(BQ) Part 1 book Electrochemical methods Fundamentals and applications has contents: Introduction and overview of electrode processes, potentials and thermodynamics of cells, kinetics of electrode reactions, mass transfer by migration and diffusion, basic potential step methods, potential sweep methods, polarography and pulse voltammetry,...and other contents.
SECOND EDITION ELECTROCHEMICAL METHODS Fundamentals and Applications Allen J Bard Larry R Faulkner Department of Chemistry and Biochemistry University of Texas at Austin JOHN WILEY & SONS, INC New Yorke Chichester • Weinheim Brisbane e Singapore e Toronto Acquisitions Editor David Harris Senior Production Editor Elizabeth Swain Senior Marketing Manager Charity Robey Illustration Editor Eugene Aiello This book was set in 10/12 Times Roman by University Graphics and printed and bound by Hamilton The cover was printed by Phoenix This book is printed on acid-free paper, oo Copyright 2001 © John Wiley & Sons, Inc 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 as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470 Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 605 Third Avenue, New York, NY 10158-0012, (212) 850-6011, fax (212) 850-6008, E-Mail: PERMREQ@WILEY.COM To order books or for customer service, call (800)-CALL-WILEY (225-5945) Library of Congress Cataloging in Publication Data: Bard, Allen J Electrochemical methods : fundamentals and applications / Allen J Bard, Larry R Faulkner.— 2nd ed p cm Includes index ISBN 0-471-04372-9 (cloth : alk paper) Electrochemistry I Faulkner, Larry R., 1944- II Title QD553.B37 2000 541.3'7_dc21 00-038210 Printed in the United States of America 10 PREFACE In the twenty years since the appearance of our first edition, the fields of electrochemistry and electroanalytical chemistry have evolved substantially An improved understanding of phenomena, the further development of experimental tools already known in 1980, and the introduction of new methods have all been important to that evolution In the preface to the 1980 edition, we indicated that the focus of electrochemical research seemed likely to shift from the development of methods toward their application in studies of chemical behavior By and large, history has justified that view There have also been important changes in practice, and our 1980 survey of methodology has become dated In this new edition, we have sought to update the book in a way that will extend its value as a general introduction to electrochemical methods We have maintained the philosophy and approach of the original edition, which is to provide comprehensive coverage of fundamentals for electrochemical methods now in widespread use This volume is intended as a textbook and includes numerous problems and chemical examples Illustrations have been employed to clarify presentations, and the style is pedagogical throughout The book can be used in formal courses at the senior undergraduate and beginning graduate levels, but we have also tried to write in a way that enables self-study by interested individuals A knowledge of basic physical chemistry is assumed, but the discussions generally begin at an elementary level and develop upward We have sought to make the volume self-contained by developing almost all ideas of any importance to our subject from very basic principles of chemistry and physics Because we stress foundations and limits of application, the book continues to emphasize the mathematical theory underlying methodology; however the key ideas are discussed consistently apart from the mathematical basis Specialized mathematical background is covered as needed The problems following each chapter have been devised as teaching tools They often extend concepts introduced in the text or show how experimental data are reduced to fundamental results The cited literature is extensive, but mainly includes only seminal papers and reviews It is impossible to cover the huge body of primary literature in this field, so we have made no attempt in that direction Our approach is first to give an overview of electrode processes (Chapter 1), showing the way in which the fundamental components of the subject come together in an electrochemical experiment Then there are individual discussions of thermodynamics and potential, electron-transfer kinetics, and mass transfer (Chapters 2-4) Concepts from these basic areas are integrated together in treatments of the various methods (Chapters 5-11) The effects of homogeneous kinetics are treated separately in a way that provides a comparative view of the responses of different methods (Chapter 12) Next are discussions of interfacial structure, adsorption, and modified electrodes (Chapters 13 and 14); then there is a taste of electrochemical instrumentation (Chapter 15), which is followed by an extensive introduction to experiments in which electrochemistry is coupled with other tools (Chapters 16-18) Appendix A teaches the mathematical background; Appendix В provides an introduction to digital simulation; and Appendix С contains tables of useful data vi • Preface This structure is generally that of the 1980 edition, but important additions have been made to cover new topics or subjects that have evolved extensively Among them are applications of ultramicroelectrodes, phenomena at well-defined surfaces, modified electrodes, modern electron-transfer theory, scanning probe methods, LCEC, impedance spectrometry, modern forms of pulse voltammetry, and various aspects of spectroelectrochemistry Chapter in the first edition ("Controlled Potential Microelectrode Techniques—Potential Step Methods") has been divided into the new Chapter ("Basic Potential Step Methods") and the new Chapter ("Polarography and Pulse Voltammetry") Chapter 12 in the original edition ("Double Layer Structure and Adsorbed Intermediates in Electrode Processes") has become two chapters in the new edition: Chapter 12 ("Double-Layer Structure and Adsorption") and Chapter 13 ("Electroactive Layers and Modified Electrodes") Whereas the original edition covered in a single chapter experiments in which other characterization methods are coupled to electrochemical systems (Chapter 14, "Spectrometric and Photochemical Experiments"), this edition features a wholly new chapter on "Scanning Probe Techniques" (Chapter 16), plus separate chapters on "Spectroelectrochemistry and Other Coupled Characterization Methods" (Chapter 17) and "Photoelectrochemistry and Electrogenerated Chemiluminescence" (Chapter 18) The remaining chapters and appendices of the new edition directly correspond with counterparts in the old, although in most there are quite significant revisions The mathematical notation is uniform throughout the book and there is minimal duplication of symbols The List of Major Symbols and the List of Abbreviations offer definitions, units, and section references Usually we have adhered to the recommendations of the IUPAC Commission on Electrochemistry [R Parsons et al., Pure Appl С hem., 37, 503 (1974)] Exceptions have been made where customary usage or clarity of notation seemed compelling Of necessity, compromises have been made between depth, breadth of coverage, and reasonable size "Classical" topics in electrochemistry, including many aspects of thermodynamics of cells, conductance, and potentiometry are not covered here Similarly, we have not been able to accommodate discussions of many techniques that are useful but not widely practiced The details of laboratory procedures, such as the design of cells, the construction of electrodes, and the purification of materials, are beyond our scope In this edition, we have deleted some topics and have shortened the treatment of others Often, we have achieved these changes by making reference to the corresponding passages in the first edition, so that interested readers can still gain access to a deleted or attenuated topic As with the first edition, we owe thanks to many others who have helped with this project We are especially grateful to Rose McCord and Susan Faulkner for their conscientious assistance with myriad details of preparation and production Valuable comments have been provided by S Amemiya, F C Anson, D A Buttry, R M Crooks, P He, W R Heineman, R A Marcus, A C Michael, R W Murray, A J Nozik, R A Osteryoung, J.-M Saveant, W Schmickler, M P Soriaga, M J Weaver, H S White, R M Wightman, and C G Zoski We thank them and our many other colleagues throughout the electrochemical community, who have taught us patiently over the years Yet again, we also thank our families for affording us the time and freedom required to undertake such a large project Allen / Bard Larry R Faulkner CONTENTS MAJOR SYMBOLS ix STANDARD ABBREVIATIONS xix INTRODUCTION AND OVERVIEW OF ELECTRODE PROCESSES POTENTIALS AND THERMODYNAMICS OF CELLS KINETICS OF ELECTRODE REACTIONS MASS TRANSFER BY MIGRATION AND DIFFUSION 44 87 137 BASIC POTENTIAL STEP METHODS POTENTIAL SWEEP METHODS POLAROGRAPHY AND PULSE VOLTAMMETRY CONTROLLED-CURRENT TECHNIQUES METHODS INVOLVING FORCED CONVECTION—HYDRODYNAMIC METHODS 331 10 156 226 261 305 TECHNIQUES BASED ON CONCEPTS OF IMPEDANCE 368 11 BULK ELECTROLYSIS METHODS 12 ELECTRODE REACTIONS WITH COUPLED HOMOGENEOUS CHEMICAL REACTIONS 471 417 13 DOUBLE-LAYER STRUCTURE AND ADSORPTION 14 ELECTROACTIVE LAYERS AND MODIFIED ELECTRODES 15 ELECTROCHEMICAL INSTRUMENTATION 534 580 632 16 SCANNING PROBE TECHNIQUES 17 SPECTROELECTROCHEMISTRY AND OTHER COUPLED CHARACTERIZATION METHODS 680 659 18 PHOTOELECTROCHEMISTRY AND ELECTROGENERATED CHEMILUMINESCENCE 736 APPENDICES A MATHEMATICAL METHODS В DIGITAL SIMULATIONS OF ELECTROCHEMICAL PROBLEMS С REFERENCE TABLES INDEX 814 808 769 785 MAJOR SYMBOLS Listed below are symbols used in several chapters or in large portions of a chapter Symbols similar to some of these may have different local meanings In most cases, the usage follows the recommendations of the IUPAC Commission on Electrochemistry [R Parsons et al., Pure Appl Chem., 37, 503 (1974).]; however there are exceptions A bar over a concentration or a current [ej*., C o (x, s)] indicates the Laplace transform of the variable The exception is when / indicates an average current in polarography STANDARD SUBSCRIPTS a с D d anodic (a) cathodic (b) charging disk diffusion dl double layer eq equilibrium f (a) forward (b) faradaic limiting / P R r pertaining to species in О + ne ±± R peak (a) pertaining to species R in О + ne ^ R (b) ring reverse ROMAN SYMBOLS Symbol С CB cd c't Meaning Usual Units Section References (a) area (b) cross-sectional area of a porous electrode (c) frequency factor in a rate expression (d) open-loop gain of an amplifier absorbance (a) internal area of a porous electrode (b) tip radius in SECM activity of substance j in a phase a aFv/RT cm cm 1.3.2 11.6.2 depends on order none none cm 3.1.2 15.1.1 17.1.1 11.6.2 16.4.1 2.1.5 6.3.1 13.5.3 1.2.2, 10.1.2 10.4 1.2.2, 13.2.2 capacitance series equivalent capacitance of a cell differential capacitance of the double layer integral capacitance of the double layer concentration of species; bulk concentration of species; concentration of species; at distance x none s" mol/cm2 F F F, F/cm2 F, F/cm2 M, mol/cm3 M, mol/cm3 M, mol/cm3 13.2.2 1.4.2, 4.4.3 1.4 Major Symbols Symbol Meaning Usual Units Section References CjCx = 0) concentration of species j at the electrode surface concentration of species у at distance x at time t concentration of species у at the electrode surface at time t concentration of species у at distance у away from rotating electrode surface concentration of species у at a rotating electrode space charge capacitance pseudocapacity speed of light in vacuo diffusion coefficient for electrons within the film at a modified electrode diffusion coefficient of species у concentration density of states for species у model diffusion coefficient in simulation diffusion coefficient for the primary reactant within the film at a modified electrode distance of the tip from the substrate in SECM density of phase у (a) potential of an electrode versus a reference (b) emf of a reaction (c) amplitude of an ac voltage (a) pulse height in DPV (b) step height in tast or staircase voltammetry (c) amplitude (1/2 p-p) of ac excitation in ac voltammetry electron energy electric field strength vector electric field strength voltage or potential phasor (a) standard potential of an electrode or a couple (b) standard emf of a half-reaction difference in standard potentials for two couples electron energy corresponding to the standard potential of a couple formal potential of an electrode activation energy of a reaction ac component of potential base potential in NPV and RPV dc component of potential M, mol/cm3 1.4.2 M, mol/cm3 4.4 M, mol/cm3 4.4.3 M, mol/cm3 9.3.3 M, mol/cm3 9.3.4 F/cm F cm/s cm /s 18.2.2 10.1.3 17.1.2 14.4.2 cm2/s cm eV~ ! none cm2/s 1.4.1,4.4 3.6.3 B.1.3.B.1.8 14.4.2 /xm, nm 16.4.1 g/cm3 V 1.1,2.1 V V mV mV 2.1 10.1.2 7.3.4 7.3.1 mV 10.5.1 eV V/cm V/cm V V 2.2.5, 3.6.3 2.2.1 2.2.1 10.1.2 2.1.4 V V 2.1.4 6.6 eV 3.6.3 V kJ/mol mV V V 2.1.6 3.1.2 10.1.1 7.3.2, 7.3.3 10.1.1 Cj(x, t) Cj(O, f) Cj(y = 0) Csc С Dj(A, E) DM £s d *\ E AE E % % E £° AE° E° E0' EA Eac Eb Edc Major Symbols Symbol Meaning Usual Units Section References Ещ EF equilibrium potential of an electrode Fermi level flat-band potential bandgap of a semiconductor initial potential junction potential membrane potential peak potential (a)|£pa-£pc|inCV (b) pulse height in SWV potential where / = /p/2 in LSV anodic peak potential cathodic peak potential staircase step height in SWV potential of zero charge switching potential for cyclic voltammetry quarter-wave potential in chronopotentiometry (a) measured or expected half-wave potential in voltammetry (b) in derivations, the "reversible" half-wave potential, Eo> + (RT/nF)\n(DR/D0)l/2 potential where i/i^ = / potential where ///d = 3/4 (a) electronic charge (b) voltage in an electric circuit input voltage output voltage voltage across the input terminals of an amplifier error function of x error function complement of x the Faraday constant; charge on one mole of electrons (a) F/RT (b) frequency of rotation (c) frequency of a sinusoidal oscillation (d) SWV frequency (e) fraction titrated Fermi function fractional concentration of species / in boxy after iteration к in a simulation Gibbs free energy Gibbs free energy change in a chemical process electrochemical free energy standard Gibbs free energy V eV V eV V mV mV V V mV V V V mV V V V 1.3.2,3.4.1 2.2.5, 3.6.3 18.2.2 18.2.2 6.2.1 2.3.4 2.4 6.2.2 6.5 7.3.5 6.2.2 6.5 6.5 7.3.5 13.2.2 6.5 8.3.1 V 1.4.2,5.4,5.5 V 5.4 V V 5.4.1 5.4.1 Em Eg E; Щ Em EP A£P Ep/2 £pa £pc £Z *л Еф E\I2 Ещ Е Ъ1А e e\ e0 ег%) erfc(x) F f /(E) fUk) G AG G G° с V V V /xV 10.1.1,15.1 15.2 15.1.1 15.1.1 none none С A.3 A.3 V" r/s s- s- none none none 9.3 10.1.2 7.3.5 11.5.2 3.6.3 B.1.3 kJ, kJ/mol kJ, kJ/mol 2.2.4 2.1.2,2.1.3 kJ, kJ/mol kJ, kJ/mol 2.2.4 3.1.2 xi xii Major Symbols Symbol Meaning Usual Units Section References AG° standard Gibbs free energy change in a chemical process standard Gibbs free energy of activation standard free energy of transfer for species j from phase a into phase /3 (a) gravitational acceleration (b) interaction parameter in adsorption isotherms (a) enthalpy kJ, kJ/mol 2.1.2,2.1.3 kJ/mol kJ/mol 3.1.2 2.3.6 дс!transfer, j j H cm/s 2 J-cm /mol kJ, kJ/mol -l/2 s Mi A#° / /(0 / А/ 8i /(0) *А Od)max enthalpy change in a chemical process standard enthalpy change in a chemical process standard enthalpy of activation Planck constant corrected mercury column height at a DME amplitude of an ac current convolutive transform of current; semi-integral of current current phasor diffusion current constant for average current diffusion current constant for maximum current peak value of ac current amplitude current difference current in SWV = if — ir difference current in DPV = /(r) - Z(r') initial current in bulk electrolysis characteristic current describing flux of the primary reactant to a modified RDE anodic component current (a) charging current (b) cathodic component current (a) current due to diffusive flux (b) diffusion-limited current average diffusion-limited current flow over a drop lifetime at a DME diffusion-limited current at tm.dX at a DME (maximum current) characteristic current describing diffusion of electrons within the film at a modified electrode (a) faradaic current (b) forward current kinetically limited current characteristic current describing cross-reaction within the film at a modified electrode kJ, kJ/mol kJ, kJ/mol 13.5.2 2.1.2 5.5.1 2.1.2 2.1.2 3.1.2 kJ/mol J-s cm A C/s1/2 7.1.4 10.1.2 6.7.1 A ^A-s1/2/(mg2/3-mM) 10.1.2 7.1.3 M-s 1/2 /(mg 2/3 -mM) 7.1.3 A A A A A A 10.5.1 1.3.2 7.3.5 7.3.4 11.3.1 14.4.2 A A A A A A 3.2 6.2.4 3.2 4.1 5.2.1 A A A A A A 7.1.2 7.1.2 14.4.2 5.7 9.3.4 14.4.2 Major Symbols Symbol Meaning Usual Units Section References Ч limiting current limiting anodic current limiting cathodic current migration current characteristic current describing permeation of the primary reactant into the film at a modified electrode peak current anodic peak current cathodic peak current current during reversal step (a) characteristic current describing diffusion of the primary reactant through the film at a modified electrode (b) substrate current in SECM steady-state current tip current in SECM tip current in SECM far from the substrate exchange current true exchange current imaginary part of complex function w flux of species j at location x at time t (a) current density (b) box index in a simulation A A A A A 1.4.2 1.4.2 1.4.2 4.1 14.4.2 A A A A A 6.2.2 6.5.1 6.5.1 5.7 14.4.2 A A A A 16.4.4 5.3 16.4.2 16.4.1 k& kc h >P 'pa *pc 'r 'S 4s h *T,oo h *0,t Im(w) /jfe t) j (c)V^I h К к k° К kf *?? k° exchange current density equilibrium constant precursor equilibrium constant for reactant j (a) rate constant for a homogeneous reaction (b) iteration number in a simulation (c) extinction coefficient Boltzmann constant standard heterogeneous rate constant (a) heterogeneous rate constant for oxidation (b) homogeneous rate constant for "backward" reaction (a) heterogeneous rate constant for reduction (b) homogeneous rate constant for "forward" reaction potentiometric selectivity coefficient of interferenty toward a measurement of species / true standard heterogeneous rate constant • A A mol c m " s" A/cm2 none none A/cm none depends on case 3.4.1,3.5.4 13.7.1 A.5 1.4.1,4.1 1.3.2 B.1.2 A.5 3.4.1,3.5.4 3.6.1 depends on order none none J/K cm/s cm/s B.I 17.1.2 depends on order 3.1 cm/s 3.2 depends on order 3.1 none 2.4 cm/s 13.7.1 3.3, 3.4 3.2 xui 456 Chapter 11 Bulk Electrolysis Methods A typical scan voltammogram in a thin-layer cell is shown in Figure 11.7.3 Note that the peak current is directly proportional to v, but the total charge under the i-E curve, given by (11.7.11), is independent of v The rigorous solution for this problem, accounting for nonuniform concentrations within the cell, can be derived (63) It has been shown that the approximate form, (11.7.16), will hold at sufficiently small values of v, that is, when (11.7.18) where e is the relative error tolerated in calculation of /p For a totally irreversible one-step, one-electron reaction, the current is given by (11.7.19) where kf = k°exp[(-aF/RT)(E - E0)] By combining (11.7.19) with (11.7.12) we obtain dC0(t) = dt \Akf(tj\ I JC {t) (11.7.20) In a potential sweep experiment, E(t) = EY - vt (see equation 6.2.1); therefore, with / = F/RT, kf(t) = k° exp[-af(E{ - E0)] exp(afat) (11.7.21) By substitution of (11.7.21) into (11.7.20) and integration between t = (C o = CQ) and t [Co = C0(t)], under the conditions that k° exp[-a/(£i - E0')] -> (i.e., an initial po- 1.0 0.5 E-EQ,V -0.5 -1.0 Figure 11.7.3 Cyclic current-potential curve for a nernstian reaction with n = 1, V= 1.0 nU \v\ = lmV/s, Co = l.OmM, Г=298К [From A T Hubbard and F C Anson, Electroanal Chem.,4, 129 (1970), by courtesy of Marcel Dekker, Inc.] Thin-Layer Electrochemistry -0.2 -0.6 -0.4 457 -0.8 Е-Е°',У Figure 11.7.4 Theoretical cathodic current-potential curves for one-step, one-electron irreversible reactions according to (11.7.24) for several values of k° Curve A: reversible reaction (shown for comparison) Curve B: k° = 10~6 Curve C: k° = 10~8 Curve D: к0 = " cm/s The values assumed in making the plots were \v\ = mV/s, A = 0.5 cm2, CQ = 1.0 mM, a = 0.5, V = 2.0 /JLL [From A T Hubbard, J Electroanal Chem., 22, 165 (1969), with permission.] tential well positive of E°), (63, 64): the following expressions for C0(E) and i(E) are obtained (11.7.22) (11.7.23) or, substituting for lq9 { о (11.7.24) ч -af(E - Е ) —— ехр[-а/(Е - Е" )] > Typical i-E curves for a totally irreversible reduction of О to R in a thin-layer cell are shown in Figures 11.7.4 and 11.7.5 The peak potential [obtained by differentiating (11.7.24) and setting the result equal to zero] occurs at Q' , F 0.0 -0.2 -0.4 -0.6 RTjARTk°\ aF \aFVv I (11.7.25) Figure 11.7.5 Theoretical cathodic currentpotential curves for one-step, one-electron irreversible reactions for several values of a Curve A: reversible reaction Curve В: а = 0.75, k° = 10~6 cm/s Curve C: a = 0.5, &° = 10~6 cm/s Curve D:a = 0.25, A:0 = 10~6 cm/s The values assumed in making the graphs were: \v\ — mV/s, A = 0.5 cm2, Cg = 1.0 mM, V = 2.0 /xL [From A T Hubbard, J Electroanal Chem., 22, 165 (1969), with permission.] 458 • Chapter 11 Bulk Electrolysis Methods The peak current is still proportional to v and CQ and is (11.7.26) Thin-layer methods have been suggested for determination of kinetic parameters of electrode reactions (63-65), but they have not been widely used for this purpose A difficulty in these methods, especially when nonaqueous solutions or very low supporting electrolyte concentrations are employed, is the high resistance of the thin layer of solution Since the reference and auxiliary electrodes are placed outside the thinlayer chamber, one can have seriously nonuniform current distributions and high uncompensated iR drops (producing for example, nonlinear potential sweeps) (66, 67) Although cell designs that minimize this problem have been devised (63, 64), careful control of the experimental conditions is required in kinetic measurements Thin-layer cells have been applied in a number of electrochemical studies, including investigations of adsorption, electrodeposition, complex reaction mechanisms, and и-value determinations They have also become very popular in spectroelectrochemical studies (see Chapter 17) The theory and mathematical treatments used for thin-layer cells find application in other electrochemical problems For example, the deposition of metals (as amalgams) into thin films of mercury and their subsequent stripping (Section 11.8) is fundamentally a thin-layer problem Similarly the electrochemical oxidation or reduction of thin films (e.g., oxides, adsorbed layers, and precipitates) follows an analogous treatment (see Section 14.3) Thin-layer concepts are also directly applicable to synthetically modified electrodes featuring electroactive species bound to the surface (Chapter 14) In many problems involving surface films, mass transfer truly is negligible over wide time domains and problems with uncompensated resistance are minimal; thus relatively fast experiments can be performed Finally, the observed behavior with a scanning electrochemical microscope (Section 16.4), where electrochemistry is examined in the gap between an electrode (tip) and a conducting or insulating substrate can be thought of as that of a leaky thin-layer cell 11.8 STRIPPING ANALYSIS 11.8.1 Introduction Stripping analysis is an analytical method that utilizes a bulk electrolysis step (preelectrolysis) to preconcentrate a substance from solution into the small volume of a mercury electrode (a hanging mercury drop or a thin film) or onto the surface of an electrode After this electrodeposition step, the material is redissolved ("stripped") from the electrode using some voltammetric technique (most frequently LSV or DPV) If the conditions during the preelectrolysis step are maintained constant, exhaustive electrolysis of the solution is not necessary and, by proper calibration and with fixed electrolysis times, the measured voltammetric response (e.g., peak current) can be employed to find the solution concentration This process is represented schematically in Figure 11.8.1 The major advantage of the method, as compared to direct voltammetric analysis of the original solution, is the preconcentration of the material to be analyzed on or within the electrode (by factors of 100 to >1000), so that the voltammetric (stripping) current is less perturbed by charging or residual impurity currents The technique is especially useful for the analysis of very dilute solutions (down to 10~ to ~ n M) Stripping analysis is most frequently used for the determination of metal ions by cathodic deposition, fol- Stripping Analysis Deposition (preelectrolysis) 459 Stripping E -0.5 Figure 11.8.1 Principle of anodic stripping Values shown are typical ones used; potentials and Ep are typical of Cu 2+ analysis, (a) Preelectrolysis at Ed; stirred solution, (b) Rest period; stirrer off (c) Anodic scan (v = 10-100 mV/s) [Adapted from E Barendrecht, Electroanal Chem., 2, 53 (1967), by courtesy of Marcel Dekker, Inc.] lowed by anodic stripping with a linear potential scan and, therefore, is sometimes called anodic stripping voltammetry (ASV) or, less frequently, inverse voltammetry The basic theoretical principles and some typical applications will be described here Several complete reviews describing the history, theory, and experimental methodology of this technique have appeared (68-74) 11.8.2 Principles and Theory The mercury electrode used in stripping analysis is either a conventional HMDE or a mercury film electrode (MFE) In current practice, the MFE is typically deposited onto a rotating glassy carbon or wax-impregnated graphite disk One usually adds mercuric ion (10 -10 M) directly to the analyte solution, so that during the preelectrolysis, the mercury codeposits with the species to be determined The resulting mercury films are often less than 100 A thick Since the MFE has a much smaller volume than the HMDE, the MFE shows a higher sensitivity There is evidence that mercury electrodes with platinum contacts dissolve some platinum on prolonged contact, with possible deleterious effects; hence platinum is usually avoided Solid electrodes (e.g., Pt, Ag, C) are used (less frequently) without mercury for ions that cannot be determined at mercury (e.g., Ag, Au, Hg) The electrodeposition step is carried out in a stirred solution at a potential Ed, which is several tenths of a volt more negative than E° for the least easily reduced metal ion to be determined The relevant equations generally follow those for a bulk electrolysis (see 460 Chapter 11 Bulk Electrolysis Methods Section 11.3.1) However, since the electrode area is so small, and td is much smaller than the time needed for exhaustive electrolysis, the current remains essentially constant (at /d) during this step, and the number of moles of metal deposited is then idtdlnF Because the electrolysis is not exhaustive, the deposition conditions (stirring rate, td, temperature) must be the same for the sample and standards to achieve high accuracy and precision With an HMDE, one observes a rest period, when the stirrer is turned off, the solution is allowed to become quiescent, and the concentration of metal in the amalgam becomes more uniform The stripping step is then carried out by scanning the potential linearly toward more positive values When an MFE is used, the stirring during deposition is controlled by rotation of the substrate disk A rest period usually is not observed, and rotation continues during the stripping step The behavior governing the i-E curve during the anodic scan depends on the type of electrode employed For an HMDE of radius r0, the concentration of reduced form, M, at the start of the scan is uniform throughout the drop and is given by М (11.0.1) nF(4/3)7rr30 When the sweep rate v is sufficiently high that the concentration in the middle of the drop (r = 0) remains at C^ at the completion of the scan, then the behavior is essentially that of semi-infinite diffusion and the basic treatment of Section 6.2 applies (75) Correction must be made for the sphericity of the drop [see (6.2.23)] In this case the spherical correction term must be subtracted from the planar term, since the concentration gradient builds up inside the drop and the area of the extended diffusion field decreases with time Thus, the equations that apply for a reversible stripping reaction at the HMDE are (75) D т nFi \СЦ(ттОма) Г х((П) ip-AD^CM (2.69 X 105)n3/2vm 2 - M 20 mV/s, and clearly, under these conditions, a large fraction of the deposited metal remains in the drop A comparison of the i-E curve predicted by (11.8.2) and a typical experimental stripping voltammogram at an HMDE is shown in Figure 11.8.2 (76) At very large scan rates the spherical term becomes negligi1/2 ble and linear diffusion scan behavior, with /p proportional to i> , results Practical stripping measurements are usually carried out in this regime At smaller rates, when the diffusion layer thickness exceeds TQ, the finite electrode volume and depletion of M at r = must be considered At the limit of very small v, when the drop is completely depleted of M during the scan, the behavior approaches that of a thin-layer cell or MFE (see below) with /p proportional to v Because the volume and thickness of the mercury film on an MFE are small, the stripping behavior with this electrode follows thin-layer behavior more closely (see Section 11.7), and depletion effects predominate The theoretical treatment for the MFE has appeared (77, 78); a diagram of the model employed is shown in Figure Stripping Analysis 461 -0.6 Figure 11.8.2 Experimental anodic stripping i-E curve for thallium Experimental conditions: 1.0 X 10~ M + Tl , 0.1 M KC1 solution, Ed = -0.7 V vs SCE, td = min, v — 33.3 mV/s Circles are theoretical points calculated from (11.8.2) [Reprinted with permission from I Shain and J Lewinson, Anal Chem., 33, 187 (1961) Copyright 1961, American Chemical Society.] 11.8.3 If the stripping reaction is assumed to be reversible, the Nernst equation holds at the surface: C M +n(O, t) = С , vt)\ (11.8.4) The solution of the diffusion equations with this condition and the initial and boundary conditions shown in Figure 11.8.3 leads to an integral equation that must be solved numerically Typical results for /p for films of different thicknesses, /, as a function of v are shown in Figure 11.8.4a At small v and /, thin-layer behavior predominates and /p « u For high v and large /, semi-infinite linear diffusion behavior predominates and /p ^ vm The limits of these zones are shown in Figure 11.8.4b MFEs used in current practice fall within the region where thin-layer behavior can be expected for virtually all usual sweep rates ( \O2 + 2H + + 2e Figure 11.10.1 Idealized current-potential curves for several systems at a platinum electrode 11.3 Based on the curves in Figure 11.10.1, sketch the titration curves for the titrations in Problems 11.1 and 11.2 for one- and two-electrode potentiometry with a small impressed current 11.4 Fifty milliliters of a ZnSO solution are transferred to an electrolytic cell with a mercury cathode, and enough solid potassium nitrate is added to make the solution 0.1 M in KNO3 The electrolysis of Z n + is carried to completion at a potential of -1.3 V vs SCE with the passage of 241 С Calculate the initial concentration of zinc ion 11.5 Iodide is to be titrated coulometrically at constant current at a silver electrode The sample is 1.0 mM Nal contained in a pH acetic acid solution with 0.1M sodium acetate having a total volume of50mL (a) Describe the course of the titration What generating current you recommend and what total titration time is expected? (b) Consider the current-potential curves that would be recorded at a rotated platinum disk upon scanning from the cathodic background limit (ca -0.5 V) to the anodic limit (at ca +1.5 V vs SCE) Draw curves for the 0%, 50%, 100%, and 150% titration points Label the waves with the electrode processes that cause them All electrode reactions other than the background discharges are reversible The following information is useful: Reaction + Ag + e^±/ ^g I3- +•2e~^± 31" Agl + e^±A>g + I~ £°, volts vs SCE +0.56 +0.30 -0.39 (с) Sketch amperometric titration curves for: (1) One polarized electrode at -0.3 V vs SCE (2) One polarized electrode at +0.4 V vs SCE (3) Two polarized electrodes with 100-mV potential difference The indicator electrodes are rotated platinum microelectrodes 11.6 Iodide in the solution in Problem 11.5 can also be determined by controlled-potential oxidation to iodine at a platinum electrode What potential should be used for this oxidation (see Figure 11.10.1)? How many coulombs will be passed? 11.7 The following is a standard procedure for the assay of uranium samples: (1) Dissolution of the sample in acid to produce UO2 + as the chloride (2) Reduction of the UO2 + solution by passage through a Jones reductor (amalgamated zinc) This solution is perhaps 0.1 M in H2SO4 Reduction takes place to U + (3) Stirring in air to give U + (4) Addition of F e + and C e + in excess and coulometric titration to an end point 468 • Chapter 11 Bulk Electrolysis Methods (a) Suppose the solution after treatment (3) contains ~ mM U + Fe + and Ce 3+ are added in quantities that yield and 50 mM concentrations of iron and cerium species, respectively Sulfuric acid is also added to bring its concentration to M Draw the current-potential curve that would be recorded at a rotating platinum disk immersed in this solution The anodic background limit is +1.7 V vs NHE and the cathodic limit is at -0.2 V vs NHE (b) Explain the chemistry of step (4) and the setup for the coulometric titration (c) Sketch current-potential curves for points at which the titration is 0%, 50%, 100%, and 150% complete (d) Sketch amperometric titration curves for one polarized electrode operated at +0.3 V and at +0.9 V vs NHE, and for two polarized electrodes separated by 100 mV (e) Sketch the null current potentiometric responses on a quantitative potential scale The following information may be useful: Reaction 4+ Formal Potential, V vs NHE Ce + e^-Ce Fe 3+ + e^-Fe + UO ^ + e ;=±UO uoj + 4H f + e • U + + 2H2O U + •+ e ~~^ u3+ 1.44 0.77 0.05 0.62 -0.61 All reactions except are reversible That process will not show a wave at platinum before the cathodic background limit is reached 11.8 A molecule of interest in research is tetracyanoquinodimethane (TCNQ): TCNQ Samples of high purity are often required Suppose you wish to develop a technique for assaying the purity of TCNQ samples Describe a means for accomplishing this goal by coulometric titration with electrogenerated anion radicals of p-chloranil (p-Chl) Acetonitrile containing tetra-n-butylammonium perchlorate would be a suitable medium Its background limits at platinum are —2.5 V and +2 V vs SCE The following reduction potentials are relevant: TCNQ + e ^± TCNQ7 TCNQ" + e ^± TCNQ " p-Chl + e ^±p-Chl T £° = 0.20 V £° = -0.33 V £° = 0.0V All of these processes are reversible (a) Specify the details of the cell, the starting composition of the solution, and the chemical processes taking place at the electrodes and in homogeneous solution (b) Draw the current-potential curves that would be recorded at a rotating platinum disk if the titration were stopped at the 0%, 50%, 100%, and 150% points (c) Sketch titration curves for: (1) amperometric detection with one polarized electrode at 1.0 V; (2) amperometric detection with one polarized electrode at 0.1 V; and (3) amperometric detection with two polarized electrodes separated by 100 mV 11.9 Consider carrying out a one-electrode amperometric titration for the system Fe + -Ce + as shown in Figure 11.5.1 at several widely different potentials and sketch the amperometric titration curves that result Consider, in each case, situations in which (a) the mass-transfer coefficients for all species Problems 469 are equal and (b) those for iron ions are 25% larger than those for cerium species Which curves would be useful in a practical titration? 2+ 11.10 When a solution of volume 100 cm containing metal ion, M at a concentration 0.010 M is elec2 trolyzed with a rapid scan at a large-area (10 cm ) rotating disk electrode, a limiting current of 193 mA is observed for reduction to metal M Calculate the value of the mass transport coefficient mM2+, in cm/s If an electrolysis of the solution is carried out at this electrode at controlled potential 2+ in the limiting current region, what time will be required for 99.9% of the M to be plated out? How many coulombs will be required for this electrolysis? 11.11 If the solution in Problem 11.10 is electrolyzed at a constant current of 80 mA under the same con2+ ditions: (a) What is the concentration of M remaining in solution when the current efficiency drops below 100%? (b) How long does it take to reach this point? (c) How many coulombs have been passed to this point? (d) How much longer will it take to decrease the M + concentration to 0.1% of its initial value? What is the overall current efficiency for removal of 99.9% of M + by this constant-current electrolysis? 11.12 A solution of volume 200 cm contains 1.0 X 10~3 M X + and 3.0 X 10~3 M Y + , where X and Y are metals The solution is to be electrolyzed at a mercury pool electrode of area 50 cm and volume 100 cm Under the stirring conditions and cell geometry, both X + and Y + have masstransfer coefficients m of 10~2 cm/s The polarographic E\/2 values for reduction of X + and Y + to the metal amalgams are —0.45 and —0.70 V vs SCE, respectively, (a) A current-potential curve for the solution is taken under the above conditions (Assume no changes in concentrations of X + and Y + during the scan.) Make a neat, labeled, quantitatively correct sketch of the i-E curve that would be obtained, (b) If the electrolysis is to be performed at a controlled potential, at what potentials can X + be quantitatively deposited (less than 0.1% left in solution) leaving Y + behind in solution (less than 0.1% Y + deposited in mercury)? (c) How long will it take to carry out this electrolysis at controlled potential? 11.13 Consider a chronopotentiometric experiment dealing with two components that are reversibly reduced in waves separated by 500 mV Derive an expression for the second transition time in an experiment carried out in a thin-layer cell Compare and contrast the properties of multicomponent systems in thin-layer chronopotentiometry with those of the semi-infinite method 11.14 In the electrolytic production of aluminum, the reduction of AI2O3 (alumina) in a bath of molten cryolite (КазАШб) (Т ~ 1000°C) is carried out at constant current with carbon electrodes A charge of alumina is placed in the cell and the electrolysis carried out until the voltage across a cell rises sharply, signaling the need to add additional alumina Explain this behavior 11.15 Suppose bromide ion is to be determined at very low concentrations This is done by depositing bromide on a silver electrode, which is held at a potential where the following reaction occurs: Ag + Br~ - e~ -> AgBr (A typical deposition potential is +0.2 V vs SCE.) Stripping is carried out by scanning in a negative direction to reverse the deposition In general, it is observed that the response during stripping shows a complex dependence on deposition time, as shown in Figure 11.10.2 Explain this effect What problems would be present in quantitative analysis? How could they be surmounted? [See H A Laitinen and N H Watkins, Anal Chem., 47, 1352 (1975) for similar results in determinations of lead.] 11.16 A study of seawater by stripping analysis reveals an anodic copper peak having a height of 0.13 /JLA when deposition is carried out at —0.5 V However, deposition at —1.0 V yields a larger peak of 0.31 fiA Account for these results Standard addition of 10~7 M Cu + elevates the peaks in both cases by 0.24 IJL A Comment on the feasibility of obtaining polarograms of any type on this solution What responses would you expect for dc, normal pulse, and differential pulse experiments? Would any of these supply useful analytical information? 11.17 An analysis for lead at the HMDE gives rise to a peak current of /xA under conditions in which the deposition time is held constant at and the sweep rate is 50 mV/s What currents would be observed for sweep rates of 25 and 100 mV/s ? 470 fc Chapter 11 Bulk Electrolysis Methods Figure 11.10.2 Cathodic stripping of AgBr from a silver electrode following anodic deposition Curves to involve successively longer deposition times The same solution gives a peak current of 25 /xA at a 100-A thick mercury film electrode on glassy carbon when the deposition time is min, the electrode rotation rate is 2000 rpm, and the sweep rate is 50 mV/s What currents would be observed for sweep rates of 25 and 100 mV/s under otherwise unchanged conditions? Compare this situation to the one observed for a deposition time of min, a sweep rate of 50 mV/s, and a rotation rate of 4000 rpm? Suppose the film thickness were varied by the use of different concentrations of mercuric ion in the analyte What effect would one see on the peak current under otherwise constant conditions? ... 17 .6 .1 A.6 13 .3.3 8.6 13 .4.2 5.2.2 13 .4.2 1. 2.3, 13 .3.3 1. 2 .1 17.2 .1 17.2 .1 2.4 6.8 18 .2.5 14 .2 .1 11. 6.4 17 .3.3 6 .1 11. 8 1. 1 .1 7.3.2 7.3.2 1. 2.3, 13 .3.3 17 .1. 1 17 .1. 1 11 .6.4 17 .2 .1 13.2.2 17 .5 Letters... eV 1. 4 .1 3.6.3 5.3 3.6.2 n 10 .1. 2 13 .1. 2 none cm cm 1. 2.3, 13 .3.3 1. 2.3, 13 .3.3 cm rr1 10 .1. 2 10 .1. 2 9.3 .1 10 .1. 2 B .1. 6 ft" cm n none ft ft cm 10 .1. 2 10 .1. 3 10 .1. 2 10 .1. 2 10 .1. 3 5.3 none 13 .3.2... IR-SEC ISE ITIES ITO LB LCEC LEED LSV MFE NHE NCE NPP NPV OHP OTE OTTLE PAD PC PDIRS PZC QCM Section Reference 12 .1. 1 12 .1. 1 12 .1. 1 18 .1 13.2.2 12 .1. 1 10 .1. 1 2 .1. 3 17 .2 .1 17.4 .1 16.2 17 .6 .1 A.6