way. No further ions interfered. The maximum inaccuracy induced by changing the calcium ion concentrations was f 2.2%. The response function was transformed to a Nikolsky-type function. The selectivity coefficient was treated as a correction factor kELca for the specific concentration range, and was iterated within the SAM procedure (see section 4.3 [90, 92, 1111). A logarithmic selectivity coefficient for magnesium against calcium of -1.05 resulted from the best fit to the experimental data. The slope in this range was lower than ideal, and was used for calculations of the selectivity factor. The conclusion drawn from these experiments was that the electrode

I 13

11 14

111

15

Figure 5-13. View of the potentiometric flow-through system thermostatted to 37 OC. (1) support (aluminum); (3, 4) body of the electrode segment (four adjoint segments); (7) flowthrough channel for the thermostatted water; (8) ion-selective solvent polymeric membrane; (9) sample channel; (10) thermoelement; (11) capillary with internal electrolyte; (12) internal electrolyte of the ion-selective half-cell; (14) body of the internal AglAgC1-electrode of the ion-selective half-cell; (15) screw to connect the ion-selective membrane tightly to the sample channel. The position of the free-flow HglHgzClz reference electrode is at the end of the flux direction. It is adjacent to a reference electrode segment. The 1 molL KCl is under a pressure of 1.2 bar; system operated with a flow rate of 2.5 mL min-I; flux of specimen from right to left


24 1

function must be fitted and evaluated exactly for the range of ion activities under biological conditions. The selectivity factors and consequently the inaccuracies were calculated and considered with respect to the tolerable errors (see Appendix 4). The continuous flow system is part of the modular system CHemsens where the polymer module, the transducing element and the sensing layer can be handled independently of each other. This extremely flexible and versatile system is used with various techniques, such as potentiometric, amperometric, and optical transducers, and sensing layers for serial and parallel analysis. A Swiss patent application has been made [I 161.

5.3.7 Significance of Magnesium-SelectiveAssays The significance of a magnesium-selective assay and of the information yielded by determinations of magnesium concentrations is generally as heatedly discussed as the role of a magnesium therapy, e.g., in acute mycardial infarction [117]. Regarding the biological impact of the ion itself, it is undoubtedly highly significant for physiological and pathological processes. However, whether measurements in blood have any meaning is a different question. Anyway, highly reliable results are mandatory for its clinical validation, owing to the narrow individual scattering range around the physiological setting point [1181. On the other hand, appropriate technology must be available if investigations are to continue to develop. The availability of a magnesium-selectiveelectrode drives medical and biological investigations, especially in veterinary medicine, where disorders of calcium, magnesium, and phosphorus homeostasis have been suggested to cause, e.g., the typical parturient paresis of dairy cows [I 191. Since the interindividual scattering range is suggested to be much broader than the intraindividual range, the reference range allows one to distinguish only very severe changes in the magnesium concentration (> k 0.14 mmol L-I). Unfortunately, only data for total magnesium ion concentrations exist so far. The individual variations need to be determined in longitudinal studies, in order to get fine-tuned reliable information. Magnesium deficiency is suggested as the underlying cause of various diseases [50,51a, 51bl. On the other hand, the magnesium-selective electrode incorporating ETHT 5506 or ETH 3832 allows one to trace impurities in buffer solutions, mimicking the intra- and extracellular medium down to the micromolar range [120]. On this basis, it is feasible to determine association constants of physiological ligands to Mg2+ accurately and to monitor the influx and efflux of Mg2+ over the cell membrane in isolated cell suspensions. With an electrode incorporating ETnT 5506, continuous monitoring of Mg2+ in 0.5-0.9 mol/L Ca2+ solutions containing the intra- and extracellular background of monovalent ions was possible down to 10 pmol/L [120]. The availability of the magnesium-selective electrode also gives rise to the suggestion of repllacing optical assays by the electrode in high-through-put analyzers for clinical chemistry [22].

242


5.4 Microelectrodes for Intracellular Measurements The term microanalysis has changed from being concerned with quantitative analysis on the microgram scale, the field of trace analysis, to a much broader concept that involves a large variety of different methods, devices, concentrations,and sample volumes, as well as analytes. Microanalysis has changed to nanochemistry and nanoanalysis which are concerned with single molecules or the molecular texture of a material [122]. Chemical sensors which transform the chemical property of a system into an electrical signal have opened up new dimensions in micro- and nanochemistry during the past decade. Overwhelming research efforts have been and are still devoted to the development of micro- and nanoelectrodes, especially in the area of biosensors, for direct measurements in tissues [70, 121-1311. Miniaturized voltammetric sensors are of special interest since the electrode characteristics are mostly improved when operated on the micro- and nanoscale level (see section 1.4.2). Developments and capabilities of ion-selective potentiometric liquid-membrane m i c m and nanoelectrodes will be discussed in this section. The term microelectrode was introduced for electrodes with tip diameters in the range of 0.2-10 pm [132]. The smallest tip diameter reported for ion-selective microelectrodes based on neutral carriers are 0.089 pm (0.05-0.07 pm inner diameter) [ 1331. Submicron tips (nanoelectrodes ) have been realized. However, even K+-selective electrodes with a tip diameter of 30-100 pm have been called microelectrodes [ 1341. As a rule of thumb for intracellular measurements, the tip diameter of a microelectrode should be < 1/20 of the largest diameter of the cell, in order to keep the cell alive [135]. This rule confines the useful tip diameter to c I pm, a cell of 20 pm diameter being considered large. With this size, the electrode tip penetrates the cell membrane bilayer without injuring the cell. In addition, intracellular potentiometric assays have to allow for the membrane potential of the living cell. That means that two electrodes, or a larger combined electrode, have to be introduced and placed within the same cell [136]. Ion-selective microsensors were reported to be "exceptional microchemical devices" because they were the smallest analytical tools available, and because they offered surprisingly low detection limits [137, 1381. The most prominent representative was a Ca2+-selective microelectrode based on a synthetic neutral carrier (ETH 129) [139]. This carrier showed an exceptionally high selectivity (fixed interference method, FIM, and SSM) against all intracellular background ions such as potassium, sodium, and magnesium ions, and a detection limit of 10-9 M Ca2+. These Ca2+-selective sensors have been inserted in single cells of frog skin epithelial tissue with diameters of S 10 pm (cell volume: 0.5 x 10-12 L). The tip diameter of the electrode was < 0.18 pm (effective spherical volume of the membrane involved: L) [140]. With a tip diameter of 1 pm and an effective spherical volume of the membrane involved of lw5L, the number of ions detected at the detection limit is equal to mol Lx mom), formally equivalent to 0.6 ions. At this detection limit, less than one ion is exchanged. This can be explained by the fact that the exchange rate has not been taken into account. However, the signal is effectively generated by a mean exchange rate of ions, the ion exchange being very fast. These extreme measurements can be performed only if the detection volume of the membrane is in equilibrium with an adequate Ca2+-buffering system. At these low detection

5.4 Microelectrodes for Intracellular Measurements

243

limits, ions can be extracted from the conditioned membrane to the sample solution. This results in a non-Nernstian, non-Nicolsky-Eisenman behavior. On the basis of these encouraging results, magnesium-selective microelectrodes were developed for applications to blood cells [ 1411. Two types of Mg2+-selectivemicroelectrodes based on a synthetic neutral carrier (ETH 7025) were realized both containing poly(viny1 chloride). The first microelectrode was designed for intracellular measurements, the second for simultaneous extracellular measurements of the Mg2+-activity.On the basis of this concept, the magnesium ion exchange between the intra- and extracellular space can be monitored. The two electrodes are different in their selectivity pattern (see Figure 5-14). The first electrode with 60 mol% KTpClPB was developed for intracellular measurements where no interference by other cations occurs. (Taurine was later found to be of great interest as an interfering cation; however it was not tested in the original investigations). The discrimination of potassium ion was enhanced up to the point at which the electrodejust shows no interference with the intracellular K+-activity. Basically, the same electrode with ETH 7025 incorporated as a neutral carrier can be applied to extracellular measurements. By adding 150 mol% borate (KTpClPB) relative to the ligand, the sodium and calcium discrimination could be further enhanced, but the electrode shifts to a Hofmeister-like behavior (see section 3.1). Lipophilic ions such as AcCh+ are preferred. The selectivity of the microelectrode against Ca2+ is not sufficient to prevent interference of Ca2+ (log = -0.7). Extracellular calcium activities, which exceed the magnesium activity by a factor of 20, have to be monitored simultaneously by a Ca2+-selectiveelectrode and treated chemometrically for the sake of accuracy. In MgC12 solutions.with a typical intracellular background (10 mmol/L NaCl, 100 mmoYL KC1, 0.001 mmoYL CaC12), microelectrodes of type 1 show nearly ideal theoretical response functions (slope: 29.1 f 0.5 and 25.5 k 0.5 mV per decade of ion activity). The detection limit is at log aMg = -4.8 If: 0.2. Over 2 weeks operation in aqueous solutions, the microelectrodes suffered practically no deterioriation of their response function and detection limit. A conditioning period of 2 4 4 8 h is recommended. The response behavior of bulk membrane microelectrodes is relatively slow (1-30 s). Hence, speedy exchange reactions in the millisecond range, like that of Ca2+ between the intra- and extracellular compartments, cannot be monitored by microelectrodes. In this case complexation of the analyte ion to fluorescence indicators is used, combined with microscopy (the complexation reaction rate of charged carriers in free solution is > lo8 mol-* s-l; the speed of light is 3 x 108 m s-l). Only slow activity changes or static activities are accessible with microelectrodes. In cytoplasm, Mg2+ is involved in exceptionally slow biochemical exchange reactions. This is in agreement with the property of the magnesium ion as a typical structure-conservingion (see section 4.4.3). A general limitation in further miniaturization of this ion-selective microsensor is the extremely high electrical resistance of the bulk liquid membrane phase (Rm = 34 k 6 x lo9 a). This requires highly developed operational amplifiers with input impedances, of at least 1014 Q, and input currents i in the range of A (fA, i >p/v) is present in the membrane phase, the shape of the response curve becomes independent of the stoichiometry of the complex ILv+. From Eq. 6-14, cases P with increased and decreased sensitivity of the response curve or Kexch can be deduced. &xch increases, e.g., with the stability constant of the ion-carrier complex and increasing pK, of the indicator, or increased hydrogen activity, or lower pH. In these cases the detection limit in the analysis of up+ is decreased. (For more details see [97, 1321). As may be noticed from the literature, different symbols for the ionophore, chromoionophore, the charges, and the stoichiometries have been used for different generations of optodes. It has proved necessary to introduce intralaboratory conventions for nomenclature to clarify the situation.

6.4.6 Medical Assays: Applications to Diluted Plasma The pH value, the influence of proteins at the surface, and the ionic strength of the sample and the membrane phase are essential parameters influencing the reliability of calibration of assays in blood. However, they are often neglected. Many assays devoted to direct quantification of analytes in blood or other biological samples show important uncertainties. Thus, the ionselective optode membranes have been applied to diluted solutions with buffered pH and ionic strength. Under these conditions total electrolyte concentrations have been evaluated, fluctuating over a small range of variation around a mean biological setting point. The measured mold ion activities are calibrated for concentration determination, comparable to potentiometric sensors. The calibration also attempts to take account of a background of interfering ions within a mean dynamic concentration range and at an optimum pH of the diluted sample. Calculations have been reported for diluted and undiluted solutions (see Appendix 9). Method comparisons between total concentration assays in diluted samples and directreading methods show the problems discussed in section 3.4. However, optical sensors and potentiometric sensors applied to the diluted plasma sample are both sensitive to molal ion activities. Comparisons with measurements by ion-selective electrodes, implemented in analyzers with large through-put for sodium, potassium, and chloride assays in the diluted sample [ 134, 1351 exhibit no fundamental methodological discrepancies. For comparisons with direct-reading assays, the analysis of a profile of analytes, such as a total protein concentration and lipid profile is recommended. As a reference, about 45%of the calcium ions are complexed to proteins. The free calcium ion concentration, i.e., the biologically active fraction of calcium, is in thermodynamic, pHdependant equilibrium with the protein concentration. The complexation of calcium to plasma proteins is a reversible process which can be described by an equilibrium between the total protein concentration [Prz-] with a mean overall charge number z- according to the isoelectric point IP of the participating protein fractions, the calcium ion concentration [Ca2+] and the

286

6 Optical Sensors, Optodes

calcium-protein complex [Ca$%](2P+Z) ,where p is the overall number of complexed Calcium ions. Kq is the equilibrium constant [136, 1371, dependant on pH and temperature (in vivo and in vitro): (6-16)

In the physiological medium, a mean IP of 4.96 is assumed [138]. For total concentration measurements in vitro, the pH is decreased to pH around 4.0 to liberate the calcium ions from the complexes. Determinations of total electrolyte concentrations in diluted samples are implemented in clinical analyzers with high sample through-put. Reference methods for the evaluation of total electrolyte ion concentrations, apart from ISES, are flame atomic emission spectroscopy for total sodium and potassium, atomic absorption spectroscopy for calcium and magnesium [ 139, 1401, and spectrophotometric methods based on ion complexation for calcium [141], magnesium and chloride [142]. Since ISE modules require a special compartment in the analyzer as well as special care and service, optode membranes have been developed as alternative tools for quantification of total sodium, potassium, calcium, and chloride concentrations. For thermodynamic equilibrium assays, constant pressure is assumed (daily atmospheric pressure), neglecting volume changes due to changes of the spatial distribution of the participating entities. Temperature is controlled; measuring systems are geneally thermostatted to 310 K for medical use. This was not possible for first manual evaluations with optical membranes as reported in the following.

6.4.6.1 Accuracy Assessment The following example, which deals with the accuracy of the chloride optode, illustrates how difficult the experimental evaluation of accuracy is. With the chloride optode, the chloride concentration is determined within the diluted sample. For calibration of the optode, the same commercial standards were applied as for the calibration of the ion-selective electrodes in clinical chemical analyzers (BM Standard). Based on constant ionic strength of the pHbuffered aqueous sample solution, ion concentrations are calculated on the basis of the measured ion activities. These calculations can be applied to real samples, 10-20 times dilution, with pH and ionic strength buffers, and assuming identical dissociation regarding the complex background. A deep-frozen (T c 253 K) Japanese horse serum (HS) was analyzed as a certified reference material. The chloride concentration of the reference sample was evaluated by coulometry. The human plasma samples as well as the Japanese horse serum were analyzed by the optode and simultaneously by the automated system at the University Hospital Zurich (USZ). All results evaluated by the optode showed values 8-10% lower than those analyzed in the USZ. This difference can be explained by the following facts (Figure 611).

6.4 ChemicalSensors Based on a Second Component: Simon Optodes

281

The concentration values of the automated potentiometric procedure (USZ) showed up to 3% higher levels for the HS sample than the assigned value. The value of the BM standard was 5% higher than the assigned value. Let us assume that the assigned value of the HS standard represents the true level of the chloride concentration. Then the BM standard must be 2% too concentrated, and the calibration level of the automated method is 3% too low. If the optical sensor is calibrated by the BM standard, a true value of 102 mmoVL is now calibrated to 100 mmo1L. This means that all determined concentrations of unknown samples will be decreased by 2%. However, the optical sensor delivers results which are 5% higher than those of the automated analysis. Consequently, the difference between the calibration of the automated analysis and the sensor rises to 7% for all samples. Thus, the true inaccuracy of the optode lies between -1 and -3%, and is smaller than the inaccuracy of the calibration of the automated system. Experience with quality assessment in clinical chemistry, related in part to different levels of know-how of the staff, indicates that identical results and reproducibility between different laboratories may be more important than true values. In this respect, it is often preferable to adjust analytical results according to the existing reference values for healthy subjects.

~

INACCURACY OF THE CHLORIDE OPTODE AS

, COMPARED TO A MAIN FRAME ANALYSER. 105 -

-

ANALYSER :

7

ANALYSER:

TRUE VALUE:

102-

T

ANALYSER: HS SAMPLE

98 -

95

I

INACCWCY CALIBRATOR *2%

*------

C

L-BM-;

TRUE VALUE:

100-

TOTAL ERROR OPTODE / ANALYSER 8 10'lo

INACCURACY ANALYSER

4.1. WACCURACY CALIBRATION -2*I*

- 2 TO -3%

Secondary standard: deep-frozen Japanese horse serum, HS (cations are determined by AAS with reference to a primary horse serum standard evaluated by isotope dilution analysis), chloride is determined by coulometry as a reference method; calibrator: BM standard for electrolytes, with buffered ionic strength.

Figure 6-11. Graphic representation of the values evaluated for a certified standard HS sample and a regular BM standard solution by the optical sensor as well as by potentiometric sensors in diluted specimens. For calibration of the chloride optode, a BM standard was used, and an automated analyzer was calibrated independently. Where both methods were calibrated by HS, the procedures agreed within 2-3% [141]

288


Assigned values are evaluated by reference laboratories which guarantee a reliable standard of analytical procedure and a high standard of instrumentation (see section 7.3.3 and Figure 3-3). A large interlaboratory variation is reported in the assignments, however. The experiences made with quality assessment in clinical chemistry, related to different levels of know-how of the staff amongst others, mean that identical results and reproducibility between different laboratories may be more useful than true values. In this respect, it is often preferable to adjust analytical results according to the existing reference values for "healthy" subjects.

6.4.6.2

Method Comparison for Calcium-, Sodium-, Potassium- and ChlorideSelective Assays

For a detailed description of the practical procedure see [104, 105, 107, 108, 1171. Two examples of a method comparison by two independent, orthogonal statistical methods are reported. The problems with calibration, standardization and method comparison for the chloride optode membrane was discussed in section 5.1. The results of the least squares linear regression procedure were compared with a nonparametric regression analysis by Passing and Bablok [143]. The results of both methods were consistent [104]. The hypothesis of linearity was not contradicted. The first-order linear regression functions are reported here. The results of the reference method are represented by X and the results of the optode membranes by Y, respectively. The following regression equation was calculated for the calcium-selective optode membrane from the comparison of the results of 14 samples in the range of 1.2-3.8 mmol/L. The interrelationship between the results of the optode membrane and the photometric procedure is approximated by the linear function: YOptode

= (0.148 f0.37) + (1.02 rt 0.15) Xphot

(6-18)

with a residual standard deviation sy.x of 0.16 mmol/L and R2 = 0.946 for n = 14 paired results of plasma samples (for correlation between optode membrane and AAS, see [65b, 104, 1441). Method comparison for the sodium-selective assay between the results of total sodium concentration measured by indirect potentiometry (ISEs) and the values of the optode membrane: A good correlation over a range of 83-153 mmol/L is equally demonstrated by both linear regression procedures. Basically, ISEs and optode membranes respond to the same physicochemical parameter. Thus, they demonstrate a closer relationship compared with FAES. The correlation between ISEs and the optode membrane is approximated by the linear regression function. Yoptde = (1.03 f 1.05) + (0.995 & 0.047) X~SE

(6-19)

with R2 = 0.976, sy.x = k 3.29 mmol/L, and a mean = 113.4 It 1.16 mmofi for paired results of 20 samples. The confidence intervals of all. first-order linear regression parameters are estimated on the 95% level of significance (correlation between the results of the optode membrane and FAES, see [65b, 104,1441).

6.4 Chemical Sensors Based on a Second Component: Simon Optodes

289

The results of the evaluation of sodium, potassium, calcium, and chloride ions have been discussed in [104,105, 107-1091, in detail, and in [65b, 144, 1451. The conclusions are reported in Table 6-2.In the references cited, it is shown that the method comparison between the optical membrane assay and FAES or AAS is clearly more problematic than with ISEs in diluted samples. Reference procedures: For the chloride assay, the two standards HS (Japanese horse serum standard) and BM (Boehringer calibration solution) were evaluated by indirect potentiometry (ISE) on a Hitachi 747 instrument. The optode was standardized by both standards. The inaccuracy was explained up to 50% by the deviation of the mean values of 2-3% between the standards. Thus, the level of the standard BS used for calibration of the indirect automated ISE procedure running on the Hitachi 747 and the optode membrane assay were corrected by HS.

6.4.7 Analytical Performance Parameters The reliability and applicability of an optode sensing membrane is decided by looking at a number of analytical performance parameters. Of primary importance are: selectivity, dynamic range, detection limit, sensitivity, life-time, mechanical and chemical stability, ruggedness with respect to the sample matrix, and the shape of the response function. The internal variables of any optode membrane derive from the theoretical response function (Eqs. 6.12 and 6.13)and influence the analytical parameters directly. These are: the absolute and relative stability constants of the complexes; the stoichiometric coefficient of the complexes; the charge numbers of the analyte, the ligand, and the chromophore; the pH of the sample (solution, vapor, gas); the activity and osmotic coefficients of all participating species; and last but not least the concentration and amount of components incorporated within the,membrane. In addition, the degree of hydration and the partition coefficients (lipophilicity,see section 4.6) of all components have an influence on the general performance. Unfortunately, displaying the relative changes in the optical spectrum of the chromoionophore provides no information on the realistic signal intensity or the requirements for an alternative optical set-up. On the other hand, it provides insight as to what extent the theoretical assumptions are matched by the experimental results. The time-related response has, so far, been much more influenced by the design of the measuring system than by diffusion processes within the optode membrane. The measuring system containing the optode membrane is characterized primarily by the geometry and the hydrodynamics of the cell and the liquid handling system. It has to be modified on account of the mode of application and the concept and logistics of the analytical procedure (see sections 4.2and 4.5).

290


Type of ion

Method and type of quality control samples

Assigned values, mean f 95% tolerance interval [ ~ O V L l

Results of ionsensing optode membranes [mmol/L]

162 486 159 589

2.28 f0.23 3.19 f0.32

1.93; 1.99 2.91; 3.22

o-cresolphtalein QC Nr.1 162 486 159 589

2.27 It 0.18 3.35 f0.27

AAS

Calcium

Potassium

Sodium

Chloride

QC Nr.'

FAES QC Nr. 162 486 159 589

4.80 f0.38 6.60 f0.53

ISE indirect QC Nr.' 162 486 159 589

4.65 f0.37 6.52 f 0.52

4.54; 4.67 6.67; 6.84

FAES QC Nr.* 120.8 k 2.4 135 f2.8

162 486 159 589

118f7 135 f 8

ISE indirect QC Nr.' 162 486 159 589

120 f 7 136 f 8

ISE indirect QC Nr. 162 486

117f12

120k 0.3 (n = 5)

106 f 3 (coulometry)

107.2 k 0.2 (n = 5)

plasmapool (USZ)

* Quality control samples Boehringer Mannheim GmbH, Diagnostica, 6800-Mannheim 31, FRG. * Repeatability (*2 SD) of 5 measurements.


29 I

Table 6-2. Results of the quantification of quality control samples (QC). Report on results obtained by optical bulk membranes compared with assigned values for the reference methods such as AAS (atomic absorption spectroscopy), FAES (flame atomic emission spectroscopy), coulometry, as well as complexometry-optical spectroscopy and ISEs (ion-selective electrodes), running on clinical chemistry analyzers with large sample through-put [ 1461 (assigned values are evaluated by reference laboratories)

Equations 6-7 to 6-15 provide the basis for predicting and describing the selectivity behavior, the active molality interval covered by the dynamic measuring range, the detection limit, and the sensitivity of optode membranes. The theoretical functions fit well to the experimental data in all cases investigated. An extraordinary flexibility of the system is observed when changing the stability constant and the PKa of the chromophore as well as the pH value of the sample buffer, making these membranes suitable for different applications. A brief overview of the main effects is given in [98]. Some characteristics will be discussed in comparison with electrodes in the following section.

6.4.7.1

The Selectivity of Optode Membranes

The consequence of insufficient selectivity coefficient of a cation-selective optode membrane against an interfering cation is shown in Figure 6-12. The insufficient discrimination of the interfering ion entails incomplete protonation of the indicator in the optode membranes discussed here which are based on an ion-exchange mechanism. The selectivity coefficient opt K-. is involved in the description of the response function, comparable to the NikolskyB Eisenman equation. As discussed in the previous section, the dynamic range is shifted by the PKa of the indicator. However, for optode membranes, the sensitivity and resolution of the signal vary along the pH and analyte activity axis. This type of presentation, where the response function of the analyte ion in pure solution and with a background of interfering ions are overlaid, allows one to control the degree of protonation and deprotonation of the indicator. Another type of presentation is shown in Figure 6-13, where the response functions evoked by the varying active molality of the analyte and the interfering ion are separated along the pH axis. An extensive theoretical treatment of selectivity coefficients is given by Bakker et al. [132] and in [97, 102, 1031. Comprehensive mathematical description of the selectivity behavior of a membrane requires information on the stoichiometry of the complexes, the charge numbers of all species involved, the induced spectral change accounting for the change in the complexation ratio of the chromoionophore (absorption coefficient), and the actual activity coefficients of the electrolytes and compounds involved (sample and membrane). Since these data are not entirely available, the response functions of competing species are calibrated in buffered pure and mixed solutions, analogously to the SSM and FIM method for ISEs (see chapter 4.3 and Appendix 8). The relative absorbance (1-q a) arising from the

292

--

6 Optical Sensors, Opiodes

F (OPTODE SIGNAL)

12

0

4z

LL

0 W W

log [ai + E

i#i

4

PROTONATED /

CATION INTERFERENCE

EE

=

\

pK OF CHROMOIONOPHORE

m

8 0 0-

Figure 6-12. Theoretical response function of a cation-selectivebulk optode membrane ((1-a) = f (log(aI+/UH+)). The dynamic range is shifted by the acidity constant pK, of the chromoionophore and the stability constant of the ligand; it is limited by interfering cations indicated by incomplete protonation of the indicator at the lower limit of analyte activity

varying active molality of the analyte a~"+and that of the interferent ajv+ relative to the H+ activity of the sample solution aMZ+ are plotted in Figure 6-13. The response function of the analyte species is separated from that of the interfering species by 'a parallel shift along the 10g(UMZ+)axis. In Figure 6-13, the response functi,on of a divalent analyte cation relative to a monovalent interfering ion and a stoichiometric ratio of 1 :1 are modeled. The formulation of the mass balance and the thermodynamic equilibrium between analyte and interfering species is analogous to potentiometnc sensors and can easily be derived from the basic principles set out in sections 3.1, 3.4,4.3, and 5.1. The optical selectivity coefficient for the ion exchange system with H+as reference ion is given by Eqs. 6-20 and 6-21, where q is the stoichiometric coefficient of the interfering ion:

(6-20) which is a factor in the following response function:

6.4 Chemical Sensors Based on a Second Componeni: Simon Optodes

'"1 TRA

'd 0.8

\

293

INTERFERING ION j Ion f fa.I

Figure 6-13. Selectivity plot according to the separate solution method (SSM) with a parallel shift of the response curve for different ions. Single ion response function denoted by l-a vs. log aM+, where M are the analyte ion I+ and the interfering ions J+. The arrow indicates the selectivity coefficient as the horizontal distance between two calibration curves at a fixed pH. The unspecified curve signifies the mixed response function of the analyte influenced by the interfering component. The corresponding response function is identified on the x-axis by the arrow pointing out the respective log ai or UM value

The ion coextraction system, in this case for anions, is treated analogously:

(6-22)

which is a factor in the following response function:

The selectivity coefficient is an experimental value and is not a constant, but rather a correction factor (compare section 4.3). First, the selectivity coefficient is pH dependent if the analyte and the interfering ion exhibit different valencies. The pH and charge-dependent selectivity behavior is induced by the deprotonation reaction of the indicator which varies with the charge-equivalent uptake of ions. It is not primarily dependent on the charge ratio of the

294


ions as long as indicator and lipophilic sites are in excess. Therefore, the charge ratio has to be taken into account through the concentration changes of the indicator species. Secondly, it var'ies with the ligand activity if different stoichiometric numbers are involved in the complexation. This variability of the membrane can be used for tuning the selectivity, to some degree. However, the selectivity cannot be optimized by the concentration of lipophilic sites in the same way as in an electrode. From the membrane models shown in previous sections, it is evident that the lipophilic sites are primarily responsible for charge compensation within the membrane. The selectivity coefficient is graphically accessible by plotting the single ion response function vs. log UM+, where M represents both the analyte ion I+ and the interfering ion J+ (Figure 6-12). For constant pH and constant membrane composition ,the distance between the response curves at a defined degree of protonation, preferably a = 1-a = 0.5, the selectivity coefficient can be evaluated from the intersection of the response curves with the x-axis, log UM+. If the selectivity coefficient is included in the fitting the experimental data, the theoretical curve indicates that complete protonation of the hydrogen ion carrier cannot be achieved. This has been confirmed corroborated experimentally. In many cases, it is not be possible to determine the selectivity coefficient of an optical bulk membrane for different interfering ions with constant pH or identical indicators (pK& Under changed conditions the activity values must be corrected and normalized to the conditions (pH, pKa) of the primary ion. In view of the complex thermodynamic equilibrium of a membrane involving all participating species and changing ligand activities with different stoichiometries and charge numbers, separate calibration (comparable to SSM) gives the most reliable information for comparison. Yet, the selectivity coefficient is not a constant, as explained above. Thus, we recommend that the analog to the SAM-method (discussed in section 4.3 and Appendix S), be used for determining the selectivity coefficient of complex samples. The effective selectivity coefficients may be particularly relevant in view of the cut-off value for complex sample compositions, especially in environmental monitoring and medicine.

q'

Table 6-3. Required and experimentally determined selectivity coefficients for sodiumselective optode membranes vs. a background of calcium and magnesium as interfering ions [132]. Data refer to an active molality of sodium ions log UNa of -2.27 (20-fold diluted serum sample, sodium concentration around the mean physiological setting point, see Appendix 3)

opt

PH

OPt

NaCa

NaMg

required

found

required

found

4.54

0.40

0.27

0.56

-2.37

5.54

0.40

0.47

0.56

-2.18

295


Finally, it must be emphasized that the selectivity coefficient of an optode membrane may differ considerably from that of an electrode incorporating the same ionophore. Since the ratio of the charge numbers of the analyte and interfering ion are not directly involved in estimating the required selectivity coefficent, the sample dilution factor is not directly involved either. This is different from potentiometric electrodes, where the total emf difference along the active molality axis has to be divided by the ideal slope of the response function due to the analyte ion (see Appendix 9). Hence, the required selectivity coefficient is estimated differently from the electrode. Estimations of the required selectivity coefficient within a relatively small physiological range of variation of the ion activities can be made by [132]: (6-24)

where Pij is the allowable analytical error (see section 4.3 and Appendix 4). This difference between electrodes and optodes has been demonstrated for the sodium-selective optode membrane relative to a calcium ion background in [132]. The graphs in [132] show that the selectivity coefficient varies with the active molality of the participating ions and with the pH, the sensitivity being additionally variable. For a comprehensive description, Eqs. 6-20 and 6-22 have to be considered.

6.4.7.2

Sensitivity and the Dynamic Range: Influence of Charge Number and Stoichiometry

On the basis of Eqs. 6-7 to 6-15, the response function of all optical ion-selective bulk membranes can be described, assuming different conditions, e.g., unique stoichiometriesof the complexes @ = 1) and unique or zero valency of the participating compounds, 10, I+, and X-. These unifications give rise to considerably simplified equations. With respect to the response curves, a higher stoichiometry of the ligand-analyte complex can have a comparable effect to that of increased charge number. In both situations the slope of the response curve, and thus the sensitivity of the assay, are decreased. If an excess of ionophore LT (LT/CT>> plv) is present in the membrane phase, the shape of the response curve becomes independent of the stoichiometry of the complex . A case were the stoichiometry of the ion-ligand complex of the primary versus the inte ering ion influences the slope of the response function has been reported. It was observed as a nonideal behavior of the electrode. In the most general case, the chromoionophore is assumed to complex preferentially to hydrogen ions with the charge z = 1 and stoichiometry 1. The response function, in which a and 1-a, respectively, are related to the logarithmic product of ion activities log (uH+)VX u x p or the logarithmic ratio of ion activities up+/ ( u H + )describes ~ a sigmoid curve AA = f (log ( u p l ( a ~ + ) y )or ) f(log(ap+ ( u H + ) ~ ) ) ,where A is the optical absorbance. The analytical uncertainty due to varying ionic strength and pH for direct measurements adds up over the two components. A change in pH of k 0.05 results in a relative error of approximately k 20% of H+p

5+

296


the activity of a divalent ion (calculated for the calcium-selective bulk membrane). A k 10% inaccuracy is calculated for monovalent ions. Assuming that the response curve is independent of the stoichiometry of the analyte-ligand complex, the sensitivity is only associated with the charge of the analyte ion, and decreases with increasing charge. a = 0.5, corresponding to 50% protonation of the indicator, marks the mean of the dynamic range of the assay. At this point, thehighest sensitivity relative to the x-axis is achieved. The available dynamic range is comparable to a titration curve and corresponds primarily to the concentration of the ligands within the membrane, among other factors (see Eqs. 6-12,6-13, 6 21, 6-23). The response function can be approximated by a straight line with optimum sensitivity in a small activity range around a = 0.5. Thus, the mean activity of the analyte in the sample should ideally correspond to this range. From Eqs. 6-7 to 6-23, the selectivity behavior, the activity interval of the dynamic range, and as the detection limit and sensitivity can be described theoretically in all cases. Despite the fact that the assumptions made are not fulfilled in some cases, the theoretical functions fit well to the experimental data in the cases investigated to date. By comparison, the linear range of the electrode response function for a cation is limited by the anion breakthrough, at concentrations of the primary ion > lo-' moVL, usually, and by the insufficient discrimination of cations in the low activity range (see Figure 5-lb). These limits are typical of each ion-selective electrode and different for different interfering ions. In some cases, the extent of the dynamic range is very similar for optodes. Dynamic ranges which are not accessible with optodes without a loss in response speed, are accessible with electrodes in the case of a high stability constant of the ligand with respect to the analyte, and efficient discrimination of interferents. The reason for this behavior is typically that the bulk membrane homogeneously equilibrates with the sample activity, whereas, in potentiometric sensors, the equilibration of the boundary ideally determines the signal. Though, in the range of 10-6-10-1 moYL nonideal behavior of the electrode response function occurs; the reasons for this are generally hard to explain.

6.4.7.3

Life-Time, Long-Term Stability of the Optode Membrane, and Lipophilicity of the Components

The Iipophilicity log PTLCof membrane components is of the utmost relevance for the lifetime of liquid membrane sensors [133] (see also section 4.6). Lipophilicity, as determined by reversed phase thin layer chromatography (TLC),is a general approach, taking account of the partition equilibrium between a more or less polar solvent and an apolar solid phase. For chromophores, evaluation of the partition equilibrium by TLC, considering the life-time of the optical system, has a limited impact since charged species follow rules given by the strong coulombic interactions within the membrane. In addition, TLC cannot be fully exploited since the basic pH indicators require very high basicity of the solid and mobile phase. Thus, in a first attempt the extraction behavior was established. by photometric measurements in a flowthrough system using whole membranes [133]. The evaluated extraction rate was in good


291

agreement with life-time values calculated by life-time equations based on Ficks diffusion laws (for a theory see [ 1331 and for the membrane model see section 4.2.2). Since blood serum and whole blood are much more lipophilic than a purely aqueous solution, they are much more efficient extractants for membrane components. The life-time decreases exponentially by a factor of for direct measurements. Hence, much higher lipophilicities of host molecules and additives are required when membranes have to be contacted with these media. The required lipophilicity log PTLC for neutral carriers incorporated in ion-selective liquid membranes with a thickness of approximetaly 200 pm and a minimum life-time of 720 h of contact to whole blood or plasma is > 11.3. For plasticizers, the required log PTLC > 14.3 [133]. An optode membrane layer of only 1 4 pm thickness has the advantage of a quick response in the range of seconds. Although, it is mainly responsible for the short life-time, limited by gradual extraction of membrane components into the sample solution. The lipophilicity of the membrane components turns out to be the most decisive parameter in this respect. For long-term applications in clinical chemistry analyzers, assuming a decrease in absorbance of only 10% over 30 days, the lipophilicity log PTLC has to be increased to a value of > 20 [133] which is only realized for the carrier ETH 4120 . The extraction of protonated chromoionophore and the lipophilic borate to the sample solution results in a decrease of absorbance, and may mimic a higher cation concentration. This effect is not compensated by a reference membrane but by the standard addition procedure reported in [112]. The possibility of checking the signal relative to the isosbestic point has not yet been evaluated to its full potential. Covalent binding of membrane components to increase the life-time of sensors should increase the life-time to infinity. Different methods of immobilization as well as molecular imprinting have been investigated by Rosatzin [101, 1471. The most relevant results will be summarized in the following section.

6.4.7.4 Immobilization of Membrane Components General strategy involves the use of very thin membranes with thickness < 2 pm, immobilization of components, and complex multifunctional polymers (see section 4.6).

6.4.7.5 Extraction of the Analyte and Depletion of the Sample Phase The theoretical description of the response behavior of optode membranes is based on a thermodynamic equilibrium involving the whole membrane phase homogeneously. As a consequence of the mass transfer, a potion of the analyte is extracted from the sample solution within the membrane. In the case of the potassium-selective optode membrane, the extracted amount of potassium ions for a concentration of 4 mmol L-I in the specimen, diluted 1+19, is L containing 1.68x in the range of 0.2-0.4 mol%. The total membrane volume of 0.192 x 10-9 mol indicator and 1.84 x lW9 mol ionophore (pm = approx. 1) is equilibrated with 340 pL

298


sample volume containing a total potassium concentration of 0.2 mmol/L and a potassium activity of 0.15 mmolk, (activity coefficient for an ionic strength I = 0.150: 31 300 pm thickness. Thus, all evaluations were made in a flow-through system with a flow of approximately 18 cm3 h-1 (0.3 mL min-l) and a cell volume of 340 pL where the stagnant layer may be in the range of 30-100 pm thickness (see [133]). Under these conditions the equilibration time is in the range of seconds. In view of these facts the detection limit must be associated with the concentration of the components in the membrane and the sample phase, the thickness of the membrane, the mode of operation (dynamic or static), and the response time of the system. The measurement of lead ions in trace concentrations has been shown to be successful in aqueous samples [110]. However, total concentrations of 10-* molL or less lead to a strong depletion of the sample solution, even if a flow- through system is applied. The actual set-up requires a minimum sample volume of several litres for the assay of total lead concentrations of l t 9 moVL. The response time depends on the saturation time of the membrane phase, and is at present 1 h or more for trace concentrations c 10-9 mom. Improvement of the design of the measuring cell as well as miniaturization of the sensing membrane should lead to sensing devices which are more suitable for a practical assay of trace elements in blood or environmental specimens. Detection modes making use of multiple internal relection elements (MIRE)should also improve the detection limit.

6.4.7.6

Interferences Due to the Sample Background

PVC membranes exhibit some propensity toward adsorption of sample components at the surface (see section 4.7). The surface shows a variable fraction of backscattered light, owing to swelling and turbidity of the surface by water uptake. A dual-membrane, double-beam arrangement was selected in the transmission mode in order to take care of these interferences, related to the membrane properties, and in order to take account of the absorbance of various samples which are more or less opalscent and colored.

6.5 The Optical Transduction Process

6.5

299

The Optical Transduction Process

6.5.1 Absorbance Measurements in Transmission Mode In the transmission mode, the measured absorbance of an analyte Aiis related to the concentration c by the Beer-Lambert law:

where I , is the intensity of the incident light and I the intensity at the optical detector after passing through the cell containing the sample solution. If the concentration c is expressed in mol/L and d is the pathlength in cm the proportionality constant is termed the molar decadic absorptivity or absorption coefficient, and is designated by [ 1 L mol-*I. Since the radiation passes through the reference as well as the sample cell in the double-beam arrangement, some light is reflected at each surface, related to a change in the refractive index. Reflection is pronounced at turbid boundaries, and is taken into account by referencing the sample signal to the signal of an indicator-free membrane exposed simultaneously to the sample flow. This differential signal is calibrate with aqueous solutions. A signal normalized to the isosbestic point was supposed to eliminated this kind of error.

A

I ,

,**% I

0.3OPTOOE I

8

O2-

z

m a LL

0

ETH 1001 ETH 5294 NaTm(CF&PB DOS PVC

cn

!2

0.1-

0.0I

I

400

I

500

I

600

I

I

700

800

WAVELENGTH [nm]

Figure 6-14. Absorption spectra of two 2 4 pm thick optode membranes incorporating ETH 1001 as ionophore. pH-buffered solutions (acetate pH 3.52) containing different molar concentrations of CaCl2 are equilibrated with the membrane within about. 10 s. The deprotonated form of the indicator ETH 5294 shows an absorbance maximum at 545 nm; the protonated form has maxima at 614 and 660 nm

300


The absorbance of photon energy in the transmission mode is used to quantify the calcium and potassium concentrations at A = 660 nrn. The absorbance is measured through two membranes, each 4 x 10-4 cm thick. The absorbance values Ai for the two totally protonated membranes referred to E 660nm = 3.7 x 104 with c = 8.75 x IC3mol/L are 0.259 and 0.1295, respectively, for a = 0.5. The measured absorbance may be different from the theoretical value since a protein-containing boundary exhibits an increased refractive index (ca. 1.35 [ 1501) and, consequently, a lower fraction of reflected light. The change in absorbance for an alteration of the potassium activity of 0.1 mmoVL in the range of 4.0 mmol/L is close to the quantification limit of 4 x 10-4 absorbance units. A high absorption coefficient in the range of 104 measured in methanol (see Table 6-4) is in favor of a relatively prominent change of the intensity of 0.0887 absorbance units for one decade of activity change in the case of potassium ions, and an associated loss of precision of < 0.0006 (n = 5) or 1.6% coefficient of variation within the activity range of 10-3-10-4. Reliable measurements are promoted by a relatively high membrane thickness (4-6 pm) a well as a high concentration of membrane components. The degree of protonation of the neutral, highly lipophilic chromoionophore with the molar decadic absorption coefficient &hax is evaluated by its absorbance in the visible range. The transformation of the two species is ideally represented by the isosbestic point of the chromoionophore (see Figure 6-14).

6.5.2

Optical Transducing Elements Based on Multiple Internal Reflection (MIRE)

Attenuated Reflection Mode (ATR) [ I 51,1521 Optical fibers can be applied in the intrinsic mode [153-1551. The membrane providing the selective chemical recognition process is attached along the fiber. In' the attenuated reflection mode the incident light beam is internally reflectqd in the waveguide of refractive index nl which is operated above the critical angle for total internal reflection 0,.A nonpropagating standing wave perpendicular to the reflecting surface is created by the interference between the incident and the internally reflected beam. The energy associated with this wave tails out into the adjacent medium with the lower refractive index n2. This tailing field is called the evanescent field and is explained by tunneling of photons to the surrounding medium. The exponential decrease of the wave amplitude with energy E(o) corresponds to an attenuation of the intensity with energy E (z) with distance z normal to the optical interface.

E (z) = E (0)e-(Z/dp)

(6-27)

where d, denotes the depth of penetration of the evanescent field. If n21 is the ratio of the refractive indices n 2 ln 1 of the media, and A1 is the mean wavelength of the monochromatic incident light relative to the refractive index of the waveguide n 1: (6-28)

301


Table 6-4. Molar decadic absorption coefficient of the protonated and deprotonated species of two Nile blue derivatives ETH 5418 and 5294 in methanol as solvent [L-1 mol-11 [151]

Indicator

Molar decadic absorption deprotonated species C

Coefficient & h a x protonated species HC+

Optode selectivity

ETH 5418

3.9 x 104 524

7.9 x 104 656

lead, cadmium

Amax, (nm)

ETH 5294 hmax,(nm)

2.3 x 104 540

3.7 x 104 660

potassium

A pseudo-Beer‘s law relationship takes into account the power distribution between the incident intensity of light and the transmitted intensity by assuming that the adjacent layer is light absorbing at a specific wavelength &ax. The intensity loss in an evanescent field sensor of length L, in the direction of the propagation is denoted by I ( z ) = I ( 0 ) 10 (-Vp

G(ck

=Z(o) 10 -A = Z(0) 10 -&;LnaxCk”2

(6-29)

where a, is the linear decadic absorption coefficient and qp =Pm/Pt, the evanescent field intensity in the external matrix P,, divided by the total light intensity in the core and in the external medium Pt [156] By the molar decadic absorption coefficient, &;~nax(see Table 6-4), the number of reflections N /2, and a hypothetical thickness de (see @. 6-30), the evanescent mode is linked to the absorbance A in the transmission mode. In order to relate ATR data to the Beer-Lambert law, a hypothetical thickness de, of the sample was introduced by Harrick [154]. The thickness de was referred to as the effective thickness, and represents the sample thickness in the transmission mode which results in the same absorbance as obtained with the real propagation pathlength d of the evanescent wave within the membrane. By this model, de is related to the wavelength &,= typically absorbed by the indicator of the chemically selective membrane according to: (6-30)

Simple application of Beer’s law to ATR data requires polarized incident light in a strict sense. However, working with unpolarized light is possible with respect to the field components in all three axes x, y and z. According to Fringeli [153, 1551 the electric field component E parallel (11) to the plane of incidence (x, z plane) is denoted by: (6-31)

302


where El is the electric field component perpendicular to the plane of the incident light. The three electric field components are calculated according to [155]. Two different values for the effective ihickness are calculated from equations and averaged for practical comparisons. The multiplicity of reflections N within the crystal is now a geometric problem and is calculated from the angle 0 (60°),of the incident light beam at the boundary of the crystal versus the membrane, thelhickness of the crystal d (1 mm), the corresponding pathlength x for one reflection, and the length of the waveguide L (52 mm). N=L/x=Lldtm 0=30

6-32]

NONPOLARIZED INCIDENT LIGHT

/-SAPPHIRE

dM MEMBRANE THICKNESS dp PENETRATION OEPTH d, OF EVANESCENT WAVE

n, , n, z n2

tg 8 = tg 60' = 1732

Figure 6-15. ATR set-up for multiple internal reflection (MIR) where a sapphire or LaSF30 crystal has been used as a waveguide in contact with an ion-selective optode membrane. 0, angle of incidence; ,511,E l , parallel and perpendicularly polarized components of the field of incident light; Em E,, E;, electric field components with respect to a coordinate system corresponding to the internal reflection plane


303

The total absorbance corresponding to the transmission mode is now calculated from the effective thickness de multiplied by the number of reflections N ,&amax,and the analyte concentration c of the sample according to Eq. 6-29. Since the sapphire crystal is only contacted by the membrane on one side, the effective number of reflections is divided by two (Nl2). For a guided wave with A = 663 nm, an angle of incidence of 600 and refractive indices of n 1 = 1.768 for the sapphire crystal and n2 = 1.474 for the PVC membrane, respectively, an effective pathlength de of 831 nm was calculated for each reflectance. de corresponds to the hypothetical thickness averaged for parallel polarized light based on calculations of the field E r o b and and for perpendicularly polarized light based on calculations of Eras. A crystal of length 52 mm therefore provides an effective pathlength of 15 x 831 nm = 12 pn. The corresponding total absorbance difference between the totally protonated relative to the totally deprotonated indicator is evaluated on the basis of e 5 6 = 7.1 x 104 L mol-l, an effective pathlength of 12 pm, and an indicator concentration within the membrane of 0.0203 mom. A total mean absorbance A of 1.75 is approximated; in contrast, the measured absorbance difference was 0.859 based on a membrane thickness of 2 pm with the same indicator concentration. As a result, the absorbance can theoretically be increased by a factor of 6, however, a 3-fold increase was realized. For a potassium-selective membrane, the theoretical absorbance is calculated at 0.3417 for a wavelength of A = 660 nm with the same sapphire and N/2 = 13 reflections in the ATR mode with respect to a mean effective thickness, de of 807 nm. The difference in absorbance between the totally protonated and the totally deprotonated indicator for the K+-selective membrane in the transmission mode is calculated to be 0.040, while 0.0347 is observed. A theoretical increase of the membrane thickness by a factor of 8 is expected for the ATR analysis, the effective thickness de being 10.5 pm. The concentration of the chromoionophore within the potassium-selective membrane is 0.0088 mom. In fact, the increase was 4-fold. The loss of light intensity as a consequence of an uncontrolled wave with an unpolarized and poorly focused light beam was remarkable [157]. Baseline shifts of up to 6%were reported due to a change in CaC12 concentration from 10-1 to l@ m o m [157]. The influence of ionic strength, ion concentration, and hydration of the membrane on the ATR absorbance was investigated. A blank membrane without indicator, lipophilic borate, or ionophore was spun onto the sapphire and exposed to pure solutions of 2, 3 , 8 and 100 mmol/L KC1. The ATR absorbance of the blank membrane in the unconditioned state is four times lower (0.1) compared with the hydrated membrane (0.4). The effects reported point out the importance of taking care of the sample background for MIRE measurements. In view of the unsatisfactory efficiency obtained with a sapphire crystal and unpolarized light, new concepts have been studied. First, the sapphire crystal was replaced by a lanthanum fluoride crystal (LASF 35) with refractive index, np587.5 = 2.022. For this refractive index, the incident angle and the geometry of the crystal to obtain the maximum effective pathlength were optimized by iterative calculations. The ATR flow-through cell was reconstructed for a planar waveguide parallelogram with 50 k 0.75 mm length, 1.5 f 0.044 mm thickness, and 20 mm breadth of the LASF35 crystal. The length of the analyte-active membrane contact was

304

6 Optical Sensors. Optodes

500

800

Figure 6-16. Attenuated reflection (ATR) spectrum. Measurement of the evanescent field of a calcium-selective optode bulk membrane. The isosbestic point characteristically does not overlap, owing to a variable penetration depth and effective pathlength of the guided wave as a consequence of the varying refractive index at different calcium concentrations in the sample. Monochromatic, but unpolarized light was used (the peak at 605 nm is an artifact)

48 mm and the incident angle of the light Q, was 520 & 24" (0.7%). The results for the same calcium-selective membrane as used in Figure 6-13 are shown in Figure 6-15. The membrane composition is given in the figure; the refractive index n2, measured with the sodium line at 587.5 nm was 1.469. The thickness was measured by interferometry and calculated to be 1.4 pm. With 26/2 reflections and an effective pathlength d, of 47 pm, the absorbance was enhanced by a factor of 8.

6.6 Trend to Miniaturized Integrated Optical Sensors (MIOS) Reducing the size, complexity, and cost of, optode-type sensors is important for their commercial success. Some possibilities for realizing miniature and totally integrated optical (10) sensors based on measuring the optical properties of sensing layers have been presented

6.6 Trend to Miniaturized JntegraiedOptical Sensors (MIOS)

305

[157]. In this section, investigations aimed at realizing such sensors by means of ion-selective membranes deposited on dielectric waveguides are reported. A typical cross-section through the transducer part is shown schematically in Figure 6-17. The working principle relies on: -

-

-

converting the chemical recognition process into a change of the real part nm of the membrane's refractive index converting this change into a change of the effective index N g of the waveguide determining this change by integrated optical means involving components such as interferometersand grating couplers.

In order to determine the sensitivity of these I 0 transducers, membranes for sensing the concentration of Ca2+ or K+ ions have been deposited on high-index waveguide gratings [ 1561. The variation of the membrane refractive index versus concentration has been determined by measuring the changes of the grating coupler resonance angle @ (see Figure 6-15). Very high sensitivities aN/anm > 0.4 have been achieved by using thin Ta,O, planar waveguiding films of a thickness hf = 100nm with a high refractive index nf= 2.2 allowing for single-mode waves. Doubly stacked grating couplers have been fabricated by first structuring fused silica substrates by a photolithographic technique and subsequently depositing the waveguiding films. Details of the experimental set-up and measurement procedures, chip design, and fabrication have been presented [158]. The sensitivities achievable for various I 0 transducer types are discussed.

MEMBRANE

nm= 1.46

WAVEGUIDE

nf = 2.2

SUBSTRATE

n S = 1.457

AMBIENT

na = 1.33

Figure 6-17. Schematic set-up of a Multiple Internal Reflection Element (MIRE) which is used to measure refractive index changes (6N/&,). The sensing pad consists of an optode membrane with thickness hm deposited on a single-mode waveguiding film (Ta2O5) with thickness hfi coated on a structured substrate (fused silica). The incident guided wave (I,) is linearly polarized (TEoand TM, mode) and is provided by a laser diode [1571. The parameter values of the refractive indices are referred to h = 690 nm

306


The experimental design (see Figure 6-17) was chosen as a prototype for initial investigations of refractive index changes in ion-selective optode membranes. Maximum coupling efficiency is achieved with the following resonance conditions [1581: Ng=n,sinOi+rngjllA

(6-33)

which relates the angle of incidence O,,measured in the ambient medium with refractive index na, to the effective index of the waveguide N g in the grating region. mg is the grating diffraction order and A is the grating periodicity. In contrast to the classical ATR design reported in the last section, the hf waveguide thickness of 100 nm in this approach is clearly smaller than the wavelength of the incident coherent, linearly polarized incident laser light ( A = 633, 690, 785 nm). Therefore the propagating wave is a single-mode wave, which changes the angle of maximum coupling efficiency upon tailing into the membrane with refractive index n, (ca. 1.46). This angle change is thus corrected and measured for the two polarization planes, the TM,and the TE, modes, at maximum wave intensity in this pilot experimental design. In this case, monitoring the TM, mode results in a higher reproducibility of the angle measurements. The TM, wave within the planar dielectric waveguide is characterized by a magnetic field component (impfly) in the y-direction and two electric field components in x- and z-directions, (Figure 6-15), whereas the TE, wave has an electric field component (i&wEy)in the y-direction , is the dipole moment, w the plus two magnetic field components on the x- and z-directions. U frequency, and E the permittivity. It was supposed that the electric field component (&uaE,) is the component that interacts selectively with the protonated indicator. The intensity of the TM, and TE, modes are related to the thickness of the waveguiding layer. A thickness of 100 nm is a good compromise for similar intensity of both modes. For a sensing pad length of 2 mm, a refractometric resolution of An,,, = lod5 in air and lo-" (ta = 0.05, = 15) in pure solutions was achieved at the detection limit using the TM,-mode. This value was evaluated with pure solutions of KSCN at A = 785 nm (laser diode) and a HeNe laser at A = 633 nm at 798 K. An important aspect of miniaturization and integration is the possibility of placing multiple sensing pads on one single chip, with no mechanical parts in the final design. A special case is a closely spaced arrangement of reference and signal pads. In situ referencing is highly relevant for practical applications to discriminate against nonspecific effects, e.g., due to swelling. Therefore pads of a "reference membrane" and a "signal membrane" have been deposited side-by-side on the same grating coupler [156]. The membranes used here are based on a single phase of plasticized PVC. Both the reference membrane and the signal membrane contain one mobile selective carrier, valinomycin in the case of potassium ions, ETH 1001 in the case of calcium ions. Anionic borates are incorporated for the charge equilibrium within the membrane. The reference membrane does not contain the indicator ETH 5294, in contrast to the analyte-active membrane. The membrane reaction responds to the ratio of the activity of the analyte to the hydrogen ion activity in the aqueous sample phase. The spectral shift of the added lipophilized pH-sensitive dye (ETH5294) in the signal dembrane is directly related to this ratio. Aqueous solutions of CaC12 with a constant pH buffer background of pH 5.2 were chosen for demonstration of the feasibility. The concentration range applied was 1W6 to 10-1 mo1L Best results were achieved with a laser-diode operating at h = 690 nm, exciting

6.6 Trend to Miniaturized Integrated Optical Sensors (MlOS)

307

the TMo mode. The refractive index decreased with increasing concentration of the analyte and deprotonation of the indicator by about ANg = 3 x 10-3 per order of magnitude Ca2+ concentration. A small increase in refractive index was observed at the HeNe laser wavelength of 633 nm, with reversed sign. The results are consistent with the dispersion spectrum derived from the corresponding transmission spectra by Hilbert or Kramers-Kronig transformation (see Figure 6-18) [156, 1671. A typical resolution of 0.003-0.0003 decades of molar Ca2+ (0.3-0.03%) in the diagnostically attractive range of 10-2-104 molL is calculated from these results. This range is also attractive for measurements of water hardness. A considerable enhancing factor of about 10 is expected with the final design of the MachZehnder interferometer, where the length of the sensing pad and the length of the propagating evanescent field plays an important role. In a dielectric medium, there is a causal relationship between the absorption coefficient, the loss factor, and the dispersion coefficient . The two characteristicsspecify the real (X) and the imaginary (XI) contribution of the electric susceptibility of the medium and are both wavelength dependent. A molecule that exhibits a permanent dipole moment reorients to follow the orientation of an applied field (polarizability). If the frequency v of an applied field matches the rotation frequency of the dipole, a high refractive index results n(v). With increasing frequency of the field, a decreasing refractive index results. In the range of the resonance frequency o, of an electron transition, absorption a( v) is expected and so-called anomalous dispersion is observed. Absorption and dispersion are the imaginary and the real parts, of the susceptibility of a dielectric medium and are related by (Kramers-Kronig)

1

ETH NaTL

LL

s

-2

1 400

Amax = 57E 500

600

700

800

WAVELENGTH [nm]

Figure 6-18.Calculated dispersion spectra of a calcium-selective optode membrane with a maximum of the refractive index change at 690 nm and a bathochromic shift relative to the absorbance spectrum of about 30 nm

308


transforms [159-1611. At frequencies well below the resonance frequency, where o > coo, minimum dispersion and absorbance are approximated. As a result, the dispersion and the absorption spectrum are closely related to each other and both are frequency dependent (see Eqs. 6-34 and 6-35) ( v = c0/A s-*, where co is the speed of light in the membrane phase, and no is the refractive index of the membrane without dye. As an approximation, the speed of light in vacuum is used.) The relationships between absorption or dispersion and frequency are given by: a(v) =-

2m (-) xyv) = (A(v) In '0) noco

(6-34) (6-35)

The dispersion spectrum of the protonated chromoionophore was modeled from its absorbance spectrum A( v) according to: (6-36)

-

The term A (= co/s, where s is equivalent to frequency) represents the integrand used to integrate the spectrum along the wavelength or frequency axis. The dispersion spectrum shows a maximum which exhibits a bathochromic shift compared with the absorption spectrum. For exact calculations, a frequency range from zero to infinity is used. In the case shown here, absorption above loo0 nm and below 240 nm was ignored. Thus, the spectrum shown here is an approximation, good enough to get the optimum and minimum frequency/wavelength of the protonated and deprotonated indicator ETH 5294 and the position of the isosbestic point for the evaluation of the refractive index changes. A difficulty is that an incorrect assumption of the pathlength through the membrane, (membrane thickness dpm), for the transmission spectrum may result in an unrealistic value for the refractive index. The model is valid only for weakly absorbing media (opposite to the basic assumptions given in section 6.4.1) The goal of the project was to use the optode membranes as analyte-selective layers in miniature monolithic and hybrid I 0 sensors. Such an example is a Much-Zehnder interferometer. It makes use of a sensing and a referencing pad located in the two arms of the interferometer. The wave uo is emitted by an on-chip light source, and generates the waves u and u' in the two arms. A chemically selective bulk membrane and a non-reactive reference membrane are cast onto the two sensing pads which are each part of one arm of the interferometer. After having traversed the sensing layers, the waves ul and ul' are superposed to form the wave u2 which gives rise to the output signal on a photodetector. The electrical output signal is a measure for the phase shift of the two interfering waves ul and 111' and related to the change in the refractive index of the chromoionophore at its resonance

6.7 NIR-Absorbing Dyes

309

wavelength relative to the blank membrane. The dispersion spectrum of the indicator is estimated from the absorption spectrum for operating under optimum wavelength conditions. An important parameter for adapting the sensor characteristics to the actual application requirements is the thickness of the membrane. While fast response times call for thin membranes, thicker membranes yield longer lif-time and increased chemical and mechanical ruggedness. Therefore, we have chosen the membrane thickness to be h, = 1 pm, distinctly greater than the penetration depth of L- 0.2 pm for the evanescent field of the guided mode in this approach. The guided mode is thus neither affected by the properties of the sample solution (e.g. turbidity) nor by deposits at the membrane surface.

6.7 NIR-Absorbing Dyes Miniaturized planar waveguide sensors, integrated optical sensor modules, and fiber optical sensors are preferably operated in the red and near infrared (NIR) range of the electromagnetic spectrum. There are at least two reasons for this. On the one hand these optical technologies are bound to the available semiconductor laser diodes, with maximum output wavelengths ranging from 680 to 1800 nm, the most prominent commercially available laser diodes emitting at A = 680, 750, 780, and 830 nm. On the other hand, hemoglobin excepted, the biological background is supposed to induce less interferences when detecting in the red and NIR (700-1000 nm) compared with detection in the UV and visible range [163, 1641. On account of these developments in the area of optical chemical sensors, various research groups have made attempts at developing new dyes absorbing or emitting in the red or NIR [164, 1651. Various applications have been discussed, such as using them as markers, indicators, or labels depending on features such as solubility, solvatochromic effects, quenching characteristics, absorption coefficient, and emission intensity. The dispersion spectra calculated for the pH indicators as used in "Simon" optodes are generally unsuitable for refractive index measurements. Therefore, a program was started to develop pH-sensitive dyes which absorb between 700 and ca. 850 nm. The required characteristics were primarily defined with a view to using such dyes in solvent polymeric membranes coupled to available analyte-selective ligands. In addition, labeling of compounds whose binding characteristics are evaluated by optical waveguides has been discussed, as well as incorporating such labeled compounds in micellar optical systems. The working principle of optical chemical sensors, discussed in the previous sections, relies on an ion exchange or coextraction mechanism where a pH-sensitive dye participates in the extraction of a specific ion by an ion-selective ligand. The most relevant features of a novel dye, in order to replace existing indicators, is: (1) the red NIR indicator must be soluble in the apolar membrane phase; producing a homogeneous membrane phase is the objective here; (2) the pK, of the indicator must match the stability constant of the ion selective ligand; (3) the indicator must be stable and lipophilic enough to reduce leaching of the dye. Several classes of dye have been synthesized; specific compounds were modified and tested in solvent polymeric membranes [113-1151. The following discussion gives a review of the results obtained. However, this research is still in the process development.

3 10


Table 6-5. Classes of unsaturated organic compounds used as red and NIR-absorbing dyes and tested in sqlvent polymeric membranes (classification according to [ 166-1681, for data and details see [1 13-1 151

No.

Class of dye

Aromatic n-systems

Poly methines

Charge transfer type nn* systems

Comments Em= / cm2mol-1;

&ax

/ nm

Oxazine dyes

Extended oxazine dyes, PPP-estimates [ 1 13, 1 151, synthesis problematic

Ethenyl acridines, L 109 [165]

DOS:

Symmetric, altemant streptocyanine

pH-sensitive Nafion membrane see [113], pH range: 2.0-7.0

Neutrocyanine croconium

Insufficient chemical stability

Neuuocyanine squarylium dye

DOS:

Dicyanovinyl dye

DOS:

pKa 11.5 f 0.04 851 (protonated) ligand ETH 1001, Ca2+-selective, 10-1 mol/L Ca2+ to < 10-5 morn, pH 4.8 (0.1 m o m Na-acetate)

La:

pKa 2.65 f 0.04 819 (neutral) O-WOE: pKa 2.77 f 0.05 Lax:, 821 (neutral) 136700 (EtOH)

km:

~ K ~ 4 .f 0 0.14 4 755 (deprotonated, pH > 5.0) O-WOE: pKa 6.45 f 0.13 768 (deprotonated, pH > 5.0) A,,,,,: cmm: 28900 (CH2C12))

A,,,=:

Reduced dicyanovinyldye ETH 5003 Nonsymmetric dicyanovinyl dye ETH 5002

km:

717 (deprotonated, pH > 14)

ha,: 11600 (CH2C12) pH-sensitive membrane pH 2-14, extremely stable

A,,,

excitation: 629 (deprotonated, CHC13) ha, emission: 728

6.7 NIR-Absorbing Dyes

311

In order to conserve as many as possible of the favorable properties of the benzo[a]phenoxazine-dyes used so far, modifications of the molecule by extending the Nsubstituted side chain at the 5-position (see Figure 6-19(1)) were studied. Theoretical estimates by PPP simulations [169, 1661 confirmed the spectral shift supposed to be feasible by prolongation of the conjugated system. The accuracy of the calculation was validated by comparison with molecules of known absorbtion spectra [113, 1701. The extended PPP mechanism allowed the prediction of the wavelength of the maximum absorbance of the visible band, the absorbance intensity, the polarization direction of the absorbance band, the MO energies, the electron densities, and the bond order. No solvent effects are considered, the predicted values refer to vacuum or environments of very low polarity. The rigidity of the side chain will prevent isomerization. Unfortunately, the compound has not be realized synthetically so far. A more successful approach was taken by Czerney and Grummt [165] as shown in No. 2 of table 6-5. This was the only dye which allowed one to realize calciumselective optical membranes [1711. Polyrnethine dyes, especially cyanines, are generally less attractive for use in apolar phases, owing to their solubility in polar phases, on account of their cationic nature. The ionexchanging polymer Nafion combines both a highly polar membrane medium with immobilized anionic sites and ion pairing with the cationic dye (compare sections 6.4.2 and 6.4.3). In this membrane, the cationic dye is stabilized by the anionic charge of the polymer. Homogeneous optode membranes incorporating dye No. 3, were obtained and allowed reproducible spectra to be registered. These membranes, as well as membranes incorporating indicator No. 4 responded reversibly to pH variations in the aqueous solution [ 1131. In the following examples, the indicator was incorporated into solvent polymeric membranes. The pH-dependent absorbance spectra of the homogeneous membranes were recorded. The most successful pH optode membrane produced so far was that incorporating dye No. 6. An exceptionally stable absorbance signal between dilute hydrochloric acid and 0.1 mol L-l sodium phosphate buffer pH 7.4 was obtained. The more polar plasticizer, 0-WOE, induced a shift in pK, to higher basicity as a consequence of the protonated form being stabilized. The same trend is observed for the squarylium dye No. 5. Surprisingly alkylation of the dicyanovinyl dye results in a different product, ETH 5003, the structure of which is currently being investigated. However, a very attractive pH optode membrane has been produced by adding cationic sites to the plasticized PVC bulk. Overall, several attractive new dyes absorbing in the spectral region between 700 and 850 nm have beeb created and tested. Membranes incorporating dye No. 8, ETH 5002, even show fluorescence emission in the far red, at 728 nm.

Membrane composition: PVC ca. 33 wt%, plasticizer ca. 64 wt% (DOS,bis(2-ethylhexy1)sebacate (permittivity: 3.9 f O.l), or 0-NPOE, 2-nitrophenyloctyl ether (permittivity: 23.9 f 0.3)), dye 10-80 mmol kg-*, (ligand 31-117 mmol kg-'), (additives), (kg refers to total membrane mass); pH buffer: potassium citrate and acetate

3 12


f:

2: L-109

' 0

N '

I

-I

clod

3: PDC

6: dicyanovinyl dye

rNi

$ $H

0-

Q

"'F'"

4: croconium dye

5: squaryliurn dye

7: reduced dicyanovinyl dye

Figure 6-19.Dyes and indicators absorbing in the red and NIR range of the electromagnetic spectrum. For chemical names see [172], for characteristicssee Table 6-5

6.8 Conclusions: Electrodes versus Optodes, Possibilities of Neutral Substrates Optical quantification of glucose and creatinine for continuous monitoring in medical applications is a challenging prospect. In order to quantify neutral analytes, the optical approach offers new possibilities (sections 6.2 and 6.4.4). Optical chemical sensors are attractive for three main reasons: their relatively easy handling, their low energy consumption, and their relatively low cost of production and instrumentation. Especially, new trends in miniaturizing optical sensors are attractive in comparison with electrochemical sensors. For neutral analytes, optical and enzymatic, amperometricelectrochemicalsensors are competitive. However, an electrochemical sensor has to be shielded from electric fields which induce noise and uncertainty, an optical sensor has to be shielded from external or internal interfering

6.8 Conclusions: Electrodes versus Optodes, Possibilities of Neutral Substrates

3 13

radiation. Nevertheless, the reference electrode is of major concern in miniaturization, since reducing its size means reducing the buffer capacity and the life-time of the whole set-up. In addition, there is the question of how to arrange the position of the reference electrode. Miniaturization of optical devices is promising. For future perspectives, labeling of a host molecule with a chromophore offers a variety of possible concepts for transducing host-guest interactions into an optical signal. The plastified PVC membrane, and even more significantly, silicone or polypropylene membranes, are perfectly permeable for gases such as C02 or NH3. The analyte in the gas phase permeates the polymer membrane. The electrochemical, potentiometric approach needs an inner electrolyte responsible for stable internal conditions since the potentiometric signal (emf) is generated by the ratio of the ion activities, a(o) and a(d), on either side of the semipermeable membrane. If E, is the sum of contributions to an emf shift, and s is the slope of the potentiometric response function: (6-37) In contrast, provided an optical membrane support is truly inert, the inner side of the membrane does not participate in the equilibrium reaction (see models in section 3.2). Optical gas sensors do not need an aqueous phase, the normal humidity is usually sufficient for hydration of the gas and the membrane. Thus, optical sensors basically do not have to tackle to problems associated with internal media. The dynamic range and detection limit of optode membranes are limited both by the stability of the ligand-analyte associate, and by the concentrations of the membrane components which determine the extraction capacity of the membrane. Since the analyte equilibrates homogeneously with the membrane, both the variations of the signal intensity and of the dynamic range show more degrees of freedom than for electrodes relying on the special equilibrium or, more likely, steady-state conditions between sample solution and membrane. In a continuous-flow systems and close to the detection limit, where the analyte is measurably consumed by the membrane, a mass transfer steady-state is operative, where the analyte is continuously replaced by the sample flow and, reversibly, continuously washed-out from the membrane. This effect can considerably reduce the detection limit. Nevertheless, the dynamic range of optode membranes will generally not be sufficient to compete with that of ionselective electrodes. Furthermore, the sensitivity and resolution vary along the dynamic response function. The reaction rate for the reversible mass transfer relies, in addition to diffusion at the boundary, strongly on the thickness of the reactive layer. However, the optical detection of very thin membranes calls for highly lipophilic or immobilized components, accumulating and amplifying optical measuring techniques. Research and joint ventures in the area of optical techniques are proceeding. Speculations about the future of such systems include integrated optical sensors, sensor arrays, visible alarm levels in environmental control, "credit card" sensors for selfmonitoring as well as digital direct reading by an intelligent arrangement of the membrane sections. Nevertheless, all approaches show that a prerequisite for low detection limits is the existence of high stability constants of the analyte-camer complex or chromoionophore. In "Simon" optodes, an adequate pKa value of the indicator is another requirement.

3 14


Another goal for the future is to evaluate ion molalities of a range of electrolytes by optodes as well as ion-selective electrodes directly in the sample, without calibration. Also pH, osmolality, and ionic strength may be quantified, coupled to multivariate pattern recognition in order to interpret data and to classify specimens. The integration of enzymes within the membrane bulk [section 6.4.4) provides new possibilities for the quantification of neutral substrates by their reactants or products. It is also possible that a more robust access to antigen-antibody and substrate-receptor reactions may be achieved. Optodes and electrodes have been shown to complement each other by their contrasting characteristics. The whole spectrum of electrodes and optodes, including amperometric sensors, provides a wide range of dedicated systems for various applications.

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[91] Gantzer, M.L., Hemmes, P.R., Wong, D., Miles Laboratories Inc., Eur. Pat. Appl. EP 153,641,04 Sep. 1985; US Appl. 583,127.24. Feb. 1984. [92] a) Spichiger, U., Internal Seminar in Zurich, Ames-Divison, Miles Laborratories Inc., Lausanne, 1985. b) Trockenchemie-TagungVillard-sur-Ollon, Ames-Diagnostica, Bayer (Schweiz) AG, 1988. [93] Mod, W.E., Seiler, K., Lehmann, B., Behringer, Ch., Hartman, K., Simon, W., Pure Appl. Chem., 1989, 61, 1613. [94] Morf, W.E., Seiler, K.,Lehmann, B., Gehrig. P., Rouilly, M., Suter, G., Rusterholz, B., Spichiger, U.E., Pretsch, E., Simon, W., in: Schmid, R.D., Scheller, F. (eds.), Biosensors, Applications in Medicine, Environmental Protection and Process Control, GBF Monographs, 1989, Vol. 13, pp. 321. [95] Simon, W., Spichiger-Keller,U., Anal. Sciences, Suppl., 1991, Vol. 7,861. [961 Seiler, K., Entwicklung von Optodenmembranenauf der Basis von hochselektiven Ionopohoren, Zurich, CH: Swiss Federal Institute of Technology (ETH), 1990;PhD thesis Nr. 9221. [97] Seiler, K., Simon, W., Anal. Chim Acta, 1992,266,73. [98] Spichiger, U.E., Simon, W., Bakker, E., Lerchi, M., Biihlmann, P., Haug, J.-P, Kuratli, M., Ozawa, S., West, S., SensorsandAcfuators B, 1993,II,l. [99] Zollinger, H. (ed.), Color Chemistry, Weinheim: VCH, Verlagsgesellschaft mbH, 1991. [loo] Bakker, E., Lerchi, M., Rosatzin, T., Rusterholz, B., Simon, W.,Anal. Chim. Acta, 1993,278,211. [loll Rosatzin, T., Bakker, E., Suzuki, K., Simon, W., Anal. Chim.Acra, 1993,280,197. [lo21 Eugster, R., Gehrig, P.,Morf, W.E., Spichiger. U.E., Simon, W.,Anal Chem.. 1991,63,2285. [lo31 Schaller, U., Bakker, E.,Spichiger, U.E., Pretsch, E., Anal. Chem, 1994,66,391. [lo41 Spichiger, U.E., Seiler, K.,Wang, K., Suter, G., Morf, W.E., Simon, W., Proceedings of the EC04, The Hague, Netherlands, 12-13 March, 1991, Proc. SPIE-Int. SOC.Opt. Eng. 1510, pp. 118-130. [lo51 Wang, K., Seiler, K., Morf, W.E., Spichiger, U.E., Simon, W . , Lindner,E ., Pungor, E., Anal. Sci., 1990, 6, 715. [lo61 Simon, W., Spichiger, U., Freiner, D., Kurattli, M., Lerchi, M., Bulletin &r Eidgeniissischen Technischen Hochschule Ziirich, Nr. 236,1991,6,14. [lo71 Simon, W., Morf, W.E., Seiler, K., Spichiger. U.E., Fresenius, 1990,336,26. [lo81 Seiler, K. ,Wang, K., Bakker, E., Morf, W.E., Rusterholz, B., Spichiger, U.E., Simon, W., Clin. Chem., 1991, 37,1350. M., Rusterholz, B., Simon, W., Spichiger, U.E., [lo91 Seiler, K., Eugster, R., Morf, W.E., Wang, K., CZ~SZ, Fresenius, 1990,337, 109. [110] a) Lerchi,M., Simon, W., Anal. Chem.,1992.64, 1534. b) Lerchi, M., Simon, W., SPIE, 1992, Vol. 1716, 336. [ l l l ] a) Ozawa, S., Hauser, P.C., Seiler, K.,Tan, S.S.S., Morf, W.E., Simon, W., Anal. Chem., 1991, 63, 640. b) West, S. ,Ozawa, S., Seiler, K., Tan, S.S.S., Simon, W., Anal. Chem, 199264, 533. [1121 Lerchi,M., Reitter, E., Simon, W., Fresenius J. Anal. Chem., 1994,348,272. [113] Citterio, D., Rhonyi, S., Spichiger, U.E.,Fresenius J. Anal. Chem., 1996,354.836. [114] Citterio, D., Jenny, L., Rhonyi, S., Spichiger, U.E., Sensors & Actuators B, 1997,39,202. [115] Citterio, D., Swiss Federal Institute of Technology (ETH), 1998; PhD thesis in preparation. [116] Wang, K., Seiler,K., Rusterholz, B., Simon, W.,Analysr,1992,117,57. [117] Tan, S.S.S., Hauser, P.C., Wang, K., Fluri, K., SeiIer, K., Rusterholz, B., Suter, G., Kriittli, M., Spichiger, U.E.,Simon, W.,Anal. Chim Act4 1991,255,35. [118] Rothmaier, M., Simon. W.,Anal. Chim. Acta, 1993,271, 135. [119] Tan, S.S.S., Hauser, P.C., Chaniotakis, N.A., Suter, G., Simon, W., Chimiu, 1989,43,257. [120] a) Kuratli, M., Badertscher, M., Rusterholz, B., Simon, W., Anal. Chem., 1993, 65, 3473. b) Kuratli, M., Pretsch, E.. Anal. Chem., 1994,66,85. [1211 Kurattli, M., Beitrag zur Entwicklung von optischen chemkchen Sensoren. Orgmisch-chemische Reaktionen als Erkennungsprozess. Zurich, CH: Swiss Federal Institute of Technology (ETH), 1993; PhD thesis Nr. 10380. [122] a) Behringer, Ch., Lehmann, B., Haug, J.-P., Seiler, K., Morf, W.E., Hartman, K., Simon, W . ,Anal. Chim. Acta, 1990, 233, 41. b) Lehmann, B., Tnfluoracetophenon-Derivuteuls carbonatselektive Ionophore in

3 18


PVC-Fliissigmembranelektroden. Zurich, CH: Swiss Federal Institute of Technology (ETHZ), 1990; PhD thesis Nr. 9255. [123] a) Ozawa, S . , Simon, w., in: Grattan, K.T.V., Augousti, A.T. (eds.), Sensor VZ Technology, System and Applications, Bristol, UK: Institute of Physics Publ., Techno House, Retcliffe Way, 1993. b) Ozawa, S., A Study on Optical GUSSensors Based on Zonophores. Zurich, CH: Swiss Federal Institute of Technology (FTH), 1992; PhD thesis Nr. 9647. [124] Demuth, C., Spichiger, U.E.,Anal. Chim. Acta, 1997 (in print). [125] a) Barker, S.L.,Shortreed, M.R., Kopelmann, R., Anal. Chem., 1997,69, 990. b) Barker, S.L., Shortreed, M.R., Kopelmann, R., SPIE 1996, Vol. 2836,304. [126] a) Wolfbeis, O.S., Anal. Chim. Acta, 1991, 250, 181. (review) b) Schaffar, B.P.H., Wolfbeis, O.S., Mikrochim Acta (Wien), 1989, III, 109. [l27] a) Stamm, C., Seiler, K., Simon, W., Anal. Chim. Acta, 1993,282, 229. b) Stamm, C., Enfwicklung eines harnstoffsensitiven Enzymsensors auf der Basis von ummoniumselektiven Fliissigmembranoptoden. Zurich, C H Swiss Federal Insitute of Technology (ETH),1994.;PhD thesis Nr. 1081 1. [128] a) Vaillo, E., Walde, P., Spichiger, U.E., Anal. Methods and Instrument. (AMI), 1995,2, 145. b) Vaillo, E., Spichiger, U.E., SPIE, 1995, Vol. 2631, 127. c) unpublished results. [129] Hauser, P.C., Pbrisset, P.M.J., Tan, S.S.S., Simon, W.,Anul. Chem., 1990,62, 1919. [130] Wang, K., Seiler, K., Haug, J.-P., Lehmann, B., West, S., Hartman, K., Simon, W., Anal. Chem., 1991, 63, 970. [131] Seiler, K., Wang, K., Kuratli, M., Simon, W.,Anul. Chim. Acta, 1991, 244, 151. [132] a) Bakker, E., Simon, W., Anal. Chem., 1992, 6 4 , 1805. b) Bakker, E., Die Bedueutng yon Phasentransfergleichgewichren fur die Funktwnsweise von ionenselektiven Fliissigmembranoptoden und -elektroden,Zurich, CH: Swiss Federal Institute of Technology (ETH), 1993 ; PhD thesis Nr. 10229. [133] Dinten, 0. Spichiger, U.E., Chaniotakis, N., Gehrig, P., Rusterholz, B., Morf, W.E., Simon, W., Anal. Chem., 1991,63,596. [134] Maas, A.H.R., Kofstad, J., Sigaard-Andersen, O., et.al., Vol. 5. Proceedings of the first meeting of the Europeun working group on wn-selective electrodes, IFCC Workshop, Oslo, 1983. Copenhagen; Private Press, 1984. ca~ [135] Meier, P.C., Ammann, D., Morf, W.E., Simon, W., in: Koryta, J. (ed.), Medical and B ~ o l o g ~AppZicat~o~ ofElectrochemical Devices, Chichester: J. Wiley & Sons, 1980; pp. 13-93. [136] Woo, J., Cannon, D.C.. in [183]; pp. 152-153. [I371 Boink, A.B.T.J, Buckley, B.M., Christiansen, T.F., Covington, A.K., Maas, A.H.J., Miiller-Plathe, O., Sachs, Ch, Siggaard-Andersen, O., Utrecht: International Federation of Clinical Chemistry (IFCC), Document 8907-15, 1989; pp 1-15. [138] Preuss, H.G., Podlasek, S.J., Henry, J.B., in: Henry, J.B. (ed.), Clinical Diagnosis &Management by Laboratory Methods, Philadelphia: W.B. Saunders Gmp., 1991; pp. 119-139. [139] Bowers, G.N., Pybus, J., in: Metes, S. (ed.), Standard Methods of Clinical Chemistry, Vol. 7, New York: Academic Press, 1972; p. 143 [140] Kiilpmann, W.R., Ruschke, D., Biittner, J., Paschen, K., J. Clin. Chem. Clin. Biochem., 1989, 27,33. [141] Lorentz, K., Clin. Chim. Acta, 1982, 126,327. [142] Schales, O., Schales, S.S., J. Biolog. Chem, 1941, 140, 879. [143] Passing, H, Bablok, W., J. Clin. Chem. Clin. Biochem., 1983.21, 709; ibid, J. Clin. Chem. Clin Bwchem., 1984,22,431. [144] Spichiger, U.E.,Seiler, K., Wang, K., Tan, S.S.S., Suter, G., Simon, W., in: IFCC I WGSE-JSCC I CBGE, Proceedings of the 13th International Symposium on Methodology and ClinicalApplications o Blood Gases, pH. Electrolytes and Sensor Technology ,Vol. 13. Hakone, October 69,1991,1992. [145] a) Spichiger, U.E., Freiner, D., Bakker, E., Rosatzin, T., Simon, W., Sensors and Actuators B, 1993, ZZ, 263. b) Spichiger, U.E., Sens. andActuators B, 1997,38,68. [146] Spichiger, U.E. (ed.), “FIA/ SFA, Automation” , Handout of the lectures in analytical chemistry V, 1990. [147] Rosatzin,T., Optische und potentiometrische Sensoren auf der Basis von Fliissigmembranen mit immobilisiertenKomponenten. Swiss Federal Institute of Technology (ETH),8092 Ziirich, Switzerland:PhD thesis Nr.9829, 1992.

References

3 19

[ 1481 Cussler, E.L. (ed.), Diffusion, Muss Transfer in Fluid Systems, Cambridge: Cambridge University Press,

1988. [149] Oesch, U., Simon, W., Helv. Chim. Acta, 1979,62,754. [150] Ciba-Geigy AG (ed.), Wissenschaftliche Tabellen Geigy, Physikalische Chemie, Blut, Humungenetik, StofJwechsel von Xenobiotika, Basel: Ciba-Geigy AG 1979; pp. 70-71. [151] Spichiger, U.E., Freiner. D., Lerchi, M., Bakker, E., Dohner, R., Simon, W., SPIE-Proceedings Vol. 1796, Bellingham, Washington: Soc.Photo-Optical Instrumentation Engineers, 1993; pp. 371-382. [152] Dohner, R.E., Spichiger, U.E., Simon, W., Chimia, 1992,46,215. [153] Fringeli, U.P., Chimia, 1992,46, 200. [154] Harrick, N.J. (ed.), Inrernul Reflection Spectroscopy, Ossining, New York: Harrick Sci Corp., 1979. [155] Fringeli, U.P., Apell, H.-J., Fringeli, M., Lauger, P., Biochim. Biophys. Acta, 1989, 984, 301. [156] Freiner, D., Kunz, R.E., Citterio, D., Spichiger, U.E., Gale, M.T., 2nd European Conference on Optical Chemical Sensors and Biosensors, Firenze, April 19-21. Sensors and Actuators B , 1995,29,277. [157] Kunz, R.E., Sensors andActuators B, 1993,11,167. [158] Kunz, R.E., Kempen, L.U., SPIE-Proceedings Vol. 2068, Bellingham, Washington: SOC.Photo-Optical Instrumentation Engineers, 1994, pp. 69. [ 1591 Boettcher, C.J.F., Bordewijk, P. (eds.),Theory of electric polarization, Vol. 2 : Dielectrics in time-dependant fwlak Amsterdam: Elsevier, 1978. [160] Naegele, K.-D., Die Anwendung der Kramers-Kronig-Analyse zur Bestimmung der Optischen Konstanten eines diinnen Platinoxid-Obe~achenfilms.Freie Universitat Berlin, 1975; PhD thesis. [ 1611 Wagniere, G.H. (ed.), Linear and Nonlinear Optical Properties of Molecules. Weinheim: VCH, Basel: Verlag Helv. Chim. Acta, 1993. [162] Campbell. I.D., Dwek, R.A. (eds.), Biological Spectroscopy. Menlo Park, CA: The BenjamidCummings Publ. Comp., Inc, 1984. [163] Thompson,R.B., in: [14],pp.151. [164] Casay, G.A., Sdealy, D.B.. Patonay, G., in: f141, pp. 183. [165] Czemey, P., G r u m t , U.-W., Sensors andActuators B, 1997,38,395. [166] Taft, R.W. (ed.), Progress in Physical Organic Chemistry,New Yolk. Wiley & Sons, 1985, Vol. 15. [167] Zollinger, H. (ed.), Color Chemistry,Weinheim: VCH Verlagsgesellschaft,1991. [168] Fabian, J., Nakazumi, H., Matsuoka, M., Chem. Rev., 1992.92, 1197. [169] a) Pariser, R., Parr, R.G., J. Chem. Pkys., 1953.21.466, b) Pariser, R., Parr, R.G., J. Chem. Phys., 1953,21, 167. c) Pople, J.A., Trans. Faraaiay Soc., 1953.49, 1375. [ 1701 program running on Silicon Graphics. [ 1711 Citterio, D., Jenny, L., Spichiger, U.E., in preparation. [172] Chemical names of dyes presented in Table 6-5 and Figure 6-19: Nr.1, 9-(diethylamino)-5-imino-5Hbenzo[a]phenoxazine substituted and extended in 5-position; Nr.2,9-[3-( 1-benzopyrane-2-ylidene)propenyl] acridinium perchlorate; Nr. 3, 1,5-bis(p-dimethylaminophenyl)-2,4-pentadum perchlorate; Nr. lH-perimidine-6-yl)-4-(2,2-diethyl-1,2-dihydr0-6H-penmidine-6-ylidene)-35, 2-(2,2-diethyl-2,3-dihydrohydroxy-2-cyclobutene-1-one;Nr. 6, 1,3-bis(dicyanomethylene)-2-[4'-(N,N-~ethy~no)-phenyli~no] indane; Nr. 7 ETHT 5003, l,3-bis(dicyanomethylene)-W-[4'-(N,N-bis(2-ethylhexyl)~no)-phenylamino]indane; Nr.8 ETHT 5002,l -dicyanomethylene-2H~4'-(N,N-bis(2-ethylhexyl)amino)-phenyla~no]indane-3one.



7 Data Validation and Interpretation

7.1 Introduction: What Does "Data" Mean? What Does "Information" Mean? A general drawback of computerization and many new technologies is the production of large amounts of data which are never transformed into information. Data are characters, signs, and terms which have not been properly defined. In analytical chemistry, data are most frequently represented by measured or calculated quantities which, according to IUPAC, are equal to the product of a numerical value and a unit [l]. The system is built upon a set of seven base quantities, each of which is regarded as having its own dimension (see Appendix 12). The unwunt of substance is of special interest in chemistry. It is proportional to the number of specified elementary entities of an analyte. The proportionality factor is the reciprocal Avogadro constant for all substances. The definitive method used in quantifying an analyte is thus, the isotope ratio evaluated by ID-MS(isotope dilution mass spectrometry). However, note that the frequently used concentration unit "moVL" is not supported by IUPAC as a base quantity, the litre is equal to 10-3 m3. The method described by W A C for handling physical data and their units in tables, as well as in.graphs, is known as quantity calculus, and uses measures with such as T / K or p / kPa [11. A dataset can also contain characters, signs, and terms which are not arranged on a continuous metric scale. The evaluation of analytical data is aimed at gaining information related to a particular specimen or sample and to an evaluated system denoted as the object. Each object is characterized by the values or terms of M variables, which are dependent on each other to some extent. To find statistical characteristics within the data of a population consisting of N objects, the M variables are described as X j = ( X i , X2, X3. &. ... XM)and arranged in a dataset. For thejth variable, a column Xi with the N values of N objects and for the ith object a row X i . with the M variables is obtained

The measured variable valuesj that belong to object i are denoted by

Xe The final result is an

N x M data matrix,with the variable values per object in rows, and the values of all objects per variable as the columns.

322


Objectives in Analytical and Clinical Chemistry The objective of clinical chemical analysis and laboratory medicine was defined by the International Federation of Clinical Chemistry (IFCC) in 1972 [3]: "Clinical Chemistry encompasses the study of the chemical aspects of human life in health and illness and the application of chemical laboratory methods to diagnosis, control of treatment and prevention of disease" (Sanz and Lous, 1972). Clinical and laboratory medicine were seen to be more "scientific" fields of clinical medicine than others. "Its task is to provide hard data, thus enhancing the objective component of the art of healing" (Gabrieli [4]).However, the results generated by chemical or physicochemical analysis are only one set of data upon which clinical medicine may base its diagnosis, therapy, and prognosis. (For approved recommendations on physicochemical quantities and units in clinical chemistry see Appendix 12 and ref. [5]. In analytical chemistry, providing "hard data" enhances the objective component in other diagnostic fields such as environmental, food, and pharmaceutical analytical chemistry. In these areas, the interpretation of hard data as a basis for decision making competes with political, ethnological, or economic considerations. Such strategies may entail a loss of hard data. Failure to data process received results in a complete loss of the information. Nevertheless, in many cases, continuous monitoring or repetitive measurements can start the ball rolling." "Data, per se, are lifeless" [4]. They become information through the "knowledge" assigned to them by a receiver. Chemical analysis attempts a step by step increase in information output which proceeds from measuring the value to taking action for medical, environmental, toxicological, sanitary, and other purposes (see Table 7-2). In this context, the management of an analytical procedure in a laboratory involves the definition of quality requirements.

Table 7-1. Analytical tools, variables, and objects defined for clinical analytical chemistry by IFCC in 1979 [2]

Tools: Clinical laboratory test

Analytical method, reagent set (test kit) for investigationsof chemical, hematological, immunologically active, etc., components in biological specimens

Variables

Analyte, laboratory parameter: analyzed, (quantified)component

Objects: Specimen

Originally drawn, unchanged material, available for analysis

Sample

The appropriately representativepart of a specimen which is used in the analysis after pretreatment (test sample)

7.2 The Results of Analytical Tests: Random Numbers or lnformation Base?

323

The following section aims at describing the general relationship between the quality of an analytical process and the yield of information, and relates these to the reliability of the decisions based on such results. The examples given focus on electrolyte total concentration measurements by flame atomic emission spectroscopy (AAS), on potentiometric and optical sensors (see also chapters 5 and 6), and on free ion concentration, in particular the molal activity of the magnesium ion.

7.2 The Results of Analytical Tests: Random Numbers or Information Base? The investigations and approaches to data interpretation presented here are intended to elucidate the general problems associated with the interpretation of analytical data, and to demonstrate some strategies to control and, consequently, to increase the yield of information, as well as to decide on the level of detail which is achieved. Presentation of information content and the procedures proposed for the discrimination of different states is closely related to the technical procedure for step-by-step yield of information (see Table 7-2). Hence some of the strategies, especially those for test validation, are based on binary data, as well as on quantitative test results, which are dichotomized through the use of a discriminator or classifier. The information content is related to the analytical performance of a procedure in each case.

7.2.1 Information, Interpretation, and Decision Making Comprehensive and critical examinations of analytical and clinical decision making are to be found in numerous papers and books. Basically, the evaluation of the efficacy, efficiency, and validity of analytical tests has to be distinguished from the evaluation of procedures for decision making. However, data evaluation and yield of information in analytical and clinical chemistry involve a step-by-step process which starts with the value measured by the analytical instrument and method. The instrumental output is most frequently represented by a metric signal on a continuous scale. By calibrating and standardizing this value, it is transformed into a reliable analytical result. Decision makers and clinicians, in contrast, intuitively regard an assay, in terms of its ability to discriminate between two values or states. This arbitrarily reduces the full information available in an assay to a binary decision. The decision is coded "toxic"/ "nontoxic" in environmental and food control, and "healthy"/ "ill", or "continue therapy"/ "change therapy" in the medical field. The cut-off value is set as a reference limit evaluated specifically for the population involved. The fact that the information obtained through the analytical process is reduced to a binary decision does not necessarily give rise to analyses of poor quality. The extent of uncertainty surrounding the cut-off value can be defined, and is decisive for the discrimination of different states. A cut-off value can be consistent with the limits of a reference interval of a "healthy" population or any threshold level for toxicological investigations, environmental, or food control.

324


The cut-off value is approached and validated from two different points of view: from the perspective of biological setting points, which frequently vary individually; and from the perspective of the validity of the analytical test or procedure applied. Different approaches for establishing the validity of analytical tests related to arbitrary decisions are presented and discussed in the following section. The increase in health expenditure in countries with a high level of welfare provision (in contrast to poorer countries) has alarmed governments (WHO Geneva), resulting in a close examination of the cost-effectiveness of medical care all over the world. There has been a dramatic increase in demand for the analysis of large chemical and hematological profiles and screening investigations with the installation of automated multichannel analysers with a data

Table 7-2.Step-by-step acquisition of information Analytical procedure:

Measured value, analyticalresult, direct reading

Calibration:

Quantitative analytical isult

Standardization, quality control:

Comparison with a reference interval or cut-off value:

Medical, toxicologicalvalidation: (in context with other more or less redundant parameters )

i

Reliable, quantitativeanalytical result

Validated value information reduced to a binary scale: diseased I nondiseased, toxic I nontoxic

i

Reliable and relevant medical or biological information

Z2 The Results of Analytical Tests: Random Numbers or Information Base?

325

output of up to 17,000results per hour. Statistically, it is easy to calculate that > 50% of persons and specimens investigated are out of the reference range "ill" or "toxic" for almost I test result if more than 12 test results are established simultaneously and if the reference value is defined as the c e n d 95% fractile (0.95) [6].One can conclude that a healthy individual is someone who has not been sufficiently tested or a nontoxic specimen is a specimen that has not been sufficiently tested. In clinical chemistry, the search for a sensible and economical use of such analyzers has led to the development of new approaches involving the quantitative validation of clinical assays, even including the interpretation of data and the reliability of the analytical procedure. Overproduction of analytical results or data generates quantities of unused information, a relatively small increase in knowledge, blurred results, and misinterpretations of significant data. This is one of the points which has to be discussed in more detail for on site testing.

7.2.2 What Does Information Mean? The relationship between a source of information (the output of the analytical procedure) and a receiver (the clinical chemist or physicist) is connected by the tern "communication" [7-91. In the field of communication, three different planes are discriminated: the plane of the technical problem, Concerning the reliability of the transfer of information; the plane of semantics, concerning the true content of the transferred information; and the plane of effectiveness, concerning the effect of the received infomation. Semantics refers to the correct allocation of a result to descernible states. In this respect, precision and accuracy are both fundamental performance characteristicsof an analytical test which influence this allocation (see section 7.3). In more detail, efJiciency and eflcucy have to be distinguished (see below, compare section 1.1). The technical problem is managed by means such as quality assessment programs and proficiency tests [6].Various attempts have been made to manage semantics and effectiveness, with varying degrees of success. The communicationchannel inevitably contributes to the quality of the transduced signal and the yield of information, depending on the capacity of the channel, the efficiency of the coding process, the noise (dissipation) and the type of information (continuous or discrete). Using these variables, the relative amount of effectively transferred information Z(D;T), called transinformation or synentropy, can be estimated (see Berger's diagram, Figure 7-1 and [9]). In communication theory, infonation usually refers to the relative amount of information which can be transmitted or yielded, and is denoted as the degree of freedom to select one piece information from the total. The total amount is equal to 1. The relative amount is defined by the logarithm of the decision possibilities, using logs to the base of 2, the Id or "logarithmus dualis". "Dual" denotes different states (bottom of the Figure 7-1) which are distinguished by two characteristics, e.g., "yes" or "no", "0" or " 1". In contrast,"binary" allows only two states (base 2), e.g. "healthy" or "ill", "true" or "false". The unit of information is called a "bit" (binary digit), proposed by J.W. Tukey [7]. If different states have two possibilities; "to occur" or "not to occur", the dual logarithm Id is used and summed over all the states resolved or discriminated.

326


The question arises whether the yield in information is linked to a stochastic process or whether it derives from previous events, The latter case is known as a "Markoff information chain" or "Markoff process" [9]. Both views are justified for specified decision processes. The term "entropy" is consistent with the description of a stochastic process which generates information. The yield of information is estimated by the reduction in entropy relative to the maximum entropy of the system. A relative entropy of 0.8 characterizes a source of information which has 80% freedom to generate a signal from the maximum degrees of freedom. Thus 20% of the signal is redundant, lost or superfluous (termed "equivocation" in the Berger diagram, Figure 7-1). In spoken English, roughly 50% of signs are determined stochastically, i.e., only 50% of words and expressions are freely chosen. With a degree of freedom of only 20%,a three-dimensional crossword could be created and solved [7]. Generally, the ratio between the information actually used for decision making laand the potential information content of a dataset lmax should be close to one to make maximum use of the reported data. In most cases, la/ Imax 95% probability of correct discrimination between neighbouring classes based only on the analytical variation s,. The number nj of discriminated events for the whole range of observed values (0.51-1.03 mmol/L) is: n j , =~(1.03 ~ - 0.51) / 0.139 = 3.741

That means that only four classes can be distinguished over the whole range of the biological variation, and two values within the reference range based only on the analytical imprecision. The probability that the single result belongs to one of the four classes is: PiNg = 1 / 3.741 = 0.267

The maximum information available from the results of the analysis of total magnesium ions in human plasma is:

I,,,

= - Id (1/ 3.741) = Id 3.741 = 1.903 bits

The reduction in entropy if a person can be assigned to one class, e.g., hypermagnesiemia, with a probability of nearly 1, is: Sinf= 0.267 Id ( 1/ 0.267 ) = 0.509 bit These results suggest that the total magnesium assay has a low discriminating efficacy. The large, relative analytical variation decreases the maximum available information compared with tests of higher precision such as the combined catheter gastric pH sensor [ 141. Alternatively, for many assays, the increase in information content is small if a limiting economical level of analytical performance is exceded. Ideally, about ten classes should be discernible for metric data in clinical chemistry and hematology for a classification of subjects (objects) based on these analytical results. The information content of different variables with respect to their classifying power can be compared and validated. The information theories introduced by Shannon have been exploited for their usefulness in analytical data analysis [15, 161 as well as in clinical decision theories by Keller and Buttner [17-20]. Biittner redesigned the Berger diagram for clinical applications and specifically for medical decision making. The Berger diagram (Figure 7- 1) represents a noisy information channel. It summarizes graphically the reduction in the maximum available information entropy, max. ( H ( D )+ H ( T ) - H(D,T)),related to two conditional events: a state D (diseased, affected) with input probability P ( D ) to be investigated,and the output probability P( r ) of a test T , which results in confirming or rejecting the state D. The maximum entropy or maximum transinformation is reduced: (1) by the equivocation (-H(D/T)), which is equivalent to the uncertainty about D when T is given; (2) by the ambiguity ( + H ( T D ) )which denotes the uncertainty about T when D is given. The equivocation can be improved only by an additional test selective for D. The ambiguity derives from the uncertainty of the test procedure itself and is not related to the state D . The final transinformation or gain in information by the test T on the

Z 2 The Results of Analytical Tests: Random Numbers or Information Base?

H(DIT)

transinformation: I(D I T) and H(D),+(T)

,A

,

329

equivocation

Dl

A

f ambiguity

Figure 7-1. Berger diagram adapted to the conditional relation between a test result T and a state D for a noisy information channel (see text) (modified according to [7,20] with permission) state D,is given by Z(D;T)={ H( T ) + H(D)}- H(D,T). If no relationship between the source D and the output T exists, Z(D,T)= 0. For a complete match of D and T, Z(D; T ) = H( T ) = H(D). The transinformation corresponds to the area of intersection of the population D and T, which is H@)nH(T). This gain in information relies on the input probability P(D) which can be improved by an effective screening process, reducing the population with true negative results. The analogy with thermodynamic entropy and Boltzmann theory has been disputed. One of the major controversies is whether the entropy of information is comparable with that of thermodynamic microstates, since in the latter there is equal probability that events will occur, whereas for information, different probabilities of events are likely [21]. Generally, three different cases of probabilities must be distinguished:the conditionaljoint probability, equivalent to the joint entropy or synentropy or transinformation; the total probability of the system, equivalent to the total entropy; and the probabilities of single states. The joint probability for two events is equivalent to the area of intersectionin a Venn diagram. The related entropy is the joint entropy [9, 20, 211. A consequent modification of the basic notation must result in taking temperature and entropy terms into consideration. Stress or missmanagement of a laboratory will act in a way equivalent to raising the temperature, associated with raising H( T ) and reducing the transinformation Z(QT). The loss of information is not only a problem of semantics, effectiveness, analytical technique, but also of the laboratory management and organization.

Conclusions A dataset used as an information base must be defined as a database where data are associated a minimum of uncertainty and a maximum of information. Thus, the required gain in information on an input state D based on the test results T is expected, and, in addition, the resolution of different states must be possible. The expected amount of information in bit is associated with the variable dynamic range, the detection limit, and the resolution of the test, and must be set for

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each analytical problem. Redundant tests do not increase the yield of information on an input state. Being able to find a strong correlation between input state D and test result T, means reducing the entropy of the system to approximatelyzero. All the investigations described below should be evaluated from the point of view of optimizing the efficiency of tests and the validity of the information base and thus the discriminatorypower of the analytical methods.

7.2.3 The Bayesian Approach Clinical data which include laboratory results are usually integrated into a complex decision process. The practice of evaluating the diagnostic performance of a test as if it were used alone has been criticized. Each analytical tool introduced as part of the decision process contributes to the decision which can be: change the treatment, classify the specimen, validate the state, allocate the patient to a diagnostic group, choose a treatment, or make a prognosis. The emphasis of early papers was focused on clinical decision makmg. The Bayes' theorem was introduced by decision trees [22-251. In decision trees, the reduction in entropy is based on the a posteriori probability of an event, as compared with the a priori probability. The difference can again be interpreted as a reduction in entropy, and thus uncertainty. Statistics and probability theory allow the quantification of an intuitively observed relationship and changes of states, and the revision of an arbitrary opinion in the light of additional infomation. The Bayesian approach is a formally optimal rule for making revisions. The weighting probability at each branch point in the decision algorithm serves to quantify the discrimination of the branching logic. Any assessment of the diagnostic performance seems to require some comparison of the diagnostic decision, based on a test result, with the "truth". The relation between a test result T and a state D can be formulated as P(ZW), the conditional probability of a certain test result T associated with state D within the selected population of interest. The relation can be inverted in answer to the question "what is the probability of an event D,if the test result T occurs P(DZS \T) ?".The Bayes theorem [22] is a method of inverting the order of the conditional probability used in decision trees [24,25]. The conditional probability P(LhT) with respect to an affected population is formulated most simply by:

P(LAhT)= P ( 7 W ) P ( D ) / P 2)

(7-5)

In medical terms, the probability P ( D ) is the prevalence, probability, or likelihood of a disease in the population under investigation. In analytical terms, it can be interpreted more generally as the probability of an event D.The expression P(T)means the total probability of a specified test result within the same population; P(m) denotes the conditional incidence of a test result T associated with state or event D (see also [6]).The basic equation has been generalized for events which occlude each other (addition rule for the cumulative probability P( T ) = CP(Dj) P (mi) for a test result characterizing different states) and for independent events (multiplication rule for the joint probability of the results of strictly independent tests P( T ) = P( T I )P(T2) ...P(Tj) in the case P(T'Q)), described by the likelihood of the coexistence of two or more events [19, 211. Boolean algebra and Venn diagrams have proved helpful. Dj


33 1

may be regarded as a set of mutually exclusive states, such as diseased (DZS) or nondiseased (REF). This notation is intended to cover the situation where the test result T can be associated with other states besides the specified D1 state. The Bayesian rule for this case is given by:

Bayes formula has been applied in the diagnosis of congenital heart disease [26],endocrine disorders [27, 281, bone tumors [29],among others [25]. However, it can also be applied to general analytical problems, where Di is any outcome of an analytical test on a more or less discrete scale, corresponding to the resolution of the test. In this case, the total probability is again given by the number of discernible states along the data scale. Bayes Theorem is generally used in risk assessment and quality assurance. The fundamental validity of Bayes' theorem in the form presented above has been demonstrated in test validations [30] as well as in ROC analysis. The notation was again borrowed from information theory [20,21].

7.2.4 General Validation of Clinical Tests and Analytical Test Results A diagnostic test has been called a "sorting device" [30].It separates more or less efficiently tested subjects according to groups of similar features, and according to the intensity of the "symptoms". The efficiency of such a test is closely related to the setting point of the discriminatorposition, which allows for more or less accurate classifications of subjects in a test population. The accuracy of the classification can be estimated only by an orthogonal, independent procedure with high reliability and diagnosticefficiency (see Appendix 2). Based on a probabilistic approach, a set of test features related to the discriminating power of a test, such as the diagnostic specificity and sensitivity, have been characterized (see Appendix) [31,32].Contrary to the Bayesian approach, the a posteriori probability for "disease" related to a test result T is expressed by the proportion of subjects classified as "diseased" (DZS ) as opposed to "nondiseased'' (REF') since it is argued that the results of a test cannot be denoted as a "probability". In this context an anterior probability or prior prevalence of "disease" or state is stipulated. Under these conditions, the Bayes' probability notation is transformed for diagnostic use in [23]: P( DZS ) P( nDZS ) P(Dzs'T)= [P(DZS)P ( 7 W S ) I + [P(REF)P(TWEF)]

(7-7)

The validity of an analytical test influences that of the related medical decision since the test is the more effective the higher the "a priori" probability or prevalence of the detected disease in the population under research is [30-321. The validity and efficiency of an analytical test result is thus related to its position in the sequence of a step-by-step diagnostic process. This justifies the strategy of using cheap, but less efficient and less well-validated tests for screening, and

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restricting the use of expensive, laborious, but efficient tests with high validity to critical results or limits. However, every screening procedure generates a relatively high number of falsepositive or false-negative results, depending on the position of the discriminator, and thus produces superfluous analysis [6].The position of the discriminator is again related to logistics, based on the test results. A false diagnosis, however, may have serious consequences for individuals, creating fear and affecting the quality of their use.

Terminology (see Appendix 2 ) The limitations of diagnostic "accuracy" as a measure of decision performance has led to the introduction of a suitable terminology to classify the validity of diagnostic tests. In studying a population, the prevalence of a given disease is defined by the fraction of diseased subjects in h population. P is the probability or likelihood for the disease to exist in this population. The sensitvity of the test measures the fraction of true-positive results among all diseased subjects. Thespeci@ity corresponds to the fraction of true- negative results among all nondiseased subjects in a study. The nonspecific@ indicates the fraction of false-positive results among all nondiseased subjects. The positive predictive value corresponds to the fraction of diseased subjects among all positive results, whereas the negative predictive value corresponds to the fraction of nondiseased subjects among all negative results. The eflciency depicts the fraction of sources or subjects correctly allocated to its classes. In contrast, the efficacy defines the probability of results with positive outcome relative to the total analyzed specimens. This fraction is often hardly populated at all in high-through-put screening, and can give rise to enormously high costs. This fraction (parameter) has to be improved by on site analysis. The accuracy or correctness of allocations can be evaluated only by "quasi- errorless" procedures which are known as primary reference procedures. Analytical procedures generally have to be traced back to these primary reference methods (see also section 1.4.4). Within the range of the overlapping frequency distributions of test results for affected and regular sources (see Figure 7-2), and close to the low detection limit of a procedure, an analytical screening test is unable to resolve two states completely,or to differentiatebetween two different levels with a probability close to 1.0. Depending on the dicriminating power (negative and positive predictive value) of the test, the frequency distributionsof the scattered analytical results which characterize two different states, overlap significantly. Hence there is uncertainty about the correct classification of the states (given by the specificity and the sensitivity) and the interpretation of the test results (given by the positive and negative predictive values). By shifting the discriminator position, the allocation may increase the specificity, but at the expense of sensitivity. This could lead to errors of omission (some drunk-drivers or polluting companies not being prosecuted) or to an innocent individual or company being wrongly accused. Figure 7-2 illustrates the interpretation of laboratory data with respect to the frequency distribution histogram of the (true) test results of regular and affected sources or healthy and diseased individuals. Gerhardt [30] presents some examples showing the overall trends in diagnostic parameter values if the discriminator is moved along the histogram of the test


333

Concentration

(b)

False Positive Rate (%I

Figure 7-2. (a) Hypothetical frequency distribution of the (true) test results; Left-hand curve represents results from regular, unaffected sources. Right-hand curve represents results from affected sources. The points indicated correspond to the discriminator positions for data interpretation. (b) Receiver operating characteristic curve. This corresponds to data (a), and is generated by moving the decision level or discriminator position along the x-axis and then plotting resulting pairs of true- and false-positive rates. The points indicated correspond to decision levels in the upper panel: (c) and (d) The test's performance in the overlap region [40]

outcomes (x-axis) in a study of subjects suspected of having, e.g., acute myocardial infarction, relative to a reference population. The reader is referred to this interesting and informative article. Moving the disciminator position along the x-axis results in pairs of true-positive relative ( T P ) to false-positive ( F P ) , and true-negative (nV)relative to false-negative (FN) ratings. Starting with the discriminator position in Figure 7-2a, creates no Fp ratings, but also no TP. Both rates are zero in Figure 7.2b. Moving the discriminator to the position in Figure 7-2c, covers > 50% TP results of affected sources and creates no false-positive results. On shifting the discriminator to lower test values Figure 7-2d, the rate of false-positive results increases, however the true-positive results corresponding to affected sources are entirely revealed. In the position indicated in Figure 7-2e, all negative results corresponding to regular sources are allocated to the affected population. In this last case, the test is clearly useless. Figure 7-2d corresponds to the target position for any screening procedure. In contrast, the discriminator position in Figure 7-2c may be a target position for affected sources where the pollution or disease is relatively inoffensive, but the costs incurred by treatment or further investigations in a reference laboratory (see section 1.4.4) are relatively high.

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Conclusions On account of the key situations discussed above, it is necessary to tackle the question whether the efsiciency or the efsicucy must be improved in the various cases presented. Let us consider Figure 7-2d, where all affected sources are disclosed, but a relatively high rate of false-positive result is involved, e.g., by a screening test. In this situation, the screening test must have a sufficiently low detection limit, however the efficacy of the whole analytical procedure (see sections 1.1 and 1.4.4) is enormously improved, since the rate of true-negative tests in a central analytical laboratory will decrease considerably compared with the situation where all sources are investigated in the central laboratory directly. In this situation, the costs of the analytical process will be decreased, even if the on-site test is not cheap. This relates the value and the returns on investment associated with an analytical test relative to its price. Generally, a gain in the efficiency of data interpretation will be obtained if the discriminator position is clearly defined and optimized between the positions indicated in Figure c and d ,and if the population to be studied has been preanalyzed.

2 x 2 Tables The diagnostic efficiency of a test can be checked by glancing at a 2x2 table (see Table 7-4). Two different states are assumed: DZS ( affected or diseased) and REF (regular or reference, see also Appendix 3); and a binary decision, NEG or POS, representing the results of a test. The paired states are classified by a defined disciminutorposition on the scale of the dynamic range of the analytical procedure. The states differentiatedin the training set are evaluated in a seprate trial by a highly reliable, analytical procedure. Among the true-negative(TN) and true-positive ( T P ) test results, false-negative (FN) and false-positive (FP) results are tolerated.

7.2.5 ROC Analysis (Receiver Operating Characteristics) Receiver operating characteristics (ROC) analysis was fmst applied in radiology and psychology to decide on the validity of an analyticaltest [37-391. The ROC curve, as shown in Figures 7-3 and 7-4, depicts the interrelationship between the diagnostic risk and the prevalence of a symptom in the population studied. It allows a rapid appraisal of the relation between the truepositive (sensitivity) and false-positive (nonspecificity)results, or of the relation between the true-negative (specificity) and false-negative (insensitivity) results, of a given test by the displacement of the discriminant curve along the whole range of overlap between the populations. Essentially, the ROC curve describes the compromises that can be made as a decision threshold is varied. ROC analysis also allows quick comparisons to be made between tests.

7.2 The Results of Analytical Tests: Random Numbers or Information Base?

335

Table 7-3.Schematic representation of a two-class test evaluation matrix, based on the binary result of an analytical test (see also Appendix 4 and text) [30]

Differentiated states

Test classifications

DIS

DIS, NEG FN

DIS, POS TP

Test classes

NEG

POS

m REF, NEG

FP REF, POS

TN I REF Specificity

PV neg

PV POS

REF I NEG

DIS IPOS

Predictive value

REF

Validity of the test

Sensitivity TP I DIS

ROC analysis relies on quantifying the information provided by viewing a dataset in terms of information theory [37]. Where there is equal probability of "signal plus noise" and "noise only", the ROC curve corresponds to the diagonal of the graph . If a dataset contains some information about the presence or absence of a signal, then the conditional probability of a positive response should be > 0. The shape of the ROC curve should occupy the space in the upper left, above the diagonal when a signal is actually present. In terms of information theory, the received message may not be the same as the transmitted message, since a noisy information channel is assumed. The "true" transmitted message corresponds to the presence or absence of the signal or the test result indicating the "true" state. The received message corresponds to the observer's decision about the presence or absence of the signal or state related to the test result. The mean information content I is then defined by the reduction in uncertainty about the state DIS after reception of the result T, averaged over all results of analytical tests received Yj, and is related to the shape of the ROC curve. The third term in Eiq. 7-8 represents the a posteriori joint entropy: I(DIS;T)= H(DIS)- H(DIS\Dy

(7-8)

where H(DIS) is given by the prevalence of the state DIS, and is complementary to the prevalence of the state REF in a training set, DIS = 1 - REF. As described in section 7.2.2, H denotes the entropy.

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In more everyday language, the shape of the is0 information curves is related to the distance d of the mean test results for two different, supposed frequency distributions; the frequency distribution of the noise, and the distribution signal + noise, weighted by the common standard deviation. Full or 100% separation of the two frequency distributions is not available mathematically since 100%is approximated assymptotically. Establishing statistically relevant levels is discussed in section 2.3. Is0 informaton curves known as either "isobias" curves or "isosensitivity"curves. Uncertainty and entropy increase with large numbers of possible states. Additional information is required to reduce the uncertainty that arises when several options exist and nobody knows which is correct [41].The information content can be interpreted as the reduction in the number of binary questions and answers required to specify the true message, exactly or the amount of information to reduce the uncertainty. Contrary to this theory, it seems that larger numbers of independent test results increase the uncertainty, related to the definition of the reference interval as the central 95% fractile of the population REF. In accordance with information theory, redundant tests do not provide full information yield, and are not adaquate for the average fraction H(DIS\ny, where Y is an exponent of the additional orthogonal information of independent tests. If the uncertainty after receiving the message is zero, the information content of the message is equal to the a priori uncertainty and is maximal. If a test result does not change the a priori uncertainty, the information content of the test is zero. In Bayes terms, the mean content of information can be denoted by:

I = I [P( BDIS), P( nREF), P(DIS)] = p(mls)

P( n D I s ) p(D1s) Id( P( nDls) P(D1S) + P( n R E F ) [ 1-P(DIS)]

(7-9)

1

(7-10)

A steep slope of the curve corresponds to a low failure rate of the classification and a high information content, dependent on the prevalence of the true signal or state [37]. The isoinformation plots show that, where there is low prevalence of a state, tests with a higher resolution are needed, which have a lower rate of false-positive and false- negative results, in order to have the same mean information content for a message. However, when comparing tests, the relative yield in information is independent of the prevalence, and it is even possible to do this without calculating the whole course of the ROC plot. To optimize the conditions for highly effective clinical data analysis, especially with respect to screening procedures, the ROC has been proposed [42]. ROC isoinformation curves have been modified for medical use. For example, for a given prevalence of 50%, the lowest failure rate corresponds to a 45" angle of the tangent to the curve. The validation of the test conditions relies on the assumption that both the background noise signal and the analyte signal have the same variation. The IUPAC recommendations for the definition of the limit of decision, detection, and quantification are based on the same assumptions [ 4 3 4 5 ] . ROC curves and ROC analysis have recently been reexamined and recommended for use in a variety of applications [46]. Software for calculating and constructing the ROC plots have been proposed. ROC plots have been used for continuous, as well as for discretely scaled data. For comparisons of the accuracy or efficiency of laboratory tests, the use


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of equal numbers of entities to be investigated was found to be more relevant than the prevalence of the true-positive result.

7.2.6 The Likelihood Ratio The development of medical decision criteria and the calculation of likelihood ratios (LR) were both based on the Bayes' approach, and were developed concurrently [47]. The approach discussed in the last section used better definitions of disease entities than previous analytic methods which relied heavily on doctors' intuition and rather vague diagnostic classifications. The likelihood ratio refers to the relative frequency of healthy subjects in a specified class with test result T compared with the relative frequency of diseased subjects with the same test result. In 1958,peripheral blood indices and symptoms were matched to hematologic diagnoses [48]. This emphasized the usefulness of weighting data with various probabilities. The procedure avoids use of the terms "false-positive" and "false-negative", and works rather with the probability of subjects belonging to REF or DIS. The likelihood ratios for both states are reciprocal. The sum of the predictive values concerned is 1 since only the range of overlap of a test result characterizing two states is involved. The chance of a single value characterizing the

1.0

0.8

0.6

0.4

0.2

0 0

0.2

0.4

0.6

0.8

1.0

Figure 7-3.Isoinformation curves for two different a priori probabilities of the true state P (DIS) = 0.5 and P(DIS) = 0.2. Each curve shows the locus of points on the ROC graph corresponding to the given mean amount of information (in bits) obtained per observation and the two exclusive probabilistic events 71DIS and I\REF, calculated by I in Eq. 2-7, where T denotes the quantity of the test result according to [37]

338

7 Data Validationand Interpretation

state REF or DIS can be predicted from the class to which the test result T belongs. The uncertainty of the decision is estimated on the basis of quality assessment statistics. LR is calculated as the ratio of two conditional probabilities and derives directly from Bayes' theorem. Bayes' probability notation for diagnostic use is:

P(DIS) x P( TPDIS) p(D'ATp) = [P(DIS) P( TADIS)] + [P(REF) x P( TPWEF)]

(7-11)

which is the same as: pvpos =

prevalence of DZS x sensitivity [prevalenceof DIS x sensitivity]+ [prevalenceof REF x (1 - specificity)] (7-12)

with the last term: P( T P W S ) (sensitivity) P( n D I S ) LRD's = P( TPWEF) = (1 - specificity) = P( n R E F )

(7-13)

This term is consistent with the likelihood of the test result T given the state DIS, divided by the likelihood of the same test result or class of test results T given state REF, if the dynamic range of an analytical test is resolved into several classes. The term "true-positive (TP)" disappears under this condition, and the last term corresponds to the likelihood ratio for the diseased state P( nDIS) / P( ZIREF). According to pVpos and pVneg the likelihood ratio must be defined as LRREFor LRDIS. This last formulation shows that the likelihood range covers values between 0 and infinity. P(ZWEF) is equal to 0, in the extreme range of test results; 1, if both likelihood ratios are equal; 0, if the odds of P ( I w E F ) for reference subjects tends to 1 and P(7IDZS) to 0. The slope of a likelihood function represents the validity of the relationship between the test result and the classified states. The likelihood ratio has even been applied in multiple tests [33] and multivariate testing, without making any assumption about the frequency distribution [32]. Hence, the LR was generalized, based on the observation that the LR was found to be the exponential function of the linear combination of a set of analytical test results:

LR(T) = exp ( OQ

+ a1T1 + , . . + amTm )

(7-14)

The problem is then restricted to estimating the weights, OQ to am,in a training set. The likelihood procedures effectively treat the range of overlap of test results in neighboring populations for different states and multiple testing (2'1 - Tm).They are not, however, robust against changes in the assumed prior probabilities and cannot be applied generally. For example, it will be necessary to evaluate such programs in the special situation where the diagnosed population attends a medical center. Although probability models have been studied intensively, the methods are impractical for most cases since they demand precise data of the prior probability for every disorder under consideration, which makes them extremely complex and laborious for multiple tests.


339

1.0

0.8

0.6

ii? 0 I

a 0.4

0.2

0 0

0.2

0.6

0.4

0.8

1.0

P

Figure 7-4. The predictive value P(DZS\ZP) as a function of the prior pobability and the prevalence, P(DZSj, at different values of the likelihood ratio LR = L =(TPDZS) / P(FPWEE;) [42]

7.2.7 Multivariate and Clustering Procedures The procedures involving decision analysis presented so far are free of assumptions concerning the frequency distribution of data. Nevertheless the probabilistic treatment of a data set composed of multiple test results for a set of subjects is tricky. On the basis of probabilistic methods, the decision process has mostly been considered to be a step-by- step process. Recently, however, more sophisticated deterministic programs have been evaluated e.g., identification [49], discriminant [50], and cluster analysis [51] as well as expert systems [25, 52, 531.A11 of these analyses involve a procedure for grouping a number of individuals or objects, each described by a set of variables into two or more groups with similar characteristics.

Discriminant Analysis Statistical analysis restricted to single variables may not be sufficiently informative. Furthermore, test statistics computed for each variable may not be independent, owing to the correlations between the variables. Discriminant analysis uses all variables simultaneously in assigning individuals and objects to previously established classes. This is different from clustering procedures (see below). The method is based on Gaussian distributions. Nevertheless, just a departure from normality can lead to discrimination, as in specification analysis. The values involved can be metrical as categorical. For typical, well-defined groups of patients (e.g., with disorders of the parathyroidal gland) multivariate discriminant analysis increases the

340


efficiency of diagnostic decisions. Discriminant analysis is easy to handle, owing to the availability of software, but this also means that, very often, large quantities of data are analyzed and classified that do not contribute to a gain in information. It is just a topic of discriminant analysis to deduce a dataset to the relevant variables. The term "multivariate"refers to a spectrum of techniques in which the random variation of several variables is used to characterize the difference in location between groups of observations. Discriminant analysis is based on the process of singling out a particular linear combination of the observed variables by a mathematical optimal criterion. Such a linear combination comprises the variables XIi...Xpi for each observation. For each group studied, a variable S i is defined whose mean and standard deviation is computed. The difference between two means, weighted by the mutual pooled standard deviation of the two groups, is the discriminating parameter which is independent on the measuring scale units. In a linear combination, the variable values X l i . . X p i are weighted by the discriminant coeficients p1 ... &, defining the weighted sum S.k (7-15)

The multivariate standard distance can now be defined as the maximum standard distance that can be obtained over all possible choices of to &. The search for the maximum distance can be envisaged as successivelychanging the angle of projection in very small steps (compare Figure 7-6). In 1936, Fisher proposed a linear model where the dependent variable was denoted, e.g., by Wi [54]. W i is a pseudovariable, coding for the groups which are expected in a training set. For the dicrimination of two different groups, the calculation of the code follows the rules: Wi can take only two values, e.g., c2 = n2 / (n 1+n2) and c l = -nl / (n 1+n2), with W i = c 1 if the object i belongs to group 1, and vice versa [50]. n 1 and n2 are the sample sizes or the sizes of the training sets. Conceptually, W i assumes fixed, preassigned values. Fisher's idea [55] relied on estimating the group code in choosing those values for p for which S becomes minimal by applying the least-squares method. Formally, this is identical with multiple linear regression: nl+n2

~~n =

Z

( W i -(&

+

X Ij +

x2i

+ & x 3 j + ... + P n x n i

(7-16)

i=l

The new variable, S.n, is one axis of the two-dimensional distribution of the values of two groups, The orthogonal projection of the discrimination plane, which separates the two groups best, and which represents the discrimination scores of the subjects, is the discrimination function 2. The dependent variable, S,n, can generally be shifted by a bias ko and a constant factor k.This shift does not, in principle, rule out the application of regression procedures to the discriminant analysis. The two methods are equivalent since adding p0 changes neither the mean difference nor the standard distance between the two groups. The multivariate standard distance Dp can therefore be obtained by applying the regression equation to the data and computing Dp 2 for the training set and the predicted group code. The coefficient of determination Rp, which involves the variance-covariance matrix, is estimated from multiple regression, and is introduced in decision analysis. Dp is then computed by:


341

(7-17)

,

The index in Dp indicates that the measure of distance is based on p variables. The remarkable similarity between the two procedures permits the use of the same tests, and hence of F- and tstatistics. Unlike all the procedures discussed so far, partial correlation betweeen variables can be analyzed. By reducing the variables one by one, those with the highest discriminating power can be selected, whereas redundant variables are deleted. In contrast to the "probabilistic" methods described above, this procedure allows a validation of the variables used, and an analysis of the efficiency of the variables, in particular related to grouping problems. Cut-off lines, i.e., discrimination limits, are represented in a multidimensional space by a discrimination plane. Thus, multivariate and clustering procedures are useful alternatives to more traditional "probabilistic"methods [56,57].Again the Bayesian approach has proved useful in multivariate procedures for decision making [46]. In practice, a research program in my group employing discriminant analysis focuses on a particular technical problem. For example, in analyzing whether the activity coefficients of sodium, potassium, calcium, magnesium, and chloride, the ionic strength, and the water concentration of human plasma discriminatebetween different groups of patients, and which of these variables contributes most to the discrimination. Groups were "healthy" students and employees, hemodialyzed patients and emergency cases (AMI, etc). If no discrimination was found, it was concluded that no significant differences between groups need be considered in further studies applying ion-selective devices and interpreting their results and the errors involved.

'Z Figure 7-5. Two-dimensional distribution of the values of two groups, Dlo and D20. Separation of the two groups by a hyperplane A, and a projection of the two frequency distributions on a new z-axis, orthogonal to S1 and S 2 (from 1-56] with permission)

342

7 Data Validation and Intelpretation

Principal component analysis is another multivariate technique. Here, one looks for the axis with the most prominent extension due to the highest variation of the linear combination of variables (equivalent to the maximum of information in the multivariate space). The principal components can subsequently be introduced in discriminant analysis and in clustering procedures, as combinations and condensates of the most relevant variable contributions.

Cluster Analysis Given a number of unclassified individuals or objects, each of which is described by a set of variables, cluster analysis provides a procedure for grouping the objects into a number of classes and subclasses with similar characteristics. Clustering is a non-parametric method for the separation of groups, based on the calculation of distances between single values or linear combinations of variables, such as the principle components. A variety of techniques and clustering algorithms are available. The results of a cluster analysis will be a number of groups, clusters of individuals and, in some experiments, a distance or similarity matrix or graph. The classes are not known in advance, but have to be discovered. Cluster analysis, a discipline of pattern recognition, has been called unsupervised learning. One reason for performing a cluster analysis may be to simplify a large dataset or to reduce data without loss of information. It may also be used to generate a hypothesis on the charcteristics of data. The hypothesis can then be tested using further observations. However, in many cases, groups are generated which cannot be interpreted and classified by the availableknowledge. In calculating distances, different algorithms such as the Mahalanobis or the Euclidean distance or even a k-nearest neighbor algorithm can be used. Different algorithms requiring different clustering techniques can be differentiated: the hierarchical techniques ( k-nearest neighbor), optimization techniques, density-seeking techniques, clumping techniques, etc. A distingushing feature of these techniques is whether the classes are mutually exclusive or not. Clustering based on the first 10 principle components generated by a linear combination of as many as 38 variables has been shown to be appropriate in analyzing a very complex problem. In this instance, a population of blood donors was evaluated and characterized by a set of 38 analytical variables. After applying an iterative algorithm to sort out the central fractile of "healthy" reference individuals, the classification and discrimination of three groups with extreme low-range values, reference range values, and extreme high-range values was tested by applying the k-nearest neighbor clustering procedure, available in SAS software [6].This algorithm, which fulfilled the statistical criteria for discriminating the three groups, provided identical results to those obtained with the iterative algorithm which generated the three main clusters and was, therefore, considered to be the best of those investigated.

Conclusions For all classificationprocedures which apply a set of differently scaled variables, standardization is a problem. Standardizationto zero mean and unit standard deviation of variables for the whole

7.3 Goals in Analytical and Clinical Chemistry

343

set of entities can blur differences between groups. Thus, weighting of variables is recommended. Further, the statistical data within groups are a priori unknown. In many cases, stepwise learning procedures must be applied. Another problem is the choice of the variables which are mainly responsible for the classification. Classification is more efficient with independent variables. For biological data, however, the range of the determination coefficient R2, as a measure for correlation between each of two variables is usually SQRT (RZ) = 0-0.4. Hence, the difference between dependent and independent variables is not very clear in many cases, and independence is therefore a weak criterion for classification. Choosing the principle components in a dataset for clustering avoids the problem since no distinction need be made between dependent and independent primary variables.

Concluding Statements In our culture, the scientific decision, the product of a rational process, represents the highest level of decisionmaking. Its characteristic elements are reasoning, consistency, logic, and prediction. The automation of decisionmaking applies only to the lowest level and is still considered a poor solution for medical or more general analytical decisions. Human memory is assumed to develop by learning. Thus, the intuitive decisions of an experienced person are superior to those of a beginner, an automation, or a computer. Consequently, new data and procedures require much more information to alter than to confirm a formed opinion. The effectiveness of additional information is lower in the prior case for changing an opinion than to confirm an opinion. This means that new methods need a much higher information content, certainty, and performance standard than traditional ones to be accepted and to become widely established. This is a difficulty, with which any new development is confronted. Hence, in many cases it is not enough just to develop a method. Rather, it is essential to show how it can be applied to data in research. The choice of analytical procedures and of the variables introduced in a decision model greatly influence the results of a classification procedure. The efficiency of the classification is associated with the variation within a group relative to the variation between groups, and the analytical and preanalytical variation. The information content and the acceptance of an analytical method is related to the analytical performance, the power of resolution, the detection limit, and the dynamic range. Thus, the definition and knowledge of the overall analytical performance of any method and procedure is of fundamental relevance for any type of application.

7.3 Goals in Analytical and Clinical Chemistry An analytical research laboratory aims to optimize technically analytical instruments and

chemical methods for particular applications. Frequently, a new technique becomes available before many applications have been found. "Optimization" is understood as the development and improvement of a technique which is a continual process. In analytical chemistry for

344

7 Data Validationand Interpretation

Table 7-4. Goals in chemical analysis

Analytical goals: Reliability

Accuracy, precision, selectivity, dynamic range, ruggedness with respect to the biological matrix, . . . . defining the "allowable error"

Availability

Statistical service in daily routine and emergency service

Ethical goals: Relevance

Reliability with respect to diagnostic errors, predictive value, efficiency

Cost effectiveness

Relation of benefit and gain in information to costs

medical use, optimization must fulfill both analytical and medical goals, as shown in Table 7-4. In this volume, the technical viability of a sensor will be discussed with respect to this goal. The technical reliability of a sensor will be discussed. The elements of the performance of sensors that are addressed in official reports [58-611 are accuracy and precision, virtual notations for real measurements, sensitivity and specificity, efficiency and ruggedness, detection limit and quantification limit, etc. (see Appendix 2). These notions are defined in the next section. For clinical, analytical tests, the word "diagnostic" preceeds terms such as diagnostic sensitivity. These terms then have a special meaning restricted to the use of tests related to diagnostic or more general medical decisions (see section 7.2.4 and Appendix 2). To replace an existing test with a new one, the new test has to perform excellently, both technically and diagnostically. However, a test which does not radically change existing interpretative practices, and which is maintains the routine levels of the reference values is preferred.

73.1 Analytical Errors and Biological Variation The total analytical error [TE]includes the systematic error (inaccuracy) and the random error [RE] (reproducibility, repeatability). Systematic errors may contribute to the total analytical error as a proportional error [PE] or a constant bias [CE] or [SE], seen as an intercept in linear regression [62].Even preanalytical errors can contribute to the total error, as indicated by the following equation:


TE = RE + SE + CE + PE

345 (7- 18)

where RE [random error]

-

It(, 50 years) need special attention [72]. Under these conditions,the preanalytical and analytical variation contribute 11.8% to the extension of the true biological reference range (1.0 or 100%). A two-tailed decision cutoff for a symmetric (ideally Gaussian) frequency distribution and a statistical decision level of

348


P = 0.95 is assumed. The allowed overlap of two neighboring frequency distributions is 2.5% each, or 5.0% in total. The relevant.classifying parameter within a group is then the intraindividual or biological variation if further contributions can be neglected. The width of a class and, consequently, the maximum information and resolving power, are determined by this variation, which is taken into account in longitudinal studies and in individual monitoring, e.g., in hemodialysis. These guidelines need to be elaborated for environmental as well as toxicological monitoring. The analytical variation may not exceed 50% of the expected allowable true changes in concentrations or activities; the class width of the resolved states is estimated on the basis of the square root of the total sum of the variances. A change in serial results obtained for an individual is defined as statistically significant,according to z-statistics, for a difference in concentration (Ac) calculated from the following equation:

where z is a multiple in z-statistics which depends solely on the probability selected for significance. This value, derived from a Gaussian distribution, is 1.65 in the unidirectional case at a level of significance of 95% and 1.96 in the bidirectional case. The difference between two single values is statistically significant (2.5% level for the one-tailed normal deviate with z = 1.96) provided that the difference between ion concentrations, &i,tot, or mold ion activities, h i , exceeds, e.g., 2.8times the total variation within this range of values ((m2+ cva2)ln). Another approach has been recommended by the German Society of Clinical Chemistry (DGKC) [73]. The definition of allowable errors focuses on the reference interval of an analyte [6,74]. The analytical goal is limited to less than 1/12 of the interval around the mean regular setting point including the maximum allowable inaccuracy: sa I1/12 reference interval 2 allowable uncertainty

(7-24)

The results of calculations using the allowable uncertaintiesfor the two approaches are shown in Figure 7-7.Most remarkably, the results of the two types of estimations do not deviate considerably. This finding suggests that most of the reference ranges are, in fact, linked to individual variation. The two methods of calculation may produce very different results, if the interindividual variation is very different from the intraindividual;The DGKC recommendations do not take this situation into account.

7.3.2 The Biological Scattering Range as the Dynamic Range The IFCC definition of the reference range relies on a statistical concept: after choosing an appropriate population of control subjects, the reference interval for any laboratory parameter is regarded as the centered 95% interval, for any type of value distribution. It may thus be inferred that the reference interval is obtained after eliminating both the 2.5% highest and 2.5% lowest values on each side of the frequency distribution curve (for a graph see [6]).The cut-off value for decisions is denoted as a reference value specifically evaluated for the population involved.

349


cv [Yo: 3.0

2.98

2.5

7

az

L . " "

CV analytical (CAP, omer)

2.33

Allowable Error in DGKC

2.0 1.5

1.oo

1.o

0.5 -1

0.0

k (4.2)

Ca2+(2.4)

Mg2+(1 .O)

Na' (140)

ci (loo)

Blood electrolytes (mean in mM)

Figure 7-7.Comparison of allowable analytical errors as defined by the CAP and DGKC norms. Experienced analytical day-to-day variations within the reference range referred to mean electrolyte concentrations in mmol L-I according to [77].Reference ranges of total electrolyte concentrations are referred to [6] (see Appendices 3 and 4).Allowable analytical errors for longitudinal studies, CAP,are based on mintra; for transversal studies on cvinter

The diagnostic interpretation of a given analytical result may be related in a very simple way to the reference interval currently in use in the clinical chemistry laboratory. When not consistent with clinical data and paraclinical parameters, the diagnostic power of a given result has to be carefully analyzed. The informativepower of a given result is tightly linked:(a) to the population of control subjects used to describe a reference interval; (b) to the total analytical and preanalytical error in laboratory results, and to the biological variation in the control population; and (c) to the position of the cut-off value, allowing discriminationbetween different populations and the subsequently fixed levels of the parameters considered in diagnosing a disease state. The reference range must be regarded as the biological scattering range of regular sources or "healthy" subjects, and is consequently the dynamic measuring range for "healthy" subjects as well. In many cases (e.g., sodium ion activity in m u m or plasma), it is very small relative to the mean biological activity (see Appendices 3 and 4). The ratio between intraindividual and interindividual variation corresponds to the so-called individuality index I, or Harris ratio, which allows one to estimate how correct it may be to compare the result for an individual with the reference interval [75]. (7-25)

350


single value uncertain

t

1

CAP-postulate f. individ. tests -

.01

.I

.5

1 m Inter

Figure 7-8. Test assessment network for quality assurance programs based on the biological parameters cvintralcvinter , Oa/CVjntra, and the diagonal OalCVinter. The CAP postulate is indicated at malcvintra = 0.5; cvintra l minter indicates the individuality index. The increasing probability of creating false-positive values is denoted by "1. order error", the increasing probability of creating false-negative values is denoted by "2. order error". The individuality index is equal to "single value uncertain" and "anal. method inadequate". The position of the magnesium concentration assay in serum by AAS is shown in face type (from [3] with permission)


351

For values of I higher than 1.4, the comparison with the reference interval creates a large number of false-positive results, for values lower than 0.6, the comparison with the reference interval is of little value. The Harris ratio I for magnesium concentrations in serum derived from Appendix 5 is 0.37. That implies that longitudinal (intraindividual) studies should be preferred as they allow more reliable comparisons and a more consistent interpretation of results. This quality assessment scheme has, however, been largly accepted in different fields of analytical chemistry, basically as a way to define the resolution as well as the detection and quantification limits by the lowest contribution to variation, often called "noise". The analytical performance and the procedures for standardization, calibration, and quality control must be optimized with respect to the recommendations.

Interpretation of the Resultsfor Serum Total Magnesium Concentrations (AAS) as an Example of the Quality Assessment Scheme The analytical variation for the median value obtained for pooled sera in the United States for quality control programs (all methods included) was 12% for a mean value of 0.5 mmol L-l, 6.4% for a mean value of 0.82 mmol L-l, and 5.5% for a mean value of 1.44 mmol L-l. For a plasma pool from the University Hospital Zurich, the Calmagite photometric method yielded an analytical variation of 6.05% for a mean value of 0.81 mmol L-l, and of 5.5% for a mean value of 0.83 mmol L-l. In the Swiss national quality control program, including all clinical chemistry laboratories and all methods, the range of analytical variation observed for various mean values was quite large, with 40% as the highest value for analytical variation. The accepted mean value for a given laboratory is 6%.

Mean:

0.8 Magnesium concentration [mM]

0.94

Figure 7-9. Minimum required difference between two values of a total magnesium test in serum in individual testing assigning a level of significance of 95% in the span of the reference interval [76]

352


According to Fraser [77], the mean intra- and interindividualbiological variationm q, for the serum total Mg2+ level of healthy individuals, expressed as the percentage coefficient of variation, was 2.2% for individual variation in a follow-up period of 2-22 weeks and 5.9% for interindividual variation. Thus, the total biological variation may be calculated as 6.4%. Therefore, when the analytical variation is approximately equal to the biological variation, the CAP criteria are not met. According to the CAP criteria, the allowable analytical variation should be less than or equal to 1.1% for individual tests and less than or equal to 3.15% (or, even better, less than or equal to 2.8%) for group screening. With an analytical variation of 6% and an individual variation of 2.2%, i.e., a total variation of 6.4% in the individual testing, the differences to be observed between two tests in the same individual needed in order to reach the 95% level of significance, for a serum Mg value of 0.8 mmol L-', would thus be k 0.14 mmol L-1. Furthermore, if the calculation includes the established analytical error between laboratories of 12-16%, the differences to be observed would be as high as 0.40 mmol L-*. In group screening, where the analytical variation is 6%, the intraindividual variation 2.2%, and the interindividual variation 5.9%, the total biological variation amounts to 6.3%. The difference between two results necessary to reach the 95% statistical significancelevel is then _+ 0.19 mmol L-1. The detailed presentation and discussion of the results of electrolyte determinations in diluted human blood plasma is presented in [34,75] and in section 6.4.6. In view of the importance of quality control, the results of commercial quality control samples will be presented there. The total concentrationsevaluated by optode membranes are compared with the assigned values and the results of reference procedures. All data are summarized in Table 6-2. In the optical approach, only the sodium-selective membrane fails to meet the requirements for medical decisions, owing to the narrow range of biological variation (mintra = 0.7%) which it can accommodate. However, sodium-selective electrodes do not meet these requirements, either. However, the chemical stability of the membrane is decisive for the analytical reliability of the sensor (see sections 6.4.7.3 to 6.4.7.5).

7.3.3 Accuracy Assessment The investigation of accuracy is the most tricky goal of analytical chemistry. The accuracy of an analytical procedure may be assessed by the following three means: 1. By analyzing primary or secondary certified standard specimens which are very close to the original composition of the native sample. For chromatography,this is identicalwith absolute calibration of the chromatogram peak areas by internal calibration or by applying a factor for absolute correction of relative values.

2. By comparing the results with those of a reference procedure or definitive method, e.g., atomic absorption spectroscopy (AAS), gas chromatography-mass spectroscopy (GC-MS), and isotope dilution mass spectroscopy (ID-MS), where the result of latter are clearly more accurate than those of the procedure examined.


353

3. By standard addition of known analyte amounts to the specimen and calculation of recovery. A special type of standard addition was applied for the potassium-selective optode membrane (see section 6.4.6). Two different known amounts of potassium ion were added and the specimen K+-concentration was estimated from the intercept and slope of the added amounts. An example, which deals with the accuracy or inaccuracy of the chloride optode, illustrates how difficult the experimental evaluation of accuracy can be (see section 6.4.6.1). With the chloride optode, the chloride concentration is determined within the diluted sample. For calibration of the optode, the same commercial standards were applied as for the calibration of the ion-selective electrodes in clinical chemical analyzers (BM standard). However, the evaluation of the inaccuracy of the developed optode was more complex than expected owing to inaccuracies between reference and calibration specimens. Assigned values are evaluated by reference laboratories which exhibit a reliable standard of analytical procedure and a high standard of instrumentation. A large interlaboratory variation is reported in the assignments, however. Experience gain in quality assessment in clinical chemistry, related to different levels of know-how of the staff among other factors, indicates mean that identical results and reproducibilitybetween different laboratoriesmay be more useful than true values. In this respect, it is often preferable to adjust analytical results according to the existing reference values for "healthy" subjects.

P==i requirements:

I

I

Figure 7-10. Graphic scheme of the suitability test (for details, see text and [45,63])

354


The pharmaceutical industry has chosen a different procedure: "catching the problem at its roots" instead of "treating symptoms". Two different documents of the European Federation of Pharmaceutical Industries'Associations (EFPIA (December 1988, Analytical Validation)) and the WHO (World Health Organization, PHA/EC/SPP/88.8) constitute the basis for the quality control assessment of analytical procedures [58, 591. They define the statistical parameters just as the clinical chemical documents do, and demand a suitability test for the complete analytical system before data production starts. Based on general recommendations, a system suitability test has been developed, which can be adapted to various chemical methods, analytical procedures, and instruments. However, the recommended general range of allowable error is much wider than the allowable error for a single analyte in clinical chemistry. Further ways of decreasing uncertainty have been tried. In biology the determination of an absolute value is often impossible. Potentiometry occupies a special position. The evaluation of ion activities, comparable to the pH, is feasible if interaction between the electrode surface and the biological sample can be prevented. Special efforts were made in our laboratory to construct a symmetric cell, symmetric membranes, and the free-flow, free-diffusion reference electrode. Additionally, an impact was made on accuracy control with the aim of producing a reference specimen with assigned values of ion activities (see sections 3.4.2and 5.2). However for optical measurements (see optodes in chapter 6), the technique of using relative measurements to compensate for interference from the biological background can be used very efficiently.

7.3.4 Conclusions and Recommendations for Planning Diagnostic Tests In planning diagnostic tests, the following steps are recommended and should be undertaken:

1. The problem to be solved should be clearly formulated, and the criteria for defining the populations which have to be compared should be as unequivocal as possible. 2. Appropriate analytical tests should be chosen. In the case of a combination of parameters, the combination to be chosen should have potential for increasing the gain in information. Weak combinations, with redundant tests, lead to an increase in uncertainty, and increase the number of false results. 3. The accuracy and precision of analytical methods must be evaluated simultaneously. It is recommended that allowable errors are assessed, and critical differences for the interpretation of results should be estimated at a reasonable level of significance, according to the t-table before starting the test and paying attention to the number of random samples involved in the test. Any concept should be based on the analysis of variance to distinguish random errors from the effects of a treatment or the efficiency of an analytical assay. 4. Preanalytical errors should be eliminated and the sampling procedure must be optimized.


355

In conclusion, the following maxim should motivate the planning of quality assessment program (of Friedrich Schlogl), and, indeed, any scientific development work.

"Acquisition of knowledge can never increase after the last observation"

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[25] Beck, J.R., Meier, F.A., Rawnsley, H.M., in: Stefanini, M., Benson, E.S. (eds.), Progress in Clinical Pathology, New York: Grune & Stratton, 19, pp. 67. [26] Warner, H.R., Toronto, A.F., Veasy, L.G., et al., JAMA, 1961,177,177. [271 Nugent C.A., Warner H.R., Dunn J.T., et al., J. Clin. Endocrinol. Metab., 1964,24, 621. [28] Patrick, E.A., Compur. Biomed Res., 1977, 7,l. [29] Lodwick, G.S., Haun, C.L., Smith, W.E. et al., Radwlogy, 1963,80,273. [30] Gerhardt W., in: [ref 201, pp. 161-204. [31] Gambino, R.S.,Galen, S.R., Beyond normality: The predictive value and efficiency of medical diagnosis. New York J. Wiley and Sons, 1975. [321 Gerhardt, W., Keller, H., Scand. J. Clin. Lab.Invest., 1986,46, suppl. 181, 1. [33] Vecchio, T.J.,New EngL J. Med., 1966,274,1171. [34] a) Spichiger, U.E., in: Lasserre, B., Durlach, J. (eds.), Magnesium a Relevant Ion, London: John Libbey & Comp., 1991; pp. 217-227. b) Spichiger, U.E., Magnesium Bulletin, 1992,14, 24. [35] Albert, A., Clin. Chem., 1982,28,1113. [36] Van der Helm, H.J., Hische, E.A.H., Bolhuis, P.A., in: Galteau, M.M., Siest, G.,Henny, J., (eds.), Biologie Prospective, Tome 11, Paris: Masson, 1983; pp. 887. [371 Metz, Ch.E., Goodenough, D.J., Rossmann, K., Diagnostic Radiology, 1973,109,297. [38] Metz, Ch.E., Seminars in Nuclear Medicine, 1978, VIlI/4,283. [39] Swets, J.A., Science, 1973,182,990. [40] Zweig, M.H., Robertson, E.A., Clin. Chem., 1982,28, 1272. [41] Clegg, D.E., Massart, D.L., J. Chem. Education, 1993,70,19. [42] Van der Helm, H.J., Hische, E.A.H., Clin Chem., 1979,25,985. [43] International Union of Pure and Applied Chemistry IUPAC, Pure & Appl. Chem., 1976,48, 127. [44] Ebel, S., Kamm, K., Fresenius 2 Anal. Chem., 1983,316,382. [45] Spichiger, U.E., Analytische Chemie IV, Statistik-Skripr, Swiss Federal Institute of Technology (ETH), CH-8092 Zurich, 1990. [46] Zweig, M.H., Campbell, G., Clin. Chem., 1993,39,561. [47] Ropes, M.W., Bennett, G.A., Cobb, S., et al.,Ann. Rheum. Dis., 1957,19, 118. 1481 Lipkin, M., Hardy; JD, JAMA, 1958,166,113. [49] Dagnelie, P., Rev. stat. App., 1966,14,55. [50] Lachenbmch, P.A., Discriminant Analysis. New York: Hafner Press, Macmillan Publishing Co., 1975. [511 Everitt, B., Cluster Analysis. Bungay, Suffolk GB:Richard Clay (The Chaucer Press) Ltd., 1981. [52] Trendelenburg, Ch, Experf Systems in Clinical Chemistry, in: [ZO]. [53] Goldschmidt, H.M.J. (ed.),The application of Multivariate Statistical Analysis in Clinical Chemistry and Haematobgy. Tilburg: Raadgevend Buro voor de GezondheidszorgGoldschmidt b.v., 1987. [541 Flury, B., Riedwyl, H. (eds.), Mulihrariate Statistics, London: Chapman and Hall, 1988. [55] Fisher, R.A., Annuls of Eugenics, 1936,7,179. [56] Winkel P., The Multivariate Approach, in: [20]. [571 Vogt, W., Nagel, D., Sator, H., Cluster Analysis as a Help in Interpretation of Complex Data, in: [ZO]. [58] European Federation of Pharmaceutical Industries' Associations (EFPIA), Working Party on the Quality of Medicines, ad hoc Working Party on Biotechnology / Pharmacy (eds.) Analytical Validation, Document III/844/87-EN Rev. 9, December 1988. [59] Accreditation for Chemical Laboratories, Interpretation of the EN45001 series of Standards, Information Sheet No 1, IS1.3-Third draft, 22/10/1991. [601 International Federation of Clinical Chemistry (IFCC), Committee on Standards, Expert Panel on Nomenclature and Principles of Quality Control in Clinical Chemistry, J. Clin. Chem Clin. Biochem., 1980, 18,69. [611 International Federation of Clinical Chemistry (IFCC), Scientific Committee, Analytical Section, IFCUWHO, J. Clin. Chem. Clin. Biochem., 1984,22,817. [62] Carey, R.N., Garber C.C., "Evaluation of Methods", in: Kaplan, L.A., Pesce, A.J., Clinical Chemistry, Theory, Analysis, and Correlation, St. Louis: The C.V. Mosby Company, 1984; pp. 338-359.

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[63] Passing, H., Bablok, W., J. Clin. Chem. Clin. Biochem, 1983, 21, 709, and, J. Clin. Chem. Clin. Biochem., 1984,22,431. [64] De BiBvre, P., Isotope Dilution Mass Spectrometry as a Primary Method of Analysis, Geel: Central Bureau for Nuclear Measurements (CBNM), 1992. [65] Spichiger, U.E.. Qualitatssicherung in der Analytischen Chemie: Lehraufrag und Bedeutung fur die Forschung . Proc. Informationstagung EurachemlSchweiz, 21. August, 1992, ETH-Zentrum, CH-8092 Zurich, Schweiz. [66] Central Bureau for Nuclear Measurements (CBNM), B - 2440 Geel (Belgium); National Institute of Standards and Technology (NIST),United States Department of Commerce, Gaithersburg, Maryland 20899; Promochem S.A.R.L., Certified Reference Materials and Primary Standards for Clinical Pathology and Medical Toxicology, 22, rue Liebermann, F - 67123 Molsheim, Cedex. [67] Young, D.S., Harris,E.K., Cotlove,E., Clin. Chem., 1971, 17,403. [68] Harris, E.K., Am. J. Clin Pathol., 1979, 72,374. [69] College of American Pathologists (CAP) (ed.), Analytical Goals in Clinical Chemistry, Proceedings of the Aspen Conference on "Analytical Goals in Clinical Chemistry", Aspen, U.S.A, 1976., 1978. [70] Fraser, C.G., JIFCC, 1990,2,84. [71] Wang, K., Seiler, K., Morf, W.E., Spichiger, U.E., Simon, W., Lindner, E., Pungor, E., Analytical Sciences, 1990,6,715. I721 Fraser, C.G., Cummings, St.T., Wilkinson, St.P., Neville, R.G., Knox, J.D.E., Ho, O., MacWalter, R.S., Clin. Chem., 1989,35,783. [73] Stamm, D., D.G. Klinische Chemie Mitteilungen, 1990,21/2 ,69. [74] Spichiger, U.E.,Freiner, D., Bakker, E., Rosatzin, T., Simon, W., Sensors and Actuators B, 1993,II, 263. [75] Harris, E.K., Clin. Chem., 1975,21,1475. [76] Spichiger, U.E., Functwnal Neurology, 1992, Suppl. N.2.41. [77] Fraser, C.G. (ed.), Interpretation of Clinical Chemistry Laboratory Data, Oxford: Blackwell Scientific Publications, 1986.



Appendices

These appendices aim to provide useful informations for those interested in analytical chemistry and sensor research, especially in the field of biological applications. Data collected here are not easily available or have not been published elsewhere. Instructions for preparation of membranes, etc., and the synthesis of the two most relevant magnesium ligands are reported.

Appendix 1 Milestones in the Development of Chemical and BiochemicalSensors [ 1,2,3]

1860 1923 1930 1938 1950 1952 1957 1961 1962

1964

1966

1967

Copper wire as a thennoelement Catalytic combustion-typesensor Practical use of the glass electrode for pH measurement Humidity sensor using LiCl film Introduction of the enzymatic Clinistix dry test (Ames) for urinary glucose Galvanic cell-type gas sensor Theory of the electromotiveforce of a solid electrolytecell Solid electrolyte-typesensor Solid crystal ion electrode sensor Basic concept for biosensors Intravascular,intracardiacoximeter for oxygen saturation and blood flow determinationin the reflection mode Oxide semiconductor-typegas sensor Piezoelectric quartz crystal sensor Discovery of the ion-selectiveeffect of valinomycin in metabolic studies ! In vivo oximetry based on two wavelength measurements of hemoglobin and a fiber optical waveguide First reports on the action of antibiotics as complexing agents in vitro and on their use in ion-selectiveelectrode cell assemblies Glucose sensor Discovery of cation-complexingmacrocyclicpolyethers (crown compounds) Studies of the effect of carrier antibiotics on bilayer membrane potentials

Siemens Jonson MacInnes Dunmore

Hersch Wagner Weissburt & Ruka Pungor Clark and Lyons Enson et al. Seiyama, Taguchi King Moore & Pressman Karpany & Silbertrust

Stefanac & Simon Updike and Hicks Pedersen Miiller and Rudin Lev and Buzhinsky

360

1968 1969 1969 1969

1970

1972 973 974 975

977 980 985

1983 1990 1990

Appendices

First use of the term "ionophore" X-ray analysis of the K+-nonactin complex Fluorosensor for oxygen determination Development of macroheterobicycliccomplexes (cryptands) First patents issued for valinomycin and other antibiotics (such as components for ion-selective electrodes) Elucidation of ion transport mechanism Theory of membrane potentials and conductances of neutral carrier membranes (bilayers) Standard procedure for the preparation of ion-selective PVC membranes First application of valinomycin electrodes for K+-determinationin blood serum or plasma ISFET &"-selective electrode based on a tailored synthetic neutral carrier + Urea sensor consisting of a NH4-selectiveelectrode coated with the enzyme urease First synthetic neutral carrier with enantiomer-selective behavior First microelectrode with a tip diameter = 1 pm based on a synthetic neutral carrier First ion-selective field effect transistor (ISFET) based on valinomycin Enzyme FET Fiber optic pH probe for physiological use Evaluation of the first optical potassium sensor based on valinomycin and dry-reagent strips marketed by Ames (Sedyzer) a, b First International Meeting on Chemical Sensors First World Congress on Biosensors, Singapore Demonstration of a working biotest based on catalytic antibodies

Pressman et al. Kilboum et al. Bergman Dietrich et al. Simon Wipf, Simon et al. Eisenman et al. Moody et al. Pioda, Simon et al. Wise et al. Bergveld Ammann, Pretsch & Simon Guilbault and Nagy

Cram and Cram Thomas, Simon et al.

Moss, Janata et al. Janata Peterson et al.

Blackburn et al.

a Charlton, St. C., Fleming, R. L., Zipp. A., Clin. Chem., 1982,29, 1857. Gantzer, M.L., Hemmes, P.R., Wong, D., Eur. Patent Appl. EP 153.641 (Cl. G01N33/00) 1985. Blackburn, G.F., Talley, D.B., Booth, P.M., Durfor, Ch.N., Maritn, M.T., Napper, A.D., Rees, A.R., Anal. Chem., 1990,62,2211.

[l] G o p l , W., Jones, T.A., Seiyama, T., Zemel, J.N., in: Gopel, W., Hesse, J., Zemel, J.N. (eds.), Sensors Vol 3; Weinheim: VCH Verlagsgesellschaft., 1992, pp. 29-60. [2] Seiyama,T., in: Seiyama, T. (ed.), Chemical Sensor Technology Vol. 1; Tokyo: Kodansha Ltd, 1988, pp. 1-14. [3] Oggenfuss, P., Morf, W.E., Oesch, U., Ammann, D., Pretsch, E., Simon, W., Anal. Chim. Acta, 1986, 180, 299.


Appendices

36 1

Appendix 2 Terminology for the diagnostic performance of a test: Characteristics of the source: DIS, diseased, affected; REF, nondiseased, nonaffected population; ALL, n , number of subjects, sources, specimens under study. Interpretation of the analytical test result (t.r.) referred to a fixed discriminator position: POS, positive t.r.; TP, true-positive t.r. (SPOSnDIS); FP, false-positive t.r. (a-error) (=POSnREF); NEG, negative t.r.; TN, true-negative t.r.(=NEGnREF); FN, false-negative t.r. (p-error) (ENEGnDIS); t.r., analytical test result; Xi,class of values of the test or ith test [14]

Terminology

Symbol

Definition

Prior prevalence of DIS, "a priori" probability

P(D1S) = DIS/ALL before test

Frequency of a disease in a population, frequency of affected sources under study before application of an analyticaltest

Anterior prevalence of DIS, "a posteriori" probability

P(D1S) = DISIALL after the test

Frequency of a disease in a population, frequency of affected sources under study after application of an analytical test

Diagnostic sensitivity

TP / DIS

Fraction of correctly allocated DIS, TP results among all DIS

Diagnostic specificity

TN / REF

Fraction of correctly allocated REF, TN results among all REF

Positive predictive value, pV+, TP / ALL POS PVPOS

Fraction of true-positive test results among all positive test results

Negative predictive value, pV-, PVneg

TN / ALL NEG

Fraction of true-negative test results among all negative test results

Efficiency

w+TN

Fraction of correctly allocated specimens among all classified (ALL = REF + DIS)

ALL

Efficacy (new)

TP

ALL

Fraction of correctly allocated positive t.r. among all classified (ALL = REF + DIS)

362

Appendices

Terminology

Symbol

cut-off value (limit) between two adjoining classes of test values, e.g., dissecting REF from DIS, basis for calculation of LR, ROC graphs, specificity, sensitivity, etc.

Discriminative value (discriminator)

Likelihood ratio LR for DIS, UDIS

Definition

P(&/DIS) LR = P(Xi/REF)

probability of DIS allocated to Xi probability of REF allocated to

Two-class test

Test in which two classes XI,X2 of test results are discriminated

Multiclass test

Test in which multiple classes XI,X2... Xi of test results are discriminated

[l] Biittner, J., in: Keller, H., Trendelenburg, Ch. (eds.), Data Presentation, Znterpreration, Berlin,

New York: Walter de Gruyter, 1989, pp. 219. [2] Gambino, R.S.. Galen, S.R., Beyond normality: The predictive value and efJiciency of medical diagnosis. New York: J. Wiley and Sons, 1975. [3] Gerhardt, W., Keller, H., Scand. J. Clin. Lab. Invest., 1986,46, suppl. 181, 1. [4] Vecchio, T.J., New Engl. J. Med., 1966,274, 1171.


Appendices

363

Appendix 3 Biological setting points for total ion concentrations and active molalities of electrolytes. Estimations of the intra- and interindividualvariations in cv/% are referred to the physiological range and had been evaluated for total substanceconcentrations(mol L-l specimen).d The mean water concentration (37 O C ) is assumed to be 0.932 kg H 2 0 L-l specimen

Primary ion

Reference interval a, b, c adults, plasma total ion concentration (mmol L-1 plasma)

Mean setting point of a, b, c active molality (mmol kg-' H20)

Activity Interindividual Intraindividual coefficient for variation d variation d I = 0.1609 mol cvjnter% cvintra % kg1,37 O C f Debye-Hiickel; pitzer f

134-143

105 f

0.742; 0.743 f

K+ b

3.34.8

3.0

0.728; 0.7263

Calcium G2+total ionized f

2.03-2.57 1.00-1.26

0.42 f

Magnesium Mg2+, total b ionized f

0.66-0.95 0.46-0.665

0.21 f

Sodium

Na+ b

& 0.6

& 0.7

4.4

5.1

0.325; 0.3417

2.2 4.1

1.7

0.336; 0.3507

5.9

2.2

11-60 x 10-3 28 x 10-3

0.724

28

pH 7.35-7.45

10-7.51

0.770

5.6

0.3-1.3

0.767

max. 0.9

0.68

Potassium f

f

Ammonium a

NH; Hydrogen concentratione activity

H3 o+(PH) Lithium a Li+, therapeut. in 14 U/mL heparinate

1.o 0.760

364

Appendices

Primary ion

Mean setting Activity point of a, b, c coefficient for adults, plasma active I = 0.160 mol total ion molality kg-I, 37 O C concentration (mmol k g ' ) Debye-Hiickel; Reference

interval a, b, c

Piwr

(mmol L-1)

Chloride c1- b

Interindividual Intraindividual variation a variation d Winter % CVintra %

99-1 11 81-87

83.9

0.741; 0.7446

1.4

1.7

22 -26

18.0

0.701

3.0

4.6

0.56-1.28 0.14-0.32 0.42-0.96

9.4

7.8

0.17 0.25

0.703; 0.330

12 (10-17)

9.8

0.763

Total bicarbonate a

HCO;

Total phosphate

H2FQiI €-PO:-= 114 Organic acids C

R-COO-, as acetate

a

Paschen K., Lammers M., Muller-Plathe, 0.(1987). Lehrbuch der Klinischen Chemie und Pathobiochemie. Greiling, H., Gressner, A.M. (eds.). Stuttgart: Schattauer, pp 368-390. Spichiger, U.E. (1989), A Selfconsistent Set of Reference Values. PhD thesis No. 8830, Swiss Federal Institute of Technology (ETH), CH-8092 Ziirich, Switzerland. Preuss, H.G., Podlasek, S.J., Henry, J.B. (1991), Clinical Diagnosis h Management. Henry, J.B. (ed.) Philadelphia: W.B. Saunders Comp, pp. 119-139. Fraser C.G., (ed.) (1986). Interpretation of Clinical Laboratory Data. Oxford, Blackwell Scientific Publications. Total buffer capacity of blood : 46-52 mmoU1; a pH value of 7.4 is aquivalent to 39.8 nmo1L hydrogen ions. Citterio, D., ZonenseleRtive Elektroden und optische Sensoren basierend auf NZR-Farbstoffen im Hinblick auf kfinische Anwendungen. PhD thesis, Swiss Federal Institute of Technology (ETH), CH-8092 Zurich, Switzerland (in print).

Chemical Sensors and Biosensors for Medical and BiologicalApplications Ursula E. Spichiger-Keller copyright 0 WILEY-VCH Verlag GmbH, 1998 Appendices

365

Appendix 4 Allowable analytical errors as required by CAP for transversal studies (College of American Pathologists), DGKC (Deutsche Gesellschaft fur Klinische Chemie) and 1% maximum allowable analytical error referred to mean physiological concentrationsand concentration ranges in (see section 7.3.1). The last column, shows the total allowable analytical error related to measurements of the active molality and refers to the mean setting point (column 3 in Appendix 3). An ideal slope s, Aemf/decade log activity of 60.6 mV for monovalent and 30.3 mV for divalent ions (310 K), is assumed; emf, electromotiveforce

Analyte

1% total allowable analytical error Ac I mmol L-1 cva/% b

Total allowable analytical error CAP f, b Ac / mmol L-1 CVa / %

Total allowable analytical error DGKC g Ac / mmol L-I CVa I %

Total allowable error emf (mV) CAP, 37 oc; ideal slope assumed

Sodium f 1.39; 1.0 free ion conc/mmol kg-' f 1.05; 1.O

f 0.42; 0.30 f 0.32; 0.30

f 0.75; 0.54

Potassium f 0.041; 1.0 free ion conclmmol kg-I f 0.03; 1.O

f 0.090; 2.2 f 0.066;2.2

f 0.125; 3.05

f0.36 x 10-3;

f 0.0050; 14

f 0.0045; k 2.84 11.5 f 0.00167; 1.37

PH

f0.001

f 0.0028; 2.8

Lithium, activity due to 14 UlmL Li-heparinate therapeutic level

< f 0.009; 1.O

Ammonium

1.o

Hydrogen activity

f0.013; 1.0

f 0.057

f 0.55

* 0.008;

f 0.01

f 3.25; 9.3

f0.26

f 0.17

Calcium total concentration f 0.0227; 1.O free ion conc/mmol kg' f 0.0113 ; 1.0

f 0.0250; 1.1 f 0.015; 1.35

fO.045; 1.98 f0.022; 1.87

Magnesium total concentration f0.0079; 1.O free ion conclmmol k g l longitudinal studies f0.0056; 1.0

f 0.0229: 2.9 f 0.0088; 1.1 f 0.021; 3.7

f0.024; 3.06 f 0.205 f 0.017; 2.9

366

Appendices

1%total allowable analytical error

Ac I mmol L-' cva I % b

Total allowable analytical error CAP Ac / mmol L-l; cv, I %

Total allowable analytical error DGKC g Ac / mmol L-l; cva I %

f0.735; 0.7

f*

Total allowable error emf (mV)

CAP,37 o c ; ideal slope

assumed

Chloride, total f 1.05; 1.0 free ion conc/mmol kg' f0.8439; 1.O

f0.76; 0.9

f 1.05; 1.0 f0.467; 0.56

0. I9

Bicarbonate as total c02

* 0.24; 1.o

f0.36; 1.5

f0.33; 1.4

0.39

f0.0094; 1.0

f0.037; 3.9

f0.060; 6.5

Total inorganic phosphate

H2PO; I HPOz-= 114 Organic anions, anion gap

f0.135; 1.0

a-f see bibliography Appendix 3. g

DGKC: Deutsche Gesellschaft fur Klinische Chemie: the allowable analytical error is limited to 1/12 of the reference range, calculated in % of the mean level. s = l/z x 61.54 mV decade-' (310.16 K).


Appendices

367

Appendix 5 Physicochemicalcharacteristicsof the five biologically most important alkali- and alkaline earth metal cations; a-h biological data for adults; thermodynamic data at 298 K, 1 bar

Features

K+

Na+

Q2+

Mg 2+

Li+

Relative molar mass Mr

39.098

22.990

40.078

24.305

6.941

Ionic radius I pm

138 (6)

102 (6)

100 (6)

72 (6)

76 (6)

Relation r I q

138

102

50

36

Surface area 0 1 pm2

239 300

130 700

125 700

65 100

Relation 0 I q

7.35 = 23

4.02 I= 22

1.93= 2l

1.00= 20

Pokuizability x 106/pm3

1.1

0.3

0.9

0.2

0.03

Softness Q

0.232

0.21 1

0.180

0.167

0.247

Coordination number

6-8

6

(6-1 8

6

4-6

Radius of the cavity (pm) 138 (6) containing the ion 151 (8) (coordination number)

102 (6)

Pref. coordination sphere 0

0

0

0,N, 0 = P(O-)3

Molar entropy of ions g So/ kJ mol -l K-'

0.1025

0.059

- 0.053 1

-0.1381

0.0134 (as>

Enthalpy of hydration dH 1k~ mol-1

- 321

- 405

- 1650

- 1920

- 520

Freeenerg of hydration / H mol-1

- 322

-411.7

-1656.9

- 1857.7

- 463.2

Molar Gibbs free energy of ion solvation h Afce I kJ mol-1

- 283.27

-261.91

- 553.58

- 454.8

- 293.31

Enthalpy of ions at infinite dilution AfHe I kJ m o t 1

- 252.38

- 240.12

- 542.83

- 466.85

- 278.49

~e~

Y

368

Appendices

Features

Rates of water exchange I s-1

10'0

Preferred Iigands

multidentate chelates macrocycles

bidentate bridged

ligands, see Na+, K+ carboxylates

92

11

0.1

2.2

In human blood plasma activity coefficientfor I = 0.15 m o m protein-bound fraction therapeutic level

4

140

2.3

0.9

0.74

0.75

0.34 0.40

0.35 0.30

Squid intracellular nerve tissue

300

10

o.oO05

7

Squid extracellular nerve tissue

22

440

10

55

Total amount of substance, mol / 70 kg

3.59

4.57

26.25

1.44

0.288 x 10-3

- 2.92

- 2.71

- 2.76

- 2.4

- 3.02

Partition I mmolL total concentration in erythrocytes

107

0.05

108

105

0.0045

1 .o

Recommended daily diatary intake (RDA) Reduction potential I V (quo complexes 25 OC)

G2+(as)

Frausto da Silva, J.J.R., Williams, R.J.P. (eds.), The Biological Chemistry of the Elements, Oxford: Clarendon Press, 1991. Christen, H.R. (ed.) Grundlagen der Allgemeinen und Anorganischen Chemie, Aarau: Sauerlander, 1988. Kaim, W., Schwederski, B. (eds.), Bioanorganische Chemie, Stuttgart: B.G. Teubner, 1991. Levine I.N., (ed.) Physical Chemistry. New York et. al. loc.; Mc Graw-Hill Book Corn. (1988). Spichiger, U.E., PhD thesis Nr. 8033, A Self-Consistent Set of Reference Values, Swiss Federal Institute of Technology (ETH), CH-8092 Ziirich, Switzerland, 1989. Morf, W.E., Simon, W., Helv. Chim. Acta, 1971,54,794. Atkins, P.W., Physikulische Chemie, Weinheim: VCH Verlagsgesellschaft, 1987. Eigen, M., Pure and Applied Chemistry, 1963,6, 97.

Chemical Sensors and Biosensors for Medical and BiologicalApplications Ursula E. Spichiger-Keller copyright 0 WILEY-VCH Verlag GmbH, 1998 Appendices

369

Appendix 6 Structures and Physical Data of Plasticizers a (for IUPAC nomenclature see Appendix 7)

Compound (H substituents not indicated)

Acronym or ETH No.

Substituents

crb

log P n c

m.p. (OC)

Halogen alkanes

chloroParaffin (CW

1-chloroatkanes

7.9

6.4-9.3

< 25

Alcohol

4190

dihydrophytol

4332

R = methyl, CH3 R = dxyl, n-C1$I21

0-WOE 0-NPPE 217 220 2480 248 1 43 14 5367 5373

-1, nc8Hl-I phenyl, c6H5 dodsyl, n-C12Hz pentadecyl, n-C15H31 2-octyldodecyl,C1gH37 2-octyleicosyl,C28H57 12-phenyldodecyl,C 1gH29 octadecyl, n-CIgH37 2-(3,7-dimethyloctyl)5,9-dimethyldodecyl, C 2oH41 5-cholestene, c27H45 dimethylpentyl,C7H15 3,7,11,15-tetramethylhexadecyl,C 22H45

R = CxHy

5382 5389 5392

74-76

23.9

5.8 kO.4 8.2 & 0.6 15 f 0.1

11.2 f 1.5 4445

13.5 f 0.5 113-1 13.5

370

Appendices


Acronym or ETH No.

Substituents

8036

4(t-butyl)benzyl, C11H15

8045

12-(4-ethylphenyI)-dodecyl, C2a33 2-((4- t-buty 1)benzyl)-dcdecyl, C21H34 13,13diphenyltridecyl, C25H35 12-(4-butylphenyI)-dodecyl, C22H37

12.8 k 2

o-fluorophenyl,C6H4F 12-bromododecyl,C 12H24Br 12-nitrildodecyl,C 13H24N 12-(o-N02-phenoxy)-dodecyl, c18H28N02 80 mol% 12-bromooctadecyl, C18H36Br 20 mol% octadecenyl,C18H35 6-(pheny1(3,5-bis(6iodohexyl)))hexyl, C 24H3912 12-iodcdodecyl,C 12H24I 1O-chlorodecyl, C1$42&1 2,6-dichlorobenzyl,C 7H5C12 12-fluorododecyl,C12H24.F 4-bromobenzyl, C7&Br 12-nitrododecy1, C 12H24NO2 12-(4-octyloxyphenyl) dodecyl, C 26H45O

2.9 f 0.2 8.7 k 1

8050 8059 8063

FNDPE 4306 4354 5402 5408 R = CxH,X 5462 8030 8031 8034 8035 8037 8055 8057

E~ b

log PTLC

m.p. (oC)

4045 65-67

*

16.1 3 38-39 129-130 69-70

Appendices


x$R Y

O’

m.p. (OC)

Acronym or ETH No.

Substituents

5401

R = dodecyl, n-Ci2H25; X = NO2 R = dodecyl, n-Cl2H25; Y =CF3 R = 12-(4-butylphenyl)dodecyl, C22H37; Z = isopropyl, C3H7 R = 12-(2-isopropyl-6-nitrophenoxy)-dodecyl, C21H3D02 ; Z = isopropyl, C3H7

49-5 I

R = dodayl, n-Ci2H25 R = 2-(3-methylbutyl)5-methylhexyl, C12Hz

49-49.5

7132

\

log PTLC

371

8064

Z

8065

4302

E~ b

53-55

BBPA DBP DOS 264 2041

5372

bis( 1-butylpentyl)acllpate dibutylphthalate bis(2-ethylhexyl) sebacate 3.9 R = 10-hydroxydecyl R = butyl tetra-n -undecyl4.9 benzophenone-3,3’,4,4’tetracarboxylate 11-(2-nitrophenyloxy) undecanoic acid 1-butylpentyl ester

9.3 st 0.6 4.7 f 0.3 11 k 1

22 5 4

312

Appendices


0

4

R-C,

Acronym or ETH NO.

Substituents

8053

R = 12-(2-nitrophenyloxy)dodecyl, c 18H28NO3

TEHP

R = 2-ethylhexyl, CgH17

Mesamoll

R = C 13H27-C 17H35 R = phenyl, C 6H4 R = hexadecyl, n-C1&3; R = 2-nitrophenyl, C 4H4NO 2 R = 2-nitrophenyl, C6H4NO2; R = dodecyl, n-Ci2H2-j R = 4-methylphenyl,C 7H7 ; R = 2-nitrophenyloxyd o d q l , C 18H28NO3

0-R

O \

4.8 '

10.250.9

"-0,

R

'0

R 0' I O=P-0, 0 I

2485 R

R'

8028

0

II

R-S-0, It 0

R'

P P

R-S-N I1 0

4305

8032

\R 8033

R = 4-methylphenyl,C7H7; R = methyl, CH 3 ; R"=heptyl, fl-C7H15 R = 4-methylphenyl,C7H7; R = H; R"=dodecyl, n-C12H25

+

8.1 0.6 58-60 49.5-51.5 38-39

< 25

73-74

a The order is chosen according to increasing number of oxidation, the acronym (alphabetically)

and the ETH number (numerically). Data from 0. Dinten, PhD thesis, ETH 8591, Zurich 1988. Supplementary data are in process by W. Zhang, PhD thesis, Zurich, in preparation.


Appendices

373

Appendix 7 The nomenclature and relative molecular mass of all plasticizers is given below. For plasticizers which are not commercially available, which are liquid at room temperature (m.p. < 30 OC) and show no signs of crystallization in the membrane phase, data for the elemental analysis are given; syntheses are given elsewhere.a The constitutions of all synthesized plasticizers were confirmed by 1H NMR (CDCl3), IR (CHC13), and mass spectra

Halogen alkanes Chloroparaffinb (ClP); 60 wt% C1, C = 11.5

Alcohol derivatives ETH 4190 (DHP, dihydrophytol, 3,7,11,15-tetramethylhexadecan-l-01);analysis calculated for C20H42O (298.55): C = 80.46, H = 14.18; found C = 80.54, H = 14.24

Nitroaniline derivatives ETH 4332 (N-decyl-N-methyl4nitroaniline)

2-Trijluoromethyl derivatives ETH 5406 (octyl-2-trifluoromethylphenylether); analysis calculated for C15H21OF3 (274.32): C = 65.68, H = 7.72

2-Nitrophenyl ether derivatives o-Nitrophenyl octyl ether (o-NPOE). o-Nitrophenyl phenyl ether (o-NPPE). ETH 217 (oNPDDE, 2-nitrophenyl dodecyl ether); analysis calculated for C18H29N03 (307.43): C = 70.32, H = 9.51, N = 4.56. ETH 220 (o-NPPDE, 2-nitrophenyl pentadecyl ether); analysis calculated for C21H35NO-j (349.51): C = 72.17, H = 10.09, N = 4.01. ETH 2480 (2-nitrophenyl 2octyldecyl ether); ; analysis calculated for C24H41NO3 (391.60): C = 73.61, H = 10.55, N =

374

Appendices

3.58. ETH 2481 (Znitrophenyl 2-octyleicosyl ether); analysis calculated for C3a61NO3 (531.87): C = 76.78, H = 11.56, N = 2.63. ETH 4314 (2-nitrophenyl 12-phenyldodecylether); analysis calculated for CaH33N03 (383.53): C = 75.16, H = 8.67, N = 3.65. ETH 5367 (onitrophenyl octadecyl ether, o-NPODE). ETH 5373 (3,7,11,15-tetramethylhexadecyl-2nitrophenyl ether); analysis calculated for C26H45NO3 (419.65): C = 74.42, H = 10.81, N = 3.34. ETH 5382 (3-b-(2-nitrophenyloxy)-cholest-5-ene).ETH 5389 (1,l-dimethylpentyl 2nitrophenyl ether). ETH 5392 (2-(3,7 dimethyloctyl)-5,9-dimethyldecyl2-nitrophenyl ether); analysiscalculatedforC28~9NO3(447.71): C = 75.12, H = 11.03, N = 3.13. ETH 5402 (2nitrophenyl-12-(2-nitrophenyloxy)dodecyl ether). ETH 8036 (4-t-butylbenzyl2-nitrophenyl ether); analysis calculated for C17H19N03(386.14): C = 71.56, H = 6.71, N = 4.91. ETH 8045 (12-(4-ethylphenyl)-dodecy12-nitrophenylether); analysis calculated for C 26H37NO3 (411S8): C = 75.87, H = 9.06, N = 3.40. ETH 8050 (2-(4-t-butylbenzyl)decyl2-nitrophenylether); analysis calculated for C27H39NO3 (425.61): C = 76.20, H = 9.24, N = 3.29. ETH 8059 (13,13diphenyltridecyl2-nitrophenylether); analysis calculated for C31H39NO3 (473.66): C = 78.61, H = 8.30, N = 2.96. ETH 8063 (12-(4-butylphenyl)-dodecyl 2-nitrophenyl ether); analysis calculated for C28H41N03(439.64): C = 76.50, H = 9.40, N = 3.19

2-Nitrophenyl ether derivatives with heteroatom-substitutedside-chain 2’-Fluoro 2-nitrodiphenyl ether (FNDPE). ETH 4306 (12-bromododecyl2-nitrophenyl ether); analysis calculated for C 18H28N03Br (386.33): C = 55.96, H = 7.31, N = 3.63. ETH 4354 (12cyanododecyl-2-nitrophenyl ether). ETH 5408 (12-bromooctadecyl 2-nitrophenyl ether); analysis calculated for C 2 m O 3 B r (470.49): C = 61.27, H = 8.57, N = 2.98. The ‘H-NMR as well as the elemental analysis showed approximately 20 mol% 2-nitrophenyl octadecenyl ether. ETH 5462 (3,5-bis(6-iodohexyl)phenylhexyl2-nitrophenylether); analysis calculated for C3fl43N0312 (719.49): C = 50.08, H = 6.02, N = 1.95. ETH 8030 (12-iodododecyl-2nitrophenyl ether). ETH 8031 (10-chlorodecyl-2-nitrophenylether);analysis calculated for C1a24NO3Cl(315.84): C = 61.24, H = 7.71, N = 4.46. ETH 8034 (2,6-dichlorobenzyl-2 nitrophenyl ether). ETH 8035 (12-fluorododecyl-2-nitrophenyl ether). ETH 8037 (4bromobenzyl-2-nitrophenylether). ETH 8055 (12-nitrododecyl-2-nitrophenyl ether). ETH 8057 (2-nitrophenyl 12-(4-octyloxyphenyl)-dodecyl ether); analysis calculated for C 32H49N04 (511.75): C = 75.11, H = 9.65, N = 2.74

2-Nitrophenyl ether derivatives with polysubstituted phenyl moiety ETH 4302 (3,4-dinitrophenyl dodecyl ether). ETH 4358 (5-methyl-2-(3-methylbutyl)hexyl3,4-dinitrophenylether); analysis calculated for C 18H28N205 (352.43): C = 61.34, H = 8.01, N = 7.95. ETH 4315 (dodecyl-2-methoxy-4-nitrophenylether). ETH 5401 (2,4-dinitrophenyl dodecyl ether). ETH 7132 (dodecyl2-nitro-5-trifluoromethylphenylether); analysis calculated for C 19H28N03F3 (375.42): C = 60.79, H = 7.52, N = 3.73. ETH 8064 (12-(4-butylphenyl)-

Appendices

375

dodecyl2-( l-methylethyl)-6-nitrophenylether); analysis calculated for C31H47NO3 (48 1.72): C = 77.29, H = 9.83, N = 2.91. ETH 8065 (2-(1-methylethyl)-6-nitrophenyl 12-[2-(1methylethyl)-6-nitrophenyloxy]dodecyl ether); analysis calculated for C30HuN206 (528.69): C = 68.16, H = 8.39, N = 5.30

Carbonic acid derivatives Bis( l-butylpentyl) adipate (BBPA) c. Bis(2-ethylhexyl) sebacate (DOS). Dibutylphthalate (DBP). ETH 2041 C (BTCU, tetra-n-undecyl-benzophenone-3,3’,4,4’-tetracarboxylate).ETH 264 (BHDE, butyric acid 10-hydroxydecylester); analysis calculated for C 14H2g03 (244.37): C = 68.81, H = 11.55. ETH 5372 (1 1-(2-nitrophenyloxy) undecanoic acid l-butylpentyl ester); analysis calculated for C26H43NO5 (467.54): C = 69.45, H = 9.64, N = 3.12. ETH 8053 (nitro2-( 12-nitrooxydodecy1oxy)be~ne); analysis calculated for C 1gH2gN206 (368.43): C = 58.68, H = 7.66, N = 7.60

Organ0 phosphates Tris(2ethylhexyl) phosphate (TEHP)

Sulfonic acid derivatives Mesamoll H81 (alkyl-sulfonic acid phenylester); alkyl chain length 13-17. ETH 2485 (hexadecanesulfonic acid 2-nitrophenyl ether). ETH 4305 (2-nitrobenzenesulfonicacid dodecylester). ETH 8028 (4-toluenesulfonicacid 12-(2-nitrophenyloxy)dodecylester)

Sulfonamides ETH 8032 (N-heptyl-N-methyl-4-toluene-sulfonamide); analysis calculated for Cl5H25N02S (283.43): C = 63.56, H = 8.89, N = 4.94. ETH 8033 (N-dodecyl4-toluenesulfonamide)

a

For synthetic procedures see Eugster, R., Rosatzin, T., Rusterholz, B., Aebersold, B., Pedrazza, U., Riiegg, D., Schmid, A., Spichiger U.E., Simon W., Anal. Chim. A m , 1994,289, 1. Techn., Hiils AG, Marl, Germany. Selectophore, Fluka AG, Buchs, Switzerland. Bayer AG, Leverkusen, Germany.


316

Appendices

Appendix 8 Materials and Methods for Magnesium-selectivemeasurements

Reagents For all experiments, doubly quartz-distilled water and chemicals of puriss. or p. a. grade were used. For the preparation of aqueous salt solutions, either metal chlorides were used and the liquid junction potential was taken into account, or 25 mol% of chlorides were replaced by acetate (35 mmoVL acetate, 105 mmoVL chloride).

Membranes The solvent polymeric membranes were prepared according to a using 0.35-3 wt% carrier ETH 7025, 155 mol% (relative to the ligand) lipophilic anionic sites, 0-3.5 wt% lipophilic salt, 36 wt% poly(viny1 chloride) (PVC high molecular mass; purum p. a., Fluka AG, 9470 Buchs, Switzerland) and 55-63 wt% plasticizer. As lipophilic anionic sites, potassium tetrakis(pchloropheny1)borate (KTpClPB; purum p. a. Fluka) was incorporated. As plasticizer onitrophenyl octyl ether (o-NPOE; puriss p. a,, Fluka) was used in standard membranes for comparisons, and as lipophilic salt tetradodecyl-ammonium tetrakis(p-chlorophenyl)borate (ETH 500) (Selectophore Fluka). The membrane components totaling 200 mg for one membrane were dissolved in 2 ml freshly distilled THF (tetrahydrofuran). This solution was cast into a 24 mm i.d. glass ring resting on a glass plate. After solvent evaporation overnight, the resulting membrane, a plastified gel, was peeled off from the glass mold and 7 mm diameter disks were cut out. The membrane disks were mounted in electrode bodies (type IS 561, Philips, Eindhoven, The Netherlands) for emf measurements.

Coating of solvent polymeric membranes The dry membranes described in the previous section were cast onto a round glass plate as used to prepare optode membranes. The glass plates were introduced into the cavity of a spinning head of a spin-on device (see Accessories, Fhka catalogue SelectophoreGO, Fluka Chemie AG, CH-947 1-Buchs, Switzerland). Solvent polymeric membranes were coated with the polymer solutions defined in Table 1 at 600 to lo00 rpm using a glass syringe. The best results were yielded with the 0.8 wt% solution of Twoflex@ EG-85A and the lowest volume applied to the PVC-membrane. The reproducible manual preparation of thin coatings is rather problematic. Coating was controlled by taking the IR-difference spectra in the ATR-setup.

Appendices

317

Table 1.Polymer solutions used for coating

Polymer

Solvent

wt%

Applied volume (ml)

TecoflexB TecoflexB TecoflexB PHBPHV

THF2 THF THF THF/CH2C12: 7 + 3 V-V

0.8 0.8 3 3

0.8 2 x 0.8 1.2 0.75

Medical grade aliphatic thermoplastic polyurethane, type EG-80A and EG-SA, Thermedics Inc., Woburn, M A 4 1 888-1 799. Tetrahydrofurane. 3 Copolymer poly[R-3-hydroxybutyrate/R-3-hydroxyvalerate].

Emf measurements Measurements of emf were carried out at 21.5 f 1 OC with cells of&e following type: Hg I Hg2C12 I KC1 (satd.)

i 3 m o m KC1 i sample solution II membrane II 0.1 m o m MgC12 I AgCl I Ag

For all measurements according to Procedure I (see below) the membranes were mounted in a flow-through electrode system based on polymethacrylate, or polysulfone. The configuration of the whole equipment is illustrated in Figure 4-3. The flow-through system is maintained at 310 K. The flow-through system is operated in a stop-flow mode. The sample is sucked in by a Perista minipump for 20 s (aqueous solutions) or 10 s (samples). The total static data acquisition time is 2 min in 40 cycles of 3 s. The last 6 cycles (6 x 3 s = 18 s) are used for further data proceeding and calculations. The emf value is the mean of the last 6 cycles (6 repetitions) or the mean over the last 18 s. The external half-cell was a free-flowing, free-diffusion liquid-junction calomel reference electrode (see section 4.1). The internal bridge electrolyte is connected with the sample channel through a capillary of 75 pm i.d. and a free-flow of about 2 plh. For all other measurements the membranes were fixed into the Philips IS 560 electrode bodies (N.V. Philips Gloeilampenfabrieken,Eindhoven, Holland). For static measurements, the electrodes were placed in a V-cuvette, furnished with a magnetic stirrer, a calibrated thermometer and three positions for two ion-selective electrodes and the reference electrode. The V-cuvette was maintained at 310 K. Potentials were recorded by a custom-made 16-channel electrode monitor (resolution -120 pV) equipped with one FET operational amplifier AD 515 KH per channel (Analog Devices, Norwood, MA; input impedance 1013 R/2 pF); input bias

378

Appendices

current < 150 fA; capacity neutralization). The signal was digitized by a 14-bit analog-to-digital converter DT 1744 (successive approximation, full scale f 500 mV, Data Translation, Natick, MA). Data aquisition was made with a Macintosh SE. Plots were made with a Hewlett-Packard HP. The measured emf values were corrected for changes in the liquid-junction potential by applying the Henderson formula (see section 3.4). Single-ion activity coefficients were calculated by the Debye-Huckel formalism.

Calibration solutions Solution low: MgC12 0.35mmolL; CaCl2 1.35 mmol/L; KCl 4.0 mmoVL; NaCl 100 mmolk; NaOAc 40 mmolL. Solution High: MgCl2 0.75 mmol/L; CaC12 to NaOAc identical. Buffering of the calibration solution to pH 7.4 increases the uncertainty in the estimates of single activity coefficients and ionic strength without any relevant contribution to complete dissociation.

Selectivity determinations Procedure I: Specific application method (SAM).After a three-point calibration (calibrators A, B and, C) 10 aqueous test solutions (see Table 5 ) were measured alternately to the middle range calibratorin a 3 min time intervall in the following sequence: A-B-C-B-1-B-2-B-3-B-4-B-5-B6-B-7-B-8-B-9-B-10-B (the letters and numbers refer to the solutions given in Table 1). The solutions were changed by removing the small beaker with the preceding solution, starting the pump, introducing the next solution, stopping the pump, and simultaneously starting the data aquisition. The magnesium activity of the test solution was evaluated from the emf difference AE (see Eq. 4) to the middle range calibrator B by a formula derived from the Nikolsky equations. The selectivity coefficient was evaluated by approaching the best least-squares fit to the response function in an iterative procedure. In order to determine the Nikolsky equation which best fits the assigned magnesium activities of the 10 aqueous test solutions, the value of < 0; stepwidth 0.05). The one 1 o g K g L was varied over a large range (e.g., -1.5 < logK with the minimum least-squares sum of the relative deviations of the measured magnesium activities from the assigned values was selected as the most reliable.

Synthesis of OH-PVC (ETH 3523, ETH 3526 and ETH 3528) Poly(vinylch1oride)hydroxy-PVC(OH-PVC) was prepared by saponification of a polyvinylchloride/polyvinylacetate-copolymer (ICI C5712/143C, I.C.I. (Switzerland) AG, Kunststoff werk CH-5643 Sins).

Appendices

379

Table 2. Elementary analysis for the used copolymer and calculated values for OH-PVC (completely hydrolysed copolymer)

Element

Copolymer (ICI C 57121143 C) (wt% determined)

Copolymer (mol%/lOOg)

OH-PVC (wt% calculated)

OH-PVC (mo1%/100g)

C

41.24 5.19 47.28

33.27 49.96 13.00

39.93 5.24 51.46

32.57 51.23 14.31

H C1

For the saponification of the ester groups, three different reaction conditions have been chosen (see I to 111, Table 3). The resulting products have been tested by the help of assymmetry potential measurements. The copolymer yielded from procedure 11 (Table 3) showed the best performance (see section 5.2) in view of stability of the emf and composition (see Table 4). To a cold solution (-10 "C) of 10 g copolymer in 200 ml of freshly distilled THF were added (over a period of 20 min) 55 ml of a methanolic NaOH solution (0.5% NaOH by weight). The reaction solution was constantly stirred at -10 "C. After 6 h the precipitated polymer was filtered off and extensively washed with 1500 ml of distilled water. The polymer was crushed mechanically and again it was washed with 300 ml of water and 300 ml of ethanol.

Table 3. Three different ways to prepare OH-PVC. The reaction conditions according to II (ETH 3528) were the most rewarding

II ETH 3528

m

ETH 3526 5 basic, 30 ml 0.5% NaOH in MeOH 0 5 25 pale yellow 3.25

10 basic, 55 ml 0.5% NaOH in MeOH -10 6 25 almost whte 6.87

10 acidic, 1 ml conc. H2SO4 in 100ml MeOH 70 24 25 white 8.69

I

Amount of copolymer (g) Saponification

Reaction temperature ("C) Reaction time (h) Drying at high vacuum ("C) Colour Yield (g)

ETH 2523

380

Appendices

Table 4. Elementary analysis for the three OH-PVCs prepared under different reaction conditions

Determination

Element

Mean value out of two determinations for ETH 3526 ETH 3528 ETH 3523 a

Right after preparation

C H

a

39.59 5.07 53.15

After 2 months

c1

48.96

After 12 months

C H c1

a

39.73 5.13 52.68

39.57 5.21 53.60

39.85 5.29 52.10

only one determination

For purification the polymer was dissolved in 180 ml THF at 40 "C an by adding 1200 ml of ethanol it was induced to precipitate. After washing with ethanol the precipitate was filtered off and dried at room temperature. Yield: 6.87g of almost white polymer (ETH 3528,see Table 4). Procedure ZZ: Selectivitycoefficients1oapot according to the separate solution method (SSM) $a were obtained in 0.1 moVL unbuffered soluhons of the correspondingchloride salts. Procedure IZZ:The interfering influence of sodium and potassium was studied by recording the emf response to solutions containing a fmed amount of magnesium and a variable amount of the interfering ion (either 90-190 mmoYL sodium or 2-8 mmoYL potassium). The emf values were corrected for changes in the magnesium activity caused by the changing ionic strength of the solutions.

Appendices

38 1

Table 5. Composition of calibrators A, B and C and the test solutions 1-10 used in Procedure I

Aqueous solution composition

A

B C 1 2 3 4 5 6 7 8 9 10

[Mg”]

[a2+]

ma7

[K+I

IINllOVL

llllnOVL

IINllOIL

mmoYL

0.30 0.50 0.75 0.60 0.60 0.60 0.30 0.40 0.40 0.40 0.65 0.84 0.50

1.oo 1.30 1S O 1.30 1.60 1 1.30 1.30 1.oo 1.60 1.20 1.35 1.30

120 140 150 140 140 140 140 140 140 140 130 140 140

6.0 4.0 3.0 4.0 4.0 4.0

.oo

4.0 4.0 4.0 4.0

4.0 4.5 4.0

Calculations

(12-1)

(12-2)

measured emf value for calibrator B measured emf value for the test solutions (1-10) magnesium activity of calibrator B magnesium activity of the test solutions (1-10) calcium activity of calibratorB calcium activity of the test solutions (1-10) selectivity coefficient slope (evaluated according to Eq. 12-2) of the calibration function in the section (B-A or B-) with the same sign for AE

382

Appendices

Resistance Resistance measurements were carried out as described by Oesch and Simon.b The reduction of the potential by a known shunt resistance is measured. The initial potential E may be 200 mV, and the known shunt resistance R, was of such a magnitude that a potential reduction A E of about < 20 mV resulted. The membrane resistance R , will then be R, = R (AE / E - AE). The precision of the determination of the specific membrane resistance p was A(1og p) c 0.2.

,

Lipophilicity The lipophilicity P of the ionophore was determined by thin layer chromatography (TLC) on reversed silica plates according to the procedure described previously.c The Pmc values obtained by this method are closely related to waterll-n-octanol partition coefficients.

Preparation of microelectrodes Single-barreled borosilicate glass (Pyrex) capillaries of outer diameter 1.5 mm and inner diameter 1.O mm (GC 150T-15,Clark Electomedical Instruments, Pangbourne, Reading, UK) were cleaned according to d by immersion in 55% HNO3 and additon of small aliquots of ethanol at intervals to maintain a vigorous but controlled evolution of N02. The glass is then rinsed and finally boiled in multiple changes of distilled water. The glass capillary is drawn into micropipettes with a vertical puller (model 7OOC David Kopf Instruments, Tujunga, CA, USA). Their tips were broken and silanized as described elsewhere e. The silanized micropipettes, with a tip diameter of -1 km, were back-filled with 10 mmol/L MgC12. The tips were dipped into the membrane phase and a slight vacuum was applied to suck the membrane solution into the micropipettes. They were then left in air for at least 4 h to let the cyclohexanone evaporate, upon which the initial filling height had decreased by 50% to 100-400 pm. The microelectrodes were completed by inserting a chlorinated Ag Wire fixed with wax. They were conditioned in 10 mmoVL MgCl2 overnight. The half-cell was coupled to a standard calomel reference electrode of the free-flow free-diffusion type.

-

Membrane phase Compositions of membrane solutions are given in the text. A mixture of 88 wt% of the membrane cocktail and 12 wt% of poly(vinylchloride), diluted with 3 times its weight of cyclohexanone, was used for fabricating microelectrodes by the front-filling technique.

Appendices

383

a Moody, G.J., Thomas, J.D.R. (eds.), Selective Ion Sensitive Electrodes, Watford, Harts.: Merrow

Technical Library, 1971. Oesch, U., Simon, W., Anal. Chem., 1980, 52, 694. Dinten, O., Spichiger, U.E., Simon, W., et al., Anal. Chem., 1991, 63, 596. Tsien, R.Y., Rink, T.J., Biochim. Biophys. Acta., 1980,599, 623. Deyhimi, F., Coles, J.A., Helv. Chim. Acta., 1982, 65, 1752.

Appendix 9 Required logarithmic selectivity coefficients based on SSM evaluations (IUPAC, see section 4.3) for the assay of a primary analyte ion I at the lower edge of the reference interval and

discrimination of an interfering ion J at the upper level of the reference interval calculated based on a minimum allowable error according to Table 2. Direct measurements in the specimen are differentiated from measurements in a 1+19 diluted sample. Data are calculated for an assay without calibration of the activities of the ion backgound as well as with calibration of a mean physiological background (2% complexation for Na+, but no complexation of further monovalent ions is assumed) [I]

Primary ion I

Mean physiological

Secondary interfering ions J

setting point of activity for background calibration (minimum activity)

Undiluted specimen a

Diluted sample (1+19) b

log required selectivity coefficient background calibration background calibration without c

withd

without c

with d

Mean active molality for calibration Allowable error in %

Sodium Na+

Na+

(0.1005)

Ch2+(i)

- 1.1 - 1.9

- 0.78

- 1.1 - 2.65

- 0.33 - 1.6

0.108

Msl’

- 1.7

- 0.45

- 2.4

- 1.2

+ 1.2

+ 0.84

+ 1.2

- 0.52

+ 0.18

K+

+ 0.84 H3O+ (pH) + 3.8 Li+ (therap.) - 0.52 NH4

k 0.3%

- 0.33

+ 4.8 + 0.18

384

Appendices

Potassium K+ (2.44 x 10-3)

Na+ K+

- 3.7

- 2.2

- 3.7

- 2.2

ca2+

- 3.0

Mg2+

-

2.8

- 1.9 - 1.6

- 3.8 - 3.5

- 2.7 - 2.3

mi

- 0.25

+ 0.2

- 0.25

+ 0.2

H30f (pH) Li+

-

1.6

- 0.91

- 1.6

- 0.91

Na+ K+ Ca2+ Mg 2+

- 3.6 - 0.7

- 2.4 - 0.16

- 2.0

- 0.77

+ 0.97

+ 1.5

- 1.9

- 0.9

- 1.9

- 0.9

N H ~ H3O+ (pH) Li+

+ 3.2

+ 3.4

+ 4.8

+ 5.0

+ 0.9

+ 2.1

+ 2.5

- 3.9 - 1.0 - 2.5

- 2.7

- 2.4

- 2.1

- 0.5 - 1.7

- 2.5

- 1.7

+ 2.9 + 8.9 + 0.2

+ 3.1 + 9.6 + 0.64

3.1 x 10-3

f 1%

Calcium Ca2+ ionized (0.690 x le3; 0.381 x 10-3) 0.765 x 10-3 (total)

f 0.85%

+ 2.7

+ 9.2 + 0.5

+ 3.7

+ 9.9

0.42 x 10-3 (ionized)

f0.85%

Magnesium Mg2+

Na

+

K+ (0.231 x 10-3; ionized 0.162 x 10-3)

ca2+ Mg 2+

0.2975 x lW3 (total)

N H ~ H3O+(pH) Li+

f 1% 0.208 x 10-3 (ionized)

f 1%

+ 0.5

+ 4.4 + 1.7

+ 1.1

Appendices

Ammonium NH; (0.80 x l e 5 )

Na+

- 6.1

- 4.6

- 6.1

K+

- 3.8

- 4.6

- 4.6 - 3.8

ca2+

- 4.7 - 5.4

- 4.4

- 6.2

- 5.2

Mg 2+

- 5.3

- 4.0

- 6.0

- 4.7

H3O+ (pH) Li+

+ 0.25 -4.1

- 3.4

- 4.1

- 3.4

Na+

- 9.4

K+

- 7.9

2.8 x 10-5

f 1%

+ 1.2

ca2+

- 8.7

(2.5 x 10-5; 3.4 x l@)

Mg2+

- 8.5

- 7.9 -7.1 - 7.6 - 1.3

4.9 x 10-5 3.98 x 10-8 (pH 7.4)

NH; H3O+ (pH) Li+

- 6.0

-5.6

- 7.3

- 6.6

- 4.7 - 3.2 - 4.0 - 3.8

- 3.2 - 2.5 - 2.9 - 2.6

- 4.7 - 3.2 - 4.8 - 4.6

- 3.1 - 2.5 - 3.7

NH; H3O+@H) Li+

- 1.3

- 0.89

+ 2.7

- 1.3

- 0.88

+1.7

HCO; RCOOSCNH2P9j

- 1.6 - 1.4

- 0.3 - 0.7

- 1.6 - 1.4

+ 0.8 + 0.4

+ 1.05

+ 0.8 + 0.4

- 0.3 - 0.7

Hpo4

- 1.54

- 0.57

- 2.04

- 1.2

Hydronium ions H3O+ (PHI

f0.13% (ApH f 0.005) ion activity

Lithium Li

+

Na+ (0.230~lW3)

K+

mean therapeutic level: 0.767 x

Mg 2+

Q2+

f 1%

Chloride C1(73.4 x 10-3) 8 3 . 6 ~10-3

f 0.7%

- 3.3

+ 1.05

385

386

Appendices

Hydrogencarbonate HCO;

c1RCOO-

(15.7 x lW3)

SCN- e H 2 q HP04

- 2.8

- 1.9

+ 0.13

- 1.5 - 1.4

- 2.8

- 1.9

- 1.5 - 1.4

+ 0.37

- 0.17 - 2.7

- 1.9

- 2.4 - 1.1 - 0.78

- 1.4 - 0.24 - 0.5

+ 0.13

+ 0.37

- 0.17 - 2.1

- 1.2

ClHCO; RCOOSCNH2P04

- 3.7 - 2.4

- 2.7 - 1.5

c1HCO; RCOO-

- 5.0 - 4.3

- 3.6

- 4.1

- 3.6

-4.1

- 3.6 - 3.2 - 3.6

SCN-

- 2.1 - 4.3

- 3.4

- 2.1 - 4.9

- 4.1

18x 10-3

k 1.0%

Phosphate HPOi(0.14 x l e 3 ) 0.25 x 10-3

- 2.1

- 1.8

+ 2.0 + 1.4

+ 1.7

+ 3.3 + 2.7

+ 3.0

f 1.0%

Phosphate H2P04

(0.098~10-3) 0 . 1 7 ~10-3

mi-

- 3.2

- 5.0 - 4.3

f 1.0%

a

C

Calculations based on molal activities as far as available (sodium, potassium, and chloride, especially). Calculations based on activities derived from total substance concentrations, assuming an ionic strength of 0.16 mmol/L. Without: activity of the interfering ion = upper limit of reference range; activity of the primary ion = lower limit of reference range. With: activity difference of the interfering ion between mean value and the limit (upper or lower) resulting in the higher difference within the reference range; activity of the primary ion = lower limit of reference range. SCN- as interfering ion is supposed to be at the mean level for smokers - ca. 0.12 mmoYL.

[ 11 Spichiger U.E.in: Encyclopedia of Analytical Science, London: Academic hess, 1995, pp. 2341.


Appendices

387

Appendix 10 Chemical Syntheses An optimized synthesis of the Ionophor E m 5506

---core

b

C

a'

recognition lipophilic bridge unit amide terminus

a

ETH 5506 A, B, C,= CH2 ; X,Y,Z = 0 First step: Connecting the core region with the bridgen (1,3,5-tris(pent-4-en-l-yl)benzene[11)

//"\/\/

Br

Mg CI

CI

Ni(C1)2(dppe),Et20, r.t. $1

To 5.4 g (222 mmol) Mg shavings in 30 ml dry Et20 were added dropwise 31.9 g (214.1 mmol) 5-bromo-1-pentene. Gentle reflux was established (Grignard-conditions). The mixture was boilt (20 min), cooled down to 0 "C and a suspension of 110 g (60.6mmol) trichlorobenzene and 250 mg (473 kmol) of nickel-(bis)-diphenylphosphine ethane dichloride in 70 ml Et20 was added dropwise. Stimng (24h, r.t.), quenching (100ml cold water, 50 ml2M HCl), extraction (150 ml AcOEt), washing (70 ml 2M HC1, 70 ml 2M NaOH, brine), drying (MgSO4). The raw product (13.2g) was distilled (11&115 "C / 0.03 Tom). Yield: 12.93 g (45.8 mmol, 76%) of $1as a colourless oil.

388

Appendices

Rf: 0.32 (hexane). bp: Kugelrohr: 170 "C / 0.08 Torr. *H NMR (CDC13, 200 MHz): 6.82 (s, 3H), 5.84 (ddt/17.0/10.4/6.6; 3H), 5.02 (d, br117.0; 3H), 4.97 (d, bd10.4; 3H), 2.56 (t, bd7.7; 6H), 2.09 (9, bd7.1; 6H), 1.70 (quintett, bd7.5; 6H). l3C NMR (CDC13, 50 MHz, D E E ) : 142.4 (s), 138.8 (d), 126.1 (d), 114.6 (t), 35.2 (t), 33.3 (t), 30.6 (t). ea: (% cdc.): C (89.30), H (10.70), (% found): C (89.37), H (10.56).

Second step: Amination of $1by iodindpotassium phtalimide (1,3,5-tris(5-phtalimidopent-ly1)benzene [2,3])

$1

I

1

l.)NaOMe, 12,MeOH

,DMF, 70" C

$2

To 32.3 ml 1M borane-THF solution (Fluka purum) in THF (-20°C) were added dropwise 5.56 g (67.7 mmol) cyclohexane. After 1 h at -10 "C a white suspension has formed and 3.026 g (10.71 mmol) 1,3,5-tris(n-pent-4-ene-y1)benzene$1 were added dropwise. The reaction mixture was stirred for 1 h at r.t., cooled to -10 O C and 1 ml MeOH and 16.31 g (64.3 mmol) I2 (Fluka purum) were added. A solution of 1.602 g (69.7 mmol) Na in 25 ml MeOH (-20 "C, 30 min.) and 120 ml 10% sodium thiosulfate solution was added. Extraction (120 ml hexane), washing (50 ml 10% sodium thiosulfate solution, 3 x 75 ml brine), drying (MgS04) and evaporation. The solid was dissolved in 55 ml DMF and stirred with 7.4 g (40.0 mmol) potassium phtalimide (7 h / 70 f 10 "C).Extraction (3 x 50 ml AcOEt/DCM, 9/1), filtration (celite), evaporation. Twice recrystallized from AcOEthexane (-20 "C): 3.50 g (4.84 mmol, 45%) white crystals of $2.According to the melting point and the lB NMR spectrum, this product reveals to be identical with the one synthesizedby ODonnell et al. [4].

Appendices

389

Third step: Reduction of the phtalimido unit $2 with N a B b

Kugelrohr

i-PrOH, 15% H20

R

R

R 0

R=

R=

-(CH.&IND

R=

{CH2)NH2 5

HO $3

$2

$4

To 2.391 g (3.51 pmol) $2 in 40 ml isopropanoVwater (17/3) were added 1.24 g (32.8 mmol) NaBQ. After stirring for 22 h at r.t. the reaction mixture was extracted (200 ml AcOEt/DCM (4/1)). This afforded 2.09 g of $3 which was transformed into $4 by Kugelrohr distillation. Yield: 1.19 g (1.72 mmo1,49%) $4.

Fourth step: Preparation of the precursor of the recognition unit and the lipophilic amide tenninus

$11

$9

a: 1.) (CF,CO),O, NEt3, THF, 2.) KOH,MeI, acetone b: KOH, 18-crown-6,THF, reflux c: toluene, reflux, 4A molecular sieve, 80% d: 1.)KOH, EtOH reflux, 2.) p-nitrophenol, DCC, EtOAc, 40%

390

Appendices

a) To a suspension of 100.2 g (533.8 mmol) l-aminoadamantane hydrochloride $5 in 500 ml THF were added 134.5 g (1.53 rnol) triethylamine followed by 82 ml (590 mmol; 1.1 eq.) trifluoracetic acid anhydride (added over 12 h, stirring at r.t.). The suspension was stirred another 2 h, poured on ice cold 2M HCl and added to 300 ml of hexane/AcOEt (2/1). The organic layer was washed (1 x 200 ml of 2 N HCl, 1 x 200 ml ice cold 2 N NaOH and 3 x brine), dried (MgS04) and evaporated. The raw product was taken up in 750 ml acetone and 258.2 g ( 1.82 mol; 3.4 eq.) methyliodide were added. KOH (128 g 2.28 mol; 4.3 eq.) was added in small portions. After stirring (30 min/50-60 "C) and concentrating in vacuo, the residue was taken up in 500 ml AcOEthexane (2/1) and 300 ml water. The organic layer was washed (3 x 2N NaOH, 3 x 2N HCl and 3 x brine), dried (MgSO4), concentrated to 200 ml. and induced to crystallize. The collected crystals 70 g (267.9 mmol; 50%) were washed (3 x ice cold ethanol) and dried. By further crystallizations68% of $6 could be isolated. Rf: 0.27 (hexane/AcOEt, Vl). bp:219-220 "C. 'H NMR (CDC13,400MHz): 3.44 (s; 2H), 2.89 (s; 6H), 2.20 (d / 2.8; 12H), 2.09 (s,br; 6H), 1.72-1.58 (m; 12H).IR (CHC13): 2911 (s), 2850 (m), 1628 (s,br), 1453 (m), 1380 (m), 1355 (m), 1340 (m), 1310 (w), 1115 (m), 1095 (m), 1060 (m), 927 (m).MS: 398 (2.2), 263 (7.1), 234 (1.9), 207 (0.9), 176 (l.O), 166 (9.8), 165 (59.1), 164 (24.3), 135 (76.2), 108 (loo), 93 (16.9), 91 (7.9), 79 (15.6), 71 (14.8), 67 (6.7), 56 (3.9), 55 (6.5), 41 (4.4). ea: (% calc.): C (75.33), H (9.61), N (7.03), (% found), C (75.43), H (9.43), N (7.00).

b) To a solution of 70.0 g (267.9 mmol) adamantyltrifluoracetamide $6 in 300 ml THF were added 37.4 g (666.6 mmol) KOH and 3.6 g (13.6; 0.05 eq.) 18-crown-6. Heating (reflux, 14 h). When no more starting material could be detected by TLC, the reaction mixture was concentrated in vacuo. The residue was distilled (0.05 Tod75-90 "C). Yield: 36.66 g (221.8 mmol; 83%) of pure amine $7. c) A solution of 34.8 g (210.6 mmol) 1-adamantylmethylamine $7 and 13.72 g (103.8 mmol; 0.493 eq.) malonic acid dimethlester $8 in 110 ml toluene was refluxed (water separator, 4A

molecular sieve). After 7 d the accumulated crystals of $9 were filtered off and the mother liquor was again put to reflux. After 4 cycles, 30.89 g (67.54 mmol; 79%) of crystalline $9 could be isolated. d) To a suspension of 35.1 g (88.1 mmol) $9 in 220 ml EtOH were added 7.49 g (133.5 mmol; 1.5 eq.) KOH. Stirring (22 h/80 "C). When TLC showed no more educt, the mixture was evaporated in vacuo. The residue was parted hetween 220 m12 M HCI and 400 ml DCM. The DCM layer was washed to neutral (brine), dried (MgS04/activated charcoal) and evaporated in vacuo. The residue was crystallized from DCMlAcOEt : 14.75 g (58.6 mmol; 66%) acid $10. e) A suspension of 11.80 g (46.97 mmol) acid $10, 6.60 g (47.4 mmol) p-nitrophenol and

10.03 g (48.6 mmol; 1.03 eq.) 1,3-dicyclohexylcarbodiimidein 155 ml AcOEt was stirred at r.t.. After 10 h the suspension was filtered off and the residue was washed with a small portion of AcOEt. The fitrate was concentrated to 100 ml. By adding small portions of hexane, the solution was induced to cystallize while cooling down to r.t. The crystals were washed with hexane/AcOEt (2/1) and dried in vacuo. Yield: 13.8 g (37.1 mmol; 74.5 %) $11.

Appendices

KOH/EtO%

391

Bio(

OH

80°C/ 22h $10

$9

r.t./ 10 h

I

p-nitrOphenol/ DCC/AcOEt

$11

Fifth step: Connection of triamine $4 with p-nitrophenylesteramide $11

$11 36

1

$4

-30 "C THF

$12

To a solution of 0.583 g (1.85 mmol) triamine $4 in 9.5 ml THF at -30 "C were added 2.13 g (5.72 mmol; 3.1 eq.) p-nitrophenylesteramide $11.The suspension was stirred for 36 h at -30 OC and for 16 h at 0 "C, poured in 100 m10.2 M NaOH and extracted (3 x 70 ml DCM) . The organic layer was washed to neutral (2 x 75 ml brine) dried (molecular sieve, 4 8) evaporated in vacuo and purified by FC (pl = 4 cm, acetoneDCM (7/3). Yield: 100 mg (0.09 mmol) $12 (EmT 5506).

392

Appendices

[I] Eapen, K.C., Dua, S.S, Tamborski, C., J. Org. Chem., 1984, 49,478. 121 Brown, H.C., Rathke, M.W., Rogic, M.M., J. Am. Chem. Soc., 1968, 90, 5038. [31 Brown, H.C., De Lue, N.R., Kabalka, G.W.,Hedgecock, H.C., J. Am. Chem. SOC., 1976, 98, 1290. 141 ODonnell, J., Hongbin, L., Rusterholz, B., Pedrazza, U., Simon, W., Anal. Chim. Actu, 1993, 281, 129.

Appendix 11 (a) Development of Magnesium-Selective Ligands. Structures and Selectivity Coefficients Carrier type: N-%-N:N'-bis{ n-[3-(R 1 -R2-amino)-l,3-dioxopropyl]-2-R3 -amino]amino(CH2),} -N-R1 -propanediamide)

Ligand+o-NPOE

n

ETH 7015

6

Ri

R2

R3

R4

-n-C12H25

-CH3

-H

-CH3

log KPo'(MgCa)

- 0.8

log P'(MgNa)

(120,150% B) -4.1 (120% B)

Appendices

Ligand+o-NPOE

n

ETH 7025 log KPO'(MgCa) log P t ( M g N a )

8

ETH 5405 log KPot(Mgca) log KPot(MgNa)

8

ETH 5442 log KPof(M&a) log KPo'(MgNa)

7

Ri

R2

R3

R4

-n-C7H15

-CH3

-H

-CH3

-CH3

H

-CH3

-CH3

-H

-CH3

393

- 1.0 (155%B) - 3.5

-n-C12H25

- 1.0 - 4.4

-nc7H15

- 1.0 - 3.9 (- 4.4 K500)

ETH 7052 log KPo'(Mgca) log KPo'(MgNa)

10 -nc7H15

-CH3

-H

-CH3

ETH 4310 log KPOt(MgCa) log KPOt(MgNa)

8

-CH3

-H

(R1)

ETH 4320 log Kpot(Mgca) log KPot(MgNa)

8

-n-C7Hi5

-n-C8H17

(R4) -H

-H

-H

(R1) -n-C8H17 (R4) -H

Future prospects

ETH 4369

-n-C7H15

- 0.7 (155% B) - 3.8 (155% B)

8

-n-c7H15

-CH3

-CH3

-H/-CH3

-n-C7H15

-CH3

-H

(R1 andR4)

-n-C18H37 log KPot(MgCa)

- 0.46 (1 14%B) - 0.70 (159%B)

log KPot(MgNa)

- 3.64 (1 14%B)

- 2.08 (159%B)

394

Appendices

Ligand+o-NPOE

n

R1

ETH 4328 log ZP"(MgCa)

8

-nC8H17

R4

-H

-H

(R1) -n-C7H15 (R4) -CH3

H

-cH3

-H

-CH3

-H

-CH3

Cyclohexyl-

-H

Cyclohexyl-

Benzyl-

-H

Benzyl-

-0.3 -3.8

8

Adamtyl-

(77 %B) (77 % B )

- 1.05 (110-155% B) - 4.2 to 4.5 (11&155% B)

log KPot(MgNa)

ETH 7160 log KPot(MgCa)

R3

- 0.46 (155% B) - 3.18 (155% B)

log P'(MgNa)

ETH 4375 log P'(MgCa)

R2

8

Admmtyl-

- 1.06 to- 1.16 (111-156% B)

- 4.2 to - 4.4

log P t ( M g N a )

(111-156% B)

ETH 4325 log P'(MgCa)

8

- 0.68 (109% B) -0.71 (165% B) - 3.91 (109% B) - 3.50 (165% B)

log KPot(MgNa)

ETH 7124 log KPOt(MgCa) log P'(MgNa)

Cyclohexyl-

8

-CH3

Appendices

Ligand+o-NPOE

n

Ri

ETH 8020 log Pt(MgCa) log Pf(MgNa)

8

-CH3

R2

395

R4

R3

Appendix 11 (b) Carrier type: N,N"- R3-(CH 2)n-bis(N'-R1-N'-R2)-R4-malonamide

Ligand + o -NPOE

n

Ri

R2

R3

R4

ETH 4087 CIP = 0-WOE (70%B) 1% Kp"t(Mgca) log KPOt(MgNa)

8

-c12H25

-CH3

-H

-H

ETH 5221 a ClP = O-WOE log Pt(MgCa) log P y M g N a )

10

-CH3

-H

+ 0.3 - 1.0 -C7H15

- 0.4 > - 3.8

396

Appendices

Ligand + o-NPOE

n

Ri

R2

R3

R4

ETH 4030 a ClP (70% B) log KPO'(MgCa) log P t ( M g N a )

8

-C7H15

-CH3

H

-H

ETH 5222 a log KPOt(MgCa) log KPOt(MgNa)

8

-C7H15

-CH3

-CH3

-H

ETH 5214 = ETH 5219 (70% B) a log KPot(MgCa) log KPot(MgNa)

8

-C7H15

-CH3

ETH 5220 a 1% KpOt(MgCa) log P'(MgNa)

8

-(%Hi7

ETH 4083 a log KPot(MgCa) log KPOt(MgNa)

8

-CSH17

Future prospects

10

0

- 3.9

-H CH3 0 >-3.6 (ClP) -2.9 (O-NPOE)

-CSH17 0 - 3.9

-H

-H

-H

-CH3

-H

> - 0.5 > - 3.8

ETH 5487 1% fl'(MgCa) log KPOt(MgNa)

ETH 5478 log P t ( M g C a ) log KPot(MgNa)

> + 0.9 > - 3.0

8

Adamantyl+0.11 - 2.16

-H

-CH3

-H

Adamantyl-

H

-CH3

-H

- 0.24

- 3.60

Appendices

Ligand + o-NPOE

n

ETH 4361

8

RI

R2

R3

-CH3

-H

397

-H

+ 0.82

log KPot(MgCa) log KPot(MgNa)

- 2.8 Lipophilic "shellsize"

a

Selectivity data according to Rouilly, M.V., Beitrag zur Entwicklung von Mg2+-selektiven lonophoren fiir den Einsatz in Fliissigmembranelektroden. Zurich, Switzerland: Swiss Federal Institute of Technology, 1990, PhD thesis ETH Nr. 908 1.

Appendix 11 (c) Carrier type: N-Rl -N-R;!-[R4-(CH2),]-diamide

~

Ligand + o-NPOE

ETH 1117 a 1% Pt(MgCa) log P'(MgNa)

R1

-C7H15

-CH3

-CH3

- 1.3 - 2.1

-H

398

Appendices

Ligand + o-NPOE

R1

R2

ETH 2220 a log KPot(MgCa)

-C7H15

-CH3

R3

Rq

-CH3

-m2

- 1.2 (pH 7.4) - 2.5 (pH 8.8)

- 0.1

log KPO'(MgNa)

- 2.6

-CH3

ETH 4025 (70% B) a log KPOt(MgCa) log KPO*(MgNa)

ETH 2222 (70% B) a

0

-C7H15

-CH3

log KPot(MgCa) log KPO'(MgNa)

ETH 5165 a (unbuffered 96%B) 1% ~ ' ( M g c a ) log KPOt(MgNa)

Future prospects ETH 1117

a

7

-CH3

- 0.4 (PH 8.8) O , -N,

-C7H15

-C7H15

-CH3

-CH3

-CH3 + 2.5 + 0.8

H I

CgH1gK 0

-CH3

- 1.7 - 1.9

GH15,N

-H

Phosphonate?

I

Selectivity data according to Rouilly, M.V.,Beitrag zur Entwicklung von Mg2+-selektiven Zonophoren fiir den Einsatz in Fliissigmembranelektroden. Ziirich, Switzerland: Swiss Federal Institute of Technology, 1990, PhD thesis ETH Nr. 9081.

Appendices

399

Appendix 11 (a) Various carriers of the propanediamide type, which show no useful selectivity; hence, no selectivity coefficients are reported

Ligand + o-NPOE

n

R1

R2

R3

R4

ETH 8073 1% V'OMgca) log P * ( M g N a )

3

-C7H15

-CH3

-H

-NO2

ETH 8078 log Pt(MgCa) log KPot(MgNa)

3

-Cyclohexyl

Cyclohexy1

-H

-NO2

ETH 8087 log KPot(MgCa) log KPo'(MgNa)

3

-Cyclohexyl

Cyclohexyl

-H

-H

400

Appendices

Ligand + o-NPOE

n

m

R1

R2

R3

ETH 4361 log KPot(MgCa) log KPot(MgNa)

5

8

-C7H15

-CH3

-H

Ligand + o-NPOE

R

ETH 4377 log KPOt(MgCa) log KPOt(MgNa)

Appendices

Ligand + o-NPOE

401

R

ETH 5381 log KPot(MgCa) log KPO'(MgNa)

Appendix 12 IUPAC Units and Statistical Considerations

Table 1. In 1960, the International System of units (SI) was adopted by the 11th General Conference on Weights and Measures (CGPM).a It relies on seven base units, each linked with one of the seven dimensionally independent, base quantities. The base quantities, units and the symbols used to denote them are:

m n

t

T 1

Z, I

mass amount of substance ime thermodynamic temperature length luminous intensity electriccumnt

with the unit

kilogram mole second kelvin metre candela

kg mol

ampere

A

S

K m

cd

All further quantities used in characterizinga dataset are derived from these base quantities

402

Appendices

Table 2. Units and quantities supported by the International Federation of Clinical Chemistry (IFCC) b

Volume Substance concentration Molality, ionic strength Buffer capacity Mass concentration, mass density Catalytic activity Energy Electric charge Chemical potential Pressure, partial pressure, osmotic pressure Temperature

1;L mol 1-1 (mol L-l; M) rnol kg' mol = mole

kg L-' mol s-l= kat N m =joule, J C (A s) = coulomb J mol-1

molar volume: molar mass:

1 mol-1 kg mol-1

entropy:

J K-1

electric potential: V (J (2-1)

Pa (N m-2) = pascal O C = degree Celsius

Statistical Overview The total analytical error [TE] includes the systematic error (inaccuracy) and the random error [RE] (reproducibility, repeatability). Systematic errors may contribute to the total analytical error as a proportional error [PE] or a constant bias [CE] or [SE], seen as an intercept in linear regressi0n.C Even preanalytical errors can contribute to the total error, as indicated by the following equation:

TE =RE + SE + CE + PE

(12-3)

where

RE [random error] SE [systematic error] CE [constant error] PE [proportional error]

x,

=

*

=

I (a + bX - XI

=

1 bias I f t (sa

/fi)

=

I R~C%- 100 I

X

t(n. The coefficients of variation Cva and CVb,intra are convenient parameters for decisions at different concentration levels. The preanalytical variance sm2 adds to the analytical variance sa2. In this case, cv, represents the total uncertainty. q . i n t m represents the coefficient of variation of the single source studied, whereas CVb.inter denotes the variation between a population of sources under investigation. The root of the sum of the squared terms is equivalent to q,in Eq. (12-5): ma

112 0b.intra

(12-4)

For group screening or screening of populations, cvinba must be replaced by the maximum variation of the regular mean setting point over all the sources investigated: (12-5)

The total observed variation sTvis equal to the square root of the sum of the variance of the sources sb2, the analytical variance sa2, and the technical and biological preanalytical errors s2,, given by the following equation: (12-6)

where the variation Srv is the variation observed within the regular range of measured values. The reference value is consideres to be any value which is representative of a selected score of sources described by similar features. cv, 2 = (0.52 ~ "22), + C V2

~

(12-7)

and 2

C V =~ (1.25 CVt,)"

= 1.118 CVb

(1 2-8)

The minimum difference in concentration (Ac) to distinguish between two values on a significance level accordingto z-statistics: bi,tot

2

2

> [(ma + CVb.inm 2 z2 I lR

(12-9)

where z is a multiple in z-statistic which depends solely on the probability selected for significance. This value, derived from the Gaussian distribution, is 1.65 in the unidirectional case at a level of significanceof 95%, and 1.96 in the bidirectional case. Any further optimization of the analytical reliability relative to the variability of the source is uneconomic for mass products of average quality.

404

Appendices

Harris Ratio The ratio between intraindividual and interindividual variation corresponds then to the so-called individuality index [I], or Harris ratio.h

(12-10) For I > 1.4, comparison with the reference interval creates a large number of false-positive results; for I c 0.6, the comparison to the reference interval is of little value. International Union of Pure and Applied Chemistry, Physical Chemistry Division (ed.), Quantities, Units and Symbols in Physical Chemistry. Oxford: Blackwell Scientific Publ., 1988. International Federation of Clinical Chemistry (IFCC), International Union of Pure and Applied Chemistry, Approved Recommendations (1984)on Physico-Chemical Quantities and Units in Clinical Chemistry with Special Emphasis on Activities and Activity Coefficients, J. Clin Chem. Clin. Biochem., 1987,25,369. Carey, R.N., Garber C.C., in: Kaplan, LA., Pesce, A.J., Clinical Chemistry, Theory, Analysis, and Correlation, St. Louis: The C.V. Mosby Company, 1984;pp. 338-359. Young, D.S., Harris, E.K., Cotlove, E., Clin. Chem., 1971,17,403. Harris, E.K., Am. J. Clin. Pathol., 1979,72,374. College of American Pathologists (CAP) (ed.), Analytical Goals in Clinical Chemistry, Proceedings of the Aspen Conference on "Analytical Goals in Clinical Chemistry" 1976,Aspen, U.S.A. g Fraser, C.G., JIFCC, 1990,2, 84. Harris, E.K., Clin. Chem., 1975,21,1475. a


absorption - molar decadic coefficient 301 accufacy 345,401 - assessment 286,352 acridhes, ethenyl 3 10 activity 4,90,114 -molal 215 - IFCCAUPAC conventions 120 activity coefficient 90,117 - blood serum 206 - Debye-Hlickel convention 118 -human blood plasma 206,361 -patients 130 - Pitzer calculus 119 - Stokes-Robinson approximation 118 -volunteers 130 active molality 4,7,114,200,215 . -abinitio 204 - IFCC/IUPAC conventions 120 - electrolytes in human plasma and serum 363 adsorption 184,298 - mechanism 186 affinity 71 alcohol dehydrogenase(ADH) 65 allowable analyticalemrs 365 amine 263 ammonia 10 amperometric sensors 19, 107, 199 -mediated 111 analyte 1 4 , 3 3 analytical chemistry 1-4 analytical errors 160 analytical instruments 1 analytical procedure 2-4 analyst 2-3 anion-selective optodes 275 antibodies 9 - antigen interaction 71

-catalytic 70 anticoagulants 192 antithrombine III (see heparin) 192 application to - diluted plasma 285 Arrhenius equation 107 artefacts 211 artificial enzymes 9 asymmetry - of membranes 205 - of the reference electrode 205,210 association - constant 95 AT-III Inhibitor 62 attenuated reflection (ATR) 300,152 - effective pathlength 300 - lanthanum fluoride crystal 302 - sapphire crystal 303 - set-up 302, 152 availability 345 avidity 71 azobenzene 272 Bates convention 118 Baysian theorem 330 Beer-Lambert law 299 benzo[a]phenoxazin 272 Berger diagram 329 bilayers 140 biocompatibility 183,189 biocompatiblematerials 212,249 - hydroxy-PVC, synthesis 376 biocopolymer 212 biological -adsorption 185 -activity 108 -matrix 183 - membranes 139,140 - setting points 363 biooptodes 280 biosensors 4,280, 199 - antigen-antibodies 71 -definition 6 - generations 109

406

Index

- graphical presentations 111 - immunological 7 1 - mediated enzyme electrodes 106, 112 - Michaelis Menten constant 109 - apparent 111 - selectivity 7,67, 155 - turnover rate 109 - turnover number 109 biotechnology 10 blood plasma - potentiometry 206,227,238,248 Born cyclic process 94 Briggs-Haldane conditions 110 calcium - selective optode membrane 290, 152 - transmission spectrum 299 -ATR-spe~trum 303 - calculated dispersion spectrum 307 calibration - potentiometric electrodes 127 - scheme for real specimen 129 CAP postulates 346,350 carbon dioxide 10 carriers 9 -chiralneutral 60 catalysis - electrophilic 64 -metalion 64 -nucleophilic 64 catalytic antibodies 9,70 catalytic rate constant 109 cation-selectiveoptodes 272 channel model 140 chemical analysis 1 4 chemical effects 33 chemical information - (see information) 33 chemical potential 83,116 chemical sensors - analytical strategies 2 4 - chemical potential 83,93 -control 83 -definition 5

- reversibility

83 - recognition process 89 -thermodynamics 83 chemoreceptors 5 chip technology 16-24 chiral neutral carriers 60 chloride - selective optode membrane 290 - selectiveelectrode 247 chromogenic ligands 41 chromoionophores 267,271 -neutral 271 clinical chemistry 9 classifications 33 cluster analysis 342 Col-Cole Plot 150 compensation - enthalpy-mtropy 96 computationalchemistry 46 concentration 114 - mold 114,121 -1igand 176 - lipophilic counterions 173 - elecrrolytes - IFCCnUPAC conventions 120 -human blood plasma 363 continuous flow analysis - chloride-selective 251 - hydrodynamics 181 - magnesium-selective 239 -system 240 coronand 268 Coulomb potential 117 counter-ions, lipophilic 173 - optimum ratio 174 coupling efficiency 305 creatinine 1,267 cross-reactivity 7 cryptahemispheraplexes 41 cyanme dyes 272,3 10 - streptocyanines 272,310 - neutrocyanines 3 10 - squarylium dye 272,310

data,hard 322 -data validation 321,331,361 Debye-Huckel - convention 118 -equation 118 - potential 117 -radius 116 -Theory 116 decision making 323, 361 dedicated system 2-4 depletion - analyte from sample 297 detection limit 179 - ion-selective microelectrodes 242 - magnesiumselective 243 diagnostic tests -planning 354 -parameters 361 - sensitivity 361 - selectivity 361 dicyanovinyl dyes 272,310 diffusion 104 -equilibrium 104 - limited response 151 - overall diffusion coefficient 151 -potential 134 dipole moments - plasticizers 165 discriminant analysis 340 discriminator 333 distribution, overall 89 Dixon-Hanes-Woolf 111 Donnan potential 103, 105, 187, 189 dry chemistry 270 dyes 272,310 dynamicrange 350 - ion-selective optodes 295 - ion selective electrodes 202 - microelectrodes 242 Eddie-Hofstree plot 111 effectiveness 325 - cost 345 efficacy 2-3,325,361

efficiency 3,325,361 electrochemical potential 99 electronic noses 20 electrode - combined catheter, pH- 248 - micro 16, 242 electrolytes 115 - conductivity 115, 134 - IFCCAUPAC conventions 120 - mobility 134 electromotoricforce (emf) 199 electron pair donor 169 electron pair acceptor 169 electrophoresis 116 electrostaticinteractions 186 enantiomers 58 environmentalchemistry 9 enzymatic sensors 63 - generations 109 - graphical presentations 111 -mediated 112 - electron transfer 112 -enzymemimics 63 -optical 280 - Steady-shte 107 enzyme kinetics 106,108 enzyme linked optodes 280 equilibrium constants -optodes 282 equilibriumreaction 83 equitransferent solutions 135 errors - allowable analytical 349,402 - random 345,401 - systematic 345,401 -total analytical 345,401 erythrocytemembrane 216 ethanol 65,263 evanescent field 300 Eyring's rate theory 146 Faraday constant 99 Ficks diffusion 153 fish acute toxicity syndrome (FATS) 5

408

I&x

flame atomic emission spectroscopy (FAES) 206 flow-through cell -optical 152 - potentiometric 240 fluorescein dye 272 fluorescence 263 fluoroionophores 268 flow-chart of electron transfer of mediated biosensors 112 forecasts 13-16 fouling 298 free analyte 4,7 frequency distribution 333 gas-selective optodes 278 gastricjuice, pH monitoring 246 Gibb's free energy 86 Gibbs-Duham equation 87 glucose 10,261,264 grating coupler 305 guest 11 guided wave 300,305 Hamaker constant 186 Hammett substituentconstant 67 Hanes plot 111 Harrisratio 350 Hawaiiancrabs 5 hemodialysis 129,211 Hendersson equation 134 Henry's law 116 heparin 62,192 - influence, effect 192 - molecular recognition in aqueous media 62 high throughput analyzers 9 history 10, 259,359 Hofmeister -behavior 91 -series 91 host 11, 39,41 -host reactand 41,63 humidity 10

hydrodynamics 181 hydrogen bonds 43,56 hydrogen sulfite 10 hydroxy-PVC 376 immobilization 297, 182 individualityindex 350 information 1-5,321 - acquisition 324 -base 323 -biological membranes 142 - entropy of 326 -gainin 327 -biological membranes 142 integrated chemical sensors 19 interaction, -s 41 - electrostatic 42, 186 -energies 42 -hydrophobic 44 - Lennard-Jones Potential 44,186 - van der Waals 43,186 interferometer,Mach-Zehnder 308 intracellular measurements 242 in vivotests 5 ion channels 141 ionic strength 90, 117, 186 -bloodser~m 206 - calculation 117 -human blood plasma 206,227,363 - real specimen 130 ionophores - chloride-selective 247 - chromogenic 267 - magnesium-selective 225 - nitrite-selective 245 - pH-selective 246 ion-selective -electrodes 199,100 - materials and preparation 376 - synthesis of OH-PVC 376 - microelectrodes 242 I R - ~ p e ~ t r ~ s260 ~~py IUPAC quantities 321,401 ISES 9-10

ISFET 19 isoinformation curve 337 Kemp's triacid derivatives 62 Kohlrausch's law 115 Kramers-Kronig transformation 307

LASF 35 -crystal 302 leaching 297 Levich equation 108 lifetime 182 -optodes 296 Lifshits treatment 186 ligands 10,41, 176 -activity 90 - concentration profile 179 - inorganic ions 48 likelihood ratio 332,338 Linewaever-Burk plot 111 lipophilic sites, counterions 173 - anionic sites 173 - optimum ratio 174 lipophilicity 90, 173, 182,296 liquid junction -potential 202,134 long-term stability 296, 182 - chloride-selectiveelectrode 250 luminescence 26 1 Mach-Zehnder interferometer 308 magnesium concentration analysis -byAAS 217 - chelating agents 219 - fluorescence indicators 218 - intracellular measurements 2 18 - photometric assay 217 -31PMMR 219 - X-ray fluorescence 218 magnesium ion - active molality in blood plasma 227 - free molar concentration 227 - required selectivity coefficient 227 - selective electrode 215

- structure-breakingproperties 171 magnesium ion chelators 219,223,235 - antibiotics 226,228 - chlorophyll 222 - natural carriers 222 - noncyclic synthetic ligands 228 -peptides 226 - polyphosphates 224 - synthetic carriers 225 - teichoic acid 224 - tripodale ionophores 232,230 - ETH 3832 233,238 - modifications of ETHT 5506 235 - synthesis of ETHT 5506 387 - ETH 7025 230,392 - model calculations 229 magnesium-selective - continuous flow analysis 239 - electrodes - applications 237 - comparison 234 - interferences 239 - instruments and results 238 - pH correction 238 - pH buffering 238 - ionophores 387,392 - measurements - significance 241 -membranes 234 market 13 mass equilibria 92 measurand 31 mediator 112 -7"lT-TCNQ 112 medical analysis 10 medical assay -optodes 285 membrane - artificial (see solvent polymeric) 139, 144 -bilayer 140 -biological 139, 140 - composition 161 - Donnan potential 189

- electroneutrality 173,189 -environment 39,162,170 - hydrodynamics, surface 181 -medium 161 -optical 151 -permittivity 162 - solvent polymeric 144, 161 - specimen, aqueous 170 - surface tension 172 - thrombocytes 189 -transport 139 -active 139, 141 - facilitated 139 -passive 139 membrane models 145,179 -asymmetric 144 -optical 151 -bilayer 143 - concentration profiles 179 - electrical circuit 149 - mixed potential 148 - multilayer, segmented 145 - Nemst-Planck 134 -optical 151 - segmented 145,179 -symmetric 144 metabolites 267,280 metabolic pathway 68 method comparison - electrolyteconcentrations 127,287 micellar optode, reverse 280 Michaelis Menten kinetics 109 microelectrodes 17,242 - magnesium-selective 243 - nitrite-selective 245 milestones 359 miniaturization 16 - integrated optical sensors 304 -pHprobe 246 mixed potentials 115,148 mobility 115 models 8, 36 mold -activity 121

- real specimen - concentration

130 121 -water 119,128 - real specimen 130 -conductivity 115 molecular recognition process 38 - analytical tools 45 - antigen-antibody 61 - aqueous media 60 - enantiomers 58 -enzymes 63 - enzyme mimics 63 - inorganic ions 4 8,50 - multitopic 7 1 - nucleic acids - nucleophiles 64 - organic ammonium ions 58,61 molecular modelling 46 - phosphate ligands 48 monactin 12 multiple internal reflection (MIRE) 300 -set-up 305 multivariateanalysis 339 NAD +-oxidoductase 65 nanoelectrdes 242 nanotechnology 16 Nemst equation 201 - diffusion layer 108 Nemst-Planck equation 134,146 neutral analytes 264,278,280 neutralcarriers 11 Nikolsky-Eisenman equation 200 NIR-absorbing dyes 309 nitrite-selective -electrode 245 -optode 275 nomenclature -electrolytes 120 - IFCC/IUPAC conventions 120 nonactin 12 nonideal behavior 117 nonthermodynamic assumptions 90, 114 Nyquist diagram 150

Index

on-site analysis 1-4 optical - absorbance 299 - characteristics,inherent 261 - effects, intrinsic 260,261 - effects, extrinsic 260 - waveguide 299 optode, optrode 13,270 optodes 270 osmolality 124 - isotonic solutions 125 - human blood plasma 126 osmometry 125 osmotic pressure 87 osmotic coefficient 124 oxazine dyes 271,310 oximetry 13 oxygen 12-13,23,260 partition coefficient 84,89,282 partition equilibrium 83,89 permittivity 162,186 phases -aqueous 88 -hydrophobic 88 phosphorescence 261 photoacoustic spectroscopy 261 photolithographictechniques - miniaturized optical sensors 305 pH indicators 27 1 pH sensor 12-13,260 -miniaturized 246 - monitoring of gastricjuice 246 physical sensors 33 physical effects 33 piezoelectricresonator 20 Pitzer calculus 1 19 plasticizers 162,369,373 - electron pair donors 169 - electron pair acceptors 169 point of care testing - POCT 21,27,265,267 polymethines 310

411

polyurethane 212 potassium 11-12 - complexation 57 - selective optode membrane 290,303 potential -electric 99,199 - electrochemical 99 -chemical 83 potentiometric electrode 199 - chloride-selective 248,251 -cell 99 -notation 99 - combined pH-probe 248 - electromotoricforce 99, 199 - magnesium-selective 225 -micro- 242 potentiometry 199 - poteatiometriccell 200 - symmetric cell 203 principal component analysis 342 predictive value 339, 361 - positive 332,361 - negative 332,361 prevalence 332 protein - adsorption mechanism 186 - Lifshits treatment 186 - plasma composition - isoelectric point (IP) 190 - specific volume 190 proton motoric force 141 pulse oximetry 13 PVC - hydroxy 212 quality assessment - optode membranes 287,290 quartz crystal microbalance (QCM) 20 Raoult's law 116 rate-controlled reactions 106 reactand 41,63,263 real solutions 116 receiver operating characteristics

412

Index

(ROC) 333,335 receptor -biotic 39 receptrodes 5-6 recognition process 33,38,89,93 reference -electrode 200,210 - half-cell 200 -material 287 -methods 288 - procedures 127 refractive index -effective 305 regression analysis - least squares 288 - Passing and Bablok 288 Reilly-Wood approximation 119 relevance 345 reliability 345 response function 179 - combined pH-probe 248 -optodes 282 - potentiometric electrodes 202,179 - miniaturizedpH-probe 248 results - false negative 333,361 - false positive 333,361 reverse micellar optode 280 reversibility 41, 83 - ion transfer catalysis 171 ruthenium(@ complexes 261 sample 1,88 - biological 206, 184 scanning electrochemical microscopy (SECM) 17 selectivity 7, 155,376 - anionic sites 173 - coefficient 201, 155,97 -required 160,383 -enzymes 7,67,155 - fixed interference method (FRM) 156 - ion-selectiveelectrodes 201,251 - ion-selective optodes 291

- lipophilic sites

173 - IUPAC recommendations 155 - mixed potential method 159 - separate solution method (SSM) 201, 376,383 - specific applied method ( S A M ) 158, 159,376 sensing layer 37,52 sensitivity - diagnostic 332,361 - optode membranes 295 sensor -array 19 -chip 17-24 - components 16 - development 10 - milestones 10 -model 8,36 - reaction, reversible 83 - recognition process 38 -transducers 34 Seralyzer 270 Simon optodes 270 sodium 11 - seIectiveoptode membrane 290 solvents 162, 369,373 - electron pair donors 169 - electron pair acceptors 169 solvent polymeric bulk membranes 161 - dielectric constant 162 -permittivity 162 specificity 7 -diagnostic 332 specimen 1,88,184 - anticoagulants 192 -blood plasma 190,206,216,249,88 - compatibility 183 -erythrocytes 216 - thrombocytes 189 -urine 249 -whole blood 214 spec- calcium-selectiveoptode 299 specific partial volume

Index

- proteins, peptides 128 squaraine dye 272 stability constants 49,95 standard electrode potential 202 standardization - electrolytes 127 STAT-ION 215 steady-state 68,83, 104, 199 - current 108 Stokes-Robinson approximation 118 stop-flow analysis 376 - chloride-selective 250 - magnesium-selective 239 - hydrodynamics 181 structure elucidation 45 structure-selectivity relationship (QSSER) 68 substrates 63,264,278,280 sulfur dioxide 10 surface acoustic wave (SAW) 20 surface compatibility 183 - thrombocytes 188 - Donnan potential 189 surface tension 172 suitability test 353 symmetric potentiometric cell 203 - miniaturized 205

toxicity tests 4-6 toxic substances control act (TSCA) 4 transport 139 -passive 139 -active 139, 141 -facilitated 139, 143, 144 transporter 140 ultramicroelectrode 17 uncertainty - a posteriori 327 -apriori 327

valinomycin 12,57 Van der Waals interactions 39 Van? Hoff plot 96 variation -biological 345,402 - analytical 345,401 volume replacement by proteins lipids 128 Warburg impedance 150 water concentration in biological specimen 128,130 waveguide 305,152 zinc-selective optode 269

teichoic acid 224 TekoflexB 212,249 thermodynamic equilibrium 83 -parameters 45 thermodynamics - irreversible 83, 105 - nonequilibria 105 -optodes 282 - reversible 83 - steady-state 105 - standard state 84 transducers 33,34 -optical 299 transmission mode 299 transduction 93 throughput 3

413

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