Advances in Electrochemical Science and Engineering, Volume 5 by Charles W. Tobias and Richard C. Alkire


275afcf48a732be-261x361.jpg Author Charles W. Tobias and Richard C. Alkire
Isbn 9783527293858
File size 55.2MB
Year 1997
Pages 430
Language English
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Category chemistry


 

Advances in Electrochemical Science and Engineering Advisory Board Prof. R. C. Alkire, University of Illinois, Urbana, Illinois, USA Prof. E. J. Cairns, University of California, Berkeley, California, USA Prof. M. Fleischmann, The University, Southampton, United Kingdom Prof. M. Froment, Universiti Marie et Pierre Curie, Paris, France Prof. K. Honda, Kyoto University, Kyoto, Japan Prof. Yu. V. Pleskov, A. N. Frumkin Institute of Electrochemistry, Academy of Sciences, Moscow, Russia Prof. S . Trasatti, Universith di Milano, Milano, Italy Prof. E. B. Yeager, Case Western Reserve University, Cleveland, Ohio, USA Advances in Electrochemical Science and Engineering Volume 5 Edited by Richard C. Alkire, Heinz Gerischer, Dieter M. Kolb and Charles W. Tobias Contributions from A. Kapturkiewicz, Warsaw 0. A. Petrii, G. A. Tsirlina, Moscow D. D. MacDonald, L. B. Kriksunov, University Park S. Gottesfeld, Los Alamos F. Beck, Duisburg 8 WILEY-VCH Weinheim - New York-Chichester - Brisbane .Singapore .Toronto Editors: Prof. Richard C. Alkire University of Illinois Vice Chancellor for Research 601 East John Street Champaign, IL 61820-5711 USA Prof. Dieter M. Kolb University of Ulm Department of Electrochemistry Albert-Einste.in-Allee I 1 D-89081 Ulm Germany This book was carefully produced. Nevertheless, authors, editors and publishers 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 inaccumte. 0 WILEY-VCH Verlag GmbH, D-69469 Weinheim (Germany), 1997 e-mail (for orders and customer service enquiries): [email protected] Visit our Home Page on http://www.wiley-vch.de All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except under the terms of the Copyright Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency, 90 Tottenham Court Road, London, UK WlP 9HE, without the permission in writing of the Publisher. Other Editorial O&es John Wiley & Sons,Inc., 605 Third Avenue, New York, NY 10158-0012, USA John Wiley & Sons Ltd Baffins Lane, Chichester West Sussex PO19 IUD, England Jacaranda Wiley Ltd, 33 Park Road, Milton, Queensland 4064, Australia John Wiley & Sons (Asia) Pte Ltd, 2 Clementi Loop #02-01, Jin Xing Distripark, Singapore 129809 John Wiley & Sons (Canada) Ltd, 22 Worcester Road, Rexdale, Ontario M9W 1L1, Canada A catalogue record for this book is available from the British Library Deutsche Bibliothek Cataloguing-in-PublicationData Advances in electrochemical science and engineering: Weinheim; New York; Chichester; Brisbane; Singapore; Toronto : WILEY-VCH ISSN 0938-5193 Erscheint unregelmilssig. Aufnahme nach Vol. 1 (1990) VOI.1. (1990) ISBN 3-527-29385-X - - Typeset by Thomson Press (India) Ltd., New Delhi Printed and bound in Great Britain by BookcraA (Bath) Ltd This book is printed on acid-free paper responsibly manufactured from sustainable forestation, for which at least two trees are planted for each one used for paper production. Introduction This publication represents the final volume in the editorial collaboration of Heinz Gerischer and Charles W. Tobias which began in 1976. Their efforts led in 1987 to the initiation of the present series entitled Advances in Electrochemical Science and Engineering with the publisher VCH Verlagsgesellschaft who committed to producing typeset volumes at regular intervals. The favorable reception of the first four volumes and an increased interest in electrochemical science and technology provide good reasons for the continuation of this series with the same high standards and purpose. Richard C. Alkire Heinz Gerischer Dieter M. Kolb Charles W. Tobias Photograph by Marianne Kischke, Fritz-Haber Institut der Max-Planck Gesellschaft Heinz Gerischer ( 1919-1994) On September 14, 1994, Heinz Gerischer died of heart failure in Berlin. His name is intimately connected with the pioneering work in electrode kmetics, semiconductorand photo-electrochemistry and electrochemical surface science. His scientific career started as a young assistant of K. F. Bonhoeffer in Berlin immediately after the war, and continued in Gottingen and Stuttgart. Then came Munich, where he accepted a professorship at the Technical University in 1962, and Berlin where in 1969 he became director of the Fritz-Haber-Institut der Max-Planck-Gesellschaft. He was a key person for the development of new methods in electrochemistry. Although a chemist by training, he recognized very early the important role of surface physics in gaining a fundamental understanding of electrode processes. Consequently, he was among the first to transform traditional electrochemistry into a branch of modern surface science. Heinz Gerischer was a man with a deep understanding of physical chemistry; his works have become landmarks for our future work. Charles Tobias (1920-1996) It is with deep sadness that we report the passing of Charles W. Tobias on March 6, 1996. Professor Tobias initiated the discipline of electrochemical engineering in the United States, and played a central role in its development for nearly fifty years. In so doing, he played a pivotal role in the development of one of the world’s leading chemical engineering departments at the University of California at Berkeley. He founded the precursor to the present monograph series in 1961 with Paul Delahay, and in 1976 continued that co-editorship with Prof. Heinz Gerischer with whom he introduced in 1990 the present series, “Advances in Electrochemical Science and Engineering”. Charles Tobias was a man of wisdom who had a profound influence on the lives of many individuals, and who contributed enormously to the advancement of electrochemical science and engineering. During the recent past, electrochemical science and engineering has seen profound changes. The consequences of changing energy, feedstock, materials, and waste treatment demands have spurred the traditional electrolytic industries, and have sparked new inventions. These trends have been accompanied by a development in the understanding of the fundamental principles, as well as rapid advancement in many areas of electrochemical science and engineering. The chapters in the present volume treat topics of fundamental and applied interest associated with electrochemiluminescencephenomena, novel superconducting materials, the prevention of electrochemical corrosion through understanding of fundamentals of transport and reaction phenomena, the advancement of polymer fuel cell technology, and the development of metal-free batteries. Andrzej Kapturkiewicz gives a thorough account on the theory of electron transfer reactions that lead to electrochemiluminescence (ECL). He discusses in detail the conditions under which the Marcus theory can give a more quantitative description of ECL processes. Oleg Petrii and Galina Tsirlina describe a wide range of oxide high temperature superconductors, their electrochemical synthesis, their properties and degradation mechanisms, and analytical methods for the characterization of their surfaces and volumes. The recent advances in this field open new possibilities for elucidating the interface and charge-transfer at extremely low temperatures. Digby Macdonald and Leo Kriksunov provide a broad perspective on the complex phenomena by which fluid flow influences the initiation and propagation of corrosion in pits and cracks. By focusing on the industrially important environment of high temperature aqueous systems, the authors provide an important link between theoretical understanding, well-designed experiments, and predictive capability. Shimshon Gottesfeld provides a valuable perspective on the advancement of polymer electrolyte fuel cells in such key areas as lowering catalyst loading, decreasing susceptibility of anode catalyst to poisoning by the fuel, improving cathode performance, and achieving high proton conductivity. These activities cover a wide range of fundamental subjects in interfacial electrochemistry and material science, as well as chemical and electrochemical engineering. Finally, Fritz Beck gives a comprehensive survey of materials that can be used as active electrodes in metal-free batteries. He discusses the advantages and disadvantages of various systems in terms of technical realization, electrochemical stability and power density, and mentions possible applications. Contents A. Kapturkiewicz Marcus Theory in the Qualitative and Quantitative Description of Electrochemiluminescence Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . 0. A. Petrii and Galina A. Tsirlina Electrochemistry of Oxide High-Temperature Superconductors .......... D. D. Macdonald and t.B. Kriksunov Flow Rate Dependence of Localized Corrosion in Thermal Power Plant Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 61 125 S. Gottesfeld Polymer Electrolyte Fuel Cells ................................ E Beck Graphite, Carbonaceous Materials and Organic Solids as Active Electrodes in Metal-Free Batteries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Index .................................................. 195 303 413 List of Contributors Fritz Beck University of Duisburg Fachgebiet Elektrochemie D 47057 Duisburg Germany Digby D. Macdonald Center for Advanced Materials The Pennsylvania State University University Park, PA 16802 USA Shimshon Gottesfeld* Materials Science and Technology Division Electronic and Electrochemical Materials and Devices Group Los Alamos National Laboratory Los Alamos, NM 87545 USA Oleg A. Petrii Department of Electrochemistry Moscow State University Vorob’evy Gory V-234 MOSCOW GSP-3 119889 Russia Andrzej Kapturkiewicz Institute of Physical Chemistry of the Polish Academy of Sciences Kasprzaka 44/52 0 1-224 Warsaw Poland Leo B. Kriksunov Center for Advanced Materials The Pennsylvania State University University Park, PA 16802 USA *With Tom A. Zawodzinski Galina A. Tsirlina Department of Electrochemistry Moscow State University Vorob’evy Gory V-234 MOSCOW GSP-3 119889 Russia Advances in Electrochemical Science and Engineering Edited by Richard C. Alkire, Heinz Gerischer, Dieter M. Kolb and Charles W. Tobias 0 WILEY-VCH Vcrlag CimbH, 1997 Marcus Theory in the Qualitative and Quantitative Description of Electrochemiluminescence Phenomena Andrzej Kapturkiewicz Institute of Physical Chemistry of the Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Kinetics of Electron Transfer Reactions . . . . . . . . . . . . . . . . . . . . . . . ...... 2.1 Mgin Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .... 2.2 Normal and Inverted Marcus Region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Radiative Electron Transfer in the Inverted Marcus Region . . . .......... 2.4 Effects of Solvent Molecular Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Unimolecular versus Bimolecular Electron Transfer Reaction . . . . . . . . . . . . . . . 3 Formation of Excited States in Electron Transfer Reactions . . . . . . . . . . . . . . . . . . . . 3.1 Routes of the Excited States Formation . . . . ........................ 3.2 Energetics of Ions Annihilation . . . . . . . . . ........................ 3.3 Triple-Potential-Step Technique in Electrochemiluminescence . . . . . . . . . . . . . . . 4 Efficiencies of the Excited States Formation . . . . . . . . . . . . .............. 4.1 Aromatic hydrocarbons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....................... 4.2 Intramolecular Donor-Acceptor systems . . 4.3 Ruthenium(I1) Chelates . . . . . . . . . . . . . . ........... ......... 4.4 Molybdenum(I1) and Tungsten(I1) Halide Cluster Ions . . . . . . . . ......... 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..................... 6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . List of Symbols C C e0 E f F FC G h H j velocity of light molar concentration of solute electron charge energyktandard redox potential force constant Faraday constant Franck-Condon factor Gibbs energy Planck's constant energy operator number of vibronically-excited sublevel 3 5 5 7 11 14 16 18 18 20 23 24 24 33 44 49 55 56 A. Kapturkiewicz reaction rate association constant for formation of precursor complex optical path length electronic transition moment refractive index of medium Avogadro constant effective radius of redox centerheactants separation distance gas constant electron-vibration coupling constant/entropy time absolute temperature electronic matrix element describing electronic coupling/potential energy energy of precursor complex formation energy functions for reactants 1 and 2 at distance r12 reaction nuclear coordinate parameter describing distance (exponential) decreasing of electronic coupling effective thickness of reaction layer static dielectric constant, dielectric permittivity dielectric permittivity of a vacuum molar absorbance of charge-transfer absorption of a photon viscosity inner/outer/reorganization energy and their ‘force constants’ dipole moment operator mean inner vibration frequency/mean outer rotation frequency relaxation time efficiency/fraction of electron transfer events electrochemiluminescence efficiency emission quantum yield dielectric permittivity in near-infrared region absorptiordemission wave number electronic wavefunction angular frequency Abbreviations A ACN BA biq BN bPY bPz bqu cip D DA DPA dPh ECL HOMO L LUMO MO PF acceptor acetonitrile bianthryl 2,2‘-biisoquiniline butyronitrile 2,2’-bipyridine 2,2’-bipyrazine 2,2’-biquinoline contact ion pair donor 10,10’-dimethoxybianthryI 9,lO-diphenyl enthracene 4,7-diphenyl- 1,lO-phenanthroline electrochemiluminescence highest occupied atomic orbital organic ligand lowest unoccupied atomic orbital molecular orbital pre-exponential factor Marcus Theory in the Description of Electrochemiluminescence Phenomena R ssip TBAP TTA 3 organic molecule solvent-separated ion pair tetra-n-butylammonium perchlorate triplet-triplet annihilation 1 Introduction The understanding of the factors determining the rate of the electron transfer processes is important, because of the ubiquity and essential role of electron transfer in many physical, chemical, and biological processes. During the past three decades they have been the subject of extensive theoretical and experimental studies. Classical and quantum-mechanical treatments predict that the reaction rate will increase with increasingly negative Gibbs energy of the reaction, maximize for a moderately exergonic reaction (the normal Marcus region), and thereafter decrease as the Gibbs energy of the reaction becomes more negative (the inverted Marcus region) [l]. One of the most fascinating consequences of such behavior is the light emission during the reaction with very large exothermicity [2]. Chemiluminescence can be defined as the emission of light resulting from the generation of electronically excited states formed in a chemical reaction. Light emission arises at the expense of the energy released from an exothermic elementary step of a reaction. The understanding of the mechanism of chemiluminescence has advanced to the point that prediction of light emission during a chemical reaction is now possible (see, for example, [3-51). However, much remains to be done in identifying the fundamental physical processes leading to electronic excitation. It is not possible to give a simple answer to the question “What are the factors controlling excited state formation?” Quantitative predictions are even more difficult, because of the large number of factors affecting the mechanism of a chemiluminescent reaction. The heart of the matter is the excitation step, which in most cases can be formulated as an inter- or intramolecular electron transfer. Kinetic considerations predict the occurrence of such electron transfer in a very short time scale (even shorter than the period of an intramolecular vibration) requiring rapid dissipation of a large amount of energy into the vibration modes of the molecular frames. This is very difficult for the reacting system, and only a limited fraction of the reacting species follows that pathway directly, leading to a direct formation of the stable ground-state products. The formation of the excited states is less exergonic and less thermodynamically favored. However, less energy needs to be vibrationally dissipated, and therefore the process may be kinetically preferred. Obviously, because the molecular energy levels are quantized, the reaction yielding the excitation must deliver, in one step, the appropriate amount of energy. In the simplest case this may be realized in chemical reactions involving strong oxidants and reductants. Both methods for the preparation of the reactants, the common chemical (e.g., [6]), and electrochemical routes (reviewed in [7-13]), can be used, and the observations from these two methods can be nicely related. Employment of chemical oxidants and/or reductants seems to be more cumbersome, especially in quantitative work. The electrochemical route seems to be much more 4 A. Kapturkiewicz useful in cases of relatively unstable intermediates. Also it is advantageous because, when working at controlled potentials, very selective oxidation and reduction can be induced. Electrochemiluminescence (or electrochemically generated chemiluminescence), ECL, can be defined as the generation of light-emitting species by means of homogeneous electron transfer between precursors in solution. Such precursors are obtained as a consequence of heterogeneous electron transfer (electrode) reactions, leading to the formation of very active oxidizing and reducing agents. To facilitate rapid encounters among themselves, precursors may be formed sequentially on one working electrode by application of the appropriate potential program (under diffusion-controlled electrolysis conditions using the triple potential-step technique [ 141) or under steady-state convective electrolysis conditions (e.g., on the ring and on the disk of a rotating ring-disk electrode [15, 161 or at double-band microelectrodes ~71). In some cases the excited states of molecules can also be achieved by means of heterogeneous electron transfer. Typically, electron transfer to or from an electrode results in formation of an excited state of the electrode [18-201. However, the oxidized form of some luminescent species may be reduced by electrons transferred from the conduction band of an n-type semiconductor, showing evidence for the production of triplet states [21-231. Electrochemical excitation, “photochemistry without light,” exhibits many phenomena that are unique to ECL as compared to photochemistry. The efficient production of emission from excimers or exciplexes as compared to excited monomers, efficient generation of excited triplet states, and intense delayed fluorescence caused by triplet-triplet annihilation are the most typical examples. On the other hand, the method offers a chance to populate the excited states that are inaccessible by the processes following photoexcitation. Three directions of the ECL investigations seem to be the most interesting: study of the mechanism of the phenomenon as such; use of electrical energy for obtaining excited molecules; and application of ECL for studying the kinetics and mechanism of electron transfer reactions. Up till now, eventual practical applications are less developed; ECL devices, such as displays and lasers [24-271, and the visualization of non-uniform current distribution on electrodes [28,29] are the most interesting examples. Quantitative study of ECL systems is a rather difficult task. The combined requirements of reductant and oxidant stability with high fluorescence efficiency of the parent molecule drastically limit the types of compounds suitable for use in the study of the ECL phenomenon. To these, we must add solubility and chemical stability in the presence of electrodes, electrolyte, and solvent. Photochemical stability is an additional requirement. Chemical complications following the initial electron transfer to and from the electrode are still a problem. The chemistry occurring in solution after electrolysis must therefore be examined carefully. Especially, the solvent-supportingelectrolyte system should be chosen to prevent lack of reactivity with the electrogenerated species. All of the above complications may lead to misinterpretation of the essentially simple processes of electron transfer excitation. However, in some cases most of these interferences may be removed by Marcus Theory in the Description of Electrochemiluminescence Phenomena 5 appropriate experimental conditions and the ECL obtained data allow for quantitative discussion. An interpretation that is more general and more quantitative than hitherto is possible in view of new data presented in the literature. 2 Kinetics of Electron Transfer Reactions 2.1 Main Concepts As mentioned above, the formation of excited states in chemical reactions may be understood in the context of an electron transfer model for chemiluminescence, first proposed by Marcus [2]. According to this model the formation of excited states is competitive with the formation of the ground state, even though the latter is strongly favored thermodynamically. Thus, understanding the factors that determine the electron transfer rate is of considerable importance. The theory of electron transfer reactions in solution has been summarized and reviewed in many reviews (e.g., [30361). Therefore, in this chapter the relevant ideas and equations are only briefly summarized, to serve as a basis for description of the ECL experiments. Although a number of theories have been proposed, there is agreement that the crux of the electron transfer problem is the fact that the equilibrium nuclear configuration of a species (in the intramolecular bond, this includes lengths and angles as well as the vibrations and rotations of the surrounding solvent dipoles) changes when it gains or loses an electron. The equilibrium configurations of reduced and oxidized forms of a redox couple, like the ground and excited states of a molecule are generally different. As a consequence, the rates of thermally activated electron transfer reactions, radiative transitions and nonradiative deactivation processes can be discussed with common formalism in which the rate is a product of an electronic and a nuclear factor. The former is a function of the electronic interaction in the reacting system, whereas the latter depends on the nuclear configuration changes between the reactants and products. Of course the larger the electronic interaction, and the smaller the changes in nuclear configuration, the more rapid is the electron transfer process. The role of both factors in determining the rate of electron transfer can be described quantitatively. The formalism describing these processes provides a unified description of homogeneous (intra- and intermolecular) and heterogeneous electron transfer reactions, either radiative or radiationless in nature. The theoretical description of the kinetics of electron transfer reactions starts from the pioneering work of Marcus [l]; in his work the convenient expression for the free energy of activation was defined. However, the pre-exponential factor in the expression for the reaction rate constant was left undetermined in the framework of that classical (activate-complex formalism) and macroscopic theory. The more sophisticated, semiclassical or quantum-mechanical, approaches [37- 411 avoid this inadequacy. Typically, they are based on the Franck-Condon principle, i.e., assuming the separation of the electronic and nuclear motions. The Franck-Condon principle 6 A. Kapturkiewicz states that the interatomic distances and nuclear moment are identical in the final and initial states during the time of electron transfer. The transfer of an electron between two states is a relatively instantaneous event compared to the slower nuclear motions that must take place to accommodate the “new” electronic configuration. Nuclear changes must occur prior to electron transfer and they are possible due to collisions between reactants and surrounding solvent. Before the transfer of an electron, the nuclear geometry of the initial state, including the surrounding solvent molecules, must be converted into a high-energy, “nonequilibrium” or distorted configuration. The transition state consists of two high-energy species which posses the same nuclear conformation but different electronic configurations. Moreover, for simplicity, the inner-molecular motions (treated quantum-mechanically) are separated from the solvent motions (treated classically). Such an approach is justified at normal temperatures. Taking into account the assumptions presented above, the probability per unit time (first-order state constant ket)that an initial state will pass to a final product may be given by the time-dependent perturbation theory as: 479 ket = -V t2(FC) h where h is the Planck constant and V12 is the electronic matrix element describing the electronic coupling between the initial and final states, being defined as follows: where !PI and !P2 are the electronic wavefunctions of the reacting system in the initial and final states, respectively. H = (HI Hz H12) is the energy operator and contains Hlz, which, unlike HI and H2, depends on the separation distance between two redox centers involved in the given electron transfer reaction. H1 and HZ, however, depend on the reaction nuclear coordinate x. H12 corresponds to the interaction between of the initial and final state, but with the electron being required to remain localized on the substract or product. The potential energies of the system in its initial (Vl) and final (V2) states are given by: + + The quantity (FC) is the Franck-Condon factor: it is a sum of products of overlap integrals of the vibrational and solvation wavefunctions of the reactants with those of the products, suitably weighted by Boltzmann factors. The value of the Franck-Condon factor may be expressed analytically by considering the effective potential energy curves, of both the initial and the final states, as a function of their nuclear configurations. Relatively simple relationships can be derived if the appropriate curves are harmonic with identical force constants. Under these conditions: 2 VI = X(xl - x) and V2 = X(x2 - + AGIZ (4) Marcus Theory in the Description of Electrochemiluminescence Phenomena 7 where X is the “force constant” (in units of energy) of the parabolas, x is the dimensionless nuclear (reaction) coordinate, AG12 is the Gibbs energy change between the initial and the final state, and xl and x2 correspond to their thermodynamically equilibrated configurations. The term X is the sum of two contributions: an inner one (Xi) required for the bond length and angle changes, and an outer one (A,) necessary for the reorganization of the solvent coordination shells. The energy Xi can be estimated using a harmonicoscillator approximation. The potential energy needed to change the inter-atomic distances from their equilibrium values in the initial state to those appropriate to the final state may be calculated, taking into account the force constants in the reactant and product ( f j , l and fj,2 respectively, where j = number of changing bond) and the change in equilibrium values of the given bond (Ag12): The quantities needed may be obtained from the IR-spectroscopic (fj,~andfj,2) and crystallographic (Agl2) data. Obviously Eq. ( 5 ) is valid only if no bonds are broken and new bonds are not formed in the given electron transfer reaction. The energy required to reorganize the solvent, A, is obtained by a different procedure. The medium outside the reactant (or reactants) is treated as a dielectric continuum with the polarization made up of two parts, a relatively rapid electronic polarization and a slower vibrational-orientational one. The latter has to adjust to a nonequilibrium value appropriate to the final state, contrary to the former. On the basis of the Born solvation theory A, (if one electron is transferred) is given by: where E and n are the static dielectric constant and the refractive index of the reaction medium; NA, eo and EO are the Avogadro constant, the electron charge and the permittivity of a vacuum, respectively; rl and r2 are the effective radii of the redox centers involved in the electron transfer reaction, with the center-to-center separation distance r12. Equation ( 6 ) is exactly valid only for spherical molecules, with a uniform charge distribution. In the cases in which the charge is nonuniformly redistributed andor for nonspherical molecules, A, may be estimated on the basis of an appropriate, more sophisticated extension of the simple Born model (e.g., [42-441). 2.2 Normal and Inverted Marcus Region Using the formalism presented above, potential energy curves may be constructed in zero-order as well as in first-order approximations. Electron transfer can then be described in terms of crossing of the system from one potential energy curve to the 8 A. Kapturkiewicz other. In the zero-order approximation, the electron is required to remain localized to the individual system. No electron transfer is possible as long as this condition is imposed: electronic coupling of the reactants is necessary for the system to pass from the initial state to the final state. Electronic coupling removes the degeneracy at the intersection and leads to the formation of two new curves, the adiabatic states of the system. The adiabatic states are obtained by solving the secular equation: The roots of the equation are: where E, and E- describe the lower and upper curve, respectively. The above considerations are valid if V12< A, the shapes of the potential energy curves are changed. Electron transfer involves a transition from one adiabatic curve to the other and therefore is inherently nonadiabatic (Fig. 2). The second region is called the abnormal or inverted free-energy region (also the inverted Marcus region) and is defined by AG12 < -A. In this region, the reaction rate usually decreases as the standard Gibbs energy becomes more negative. Marcus Theory in the Description of Electrochemiluminescence Phenomena 9 initial st Energy - Nuclear coordinate x Fig. 1. Electron transfer in the normal Marcus region. Potential energies of the reactant and product as a function of the nuclear (reaction) coordinate: the zero-order (left) and first-order (right) representations. t Energy I x2 X1 x2 Nuclear coordinate x -+ Fig. 2. Electron transfer in the inverted Marcus region. Potential energies of the reactant and product as a function of the nuclear (reaction) coordinate: the zero-order (left) and first-order (right) representations. In electron transfer reactions with relatively low exothermicity, -AG12 < A, the excess of the Gibbs energy leads only to vibrational and orientational excitation of the surrounding solvent shell. If the reaction is more exergonic, vibrational andor electronic excitation of reaction products is generally possible. The overall reaction rate is then the superposition of many channels. 10 A. Kapturkiewicz Electronic excitation is possible only for very exergonic electron transfer reactions with the energy excess larger than the energy for the given excited state, typically greater than 1.5 eV. Vibrational intramolecular excitation is, however, already possible for moderately exergonic processes (typically the energy of vibronic quanta is 0.1-0.3 eV). Consequently, the reaction rate in the inverted Marcus region (with -AG12 > A) may be faster than that expected from the simplified theory. Vibrational excitation of the high-frequency modes accompanying the electron transfer lowers the energy gap in the inverted Marcus region. This results in lowering of the effective activation energy and in enhancement of the reaction rate. Of course, the enhancement is even greater if additional channels (leading to electronically excited products) are also accessible. In the theoretical description of the resulting reaction rate the same main assumptions are applicable, but different Franck-Condon factors (FC) should be applied for all the accessible channels. In the theoretical description of the overall reaction rate the modified Eq. (1) may be applied (with the assumption that the electronic coupling element does not depend on the quantum number, j , of the excited vibrational mode): Each summand in Eq. (11) represents the rate for a single contribution to the total rate from a 0 -+ j nonradiative vibronic transition (Fig. 3). The Frack-Condon principle applies for each of the single contributions. Similarly, as in the single mode approximation, the corresponding Franck-Condon factors (FC,) are a sum of product of overlap integrals of the vibrational wavefunction of the reactants with those of products, weighted by appropriate Boltzmann factors. It is assumed (for simplicity) that only one (averaged over all of the changing bonds and angles) high-frequency initial state final states initial final states 1 AG, 2 Fig. 3. Schematic illustration of non-radiative electron transfer (horizontal mows) in the normal (left) and inverted (right) Marcus regions. Associated with each vibronic state is a stack of sublevels representing low-frequency (mainly) solvent modes. In the initial state only one vibrational mode, with j = 0, is mainly occupied, whereas in the final state various vibrational modes, with j = 0, 1 ,2...,may be accessible. Diagonal arrows (in the inverted Marcus region) correspond to radiative electron transfer (charge-transfer fluorescence). Adapted from [55].

Author Charles W. Tobias and Richard C. Alkire Isbn 9783527293858 File size 55.2MB Year 1997 Pages 430 Language English File format PDF Category Chemistry Book Description: FacebookTwitterGoogle+TumblrDiggMySpaceShare This series, formerly edited by Heinz Gerischer and Charls V. Tobias, now edited by Richard C. Alkire and Dieter M. Kolb, has been warmly welcomed by scientists world-wide which is reflected in the reviews of the previous volumes: ‘This is an essential book for researchers in electrochemistry; it covers areas of both fundamental and practical importance, with reviews of high quality. The material is very well presented and the choice of topics reflects a balanced editorial policy that is welcomed.’ The Analyst     Download (55.2MB) Advances in Chemical Physics Chemical Modelling: Applications and Theory, Volume 10 Compositional Analysis of Polymers: An Engineering Approach Handbook of Food Science and Technology 1 Chemistry of High-Energy Materials, 2nd edition Load more posts

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