OVERDUE FINES: 25¢ per du per item RETURNING LIBRARY MATERIALS: ———_____‘_ Place in book return to remove charge from circulation records THE CHARACTERIZATION AND APPLICATION OF SOHE ELECTROCHEMICAL RELAXATION TECHNIQUES IN CORRELATING INTERPHASIAL STRUCTURE WITH ELECTROCHEMICAL REACTIVITY by Paul Daniel Tyma A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 1930 ABSTRACT THE CHARACTERIZATION AND APPLICATION OF SOME ELECTROCHEMICAL RELAXATION TECHNIQUES IN CORRELATING INTERPHASIAL STRUCTURE WITH ELECTROCHEMICAL REACTIVITY by Paul Daniel Tyma This study describes experiments which expose correlations between electrochemical reactivity and the structure of the region of solution immediately adjacent to the electrode surface (the "interphase"). The variation of the electrochemical transfer coefficient (corrected for double-layer effects) with electrode potential was studied over several orders of magnitude in rate for the 3+IZ+ aquo complexes (M - Cr, Eu, oxidation and reduction of M V) and for-Co(NH3)5F2+ reduction. Little or no change in the transfer coefficient was seen for the reduction reactions, whereas a striking potential dependence was observed for the oxidations. This variation is more than that predicted by dielectric-continuum models of ion solvation and is shown to be compatible with a previously reported model involving specific (Hydrogen-bonding) interactions between solvent molecules and ligands in the primary coordination sphere. The effect on electrochemical redox kinetics of deuterating both the solvent and ligands of transition-metal complexes was considered. it was shown that ratios of double-layer corrected standard rate constants obtained in the two solvents provide information about differences in the intrinsic free-energy barriers to electron transfer which are brought about by solvent deuteration. Larger rate ratios were found than are predicted on the basis of molecular-orbital calculations of the inner-shell contribution to the reorganization energy and predictions made by a dielectric- contlnuum model of the outer-shell portion. Again, the results were seen to be compatible with a model which postulates specific rather than general solvent structuring by the reactant ion. A pulse-polarographic display format and analysis method applied to a collection of current-time transients which result from potential-step perturbations of an irreversible electrode reaction were demonstrated to provide more reliable rate information than a chronoamperometrlc analysis of individual transients. in addition, pulse polarography was shown to indicate directly the presence in the data of unexpected features which were found to be due to nonideai instrumentation and to adsorption effects. High-speed dc polarography was evaluated in terms of its suitability for providing electrochemical change-transfer rate information which might be inaccessible by conventional large- or small-amplitude perturbation techniques. Dropping mercury- electrode flow rates between i and 2 mg/sec were shown to be appropriate; larger flow rates were seen to be unacceptable due to stirring or depletion effects. The method under some circumstances separated kinetically controlled polarographic waves which overlap at conventional times and reduced in some cases the effects of polarographic maxima enough to provide access to rate data. Conventional instrumentation was employed where feasible for the experiments described in this study. For those cases where commercially available equipment did not possess sufficient speed or timing flexibility, a microcomputer-based system for the acquisition and management of electrochemical data was developed and utilized. Its features include the capability to make measurements with 12-bit resolution at rates up to 100 kHz and the ability to provide with 12-bit resolution a voltage output with a submicrosecond settling time and less than 2 mV peak-to-peak noise. Optical and high-speed electrochemical drop-fall detectors were constructed for the purpose of synchronizing timing circuitry with the birth of the new drop. The former were shown to be unacceptable as a consequence of a nonreproducible delay between 20 and 100 msec. The electrochemical detector showed several advantages: it is compatible with potentiostats; it does not constantly impose an ac perturbation on the cell; it requires infrequent adjustment; and it is about 200 times faster than those of comparable design. ACKNOWLEDGEMENTS There is, unfortunately, too little space for me to express my gratitude to all the friends who contributed to lightening my burden and to making more pleasant my tenure in the groves of academe. First and foremost, I wish to thank my colleagues in the research groups of Professors Enke and Weaver for their assistance in setting up and maintaining the equipment and ambience appropriate to laboratory research. In this regard, the low emotional center-of—gravity provided by Ed Yee, the transmission of some instrumentation designs to reality by Ken Buyer, and the horizon-broadening discussions with Milton Webber warrant special mention. The assistance of Scott Nettles produced a key portion of the isotope-effect studies described herein. Among the members of the university staff are several who have been particularly helpful. Dr. T. V. Atkinson is one graphic example, especially when the chips were down; and it would be unfair to describe Marty Rabb as anything less than instrumental in the construction of several pieces of equipment. There were many occasions on which I drew on the considerable talents of Kathy Nyland and Bev Adams. Suffice it to say that you wouldn't be able to read this now were it not for the work of Cathy Caswell. Above all, I wish to thank my wife Kelly, whose patience and hard work has been an inspiration to us all. - "Forsitan et haec olim juvabit." TABLE OF CONTENTS LIST OF TABLES ............. . LIST OF FIGURES . ....... . ............. CHAPTER I. INTRODUCTION . . - . - . . . . OVERVIEW ENERGETICS OF HETEROGENEOUS ELECTRON-TRANSFER PROCESSES THE ELECTROCHEMICAL TRANSFER COEFFICIENT DEMONSTRATIONS OF SOLVENT STRUCTURING USE OF RATE RESPONSES TO PROBE INTERPHASIAL STRUCTURE EXPERIMENTAL TACTICS IN THE USE OF PERBROMATE PROBES ASSESSMENT OF MEASUREMENT RELIABILITY CHAPTER II. A MICROCOMPUTER-CONTROLLED ELECTROCHEMICAL DATA- ACQUISITION SYSTEM . . . . INTRODUCTION AND GENERAL DESCRIPTION POTENTIAL GENERATION AND MEASUREMENT THE TIMING OF COMPUTER-CONTROLLED MEASUREMENTS ADDITIONAL MEASUREMENT ACCESSORIES AN ILLUSTRATIVE EXAMPLE . . . . . . . . CHAPTER III. SYNCHRONIZATION OF NATURAL DROP-FALL EXPERIMENTS INTRODUCTION . . . . AN EVALUTION OF OPTICAL DETECTION TECHNIQUES A HIGH-SPEED ELECTROCHEMICAL DETECTOR acumen» 10 12 16 17 20 23 26 . 28 32 33 3t. 37 iv CHAPTER IV. FURTHER OBSERVATIONS ON THE DEPENDENCE OF THE ELECTROCHEMICAL TRANSFER COEFFICIENT UPON THE ELECTRODE POTENTIAL . . . . . . . . . . . . . . . #5 INTRODUCTION . . ................ . . . . . . . #6 EXPERIMENTAL . . . . . .................. . . A9 RESULTS AND DATA ANALYSES ..... . . . . . . . . . . . . . 50 DISCUSSION . . . . . . . . . . . ....... . . . . . . . . 73 ADDENDUM . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 CHAPTER V. SOLVENT ISOTOPE EFFECTS UPON THE KINETICS OF SOME SIMPLE ELECTRODE REACTIONS . . . . . . . . . . . . 86 INTRODUCTION ................ . . . . . . . . . 87 EXPERIMENTAL . . . . . . . ....... . ~,- . . . . . . . . 89 RESULTS . . . . . . . ..... . . . . . . . . . . . . . . . 91 Aqua CompIexes . ...... . . . . . ..... . . . . 91 Ammine and Ethylenediamine complexes . . . . ..... . 99 DISCUSSION . . . . . . . . . . . . . . . . . . . . . . . . . . 10h Interpretation of observed isotopic rate ratios . . . . . IDA Comparisons between isotope effects for corresponding electrochemical and homogeneous reactions. . . . . . . . 115 CONCLUS 'ONS a o o a o o o a a a o a o o o o a a o a o a o o o 120 CHAPTER VI. THE UTILITY OF PULSE-POLAROGRAPHIC ANALYSIS TECHNIQUES IN THE ASSESSMENT OF ELECTROCHEMICAL KINETIC PARAMETERS FROM TOTALLY IRREVERSIBLE CHRONOAMPEROMETRIC TRANSIENTS . . . . . . . . . . . . 121 INTRODUCTION ............ o . . o . o . . a o . . 122 EXPERIMENTAL . ...... . ...... v . ..... . . . . 125 Reagents . . . . . . . . . . . . . . . . . . . . . . . . 125 Measurement System ...... . . . . . . . . . . . . . 126 RESULTS . . . . . . . ....... . . . . . . . . . . . . . 128 DISCUSSION 0 0 O O O O ..... O I O O O O O O O O O O O O . 135 A Comparison of Chronoamperometric and Pulse-Polarographic Data Analyses . . . . . . . ..... . . . . . . . . . The Maximum Reliable Rate Constant . . . . . . . . . . . Chemical Causes of the Polarographic Peaks . . . . . . . The Effect of Instrument Performance on Pulse Polarograms CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . CHAPTER VII. THE ACCESSIBILITY OF ELECTROCHEMICAL CHARGE-TRANSFER RATE INFORMATION FROM TIME-RESOLVED, DIRECT-CURRENT POLAROGRAPHIC DATA . . . . . . . . . . . . . . . . . INTRODUCTION . . . . ...... . . . . . . . . . . . . . EXPERIMENTAL . . . . . . . ............. RESULTS AND DISCUSSION . . . . . . . . . . . . . . . . . . . The Effect of Large flow Rates . . . . . . . . . . . . The Effect of Intermediate Flow Rates . . . . . The Effect of Small Flow Rates . . . . . . . . . . . . . A Comparison of Techniques . ...... . . . . . . . . Comparison of Limiting Currents With Reported Behavior The Effect of Sampling Time on Polarographic Maxima . . The Effect of Sampling Time on Kinetically Controlled waves 0 O O O O O O O O O O O I O O O O O O O O I O O 0 CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . CHAPTER VIII. SUGGESTIONS FOR FURTHER STUDY . . . . . . . . . . . MEASUREMENT-SYSTEM IMPROVEMENTS . . ..... . . ..... . STUDIES OF SOLVENT STRUCTURING . . . . . . . . . . . . I . . DC-POLAROGRAPHIC MEASUREMENTS . . . . . . . . . . . . . . . . REFERENCES ..... O O O O O O O O O O O O O ..... O O O O O 135 I37 142 m 151+ 156 157 161 162 162 166 '17:. .178 186 . 187 189 193 19A 195 197 198 200 Table 1, Table 2. Table 3. Table A. LIST OF TABLES Apparent anodic transfer coefficients C‘pr for Cr2+, Eu2+ aq aq as a function of electrode potential. . . . . . . . . . . . 55 , and V2+ oxidation aq The effects of varying the electrolyte composition upon the average potential at the reaction plane (brp for 2+ 2+ + . . aq’ Euaq’ and Viq oxIdatIon and Co(NH3)5I-'2+ reduction, obtained using eqn (5). .. . . . . . 59 Cr Double-layer corrected anodic transfer coefficients 2+ 3 2+ + a for Craq, Euaq’ and Viq COI'I' oxidation as a function of electrode potential, compared with the corresponding intrinsic transfer coefficients ( of) oscillator model. . . . . . . . . . . . . . . . . . . . . . 65 calc calculated from the harmonIc Solvent Isotope Effects Upon the Electroreduction Kinetics of Some Transition-Metal Complexes at the Mercury-Aqueous Interface.. . . . . . . . . . . . . . . . . . . . . . . . . 96 vi Table 5. Table 6. Table 7. Table 8. Table 9. Table 10. vii Solvent Isotope Effects upon the Standard Electrochemical Rate Constants of Some Transition-Metal Aquo Couples. . . . Primary and Secondary Isotope Effects upon the Electroreduction Kinetics of some Co(III) and Ethylenediamine Complexes. . . . . ...... . . . Primary and Secondary Isotope Effects upon the Electroreduction Kinetics of some Cr(lII) Ammine and Ethylenediamine Complexes. . . . . . . . . . . . Comparison of Solvent isotope Effects for Corresponding Electrochemical and Homogeneous Reactions. .. . . . . . . . . . . . . . . . . . . . . . . Laplace analysis of chronoamperometric data obtained for reduction of 2 mg Cr3+ in I I1 NaCIOh/Z m5 11+. . . . . Values of i/iiim for four polarographic techniques for the reduction of Co(NH3)5F2+ in 1 M_KF. . . . . . . . 98 100 101 117 138 183 Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure 10 11 12 13 1‘1 LIST OF FIGURES Free-energy diagram for electron-transfer reactions. . . . Block diagram of measurement system. .. . . . . ..... Interface to D/A converter. . . . . . . . . . . . . . Clock-Interface circuitry. a) Remote start. b) Remote trigger for A/D converter. . . . . . . . . . Interface to Biomatlon transient recorder. .. . . . . . . Drop-fall trigger input. . . . . . . . . . . . Flow charts for polarography. a) Conventional b) First-drop. .. . . . . . . . . . . . . . . . . . Schematic diagram of optical drop-fall detector. . . Differentiated current from photodarlington transistor. . Block diagram of ac drop-fall detector. . . . . . . . . . Schematic diagram of ac drop-fail detector. . . . Rate-potential plots for the one-electron oxidation of 2+ in KPF6, NaCIOh, and KCI electrolytes at Cr aq the mercury-aqueous interface. . . . . . . . . . . Rate-potential plots for the one-electron oxidation of 2+ Euaq in KPFG, NaCIOk, and KCI electrolytes at the mercury-aqueous interface. - . . - . . . . . . . . . . Rate-potential plots for the one-electron oxidation of Vi: I" KPF5: NaCth, and KCI electrolytes at the mercury-aqueous interface. . . . . . . . . . . Viio-r 22 25 27 29 30 35 38 39 AD 51 52 53 viii Figure 15 Plots of the potential across the diffuse-layer ¢ 3C5 against the electrode potential E for o.h !. and 0.1 H_KPF6. . . . . . . . . . . . . . . . . . . 53 Figure 16 Plots of the logarithm of the rate constant corrected for 3+/2+ aq against the electrode potential E at the mercury-aqueous IonIc double-layer effects log kcorr for Cr interface. . . . . . . . . . . . . . . . . . . . . . . . . 68 Figure 17 Plots of the logarithm of the rate constant corrected 3+/2+ for ionic double-layer effects log kco r for Eu r against the electrode potential E at the mercury- aqueous interface,. . . . . . . . . . . . . . . . . . . . 70 Figure 18 Plots of the logarithm of the rate constant corrected for ionic double-layer effects log kcorr for Vi§I2+ against the electrode potential E at the mercury- aqueous interface. . . . . ..... . . . . . . . . . . . 72 Figure 19 Rate-potential plot for Co(NH3)5F2+ reduction in i‘fl KF.. . . . . . . . ...... . . . . . . . . . . . . 83 Figure 20. The excess electronic charge density qm of mercury in contact with 1 M KF(HZO) and 1 M_KF(DZO) electrolytes versus the electrode potential E . . . . . . . . . . . . . 93 Figure 21 Current-time—potential surface for the reduction of Cr(OH2)g+ in 1.! NaCth (pH 2). . . . . . . . . . . . .123 Figure 22 Transient stabilization of current-to-voltage converter. . . . . . . . . . . . . . . . . . . . . . . . .127 Figure 23 Current-time transient responses to potential steps for Cr(OH2)g+ reductiOn. . . . . . . . . . . . . . .129 Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure 2A 25 26 27 28 29 30 31 32 33 38 35 36 37 ix 3+ Pulse polarograms for Craq reduction at 0.5 msec intervals. .. . . ........ Pulse polarograms for Cris reduction at 0.1 msec Intervals. . . . . . . . . . . . ............ Pulse polarograms for Co(NH3)5F2+ reduction at 2 msec Intervals. .......... Pulse polarograms for Co(NH3)5F2+ reduction at 0.2 msec intervals.- Laplace-space analysis of current-time transient for Crag reduction (-1200 mV) ............. Schematic representation of an electrochemical cell. -- Schematic representation of the potentiostat circuity. ..................... Summing-point deviations for Griz reduction at Hg. """"""""""" o oooooo Summing-point deviations for Co(NH3)5F2+ reduction at Ag. .............. . ...... Applied-potential waveforms for Crag reduction at Hg. .......................... Simulated pulse polarograms at 0.2 msec. ....... 3+ Time-resolved dc polarograms for Craq reduction (m - 17 mg/sec) .................. Comparison of Ilkovic-equation predictions and experimental results. . . . . 3+ aq Knocked-drop dc polarograms for Cr reduction (1.8 mg/sec). .131 132 -133 .13h . mo . 1A5 . 1A6 . 149 . 150 152 . 153 . 164 165 . 167 Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure 38 39 40 A1 #2 #3 AA 45 A6 A7 #8 “9 X Knocked-drop dc polarograms for Crg: reduction (3 mg/sec). .. . . ...... . . . . . . ...... Knocked-drop dc polarograms for Org; reduction (h mg/sec). .. ...... . . . ........... Natural-drop dc polarograms for Griz reduction (1.8 mg/sec). . . . . . . . . ....... Natural-drop dc polarograms for Crag reduction (3 mg/sec). fl ................. Natural-drop dc polarograms for Crg: reduction (h mg/sec). . . . ..... . . . ..... 3+ Knocked-drop dc polarograms for Cr reduction (0.97 mg/sec). 3+ Limiting currents for Craq reduction (0.97 mg/sec). ....... . . ..... Tafel plots derived from 50 msec and 2 sec knocked- 3+ aq drop polarograms for Cr reduction (0.97 mg/sec). . . . . . . . . . ...... Comparison of polarographic techniques for Co(NH3)5F2+ reduction (50 msec). . . . ........... . . . Comparison of polarographic techniques for Co(NH3)5F2+ reduction (0.5 msec). . . . . ...... Effect of drop-knocker solenoid response time and displacement on polarographic current-time curves (large displacement). .. . . . . ........... Effect of drop-knocker solenoid response time and displacement on polarographic current-time curves (small displacement). .. . . . . . ..... .168 . 170 . 171 . 172 175 .176 ~177 - 180 . 181 . 18S Figure 50 Figure 51 Figure 52 Figure 53 xi Dc polarograms for the reduction in I‘M NaCIOh (pH 2). . . . . . . Dc polarograms for the reduction in 1'! RF. .. . . . . . . . . . Dc polarograms for the reduction in 1 M NaNO3. . . . . . . . . . Dc polarograms for the reduction in 1‘5 NHAF. . . . . ...... of Cr(NCS)g' of cis-Co(en)2(N3); . 188 . 190 . 191 . 192 CHAPTER I . INTRODUCTION OVERVIEW The goal of the work described in this thesis is to determine relationships between rates of electrochemical reactions and the structure of the reactants and of the solution region adjacent to the electrode, the so-called "interphase", using conventional approaches when feasible, devising and applying new instruments and methods when previously available strategies are Inappropriate. This chapter presents a summary of the information which is sought, the motivation for seeking it, and the tactics for garnering it. A brief description of the energetics of heterogeneous electron- transfer reactions is given, along with a discussion of the use of the electrochemical transfer coefficient and isotopically substituted reagents to provide information about the structure of the solvent in the Interfacial region. The use of rate responses to infer structural properties and the characterization of new techniques for developing additional probe reactions are discussed. Intercomparison of teChniques is presented as an approach for assessing the reliability of measured rate data. In spite of recent successes in the chemical modification of electrodes,1 the ability to tailor an electrochemical surface to suit specific needs continues to elude the electrochemist. The effects of reactant structure on the rates and mechanisms of homogeneous electron transfer between members of inorganic redox couples have received thorough scrutiny,2 but the same degree of attention is just beginning to be focused on the electrochemical (heterogeneous) reaction analogs. A complete understanding of the factors which control electrochemical reactivity would pave 3 the way both toward the inexpensive realization of clean and efficient energy conversion which electrochemistry has promised 3’“ but not yet provided, and toward the effective 5 for many years arrest of the ubiquitous and costly corrosion for which electrochemical charge-transfer phenomena provide a most useful model.6 The work described herein is one contribution to a major ongoing effort to correlate rates and mechanisms of electrochemical redox reactions with the structure of the reactant and of the environment of the electrode-solution interface. The study of homogeneous redox processes has identified reaction types of two extremes:2 those which proceed with imperceptible perturbation of the primary coordination spheres of ligands about the two reaction centers ("outeresphere"), and those in which a ligand forms a bridge between the two reactants ("inner-sphere"). Analogous heterogeneous examples and techiques for discriminating between the mechanisms have been described.7 A distinguishing feature of outer-sphere electron-transfer processes is that they are believed to be non-adiabatic or only weakly so; that is, the reactant and product free-energy surfaces are only weakly coupled if at all in the vicinity of the activated complex. Because the rates of redox reactions can be significantly larger at electrodes made of some materials than of others and because the composition of the ligands about a transition-metal ion can have a drastic effect on the rates, it is of interest to determine how this "electrocatalysis" arises. One study at Hg electrodes has demonstrated that for some kinds of substituted Cr(I|I) ammine complexes the rate enhancement afforded by an inner-sphere pathway I. is due principally to the increased availabilty of electroactive species provided by adsorption rather than due to any decrease in the elementary activation barrier.8 In another context, experimental evidence has been presented that some metals do indeed lessen the activation energy.9 ENERGETICS OF HETEROGENEOUS ELECTRON-TRANSFER PROCESSES To provide a conceptual basis for the understanding of electrode processes, one may consider a model in which five states are identified, the free-energy profile of which is shown in Figure 1. The states and their respective free energies are as follows: reactant in the bulk of solution (with free energy 6'); reactant at its plane of closest approach to the electrode (6"); the activated complex in which, due to the Franck-Condon restriction for a radiationless process, the free energy and interatomic distances of the reaction species prior to the electron transfer equal those of the product species immediately following the transfer (61.); the reaction product adjacent to the electrode (GI'I); and the product in the bulk solution (GIV)' Several free-energy differences can be described: the work in bringing the reactant to the surface (wr a A'GlI-I - Gll - GI); the work in removing the product (wp - A GIV—III - le - Glll); the free energy of the reaction (A Go - A GIV-I - GIV - GI; the experimentally measured activation energy (A 613p - A 6+ _' - 6+ - GI); and that portion of the activation energy which is characteristic of, or ”intrinsic" to, a given reactant and electrode combination + (A61 " AGT-II " 6+ ' GI|)' I III‘I’III I! reaction coordinate Figure 1. Free-energy diagram for electron-transfer reactions. 6 Among contemporary theories to describe redox-reaction kinetics, one due to Marcus has enjoyed considerable success. ,According to this formulation, the electron-transfer rate constant is described to a good approximation by . -_1_A P-rr -] In kapp In Ze RT [ E-+ ai(w w ) + w +<1iF(E Ef) (1) where wr and wp are defined as above; 2e is the electrochemical collision frequency; A/A is the "reorganization energy", namely A 6+ _'| for the case where there is no ”surface driving force" (Gil ' GIII)‘ °" ' is an integral Intrinsic transfer coefficient (gigg‘igfrg); E is the electrode potential; and Ef is the formal potential of the couple under scrutiny. The first term within the braces in Equation 1 is called the "intrinsic" portion of the activation energy, the second the "surface therodynamic" contribution, and the last the "bulk thermodynamic" term. THE ELECTROCHEMICAL TRANSFER COEFFICIENT That the electrode potential has an effect of the reaction rate provides one of the most commonly employed probes in the study of electrochemical kinetics. Through the well-known correspondence between the electrode potential and the free-energy change occurring in an electrochemical cell, and through the linear free-energy relationship embodied in Equation 1, a change in the electrode potential changes the rate vlg_the bulk driving force. Because the work terms wr and wp can be implicitly potential-dependent, additional effects due to potential can be seen. A fraction of the overall cell-potential change is ascribed to the electrochemical rate difference It produces, so that one can define the quantity 3A6 BAG 3 In k a - app - -1 app . -RT app (2) 3PP ‘— BACO Ll nF 3E u nF 3E u to describe the symmetry of the free-energy barrier, including ”environmental" effects. The corresponding relationship can be written exclusive of double-layer effects r “(183%) . “app 1% (‘35—): p (3) we) we) I: 3 E u F 25E II The integral version of this quantity shown in Equation 1 uses the chord suggested by Equation 3 instead of the slope (partial derivative). A geometric argument can be used to show that for free-energy surfaces which are roughly parabolic, “I is about 0.5 for small or moderate values of the bulk thermodynamic term. An important consideration in the assessment of electrochemical reactivity patterns is therefore to apportion the measured activation energies into the intrinsic and thermodynamic segments, the latter not only for the driving force AGo but also for the ”double- layer“ efects of wr and wp. DEMONSTRATIONS OF SOLVENT STRUCTURING A significant component of the reorganization energy A/A for an outer-sphere reaction consists in the rearrangement of the ligands and solvent molecules surrounding the reactant ion so that, in keeping with the Franck-Condon limitation, the transition state reflects a condition of metal-ligand bond distances and solvent polarization which is between the reactant and product conditions. Recent study of the effects of ligand composition about transition-metal redox couples on the half-cell reaction 11,12 entropies has provided compelling evidence for the existence 8 of specific, secondary structuring of solvent molecules which is engendered by solution species. For those cases where the double-layer effects are negligible or known, the potential dependence of the intrinsic electrochemical transfer coefficient could provide an additional test of such a model. A theoretical prediction13 based upon the treatment of the solvent as a continuous dielectric medium has received some examination‘h. Although the results of this study produced less variation with potential than the dielectric-continuum model presages, evidence ls presented in Chapter IV below that under certain circumstances the transfer- coefficient dependence upon potential is even stronger than the model anticipates. Indeed, the results can be seen to corroborate the structured-solvent argument.15 Furthermore, because of the participation of hydrogen bonding in secondary solvent structuring,11 coupled with the sensitivity of the hydrogen-bond strength to the mass of the hydrogen isotope,16 the measurement of electrochemical reaction rates in 020 solvent in comparison with those in water presents the opportunity to examine those aspects of the model which relate to the specific nature of the secondary structuring. The results of experiments described in Chapter V involving the use of isotopically substituted ligands and solvents substantiate still further the applicability of the structured-solvent model. USE OF RATE RESPONSES TO PROBE INTERPHASIAL STRUCTURE A recent discussion has shed light on the measurability and indeed on the significance of electrochemical activation parameters, by explicating the confusion surrounding the temperature dependence 9 of electrochemical potential scales.17 Because an experimentally measured ("apparent") activation energy represents an intertwining of work terms and activation information (cf. Equation 1), it is imperative that the adsorption energetics be determined. Two limiting cases can be described: that in which there is significant interaction, often covalent, between an adsorbing species and the electrode ("specific adsorption"); and that in which the interaction is of a fairly weak, nonspecific coulombic nature between a charged reactant species and the electrified electrode-solution interface. When the adsorption is very strong, as is often encountered in the former case, a rapid potential- perturbation technique such as chronocoulometry can be employed to determine the amount of electroactive material immediately adjacent to the electrode.18 Should the latter situation prevail, however, one must resort to more indirect means. The adsorption coefficient Kr is then given by Kl‘ - 2r(exp(-2F (OZ/RT )) (‘1) where r is the radius of the reactant ion of charge 2 and ¢2 is the Galvani potential difference between the bulk of solution and the plane of closest approach of the ion to the electrode.9 This potential difference arises from the anisotropy generated in solution by the presence of a charged electrode in a medium of mobile charge carriers (electrolyte ions) whose coulombic attraction or repulsion for the electrode charge is compensated in part by thermal motion of the solution. The factors which determine A2 are the charge density qm on the metal and the 10 specifically adsorbed charge density q', both of which can be assayed for liquid electrodes such as Hg by means of electrocapillary thermodynamics.19 One theory which is due to Guoy and Chapman20 to describe the dependence of ¢2 on -(qm + q') has enjoyed 1#,15,21,22 The measured success despite a recent challenge. rate responses of mechanistically simple electrode reactions to systematic and known changes of double-layer composition can then be utilized as "kinetic probes" of unknown OZ values, an application of considerable advantage for solid-electrode studies9 where the metastable nature of the solid surface precludes the uSe of electrocapillary thermodynamics. EXPERIMENTAL TACTICS IN THE USE OF PERBROMATE PROBES Cationic complexes of Co(III) have been well categorized as outer-sphere probes for various potential ranges on Hg electrodeszz’23 and have seen employment at solid electrodes.9 The electroreduction of perbromate anion has been suggested as an anionic probe.2h For it to probe successfully the unknown specific adsorption of solution species, the reduction rate of perbromate must be scrutinized in media for which specific adsorption data are available. Typically, these solutions would contain concentrated fluoride salts so that the specific adsorption could be quantified by the Hurwitz-Parsons method.25 Two experimental complications 26 The reduction rates are close to militate against its use: the maximum measurable by ordinary dc polarography; and the potential "window" on Hg electrodes has complications at its extremes, namely Hg oxidation in the region of kinetic interest and bromate or solvent reduction very near the onset of the requisite limiting- 11 current segment. While pulse polarography can be used to measure 27 faster rates, a condition necessary for its employment is the existence of a potential range in which the electrode is ideally polarizable (no charge transfer occurs across the electrode-solution interface). That this region is not present at Hg electrodeszl"26 vitiates the application of pulse polarography. Time-resolved dc polarography offers the prospect of access to faster rates for such a situation.28 Because the experimental perturbation is the electrode-area growth, no ideally polarizable region is required, which renders the technique amenable to perbromate measurements. The predicted shift29 of the kinetically controlled analyte wave and interference waves described above, which occurs with decreasing current-sampling time following drop birth, suggest that rates may be measurable at potentials closer to those where the Hg-oxidation wave is normally significant and that the limiting current may be less ambiguously determined in concentrated electrolytes. Another advantage of the technique is the reported elimination of complications due to polarographic maxima in electroanalytical work involving Hg drops of forcibly shortened lifetimes.30 Whether the same advantages accrue to measurements of electrochemical reaction rates under the same circumstances has yet to be reported. A systematic evaluation of time-resolved polarography is presented in Chapter VII with an eye toward its suitability for electrochemical rate measurements. For such purposes, it is desirable to compare rapidly sampled polarographic currents at dropping Hg electrodes where the drop 12 detachment occurs by natural fall and by forced dislodgement. The latter are experimentally more expedient at the expense of producing additional convection within the solution, a complication absent in the latter case. A signal to synchronize timing circuitry with the birth of the drop is easily derived from the circuit which drives a solenoid to knock drOps from the capillary, but some external means of detecting drOp fall accurately must be fashioned for natural-drOp experiments. Two types of drop-fall detectors were constructed; the characterization of the optical class of detectors and the fabrication of a high-speed electrochemical detector form the subject of Chapter III. ASSESSMENT OF MEASUREMENT RELIABILITY Underlying the electrochemist's interpretation of kinetic parameters is an implicit confidence that the rates have been measured reliably. It is worth considering whether this conclusion is warranted: one would find it helpful to know if the surface conditions are reproduced from one experiment to the next; how fast a rate can be measured accurately with the available equipment; and to what extent the choice of experimental technique, data analysis, or instrument design distorts the rate Information presented. Quite apart from the anticipated considerations of reagent purity in the solutions tested, the difference between liquid and solid electrodes is crucial to the first question. There are several well-documented reasons for this. Because the adsorption energetics of solution species at electrodes seldom if ever are less favorable on solid electrodes than on Hg, trace cOntaminants 13 whose effects on electrode kinetics are magnified by their concentration In the double layer by adsorption processes are of less consequence at Hg electrodes. Liquid-liquid interfaces are smooth on a molecular scale, and unlike solids the arrangement of surface atoms is not metastable. The surface and geometric areas of liquids therefore always concur, whereas the "surface roughness" of solid electrodes as expressed In the ratio of these areas can differ from unity and can be reproduced only if some pains are taken. The surface of a liquid electrode can be easily renewed, and therefore liquid eleCtrodes do not carry with them a history of previous experiments as solids do.31 That Hg-electrode surface conditions can be copied faithfully has received frequent demonstration, making scrutiny of the other two considerations possible through the study of Hg behavior. Measurements of Cr(III) reduction rates in perchlorate electrolytes from two different studies in two different laboratories agree well.32’33 Within a given location, one study‘h has shown that systematic differences of 102 in rate parameters assessed by two different analyses of dc polarographic data are readily discernible from those calcutated from chronocoulometric results. In another case, two applications of Co(III) ammine probes‘s’23 produced rate constants in good agreement. In studies at solid electrodes, on the other hand, rate disparities from one experiment to the next of 502 or more are not uncommon.31 As to the second and third reliability considerations, an intercomparison of techinques often provides valuable information. 1h The ranges of rate constants accessible from pulse- and dc-polarographic 27.29 data overlap considerably, 3A and experiments described in Chapter V and elsewhere using these two methods can produce essentially identical rate parameters. Weaver and Anson have described the convergence of reaction rates measured via chronocoulometry and dc polarography and have used this technique-comparison to show the inappropriateness of a spherical-diffusion correction to their polarographic results.‘h Chronocoulometry has been described on purely theoretical grounds as providing a higher information content for kinetic studies than chronoamperometry,35 but an empirical examination of this point has not been reported. Once a give experimental technique has been chosen, the method for the treatment of data can be important. Various time-domain approximations to the complicated rigorous solution of the diffusion 36 equation characterizing chronoamperometry are available , each with its own range of applicability. The use of Laplace-domain 37 analysis has been proposed as a way to utilize all of the current- time data rather than selected portions, but a demonstration of the relative merits of these methods has not been forthcoming. Enke et. al. have discussed thorougly the determinate'error which results from the use of approximate solutions or nomographic methods in the coulostatic technique, as well as experimentally accessible criteria which can indicate the suitability of a particular approximation. Chapter VI describes an assessment of high-speed rate measurements made at Hg electrodes with equipment constructed in this department and provides an experimental demonstration of the superiority of a pulse-polarographic type of display and 15 data analysis for irreversible chronoamperometric transients. Also presented is a strategy for determining the extent to which the boundary conditions assumed in the solution of the diffusion equations are satisfied by the instrument employed. There are many instances in which the performance of commercially available instruments is adequate for the rate measurements required by a given study. Most of the experiments described in Chapter IV and V below fall into this category. However, the technique evaluations reported in Chapters VI and VII necessitated considerably more timing flexibility and speed than are possible with conventional instrumentation. For instance, it is desirable In potential- step techniques to sample the cell current or its time integral within time ranges characteristic of double-layer charging phenomena. Typical double-layer integral capacitances at Hg electrodes are around one microfarad: for uncompensated solution resistances less than 100 ohms, cell time constants would be as large as 100 microseconds. Sampling intervals of 10 microseconds would be sufficient for this task, but such a time is more than three orders of magnitude smaller than the current-sampling time of the pulse-polarographic mode of the redoubtable PAR Model 174 Polarographic Analyzer (EGSG Princeton Applied Research, Princeton, NJ), one of the most commonly used electrochemical instruments. For those cases in which conventional electrochemical instruments did not possess the speed or flexibility required for the studies described herein, a microcomputer-controlled electrochemical data acquisition and management system, the documentation of which comprises Chapter II, was utilized. CHAPTER II. A MlCROCOMPUTER-CONTROLLED ELECTROCHEMICAL DATA- ACQUISITION SYSTEM 16 17 INTRODUCTION AND GENERAL DESCRIPTION A general description of the microcomputer system and its laboratory-type peripherals forms the subject of this chapter. Some attention is paid to the steps in its development which were necessary to obtain satisfactory speed and signal-to-noise ratio performance in the potential-generation subsystem. The maximization of the data-acquisition rate is discussed, and special- purpose accessories which were required for some experiments are described. Finally, an example is presented of a technique which cannot be performed by ordinary instruments but which is readily implemented by a computerized experimental-control system. A decade ago, a review of electrochemical relaxation-techinque methodology claimed that "...apparently the ultimate in (electrochemical) Instrumentation these days is to have your own digital computer in the lab."38 Scarcely two years later, the same author opined that "...today's polarographer is apt to feel obsolescent without a minicomputer."39 The virtual explosion of computer technology since then has put a wide range of processing power into the hands of electrochemists. Recent applications range from a highly sophisticated "soup-to-nuts" Fourier-transform based system capable of viewing in the frequency domain simple diffusion processes as well as complicated reaction mechanisms,"0 to monitoring measurements of ion-selective electrode potentials.h1 Similarly spectacular learning-curve progress in memory fabrication has made possible the manufacture of microprocessors which are capable of mimicking the instruction-set performance of other computers, thereby emulating inexpensively their more costly, albeit more powerful, cousins. 18 The computer system which was built in our laboratory is based upon the Digital Equipment Corporation LSl-ll central processing unit (CPU), which emulates the instruction set of the POP-11 family."2 Access within the university to the real-time, dual- task operating system RT-lllI2 made high-performance software- development tools such as symbolic editing, high-level language- processing, and file-minipulating programs immediately available for use in the creation of applications software for the acquisition and reduction of electrochemical data. Because of the considerable time-saving this made possible, efforts could be concentrated on construction of the computer from the circuit-board level, a process which makes computation available at substantially less expenSe than in ready-made "turn-key" computers. Figure 2 shows a schematic representation of the computer system. Those subsystems shown in solid-line rectangles are components which are included with the CPU in virtually any computer system of recent vintage: namely, high-speed memory, a console terminal, mass-storage memory, and a hard-copy printer. Interfaces to all but the last of these peripheral devices were used without modification as they came from the manufacturers. This is indicated in Figure 2 as solid-line connections between subsystems. The printer-interface circuitry was constructed from a MDB Model MLSI-1710 general-purpose parallel-interface module (MDB Systems Inc., Orange, CA) and the random logic necessary to pass data between the bus-tending circuits and the Centronics-type input- output (I/O) structure of the Printronix Model 300 graphics line printer. l9 Am some A_mmonommov hm_z_Iooz_v Am.e:olooe:ov A< away “sac. usauao .oca_m can a ouoo coon...._. _ __o om . _m__wtom . II n \\ "lllllllllllllltllllllliu mue2_mm o\_ .:L muemm>zoom mo.:¢zoom mwmwl‘(‘ >.~_nu“mmg‘ Till“ A“_\< m n ..................... .m Figure 2. Block diagram of measurement system. 20 POTENTIAL GENERATION AND MEASUREMENT What distinguishes a laboratory computer from an ordinary computer is the presence of those accessories which can transform analog voltages to digital binary representations and vice versa (analog-to digital (A/D) and digital-to analog (D/A) converters) and that which can provide accurately spaced timing pulses for sequencing measurements (real-time clock), enclosed in Figure 2 by broken-line rectangles. Twelve-bit A/D and D/A converters are contained on a Data Translation Model DT 1761-SE-C-DMA Analog Input/Output Board (Data Translation Inc., Natick, MA), and the clock is a MDB model MLSI-KWIIP circuit. The laboratory peripherals required modifications to perform to the standards required by our experiments. While the "quasi-differential" nature of the A/D input system (single-ended analog multiplexer and differential input amplifier) provides sufficient noise immunity even in the relatively noisy mainframe environment, the same performance was not seen for the D/A converter. The output of the latter was discovered to contain rather large-amplitude, high-frequency noise, mainly about 200 mV peak-to-peak at a frequency near #00 kHz. Because a design criterion for the potential-generation circuitry was the ability to deliver potential steps with submicrosecond rise time to the potentiostat used for electrode-potential control (see Chapter VI), low-pass filtering of the D/A converter output to remove the noise was not an acceptable alternative inasmuch as a filter time-constant of sufficient magnitude to reduce the noise would also increase the rise time to several hundred microseconds. 21 Rather than being common-mode (that is, Induced equally in both the D/A converter output and its analog return), a condition which could in principle be remedied by employing a differential amplifier at the potentiostat,l'3 the noise originated in the dc-dc converter whose function is to produce +15 and -15 V analog- circuitry power isolated from the 5 V logic power supply from which it Is derived. Such behavior is characteristic of these switching power supplies when they have insufficient output filtering.hh AS A miniature LC-type low-pass filter with a nominal attenuation over 1000 at 100 kHz was installed on the analog power supply; its effect was to reduce the noise in the D/A converter output to a third of its original magnitude, an amount still too large for precise potential control. Clearly additional noise must be induced in the power-supply leads between the filter and D/A converter, a situation difficult to remedy by retrofitting. A second D/A converter was available in a staircase-waveform generator built in this department."6 This converter met the rise-time specification for our experiments: its settling time is I microsecond to within 1 L53 (1 part in #096) for a 20-volt step. Furthermore, because the long-distance information transmission is accomplished in the digital domain,"7 noise in the output was found to be less than 2 mV peak-to-peak. An interface, shown in Figure 3, was built to allow the computer to program the D/A converter through the ORV-11 parallel digital port."2 In addition, a digital trigger signal generated in response to the LOAD B AND CONVERT command"6 was derived from gates within the waveform 22 Hnrw NIrm murm ¢I¢m mirm mitm hirm mIrm mlrm mmmznz ZHQIQH Q>\®#v /~.r\(t123._12:(rik- QM ‘K\\\\\ ‘\'\.d'[\-GD(\I3'(O mmmc—Ic—Iv-Ic—Ic—o VVVVVVVV mfihzo I moz hQHDO wGHDO mOPDO rQHDO mshno NQHDO ashno oohno onhmo Interface to D/A converter. Figure 3. 23 generator so that synchronization of electrochemical experiments with potential steps could be effected. THE TIMING OF COMPUTER-CONTROLLED MEASUREMENTS Once a sample-and-convert measurement cycle has been completed, the information in the A/D output register must be transferred to the computer's memory for further processing. Two different types of transfers are possible: one in which the CPU interrogates the A/D converter and writes the result into memory ("program control"), and one in which logic associated with the converter uses the computer bus when It is idle to transfer the conversion to a pre-programmed memory location without the intervention of the CPU ("direct memory access", or DNA). In circumstances where the time taken by the computer to ascertain that the conversion is available and to store the result poses no threat to the timing fidelity of subsequent measurements, the former, less complicated approach may be taken. Observations show that the LSI-ll is capable of making measurements under program control at AO-microsecond intervals without introducing timing errors. The length of this period clearly precludes another system-design criterion, namely the ability to make measurements separated by only 10 microseconds. However, the analog I/O board was purchased with an A/D converter which has a conversion time of 8 microseconds or less and DMA logic with typical transfer times of 1 microsecond, thereby ensuring 100 kHz data-acquistion rates in this mode. The real-time clock counts pulses of a prOgram-selectable, four-frequency oscillator; 100 kHz, 10 kHz, 60 Hz, and external rates are nominally available. However, construction and design 2h flaws in the clock introduced two unexpected features: first, the behavior of the underflow or overflow signals of the 7h193 decade-counter integrated circuits which comprise the programmable modulo-N counter circuit“8 is such that an extra eight-tenths of the clock period must elapse before the first overflow or “9 underflow signal is generated; and second, the mask-programmable MOS frequency divider which is supposed to produce a 60-Hz output frequency from the 3.5795 MHz crystal oscillator actually provides pulses at 20-Hz intervals. Neither of these anomalies causes anything more than a minor inconvenience in practice inasmuch as the data-acquistion programs can easily take them into account. Ostensibly the combination of a clock and A/D converter which are both capable of running at 100 kHz can acquire measurements spaced by IO-mlcrosecond intervals. The fly in the ointment is that as these modules are configured by their manufacturers the CPU must arbitrate every clock-expiration and measurement- initiation transaction, tasks which It is clearly incapable of performing singly every ten microseconds, much less in tandem. Although the A/D converter has externally accessible trigger inputs which can initiate measurements without CPU intervention, the clock is somewhat less than ideals0 in that it can neither make use of this feature nor in Itself be triggered by an external event, such as the application of a potential step in chronoamperometry or chronocoulometry experiments. Modifications shown In Figure ha enable the latter objection to be overcome, which enhances the overall timing accurancy. Making the clock's overflow/underflow signal CTFLW available to other circuits, coupled with the pulse- 25 (A) +5 F18 VPUP EXT 1K __ 11 [\19 START : , L// 15 7407 2 PR 5 once >2 0 O-———»RUN 53 __ 3 7.174- KHCSRO: CLK Q CLR 35 605 9813 50“ > a11313,12é13, 13313 (a) TD ”RTCTRG” ON CTFLN > 1>B O-———+A/O CONVERTER 74121 (J uSEC) Figure A. Clock-interface circuitry. a) Remote start. b) Remote trigger for A/D converter. 26 stretching monostable (shown schematically in Figure Ab) on an external circuit board which can be connected to the clock-trigger input RTCTRG of the A/D converter, removes the former obstacle. Once these enhancements were included, 100-kHz data-acquisition rates were made possible. ADDITIONAL MEASUREMENT ACCESSORIES There are circumstances in which data rates even faster than this are required. Instruments are available with so-called "flash-encoder” A/D converters which can digitize voltages twenty or more times faster, usually with some sacrifice in converter resolution. The Biomation Model 820 transient recorder (Could- Biomation Inc., Santa Clara, CA), an 8—bit, twenty-million samples- per-second waveform recorder, was used for some ultrahigh-speed measurements described in Chapters VI and VII. To take advantage of the digital form of its recorded data, an interface between the transient recorder and the ORV-11 parallel port was constructed (Figure 5). Commands to the transient recorder are distinguished from those to the D/A converter In two ways: data for the latter device must have bit 15 (M58) set, whereas the "handshake" strobe line CMD (run by bit 0 of the command-status register of the ORV-11) must be turned on as a transient-recorder command is issued and turned off before the next command is sent. In this way, complete remote control of the transient recorder could be brought about. Time-critical, high-speed signals could be digitized 20h8 times in as little as 100 microseconds and read into the computer in about 50 milliseconds, all without changing the voltage output by the D/A converter. 11 BERG/3M CONNECTOR DESIGNATION ORV- LNG Figure 5. N AAAA AAAAAAAAAQHNO‘) v-‘NGJTIOCDBQOD—H-IH—I vvvvvvvvvvvvv O—IN onmmrmmhmoHI—IH mmmmmmmmmmmmm AAAAAAAAAAAAA A I A A A A A A A A A A A AAA/\AAAAAAAAA HHHHHHHHHF‘HHH 773713137753“) VVVVVVVVVVVVV AA AAAAAAAmr .szI-CDQNNN \\\\HNN\\ /U) SammtmmhmmoHN QQGQQQQQQGv-‘H—I PHHPPHPPPHHHF 3333333333333 0000000000000 ‘AAAA AAA/\AAAAAAA (\mmbmeF-‘NMQ «ammmmmmmmm VVVVVVVVVUV A . I V I OLD O ZAOfiNCOfl'IDLOfiZ OLLDDDDODDOI A A A A A A A A A A A A A A A A A A NNNNNNNNNNN 733133-3773? VVVVVVVVVVV A ‘ l\ AA \AAAAA AmNIns-ncmxmn AIOUNY)\N0‘)NNNH mv-o\\I\\\\\v-I \\1-_I ~m¥ILLIQ\ xwi-JLIJCDXILIJQZ VVVVVVVVVVV m G QHNma'IDLOINID COSQOQQDGQH (OLIJZZZZZZZZZ er—Oo—oe—ae-aO—OHO—OO—OI-o Interface to Biomation transient recorder. 28 One additional channel for timing or status information between experiment circuitry and the computer was set up with the remaining unused ORV-11 command-status register output bit CSRI and input bit REQ A, shown in Figure 6. This interface was used to synchronize measurement sequences with an external event in a situation where the computer's cycle time or interrupt latency has an immeasurable effect on the accuracy of the experimental information. The most common application of this channel was to receive a trigger signal from a drop-fall detector or the modified driver for the 51 drop-knocking solenoid. Measurements were not made until at least 50 milliseconds after the trigger (see Chapters VI and VII), which results in an inaccuracy that is only a fraction of a percent for the first point and substantially less thereafter. AN ILLUSTRATIVE EXAMPLE A chief advantage of computer-controlled instrumentation is that once timing and measurement hardware has been suitably assembled, the control is in software. That is, a change in experimental technique can be brought about by the simple expedient of editing a program. Hardware-sequenced instruments, on the other hand, require changes in the control circuitry in order to become capable of measurements for which they were not originally designed. The ease with which a computer-controlled polarographic instrument can be adapted to perform the technique known as first- drop polarography illustrates this point well. Figure 7a shows a flow chart for a dc polarographic-measurement program, a technique available on many commercial instruments, albeit not with the same timing flexibility and data-management 29 +5 1K TRIGGER e ‘ CLK ———»REO A CSRI > Figure 6. Drop-fall trigger input. 30 as sea a gsaa a. coEEoo~ “a. *a_ "all -0 do- :1“; . .3 ma - n so 3) Conventional b) First-drop. Figure 7. Flow charts for polarography. 31 capability provided by the computer. In the characterization of depletion effects in time-resolved polarography (see Chapter VII), it is necessary to determine to what extent the concentration polarization brought about by electrolysis at the previous drop has been alleviated by the stirring of the solution produced when the drOp fell from the capillary. To do this, one must compare conventional measurements with those made under circumstances in which the concentration is distributed uniformly near the electrode. If one maintains the electrode potential throughout- several drop lifetimes at a value where no electrode reaction occurs and, upon detection of the next drop fall, steps the potential to the measurement value, the concentration conditions will be satisfied. A flow chart to perform these "first-drop" measurements can be made from the conventional chart (Figure 7a) by interposing a step to return to the ideally polarized potential ESTART after the measurement has been completed and waiting several drop lifetimes before the next measurement. Figure 7b shows these small modifications; in this way, a technique which cannot be performed by conventional instruments has been made possible by minor changes in the data- acquisition software. CHAPTER II I. SYNCHRONIZATION OF NATURAL DROP-FALL EXPERIMENTS 32 33 INTRODUCTION There are many types of experiments performed with dropping mercury electrodes (DME) in which measurements must be made at times that are well defined relative to the birth of the drop. The simplest method for measurement synchronization Is to dislodge the drop forcibly and simultaneously trigger a timing circuit. However, mechanical drop dislodgment may cause significant disturbance of polarographic diffusion profiles in the growing drop, particularly 52 at subsecond current-sampling times. An alternative approach is to detect the birth of a new drop following natural gravitational drop fall. Such drop-fall detectors also enable natural drop times to be determined, providing a simple route to the interfacial tension.53 We have been investigating dc polarographic current-time curves at short times (0.01-1 sec) following drop birth to evaluate rapid dc polarographysz’sh as a method for monitoring the kinetics of electrode reactions.28 For this purpose, as well as other applications where accurate knowledge of the drop time or electrode area is required, it desirable to detect the time of consecutive natural drop fall with millisecond accuracy and In a manner which Is compatible with potentiostatlc circuitry and automated data acquisition by a laboratory microcomputer. Although a sizable number of detection techniques have been reported (for example, see citations in refs. 55 and 56), few fulfill the above criteria. Nearly all use either a superimposed ac voltage or light as probes, although an FM transmitter and receiver have been employed to exploit the behavior of a DME 34 56 as an antenna.57 While the optical detectors offer the advantage of requiring no electrical connection with the cell, they are subject to serious errors of up to 100 msec,28 as will be shown below. A number of the ac devices described either are not compatible with conventional potentiostat-based instrumentation (e.g., ref. 58), have response times on the order of tens of milliseconds,59 or continuously impose an undesirable ac perturbation on the cell and require remote activation and disabling because of limited noise lmmunity.55 A recently reported techique6o for making drop- time measurements averaged over successive drops is simple in concept but requires adjustment as the cell current is changed, and in the vicinity of the potential of zero charge (pzc) it relies on stray impurity currents. Since these limitations render the previously described detectors inadequate for our purposes, we have developed a faster, more sensitive and versatile device which is described below. AN EVALUTION OF OPTICAL DETECTION TECHNIQUES We initially chose the optical method of Hahn and Enke56 based upon its lack of interaction with the potentiostat circuitry and simplicity of implementation; Figure 8 presents a schematic diagram. The sudden change in light scattered up the capillary when the drop falls is converted to an electrical signal which is differentiated and amplified to provide a detector pulse which is compatible with transistor-transistor logic. Preliminary time-resolved dc polarographic measurements (see Chapter VII) produced rate constants which decreased monotonically as the sampling time increased and which were inconsistent with previously 35 PHOTOSENSOR AND OEILJ Luv—n 00 r— no. LL.CD Figure 8. Schematic diagram of optical drop-fall detector. BUFFER V DIFFERENTIATOR AMPLIFIER .Jluu [LIP- =>IJ. Luv-I .JIJE 36 32 reported values. Efforts were undertaken to determine If systematic errors were introduced by any portion of the measurement system. Upon closer scrutiny it was found that the signal produced by the drop-fall detector occurred no less than 80 msec following the fall of the drop. What appeared to be the source of the delay was that the original designers did not reckon with the inversion produced in the comparator stage of the level shifter (amplifier AA in Figure 2 of ref. 56). The desired negative- going logic transition occurred only as the result of noise in the differentiator output on the trailing edge of its output spike. Once this level-inversion discrepancy was rectified, however, a nonreproducible 20 msec delay remained. Since one of our design goals was the capability to sample currents after 50 msec, this performance remained unacceptable. To meet this goal, it is necessary that the detector error be less than 1 msec. For it to be capable of this, however, it must have preferential frequency response In the 1-10 kHz region. Examination of the original passive components of the differentiators6 showed that they limit frequency response to between 0.16 and 3 kHz (unity-gain limits), with maximum gain at 22.5 Hz and gain in excess of 10 at the archetypal noise frequencies 60 and 120 Hz. Even with more appropriate passive components, however, insufficient signal amplitude was present in the necessary frequency range; efforts to remove sources of stray light by optical shielding and to increase the gain of the amplification stage proved equally unsuccessful. Because the light is attenuated appreciably by the fiber optic system, even with the recommended 37 polishing of the capillary groove and fiber optic ends, we tried attaching a more sensitive photodarlington transistor (2N5777) directly to the capillary groove with the die facing the Hg drop. The buffer amplifier in the detector was replaced by a current- to-voltage converter (10 uA/V); the a-c component of a typical differentiated output is shown in Figure 9. While the signal- to-noise ratio would undoubtedly be increased if the current- to-voltage conversion were preformed directly at the phototransistor, the necessary mounting considerations vitiate such an undertaking. Furthermore, Inspection of Figure 9 will reveal that the rise time of the differentiator spike produced by the fall of the drop is approximately 20 msec. This result is not surprising in view of the fact that the drop continues to reflect light after detachment until it falls below the light path, and a 20 msec delay corresponds to the time required for a 2 mm displacement of a freely falling object. The Inevitable conclusion is that the optical detection system is inappropriate for this or any other application where inaccuracies of 20 msec cannot be tolerated. It is still useful in systems 56 such as its original utilization where a precise albeit inaccurate time delay following the birth of the drop is all that is required. A HIGH-SPEED ELECTROCHEMICAL DETECTOR Successful performance was obtained from an alternating-current electrochemical detector. Operation of the detector can be understood with reference to the block diagram (Figure 10) and schematic (Figure 11). Late in the drop life, the monostable which produces the delay for measurement of the dc current (D) returns to Its 38 I second 0.5V I- 0v Figure 9. Differentiated current from photodarlington transistor. (I) LEVEL OETECTOR (A) I 39 (0) PULSE DETECTOR (Bl :- “III- :- =4 0"“- N15- lull-l moo: can :II-I- 0.1:: cu a>> 012 coo 1.1-0 1“I5 >0“ (II-Z .l—< “in: acu- O.5 TO 5 SEC 10 “SEC Al: [OSCILLATORI .u- <- <0) 08 cm I-- 2“. o— 0.1 O: I-< Figure 10. Block diagram of ac drop-fall detector. A0 III! ask If}- g rnon ocuIIHENT- - _ _ C'VV ' 1 To-V >——4 s an 3.3: 3 convng ‘:‘ R R R vAVAVA i vAvAvk * Isak *70'P (A2) 1.sx I II! A zzarr zzarr .,. all 88"? 220?? (“1) ("2) (III) TI! IIEH ‘4 To CONTROL IN TLC AIPLIPIII t - vzvzv. 13 n (A9) Figure 11. Schematic diagram of ac drop-fall detector. hi stable state and closes the analog switch. An ac perturbation of 10 mV peak-to-peak at 100 kHz is imposed on the cell, and the resulting ac component of the cell current is detected by a tuned amplifier (A). When the electrode area is large enough so that the magnitude of the ac current exceeds the threshold selected by the potentiometer, the logic-level output of the level detector (B) will change states at the frequency of the ac source and activate the missing-pulse detector after a delay to allow for switching transients. The precipitous decrease in electrode area concomitant with drop fail causes the tuned amplifier output to remain below the threshold throughout several ac cycles, long enough for detedtion of the missing transitions in the level-detector output. Within 100 to 200 usec of the fall of the drop, the ac source is disconnected from the potentiostat so that dc measurements can be made. The missing-pulse detector input is Inhibited by the gate (C) to prevent noise transients from retriggering the detector, and a signal Is sent to the current- sampling circuitry. The time interval between the fall of the drop and Its detection is due to three causes. First, at potentials away from the pzc, the potentiostat must supply charging current to the nascent drop. The resultant current spike (typically 50 usec) contains frequency components which can be detected by the tuned amplifier and which may keep the amplifier output above the level-detector threshold for a brief time after the drop has fallen. Second, the tuned amplifier must respond to the sudden change at its input with a deliberately constrained frequency response. Several 42 periods of oscillation at the center frequency are required to accomplish this. Third, a full period (15 to 20 usec) of the missing-pulse detection monostable must elapse between the last output transition of the level detector and the production of the trigger signal for the current-sampling circuitry. Finally, noise in the current-to—voltage converter whose power spectrum overlaps the frequency range of the tuned amplifier can delay detection of drop-fall a few additional ac cycles. The drop-fall detector operates reliably even in noisy environments provided the potentiostat employed has sufficient response at the frequency of the ac perturbation. Although we have chosen a frequency of 100 kHz, the detector is suitable for slower potentiostats providing that a lower frequency is selected, albeit with some lengthening in drop-detection time. This modification needs to be performed only once and is accomplished by varying the passive components in the twin-T networks around amplifiers A1 and A1161 and the timing capacitor on M51. A single selection of the suitable gain (two are available) for the tuned amplifier and of a threshold level appropriate to the current-to—voltage converter setting, to the electrode capacitance, and to the cell resistance generally suffices over a wide potential range (2V or more) for a given set of cell conditions. Since no further adjustments are required, this Circuit is very useful as a trigger device for automated instruments, especially those under the control of a laboratory computer. The circuit's independent nature allows the computer to perform lower priority tasks between measurements, instead of requiring that the processor continually #3 monitor portions of the detection circuitry in order to discern drop Fa11.55 The features of the detector include the temporary disconnection of the self-contained oscillator from the potentiostat by means of an analog switch as soon as drop fall has been detected, which eliminates the need for filtering. A single adjustment generally suffices for a wide range of potentials, and the operation of the detector is unaffected by the presence of the pzc within that range. The response time, between 100 and 200 usec is dictated by electrochemical cell characteristics, the frequency of the ac perturbation, and the time window of the missing-pulse detector. Unfavorable cell conditions are those in which large faradaic and nonfaradaic components are present so that the output of the tuned amplifier remains substantial even after the drop has fallen. Such circumstances are encountered, for example, with 3+ a solution of I m! Cr in 1 M NaCth(pH 3) at an electrode potential of -1100 mV. vs. SCE where the diffusion-controlled reduction of Cr3+ occurs, and the excess electrode charge density is large and negative (ca. ~13 uC cm.2).32 The response time was assessed by observing the current-to-voltage converter output on a Biomation Model 820 transient recorder in the pretrigger mode. Detection was considered to have occurred when sinusoidal variations at 100 kHz could no longer be distinguished in the cell current. Thirty determinations yielded an average detection time of 185 usec with a standard deviation of 36 psec. Measurements at the growing mercury drop are essentially unaffected by the ac perturbation since It is automatically disconnected within this time scale. Ah Either individual or successive natural drop times can be conveniently determined to this accuracy, so that current-time curves may be monitored even at subsecond sampling times with high accuracy. In addition to its use as a synchronization device for rapid dc polarography (see ref. 28 for details) and determinations of the excess electrode-charge density from charge-time curveséz, we have also found it to be highly suitable for obtaining precise surface-tension data from drop-time measurements6o. CHAPTER IV. FURTHER OBSERVATIONS ON THE DEPENDENCE OF THE ELECTROCHEMICAL TRANSFER COEFFICIENT UPON THE ELECTRODE POTENTIAL 115 #6 INTRODUCTION A considerable amount of effort has been devoted to providing experimental tests of the prediction of contemporary theories 10,63 of electron transfer that the electrochemical transfer coefficient a for outer-sphere electrode reactions should depend upon the elctrode potential.m’6h"73 It turns out that stringent tests are relatively difficult to design since the predicted dependences are usually small, and the measured (apparent) transfer coefficient a app will generally differ from the required ”intrinsic" transfer coefficient7h a. as a result of the influence of the interphasial environment ("double-layer" effects). Thus a app is often observed to vary markedly with electrode potential as a result of ionic double-layer effects, and the uncertainties in the required correc- tions are frequently larger than the residual predicted variations in al. This difficulty is most acute for multicharged reactants and for reactions monitored at solid electrode surfaces where there are considerable uncertainties in the double-layer composi- tion. However, persuasive evidence for a variation of a in approximate accordance with the theoretical predictions1 has been observed for the electroreduction of tert - nitrobutane and other organic nitro compounds in acetonitrlle and dimethylform- 70’73 On the other amide at mercury and platinum electrodes. hand, the electroreductions of Cr(OH2)SOSO+, Cr(OH2)5F2+, and Cr(OH2)g+ at the mercury-aqueous interface exhibit transfer coefficients both before and after double-layer corrections that are essentially constant over a wide range of electrode potentials, under conditions 47 where noticeable variations in a are predicted by the theoretical models.17 In view of these disparate sets of results, it seems desirable to examine a wider range of Inorganic systems at anodic as well as cathodic overpotentials in order to check the generality of the latter behavior. Despite their large charges, redox couples of the type Mag/2+ (where M is a transition metal and "aq" represents aquo ligands) provide useful model systems for this purpose. Thus a number of such couples, particularly Griz/2+, Eugz/2+, V2+/2+, and Fe23/2+, can be studied that exhibit widely varying formal potentials and yet are of similar size and structure so that the nature of the ion-solvent interactions,11 and therefore the solvent-reorganization process, should be similar in each case. Also, these couples exhibit relatively small heterogeneous electron-transfer rates so that measurements of “app can be made over wide ranges of both cathodic and anodic overpotentials. An obvious difficulty faced with these systems is that the double- layer corrections upon “app are usually significant. These corrections are smallest and can be aplied with the greatest confidence for supporting electrolytes at high ionic strengths 17’32 The reduction In the absence of specific ionic adsorption. of Org: and Bug; can be monitored at negative potentials at mercury electrodes where noncomplexing anions such as perchlorate are not significantly specifically adsorbed.32 However, the oxidations 2+ 2+ + - - of Craq, Euaq’ and Viq proceed at potentials poSItIve of 23. -500 mV. vs. s.c.e. where most anions, including perchlorate, are strongly adsorbed. The required double-layer corrections 48 upon aapp can involve sizable uncertainties under these conditions as a result of the discrete nature of the specifically adsorbed anionic charge and its tendency to induce ligand-bridged reaction pathways.7’75 Therefore it is desirable to search for anions that are only weakly specifically adsorbed at potentials positive of the point of zero charge (p.z.c.) and which do not significantly complex with the cationic reactants. Suitable electrolytes are sparse. Although fluoride and hydroxide anions exhibit the smallest tendency to be specifically adsorbed at mercury,76’77 they both strongly complex aquo cations. However, hexafluorophosphate(V) 78 anions have even less complexing ability than perchlorate and yet are only weakly specifically adsorbed at potentials positive of the p.z.c. even in concentrated solutions.79 Consequently,. -q' ” q”, where q' and qm are the specifically adsorbed and excess electronic charge densities, respectively.22’79’80 In the present chapter, we report rate constants for the oxidation of chZ’ Euiz, and V2: in KPF6 and NaCth supporting electrolytes at the mercury-aqueous interface over a wide range of electrode potentials (ca. -600 mV to +200 mV vs. s.c.e.) using normal pulse and d.c. polarography. Rate-potential data for the corresponding electroreduction reactions are also given. In addition, it was 3-!- found that the electroreduction of Feaq could be monitored in KPF6 media at mercury electrodes. Taken together, these results strongly suggest that substantial decreases in the intrinsic transfer coefficient “I occur for aquo electrooxidation reactions with increasing anodic overpotentials. They also lead to a reinter- pretation of the apparent failures of the Frumkin model in describing “9 2+ V2+ double-layer effects upon the electrooxidation of Eua and q as which were reported recently.81’82 EXPERIMENTAL 3+ Stock solutions of Cr aq were prepared essentially as described in Ref. 32; Eug; was made by dissolving Eu203 in a slight excess 2+ 2+ + of either HCth or HPF6. Solutions of Craq, Euaq, or Viq were prepared by exhaustive electrolyses of Crzz, Buzz, or V'O2 in the appropriate electrolyte at £3. -900 mV, -1000 mV, or -1100 mV vs. s.c.e., respectively, using a stirred mercury-pool cathode; Vi; was obtained by reoxidation of V2; at -300 mV. Their electrode kinetics were examined Immediately after preparation In the electro- lysis cell to minimize reoxidation by trace impurities such as oxygen. The source of Fez: was Fe(Cth)3 (G.F. Smith Co.). The supporting electrolytes contained sufficient concentrations of the appropriate acid, usually 5-10 m!, to suppress hydrolysis of the aquo reactants. Stock solutions of HPF6 were prepared by adding concentrated HCIDh to saturated ( 0.5 M) solutions of KPFG, cooling to 0°C and filtering off the KCIOu. They were kept frozen prior to use to avoid any significant hydrolysis of PFg.83 Sodium perchlorate, prepared from sodium carbonate and perchloric acid, and potassium hexafluorophosphate (Alfa Ventron Corp.) were recrystallized twice from water. The absence of significant amounts of F' in PF; solutions was confirmed using a fluoride-ion selective electrode (Orion Model 9h-09A). Solutions were prepared using water purified by double distillation from alkaline permanganate followed by "pyrodistillation"1‘ in order to remove trace organic impurities. All solutions were deoxygenated 50 by bubbling with prepurified nitrogen, from which residual traces of oxygen were removed by passing through a column packed with B.A.S.F. R3-11 catalyst (Chemical Dynamics Corp. South Plainfleld, N.J.) heated to 140°C. The electrolysis cell consisted of a working compartment of volume 33. 5-10 ml. which was separated from compartments containing the calomel reference and platinum- wire counter electrodes by one and two glass frits, respectively (”very fine" grade Corning, Inc.). The working compartment was surrounded by a jacket through which was circulated water from a thermostat. Normal pulse and d.c. polarograms were recorded at a dropping mercury electrode (flow rate 1.8 mg/sec) using a PAR 174A Polaro- graphic Analyzer coupled with a Hewlett-Packard 7045A X-Y recorder. The kinetic analyses of these polarograms employed the methods due to Oldham and Parry.sh Back-reaction corrections were applied where necessary as outlined in Ref. 32. All potentials are reported with respect to the saturated (KCI) calomel electrode (s.c.e.), and all kinetic parameters were obtained at 25.0 : 0.l°C, unless otherwise stated. RESULTS AND DATA ANALYSES Figures 12-14 consist of typical rate data obtained for the oxidation of Cris, Euiz, and V2: in KPF6 and NaCth electrolytes at the mercury-aqueous interface expressed as (Tafel) plots of the logarithm of the observed (apparent) anodic rate constant log kzpp versus the electrode potential E. Apparent anodic 51 Iog,o(kopp/Crn.sr') I I I I | 200 O -200 -400 -600 E/mv. VS. s.c.e. Figure 12. Rate-potential plots for the one-electron oxidation of erg: in KPFG, NaCIOh, and KCI electrolytes at the mercury-aqueous interface. Key to symbols: 0.11 14. I 750 mV) where perchlorate specific adsorption is negligible, 57 it appears that ¢rp = 0.6 ¢gcs, at least for ionic strengths 16 in the range u - 0.3-1 Q. The rate responses obtained upon the addition of specifically adsorbing halide anions at a constant ionic strength of 1 fl_again yielded A¢rp z 0.6 A¢SCS that such discrete adsorbed charge q' has an effect similar to 75 , indicating the electrode charge qm itself. On the other hand, it has been argued that specifically adsorbed perchlorate charge exerts a substantially smaller effect than the electrode charge upon the rates of Sufi; oxidation.81 If correct, this latter finding would severely complicate the applica- tion of double-layer corrections to kinetic data gathered in electrolytes containing PF; as well as 010; in view of the structural similarity of these anions. However, the kinetic data in Figures 12-1h strongly indicate that the analysis employed in Ref. 81 is incorrect, as will now be demonstrated. By integrating the capacitance data for KPF6 and HCth electrolytes given in Refs. 79 and 85, the qm -E curves for these two electrolytes at a given ionic strength were found to be closely similar. (Suitable data in NaCth electrolytes are unavailable.) Consequently, the large differences in log kgpp observed for Bug; oxidation between KPF6 and NaCth electrolytes at 0.1 and 0.0 fl ionic strengths (Figure 13) must be due to the greater specific adsorption of 33 Clo; compared with PFg. It is convenient to compute the difference in the potential at the reaction plane at a given electrode potential, A¢ Ep’ from the corresponding rate difference (A log k for a pair of electrolytes using (cf. eqn (7)): app)E (A log “apple - -(r.2.303) +~=m +~co o unzu ac.s:mmm .Amv coo mc_m: .o_ucouoa coccuuo_o cox—u um coax .Auxou oomv m.o I 50.. no:.mugo .cE=_ou ocmzuumo_ to; ecu c. co>_m mm ._ux co ac_umz Ou wumx sac» ou>_05uuo_o uc_mcmnu >a uaonm unnecen .m_u:ouoa utocuuo_o co>.m up ecu—n co_uuou. ozu um _m_u:ouoo ommco>n to» mcouoEmcmo mo. c. momcmco m:.ucoaoam ogu ecu :_.omcm:o_ mm a: can .ug.m _.c\¢..x z ..c cm a up cw 5 cc: m.mm m.:~ mm m. can m.mm mN mm - co~ ao.umz_m .\o..x.m _.o m- m.m_ o. m.m co: m.- m.£ .N i can mN m. m.m~ a. o=~ {c.9mz m_:.=\e..x_m s.° :N v. Q— s cc: mm MN m... can mm “a m. °=~ ao.uaz.m ..=\e..x_m _.o .o.u.m n> >5 +~mmfimzzvou mo_xo WM> mExo ”M .xo ”who u: mou>_05uuo_m >..._... 3 - m m on .uo .uu at .Amv coo ac_n: ooc_uuao .:o_uu:ooc +~m A :zvou can co_uou.xo +~> pen +~=m +~cu cam e ecu-o :o_uunoc «go up _m_u:ouoo omoco>o ecu con: co.u_nooEou ou>_oLuuo_o ozu m:_>ca> mo nuuommo oak .~ o_nmh 60 +33 q to react closest to the electrode, yielding the largest values of A¢ 33. (Smaller, yet compatible differences in the rate rP responses to anion adsorption were also seen for Eu3+ versus aq 75) 2+ + 2 2+ the sequence Euaq < Viq < Cra so that Euaq should be able 3+ Craq reduction. It therefore appears to be very likely that the earlier asser- tion81 that adsorbed Clo; induces anomalously small changes in ¢rp for Bug; oxidation is incorrect. The analysis employed in Ref. 81 consisted of comparing the experimental plots of log k versus E for Eu2+ aq app oxidation with an estimate of the "double-layer corrected" plot of log k corr versus E to obtain ¢ rp using eqn (7). The latter plot was obtained by extrapolating rate data from markedly more negative potentials, where 010; is not adsorbed, 81 by assuming that a - 0.5. The validity of this procedure COFF relies critically upon the correctness of this assumption. Although c a was found to be close to 0.50 for Eu3+ reduction over corr aq the potential range -700 to -900 mV,32 any changes in a corr at more positive potentials can lead to substantial errors in these estimates of log kcorr and therefore in the derived values of ¢rp using eqn (7). Indeed, the values of agpp in KPF6 electrolytes (Table 1) 2+ provide strong evidence that a < 0.5 for Buzz and Craq oxidation over a wide range of anodic overpotentials. An extreme a COP? upper limit to azorr under these conditions can be obtained by ignoring the effect of PE; specific adsorption. In the absence of specific ionic adsorption, the term ( 3¢ rp/a E)u appearing in eqn (8) is equal to cdl/cdiff’ where C and C f are the dl dif 61 overall double-layer and diffuse-layer capacitances, respectively. For concentrated solutions of symmetrical electrolytes such as KPFS, cdiff is calculated to be only weakly dependent upon the 88 absolute value of qm and independent of its sign. Therefore the magnitude of ( a¢ rp/ 8E)u should be approximately the same at a pair of electrode potentials on either side of the p.z.c. having similar values of I qml and C By inspecting the published 79 dl' double-layer data, such a circumstance is seen to be encountered for 0.0 fl.KPF5 for E a -200 mV and -700 mV vs. s.c.e. (where I qml is approximately 6 uC/cm2 and Cd, 2 22 and 20 uF/cmz, respectively). However, PF; is significantly adsorbed at -200 mV but not at -700 mV,79 so that any effect of PF; adsorption will make ( 8¢ rp/ 3E)u smaller at -200 mV. At these two electrode potentials, aa for Eng: oxidation equals 0.15 and 0.31, respectively app c a (Table 1). Since acorr a 0.50 and therefore acorr a 0.50 at E . -700 mV32 (eqn (6)), we conclude from eqn (8) that a :orr < 0.35 at -200 mV. Consequently it appears that the small values of aa seen for Eu2+ oxidation in KPF at anodic overpotentials app aq 6 must be due to values of aa that are also well below 0.5. COi'i' . a 2+ This finding leads to estimates of log kcorr for Euaq oxidation, obtained by extrapolation from more negative potentials, that are markedly smaller than those given in Ref. 81, yielding estimates of ¢ rp in perchlorate and chloride electrolytes that are much closer to the corresponding values of dgcs. In view of these results and those presented in Table 2, it appears that semiquantitative estimates of log kzorr and agorr can be obtained by using eqns (7) and (8), ¢rp being obtained 62 in the conventional manner from the net diffuse-layer charge density -(qm + q'). Figure 15 contains plots of ¢2CS versus E in 0.1 and 0.h fl.KPF5 which were obtained from the corresponding plots of (qm + qéF-) versus E derived from the double-layer data 6 given in Ref. 79. It is seen that for 0.0 !.KPF59 I ¢gcs I < 5 mV when -E < 450 mV. This is because qfiF = -qm at electrode 79 potentials positive of the p.z.c. In view of the relative 2+ values of A¢rp for Craq, Eu2+, and Vi; oxidation and Co(NH3)5F2+ aq reduction given in Table 2, together with the consistently good agreement between ¢rp and ¢3CS seen for the last reaction,22 . 2+ 2+ rough estimates of ¢rp and hence (3 45 ml 3E) for Craq, Euaq, and Vi: oxidation in 0.0 §_KPF6 were obtained by assuming that it rp equals 0.6 discs, 0.9¢gcs, and 0.8 4):“, respectively. The resulting estimates of ( 34> rp/ 3E) 11 were then inserted into eqn (8) along with the values of (lgpp obtained in 0.0 fl_KPF6 (Table 1) to yield the estimates of (izorr given in Table 3. (Although this procedure is subject to sizable uncertainties, these are unlikely to affect greatly the derived values of corr for -E ‘< #50 mV since the double-layer corrections are quite small under those conditions.) Similar estimates of (lzorr were obtained from the values of (lgpp obtained in 0.1 fl KPFG, and also in NaCth electrolytes using the published double-layer data for I-IClOA.88 However, the double-layer corrections are larger and more uncertain In perchlorate media as a result of the substantially greater specific adsorption of Clog. 2+ aq and Bug; oxidation decreases markedly as the electrode potential Inspection of Table 3 reveals that indeed <13 corr for Cr 63 20- 963” /mV. VI l I i . I -200 -400 -600 -8OO E/mV. vs. s.c. e. Figure 15. Plots of the potential across the diffuse-layer ¢ :CS against the electrode potential E for 0.0 fl and 0.1 fl KPF6. Key to symbols: 0.h fl'( 0 ), 0.1 fl.( l ) 6h .m.: um.: m—.: m_:.: ::p an.: n—.: mm.: :N.: m_:.: : mam.s m..= km.c s~.= ~s.s a..- m—:.: :~.: mm.: :~.: mmm.: :~.: ~:.: ::~n m::.: m~.: m_a.: -.: ~:.: _~.: m~:.: ::mu :a.: m:.: :c.: :m.: #4.: m~.: m~:.: :::n _m.: hm.: ~:.: 54.: mm:.: :a.: N..: ::mu am.: um.: m:.: m__.: :::u ~m.: am.: .m.: ~m.: :_.: ::uu mam.: ~m.: mmm.: :m.: mm:.: ::m. mmm.° sm.° °m°.= com- u_muAha v chow: u_muawa v ecowa o_ouahe V gnome .o.u.m m> >5 m N m N m N co_uao_xo WM> co_uno_xo ”mam co_umo_xo ”We: :Allwmmv m .m:: ._ovoE c0u0__.0mo u_cOEcns on: so.» ovum—no.0u u_muao.e v mucu_u_uuoou comment» u.mc_cuc. mc_ocoamuceou oz: cu.) vocnosou ._o_ucouoo opacuuo_o no co.uuc:m a no co_uno_xo WM> new .wwaw .WMcu can ccomo nuco_u_uuoOo commencu u_vo:c oouuoccou co>o_io_n:o: .m o_aoh 65 Notes for Table 3. l GCS d potential E in 0.4 §_KPF6, obtained from slopes of plot in Figure 15. Variation of diffuse-layer potential ¢ with electrode 2Anodlc transfer coefficient at stated value of E, corrected for the effect of the ionic double layer. Obtained from values of ea in 0.0 fl KPF6 given in Table 1 from eqn (8) using the app Ilisted values of ( 8¢ GCS d equals x( a¢ SCSI 3E)u , where x - 0.6, 0.9, and 0.8 for Cr 2+ aq / BE)u , assuming that (3¢rp/ 3E)u 2+ aq’ Eu , and Vi; oxidation, respectively (see text). 3 Intrinsic anodic transfer coefficient, calculated using eqns (11) and (12) (see text). 66 E becomes less negative so that (Izorr < 0.2 for -E '< 300 mV. These data are also presented as plots of log kzorr versus E in Figures 16-18, which were obtained by inserting the appropriate a . estimates of (brp together with log kapp In 0.0 fl KPF6 from Figures 12 and 10 into eqn (7). The corresponding cathodic segments log kzorr versus E that were obtained from measurements of kgpp in 0.0 §_KPF6 are also included in Figures 16-18. 3+/2+ Although the large positive formal potential for Feaq (+500 mV at an ionic strength of 0.211) precludes monitoring the kinetics of Fe:: oxidation at mercury electrodes, it turns out that the kinetics of Fez: reduction in KPF6 electrolytes are sufficiently slow so that pulse polarography can be used to obtain cathodic Tafel plots in the potential range 22' 300 to 0 mV. In 0.0 ! KPF6, kgpp is 1.3 x 10"2 cm/sec at a potential of +100 mV, and (Igpp is 0.50 I 0.00 for potentials between 200 a .. and 50 mV. Consequently, from eqn (6), a app - 0.50 under these conditions. Applying the same double-layer correction as for 2+ a ~ 2+ . . Craq oxidation using eqn (8) yields a’corr - 0.55 for Feaq oxidation at a potential of +100 mV. Rate measurements were also made as a function of temperature in the range 150 - 05°C for Cris and Eng; oxidation in 0.0 fl.KPF5' Using a nonisothermal cell arrangement with the reference electrode 11,89 so-called "ideal" enthalpies of 17.39 held at room temperature, activation AHIdeal were obtained from the Arrhenius slopes. Values of ‘A"(deal close to zero (0-2 kcal/mole) were obtained over a wide range of anodic overpotentials (+100 5. E .1 -050 mV); i.e., the anodic rate constants were found to be almost independent Figure 16. 67 Plots of the logarithm of the rate constant corrected 3+/2+ for ionic double layer effects log kcorr for Craq against the electrode potential E at the mercury-aqueous interface. Key: Solid lines are experimental values. Anodic rate constants shown for -E < -Ef, cathodic rate constants shown for -E > -Ef. Values of log k corr obtained from corresponding values of log kapp in 0.0 5 KPF6 (Figure 12) using eqn (7). assuming that GCS. 3+/2+ GCS ¢ rp equals 0.6 ¢d for Craq . ¢d for 0.0 g KPF6 taken from Figure 15. The dashed lines are the theoretically predicted curves from the harmonic Values of oscillator model which were obtained using eqns (10) and (11). The dotted lines are the anodic Tafel plots obtained by assuming that a - 0.50 at all potentials. Iog,o(kcm/cm.s") 68 l J l J / . -zoo -4oo -600 E/mV. vs. s.c.e. -800 Figure 17. 69 Plots of the logarithm of the rate constant corrected 3+/2+ corr q against the electrode potential E at the mercury-aqueous for ionic double-layer effects log k for Eua interface. Key: Solid lines are experimental values. Anodic rate constants shown for -E < -Ef, cathodic rate constants shown for -E > -Ef. Values of log kcorr obtained from corresponding values of log kapp in 0.0 fl KPF6 (Figure 13) usigg/gqn (7). assuming that GCS + + GCS ¢ rp equals 0.9 ¢d for Euaq . Values of ¢d for 0.0 g KPF6 taken from Figure 15. The dashed lines are the theoretically predicted curves from the harmonic oscillator model which were obtained using eqns (10) and (11). The dotted lines are the anodic Tafel plots obtained by assuming that a - 0.50 at all potentials. Iog|o(km/cm.s") .70 l I .Ef [1/ =-625m\l 1 E/mV. vs. s.c.e. '200 '400 ‘600 -BOO Figure 18. 71 Plots of the logarithm of the rate constant corrected _ 3+/2+ for ionic double layer effects log kcorr for vaq against the electrode potential E at the mercury-aqueous interface. Key: Solid lines are experimental values. Anodic rate constants shown for -E < -Ef, cathodic rate constants shown for -E > -Ef. Values of log k corr obtained from corresponding values of log kapp in 0.0 fl KPF6 (Figure 10) using eqn (7). assuming that ¢GC$ for V3+l2+ 0 equals 0.8 . '9 cos d '9 Values of ¢d for 0.0 fl_KPF6 taken from Figure 15. The dashed lines are the theoretically predicted curves from the harmonic oscillator model which were obtained using eqns (10) and (11). The dotted lines are the anodic Tafel plots obtained by assuming that a - 0.50 at all potentials. Iog.o(kcm/cm.s.") 72 I 1 I l L E a=--475m\/. ‘f l : -2oo ' -4oo E/mV. vs. s.c.e. “600 73 of temperature. The corresponding "ideal" entropies of activation AS+ ideal were found to change from £3. -30 to -20 3,". with increasing anodic overpotential over the same potential range. DISCUSSION The very marked decreases of 0.3 seen for Cris, Euiz, corr and Vi; oxidation with increasing "formal" anodic overpotential n a(.E-E:) contrast with the approximate constancy Of a 20,, 3+ aq reduction)“ over a substantial range seen previously for Cr (100 - 500 mV) of formal cathodic overpotential nc(-Ef-E). Decreases in the intrinsic transfer coefficient “I with increasing overpotential are indeed predicted by contemporary theories of electron transfer, arising from the expected curvature of the reactant and product free-energy surfaces in the intersection region.m’63 However, the theoretically predicted variations in the anodic and cathodic transfer coefficients (a 7) and calc (of) are very similar to, and markedly smaller than, the experimental calc with increasing anodic and cathodic overpotentials variations in (Izorr at anodic overpotentials. Using the harmonic oscillator model,1 (0')calc is obtained from* F(Ef‘E) (10) ( ai)calc . 0'5 + 2X where A is the Marcus intrinsic reorganization term. (Forms of eqn (10) have been written with either 2A or 01 in the denominator of the last term.10 As explained in Ref. 10, the form of eqn (10) written here follows from the definition of the electrochemical transfer coefficient at a given electrode potential E in terms of the tangent to the Tafel plot at E, i.e., a is taken as :(2-303/f)( 3log k/ 3E) , and is therefore consistent with the 70 experimental values of a a which were obtained using eqn (5).) 3P9 A is related to the double-layer corrected rate constant kzorr at the formal ("standard") potential by10 ks RT In(-552’-15) ' ’0 (11) where Z is the heterogeneous collision frequency, which is usually calculated from1 Z - (kT/ZITm)*. Taking the effective mass m of the present reactants equal to 200 yields 2 - 5 x 103 cm/sec. Values of kzorr were obtained from eqn (7) using ka obtained pp 3+/2+, k5 = 3 x 10'6 cm.s.-1; Eu3+l2+ aq corr aq :’2+, 7.5 x 10'” cm.s.-1. (Although these values naturally depend somewhat upon the assumptions used in Q in 0.0 !_KPF6: for Cr 3.5 x 10'5 cm.s.-1; Vi applying the double-layer corrections, the uncertainties in this procedure do not significantly affect the resulting values of (all The values of (a?) calc obtained from eqn (10).) 2+ aq’ Buzz, and Vi: oxidation are listed in Table 3 along with the a a a corresponding values of ‘xcorr' It is seen that (1corr < (a I calc calc obtained from eqn (10) for Cr over a wide range of anodic overpotentials. On the other hand, for electrode potentials negative of Ef, little change in 0 =(a,) The predictions of eqn (10) are also expressed as dashed lines COl'i' ac 0.5. (and therefore co rr) is observed, and a 3 corr calc in Figures 16-18. For comparison, Tafel plots generated by assuming that a - 0.50 at all potentials are given in Figures 16-18 as dotted lines. The experimental double-layer corrected Tafel plots clearly exhibit markedly more curvature than the theoretical plots at anodic overpotentials, whereas the opposite appears 3+ to be true at cathodic overpotentials, at least for Cra reduction.lh 75 In order to unravel the physical reasons responsible for these unexpectedly large variations in (,a it is instructive corr’ to ascertain whether they arise as a consequence of a given anodic overpotential for the reaction under consideration or from the particular electrode potential region where the effect is observed. -The latter situation would be expected If there are sizable contri- butions to the double-layer corrections beyond the averaged coulombic terms considered in eqn (8), so that acorr differs from the required intrinsic transfer coefficient 0'. Such contributions could arise from differences in reactant-solvent interactions in the bulk solution and in the Interphase or from discreteness- of-charge effects. All these double-layer influences can generally be taken into account by expressing them as "thermodynamic" work terms (c.f. refs. 7 and 90): a I- “a '- otapp ' 0‘l i 9% 6—3—5511 2'; ( ‘f—l‘) ("g-EL)” (12) where wr and wp are the work required to transport the reactant and product, respectively, from the bulk solution to the reaction site. If these work terms arise solely from averaged coulombic effects so that C! - 0', then wr - ZF ¢r corr and wp - (Z i a I)F¢rp; p and eqn (12) reduces to eqn (8). In all probability, the work terms ( awp/ 3E)u in eqn (12) will be approximately the same for the redox couples under scrutiny here for a given electrolyte and electrode potential, irrespective of their origin; the same is true of (awr/B E) u . From the form of eqn (12), if 0:” (or agorr) values for a pair of aquo oxidation reactions are markedly different at a given electrode potential, this difference must at least partly arise from differences in a? for the two 76 reactions. Also, if (a wp/ 3E) 11 = (awr/a E)u , the magnitude of the double-layer corrections will be approximately independent of a? anyway. The relative values of aa for Fe2+ and Cr2+ aq aq oxidation corr at a given electrode potential are of particular interest in this connection since Ef for Pegs/2+ (500 mV) is substantially more positive than Ef for Crag/2+ (-660 mV). In the region of electrode potential (+100 to 0 mV) where kinetic data for both a for Fe2+ corr aq Q reactions are available, oxidation ( = 0.5) is substantially larger than for Crgz oxidation ( = 0.20). In view of eqn (12), a? is also substantially larger for the former reaction, even if a i From eqn (10), the corresponding a . corr I at E - +100 mV are 0.60 and 0.33. respectively. s 2+ 2 -5 (An estimate of kcorr for Feaq of 1 x 10 cm/sec was obtained a values of (a i)calc by linearly extrapolating the cathodic Tafel plots to the formal potential.) . a + . The relative values of (xcorr for Viq oxidation In comparison with those for Cr:: and Eugz oxidation are also instructive since Ef for Viz/2+ oxidation (-075 mV) is significantly more positive than for Crag/2+ and Eugzlz+ (-660 and -625 mV). It Is seen (Table 3) that at a given electode potential, (1cor for the r former reaction tends to be larger than for the latter two reactions. However, at given values of na, all three reactions exhibit closely similar values of agorr' It therefore appears that the observed marked dependence of upon electrode potential (I COI’I‘ arise from variations 07 as a consequence of the anodic overpoten- tial itself. 77 Assuming then that the plots of log kco 3+/2+ aq ’ in Figures 16-18 approximate the desired plots after correction rr against anodic 3+/2+ 3+/2+ Euaq , and Vaq given and cathodic overpotential for Cr for all environmental effects, it remains to consider possible ways in which such asymmetry in the dependence of 0' upon the anodic and cathodic overpotentials could be generated. Some asymmetry will appear when the vibrational force constants for 10,91 the reduced and oxidized species differ. However, this effect 10 Another way in which such asymmetry is predicted to be small. can arise is when the work terms wr and wp markedly differ. Then if ( awr/ aE)Il and (3wp/38)I1 equal zero, it can be shown (eqn (87b) of Ref. 10) that instead of eqn (10) we should write (a,) - 0.5 1 Wu )(Ef-E) + (Np-erZA (13) calc Physically, the final term in eqn (13) accounts for the difference between the thermodynamic driving force F(Ef-E) for the overall reaction and the driving force associated with the free-energy barrier for the elementary electron-transfer step which determines a l' Consequently, a possible explanation of the observation a a that. acorr < ( a' calc (Table 3) is that there is at least one component of the work terms wr and wp other than the coulombic terms so that wr>°’ wp. However, in order to fit the values of in Table 2 with ( a7)calc obtained from eqn (13), values a “corr of (wp-wr)==11 kcal/mole are required. Such large differences in work terms between H3+ and M2+ seem unlikely. aq aq It is interesting to note that the observed shapes of the anodic and cathodic Tafel plots closely resemble those which are obtained from a theoretical nonadiabatic model involving 78 resonance tunneling via a localized electronic state in a surface film.92 Although such films are absent from the mercury-aqueous Interface, the inner-layer solvent could conceivably act in a similar fashion. However, the physical nature of the localized electronic states in this case are unclear. The remaining explanation for the observed behavior is that the free-energy surfaces which provide the elementary Franck- Condon barrier to electron transfer are inherently nonsymmetrical or of complex shape. An important property of Hi; oxidation reactions that may be responsible for such a circumstance is the substantial increase in solvent ordering that apparently 2+ 3+ attends the conversion of Maq to "aq’ which is manifested in extremely large "reaction entropies" A536 for such H232+ couples (where A53: equals the difference between the ionic entropies “1. of the reduced and oxidized halves of the redox couple At the formal ("standard") potential for the redox couple, the free- AH0 17 energy driving force AGO equals zero” so that TA 5° - A o 3+/2+ 3+/2+ 11 Since Src for Craq and Euaq equals 33. 50 e.u., then A.H° for Criz and Euiz oxidation equals ca. -15 kcal. mol."1 at their respective formal potentials. Consequently, these oxida- tions are highly exothermic so that the potential energy surfaces will be highly nonsymmetrical, and Increasingly so as the anodic overpotential is increased, since -A H° - TA 5:: + F(E-Ef). As explained in detail in Ref. 92, the measured "ideal" activation parameters are approximately equal to the actual enthalpic and entropic barriers to electron transfer. The finding that ZSH+ = 0 ideal for Criz and Fug; oxidations at anodic overpotentials therefore 79 indicates that those reactions are sufficiently exothermic so that the reactant's and product's potential-energy surfaces inter- sect close to the reactant's energy well. Admittedly, the depen- dence of the free energy of activation upon the overpotential (i.e., upon the free-energy driving force 136°) should be given by eqn (10) irrespective of the individual enthalpy and entropy of activation, providing that the resulting free-energy surfaces are parabolic. In the present case, the observed small values of AH+ would be expected to be accompanied by small values of A S 1.because the transition-state structure should closely resemble that of the reactants. Instead, substantial values of 155+ are obtained for the oxidation reactions so that 05+ 5 0.5 05° even when AH r550. This anomaly may arise from the need for the solvent molecules in the immediate vicinity of the Hi: reactant to be oriented strongly via hydrogen bonding with the aquo ligands11 in the configuration similar to that appropriate for the solvent 3+ 11 _ 11 structure making Maq product prior to formation of the transition state. These solvent structural changes may be envisaged as occurring in a separate step prior to the normal inner-shell reorganization and long-range (dielectric-continuum) solvent polarization leading to the formation of the transition state.10 Such a mechanism would indeed lead to the observed asymmetric shape of the anodic and cathodic Tafel plots since one can show that ( d.) would then be given by a relation similar to eqn (13). calc only with (wp-wr) replaced by the free energy required for the prior solvent-reorganization step. 80 Irrespective of the detailed reasons for the observed behavior, it seems likely that the observed Tafel plot asymmetry is associated with major differences in short-range solvent polarization between the reduced and oxidized aquo species. The electrochemical reac- tivities of these aquo redox couples also exhibit anomalously large dependences upon the nature of the electrode material, which have been ascribed to varying interactions between the aquo ligands and inner-layer water molecules.93 The present conclusion that adsorbed perchlorate as well as halide anions induce changes in ¢rp for Euiz oxidation that are comparable to the effect of the electrode charge removes the puzzling anomaly arising from the earlier conclusion of Ref. 81, being in harmony with the similar results seen for the effects of a number of anionic adsorbates upon the outer-sphere reduction rates of Co(lll) amine co111plexes.22’23 Taken together, these results demonstrate that the simple Frumkin model embodied in eqn (7), if generalized to take into account differences between ¢rp and ¢rp arising from the possible noncoincidence of the reaction plane and the o.H.p., has so far been consistently and surprisingly successful in describing the effects of specific anionic adsorption upon the electrode reaction rates of simple cationic metal complexes. Although individual discreteness-of- charge effects could well play an Important role, their net influence appears to be relatively small for these outer-sphere reactions. Substantial differences have been reported between the prediction of eqn (7) and the experimental double-layer influences upon the rates of Eu:+ q and Vi; oxidation in extremely dilute (millimolar) 81 supporting electrolytes. However, these discrepancies partly arise from the use of the same double-layer analysis as in ref. 81, i.e., from assuming that (I: - 0.50 for Eu2+ and V2"- oxida- orr aq aq tion at all electrode potentials. ADDENDUM As a complement to studies on (structuring) aquo complexes in structured solvents such as H20, the electroreduction kinetics of Co(NH3)5F2+ was examined over several orders of magnitude in rate to see if the lack of curvature in reduction Tafel plots in water is specific to (structuring) complexes with water in the primary coordination sphere. Results described in Chapter 111 indicated that reliable rate data could be obtained for this complex in neutral 1 §.KF from pulse-polarographic data taken at sampling times as short as 300 usec. Pulse measurements in the range of 500 usec to 50 msec were coupled with dc measurements, including foot-of-the-wave (activation-controlled) measurements on concentrated solutions. A 30 mg solution was prepared by dissolving solid [Co(NH3)5F](Cth)2 in 1 !_KF. Its dc poiarogram was well behaved until close to the top of the wave, which at about -000 mV against SCE is very close to the pzc. Pronounced depression in the currents was observed for more negative potentials, making rate measurements unreliable. (However the kinetic parameters are to be derived, the limiting current must be known, even if only aproximately: use of 90: of the wave (in terms of llilim) requires accurate knowledge, and the applicability of the assumption that the current is activation-controlled relies on the current being less than 82 15 to 20% of the limiting value.) The use of a pulse-polarographic limiting current in conjunction with previously characterized ratios of pulse to do limiting currents was vitiated by the observation of similar, albeit less extreme, behaviour in the pulse polarogram. A tenfold dilution of this solution by supporting electrolyte produced well-behaved dc and pulse polarograms; the poor limiting- current behaviour of the concentrated solutions is probably due to base-induced precipitation which results from the release of ammine ligands at the electrode surface from the labile reduced cobalt moiety. However, kinetics analysis of the concentrated-solution polarograms using limiting-current values which were ten times larger than those obtained from the diluted solution produced - rate constants and apparent transfer coefficients which were significantly disparate from those of the dilute solution. The roughly 82 difference in ionic strength due to concentrated complex may be responsible for this. Use of limiting-current estimates from the original concentrated-solution data prior to the onset of current depression yielded kinetic parameters which agreed well with values from the dilute solutions in the potential regions where kinetic parameters are accessible from both data sets. The Tafel plot for the system, shown in Figure 19, spans more than four orders of magnitude in rate and shows upward concavity, in contrast to the plots for aquo oxidations and to theoretical predictions. Essentially linear behaviour was seen at the highest rates, rather than downward curvature. Because the smallest rate constants were obtained from concentrated solutions prepared from the perchlorate salt, the possiblity exists that the upward 33 Co(NH3)5F2+ reduction 00m tillllTlllrllelelTIlTTlllllllllTlllTll[liTllllW‘lTlWlillll‘ - 1— d p 1- d — c1 1— .- I- an - cl _ ‘ I. . 1 t '1 .1 - - h d I. d b d h d — - I— d A P d - _ q I - .. t .1 q .— .1 P - p - — ‘ t -1 .1 v I- q 8 " " 1- .1 - d b a l- .1 I- d — q - -I l— - 1 I— -1 — III - -1 I- d - -1 i- d — - 1- q - -I — u 1— d In I- D d D I I- d 1 1 1 1 1 . 11111L111 11111111 111111111111111111111111111 111111114 -B.OO 0.0 -O.6 Pouwukfl 6me) Figure 19. Rate-potential plot for Co(NH3)SF2+ reduction in I " KF. 80 curvature of the Tafel plot results from a rate enhancement which is produced by anion adsorption, particularly the specific adsorption of perchlorate. An ion-exchange technique was used to make a stock solution of I)o(NH3)5F2+ which was ostensibly free of perchlorate. An anion-exchange column of AG 1-X2 in the fluoride form was made from enough resin to present an approximately ten-fold excess . of exchange capacity over the amount of perchlorate in the sample. The solution of the prechlorate salt (enough to make 5 ml of a 15 mg stock solution) was introduced into the column and eluted by water. The absence of perchlorate was inferred from the lack of a precipitate produced by a drop of eluate in 2 H_KF; since a saturated potassium perchlorate solution is about 30 NE at room temperature, the residual perchlorate concentration was less than 0.5 mg. The complex-containing eluate was reduced in volume by vacuum distillation, enough solid KF having been added to make a 1 fl_solution, and diluted to volume. Both the stock solution and a solution diluted tenfold by electrolyte gave reasonable pulse and dc polarograms. The foot- of-the-wave kinetic parameters obtained from the dc polarogram of the stock solution produced less curvature in the Tafel plot than those from solutions containing perchlorate, but again upward concavity is present. It remained to correct the rates for coulombic double-layer effects; corrected transfer coefficients were obtained from (3¢/3E)u and the apparent transfer coefficient. Values of this derivative were approximated from capacitance ratios by assuming that (1) 85 there is no specific adsorption of electrolyte or reactant; (2) the Galvani potential at the reaction site is given by the Gouy- Chapman theory; and (3) the inner-layer capacitance depends only on the electrode charge. Using double-layer capacitance and electrode-charge values from Parsonsgh for 0.79 H NaF, and diffuse- layer capacitances from GCS theory, the inner-layer capacitance as a function of electrode charge was calculated. These values, coupled with diffuse-layer capacitances calculated for llfl solutions, produced the necessary transfer-coefficient corrections. The corrected values of the transfer coefficient showed even more disparity from the theoretical predictions. It would seem that the specific solvent-structuring argument for the pattern of the potential dependence of the transfer coefficient continues to be appropriate. CHAPTER V. SOLVENT ISOTOPE EFFECTS UPON THE KINETICS OF SOME SIMPLE ELECTRODE REACTIONS 86 87 INTRODUCTION It has been known for some time that sizable changes in the rate constant of homogeneous electron transfer reactions between transition—metal complexes occur when heavy water (020) is substi- tuted for 1120.95"97 These solvent isotope effects have been attributed to "secondary" isotope effects arising from differences in reactant- solvent interactions as well as to "primary" isotope effects arising from the replacement of hydrogen by deuterium in the 96'98 Studies of coordination sphere of the reacting cations. deuterium-isotope effects in electrode kinetics have largely been limited to the important but atypical cases of hydrogen 99’100 and no isotope effects upon the kinetics and oxygen evolution, of simple outer-sphere electrode reactions have apparently been reported. Nevertheless, it is anticipated that such studies could shed light on the role of the solvent in outer-sphere processes. In particular, the dielectric properties of H20 and 020 are almost identical; and yet the mass difference between H and 0 yields significantly different hydrogen-bonding properties, so that these measurements could in principle provide a means of assessing the importance of specific solute-solvent interactions to the kinetics of electron transfer. In some respects, electrode reactions are more suitable than homogeneous redox processes for such fundamental studies since the former type involves the thermal activation of only a single redox center. Also, the comparison between the solvent isotope effects observed for corresponding homogeneous and electrochemical reactions involving transition-metal complexes could provide clues as to the similarities and differences between 88 the reactant-solvent interactions in the bulk and lnterphasial redox environments. For this reason, we have examined the effect of replacing H20 solvent with 020 upon the electrode kinetics of a number of aquo and ammine complexes for which the solvent isotope effects upon outer-sphere homogeneous reactions involving these complexes have previously been scrutinized.96’98’1m"103 These reactions 3+/2+ 96,101 a include Fe q self-exchange and the reduction of Co(IIl) ammines by V2: and Cr:;.102’103 Although the sizable (factor of two) ratio of the rate constants in H20 and 020 (kH/kD) for Fegzlz+ self—exchange was originally attributed to the presence 101 of a hydrogen-atom transfer mechanism, similarly large values of kH/kD have been observed for cross-reactions involving aquo 96,102,103 Ne complexes for which this mechanism is ruled out. have recently measured the solvent isotope effect upon the formal electrode potentials Ef of a number of transition-metal redox couples.10h For couples containing aquo or hydroxo ligands, large differences in Ef between H20 and 020 were observed that appear to be at least partly due to hydrogen bonding between these ligands and the surrounding solvent.104 It is of Interest to determine how these thermodynamic differences are reflected in the electrode kinetics of such complexes. Studies of isotope effects for substitutionally inert ammine and ethylenediamine complexes are also of particular interest since, in contrast to aquo complexes, the deuteration of the ligands and the solvent, i.e., the primary and secondary isotope effects, can be investigated 89 105’1°6 The results of these experiments are reported separately. in the present chapter. EXPERIMENTAL The Co(III) and Cr(lll) complexes were synthesized as solid perchlorate salts using the procedures noted in refs. 23 and 3+ aq were prepared by dis- 33, respectively. Stock solutions of Eu solving Eu203 in a slight excess of perchloric acid, and those of Cr3+ as described in ref. 32. Solutions of Eu2+, Cr2+, and aq aq aq Vi: were obtained in the appropriate electrolytes by electrolyzing 2:, Griz, and V(V), respectively, over a stirred mercury pool at -1100 mV. vs. s.c.e.; V2: was formed by reoxidizing 3+ Bq solutions of Eu Vi; at -300 mV. vs. s.c.e. The source of Fe was Fe(CIOh)3 (G.F. Smith Co.). Potassium hexafluorOphosphate (Alfa Ventron Corp.) was thrice recrystallized from water.' Sodium perchlorate was prepared from sodium carbonate and perchloric acid and recry- stallized prior to use. Stock solutions of lanthanum perchlorate were prepared by dissolving La203 in a slight excess of perchloric acid. The use of aqueous reagents such as 702 perchloric acid generally introduced only small ( <12) amounts of water into the resulting DZO solutions. The Co(III) and Cr(III) ammine and ethylenediamine complexes were deuterated by dissolving the protonated perchlorate salts in the minimum amount of 020 containing 1 m! hydroxide ions. The amine hydrogens are rapidly deuterated 105 under these conditions. These stock solutions were then added to the appropriate electrolyte in H20 or 020 acidified with suf- ficient perchloric acid (usually 5-10 mg) to suppress completely the exchange of amine hydrogens on the timescale of the kinetics 90 experiments. Water was purified either by means of a "MilliQP purification system (Mlllipore Corp.) or by distillation from alkaline permanganate followed by "pyrodistillatlon",11 with identical results. Deuterium oxide (99.82, Stohler Isotope Chemicals) was used either directly or following distillation from alkaline permanganate, again with identical results. All solutions for electrochemical scrutiny were deoxygenated by bubbling with pre- purified nitrogen, from which residual traces of oxygen were removed by passing through a column packed with B.A.S.F. R3-11 catalyst heated to 100°C, and then humidified by bubbling through either H20 or 020, as appropriate. Kinetic parameters were obtained at a dropping mercury elec- trode (flow rate 1.8 mg/sec, mechanically controlled drop time 2 sec) by means of normal pulse and d.c. polarography using a PAR 170A Polarographic Analyzer coupled with a Hewlett-Packard 7005A X-Y recorder. The kinetic analyses of these irreversible polarograms employed the methods due to Oldham and Parry,8h which allowed rate constants in the range 22. .IO-h to 0x10.2 cm/sec to be evaluated reliably. The electrochemical cell used for the kinetic measurements consisted of a working compartment containing ca. 5 ml of the solution of interest in either H20 or 020, which was separated from the reference compartment by means of a glass frit ("very fine" grade, Corning, Inc.). For experiments where bulk electrolyses were performed, the platinum-wire counter electrode was located in a third compartment which was also separated from the working compartment by a glass frit. The reference compartment was filled with an aqueous solution of the same ionic composition 91 as in the working compartment, in which was immersed a commercial saturated calomel electrode (s.c.e.). When using strongly acidic electrolytes, the reference compartment was filled instead with saturated aqueous NHhCl in order to minimize the liquid-junction Oh The solvent liquid-junction potential between the potential.1 H20 and 020 solutions is probably negligible ( <"1»2 mV) using this cell arrangement , as evidenced by the essentially identical formal potentials obtained in H20 and 020 for ferrocene/ferrocinium 10” (Both and Fe(bpy);+/2+ (bpy - 2,2'-bipyridine) redox couples. these couples are expected to exert only a small, nonspecific influence upon the surrounding solvent.) Consequently, a given cell potential E measured in a given electrolyte in H20 and 020 will correspond to essentially the same, albeit unknown, value of the Galvani metal-solution potential difference 0m in both solvents. (See ref. 100 for a detailed discussion of this point.) All electrode potentials are therefore quoted versus an aqueous s.c.e. using this cell arrangement, unless otherwise noted. All kinetic parameters were obtained at 25.0 3.0.10C. RESULTS 5322 Complexes Since large differences in the formal potential, 15E2-H, are observed for redox couples containing aquo ligands when changing from H20 to 020 solvent,10h it is of particular interest to examine the corresponding differences in their electrode kinetics. Reac- tions that have been found to be suitable for scrutiny at the mercury-aqueous interface are Fegz/2+ at cathodic overpotentials, and Cr3+l2+ V3+/2+ 3+/2+ at both cathodic and anodic aq , aq , and Euaq 92 overpotentials; "aq" denotes OH2 or 002 ligands in the appropriate 3+/2+ 89 u - 0.5(H20)] is positive of the potential where mercury dissolution solvents. (Although the formal potential for Fe [095 mV, occurs in noncomplexing media ( >350 mV), we have found that well-defined normal pulse and dc polarograms can be obtained for Fez: reduction in acidified KPF6 or NaCth over the potential range 53. 300 to -100 mV. on account of apparently very slow exchange kinetics for Feiz/2+. To our knowledge, no previous 3+/2+ measurements of Fe 89 kinetics at the mercury-aqueous interface have been reported.) When comparing electrochemical rate constants in H O and 020, it is desirable to correct the relative rates 2 for differences in the ionic double-layer effect between these . solvents. By assuming that this correction can be calculated using the simple electrostatic (Frumkin) model, we can express the ratio of the observed (apparent) rate constant for a given one-electron reaction in H20 to that in 020, (kH/kD)app, as (cf. ref. 22): H D _ H D _ A D-H log(k /k )app log(k /k )corr (f/2.303)(<3corr :_Z) ¢rp (10) where (kH/ko)corr is the corresponding isotopic rate ratio corrected for ionic double-layer effects,22 A¢ 3;" the average potential on the reaction plane in changing from is the alteration in H20 to D20, Z is the reactant charge, a corrected transfer coefficient, and f-F/RT. (The plus/minus corr IS the double layer- sign in eqn (10) refers to electrooxidation and electroreduction reactions, respectively.) In order to estimate A¢>2;H, plots of the excess electrode charge density qm against the electrode potential E are required in both H20 and 020. Figure,20 consists 93 I I I I I __ 1M KFiHZO) 0" -..-- 1M KF(DZO) -2— N l . s -4... U . =1. ‘\ E CT -6?- -8..— -lo I I I I -400 '600 -BOO E/mV vs. aqueous see. Figure 20. The excess electronic charge density qm of mercury in contact with 1 M KF(H20) and l‘M KF(DZO) electrolytes versus the electrode potential E . 90 of a pair of such plots for 1 M_KF. These were obtained by inte grating the capacitance-electrode potential curves for these 90,107 electrolytes along with the following values of the potential of zero charge that were determined by the streaming potential method:77 1 M_KF(HZO), -030 mV; 1 !_KF(D20), -000 mV vs aqueous s.c.e. It is seen from Figure 20 that the qm-E plots for H20 and 020 are quite similar, although it is interesting to note that the plot for 020 is displaced significantly relative to H20 at the most negative potentials. Since fluoride anions are not significantly specifically adsorbed within this potential range,76 these electrode-charge displacements at fixed values of E, (A qm):-H, presumably arise from differences in the inner-layer structure between H20 and 020. For most of the reactions considered here, either 0.0 !_KPF6 or 00 m5 La(Cth)3, rather than fluoride, supporting electrolytes were used In order to minimize the extent of ion- pairing and to enable acidic solutions to be used; there is exten- sive information available on the magnitude of the double-layer corrections for the present reactants in these electrolytes.‘5’22’23’32’33 Although both 0.0 !.KP55 and 00 mg La(ClOu)3 exhibit significant anion specific adsorption at positive electrode charges, the extent of adsorption is small at potentials more negative than ca. -500 mV and -650 mV, respectively. Under these latter condi- tions, the relative qm-E curves for these electrolytes in H20 and 020 will be closely similar to those given in Figure 20, so that the required double-layer corrections to the observed rate ratios (kH/kD):pp could be obtained to a reasonable approximation 95 in the following manner. The value of ( Aqm)g'H at the appropriate value of E was read from Figure 20 and the corresponding difference in the diffuse-layer potentials pd between 020 and H20 in a given electrolyte, ( 04> (pg-H, obtained using Gouy-Chapman theory. The corresponding values of ( 0¢ d)g-H were obtained by assuming that 045”) - 0.7 A ¢d and A¢rp - (“id for 0.0 M KPF6 and 00 mg La(Cth)3, respectively, as indicated from earlier studies.15’32 These values of ( A oouoac mc_ocoemueeou Eocm ooc.ouao mou>_oLuuo_o mc_ueooeam 05mm c. _m_ucouoa Au \ sm.: mm.: s:.: n:.: m:.: mm.: mm.: sm.: ma.: ma.: can 6 x no. ox scam oo:_auno .nucmuuooc once mo n_m>_oLo>: mmoeaqam ou ::_uzl :5 :—1 1m so.) oo_m.o.u<~ m-e.xe.m m-e.xm.m m-e.xs.s m-e.xm.m m-e.x..~ m-e.xm.~ :1c—xm.m e-e_xm.~ m-e.xm.m m-e.xm~.~ .00m .50 can ux Fl N Leou new a ::N .o.o.n N: .n> >5 m o x acoumcou oumc oouuoccou Lo>m_1o_a:oo :0 Oman: .. o~e mAeo_o:eu me e: e~= .. e~e :uex_m e.e o~= .. owe eeex_m e.e eN: .. e~e m.ee.e... me es ow: .. eNe :uex m.e.e oN: ou>_oLuuo_m acu>_om — .ooomcouc. naoooo<1>czucux as» an mu_uoc_x co_uo:ooe0euuo_u as: con: uuuoemu vacuom_ aco>_om : soc: owe—ouao .uco_u_mmoou commune: acoeoooa o_oozumum. u use co_uon_eo_oo co_m:mu_o Lo» oououceou >u_mcoo ucoeeao ._o_ucouo: uooLuuo_u ooumum um acouchU came “anemone u_oo;uo:~ _ acmuumox .e u.euh 97 selected electrode potential and an apparent cathodic transfer coefficient aapp’ found from aapp =- -(f/2.303)( 3 log kapp/a E)u . The corresponding double-layer corrected rate ratios at a fixed electrode potential, (kH/kD):°rr, are also given in Table 0. (Since essentially identical values of <1 and hence (I app corr were measured for a given system in H20 and 020, these rate ratios will be approximately independent of the value of E chosen.) D)E H It is seen that the values of (k /k corr are comparable to, or somewhat less than, unity. However, a given electrode potential corresponds to larger cathodic overpotentials in 020 than in H20 since values of Ef for these couples are markedly less negative in the former solvent.107 The cathodic Tafel plots were there- fore extrapolated to the appropriate formal potentials for each couple measured in H20 and 02010“ to obtain the "standard" apparent rate constants (ks)app listed in Table 5. These results are also presented as ratios of (k ) 5 app These rate ratios were corrected for a given redox couple in H o and 020, (kg/k0) 2 s app' for the effect of the ionic double layer as noted above, except M)D'H that values of ( Aq and hence Am_ u_a:oo u_:o. agu no aoouuo ocu ace oouuoccoo .oN: ocm :N: :. acnumcou oume ocmocoun mo o_umm A.— m.— m.N m.— LLOU n e m A:x\: 1:0.a_mcoch 050m :0 mucouncou ouoz Ann—EosuoLuuo_m ocoocoum as» con: auuomum cacao»..ucu>_0m x. oum_L:oLq:o on: o: m mnmeo> N.— m.— a.: mm.- 000 EU Fl can a Ae : m x\:xv .Auxou oomv Aa—v coo m a N .e e e. one» o. e~ : c. ueaumcou puma ocmocmum acoemaao mo o_um¢ .mm mo o:_m> aeox no. mo mac—a m:_um_o:meuxo >n oo:_ouao .ucoumcou bane :oeoocmum: acoemaa< m .a:_ .eoc seem coxoh .uco>.0m :N: Lo» :N: mc_u:u_umn:m :. mm c. unamLUN .a:_ .moe Eco» .numcueum u_co. ouo_caocoqo um o.::0u xooae com _o_ucouoa .mELom. e-e_x:.~ : m_e- eNe : m . m a 1. 1 ~ on :1:—x: m A :Auvo: :5 :: NNo : : +N\+m:u :-e.xe.m . : «me- e~e : .xu. : .1 . mm N 1 :N: om> :1e.xm.e : . eee- cue : e 1 mm N m1:—x:.N max z a.: mmw1 : : : QIQ—XN.N : 0°01 ONO 2 x . m a a IE mm m 1 N one m1:— : — A :.u: 4 z :a m m : : +N\+m : s-c.xm.m e emm e~e : x e I. . m: m N one 91:. m max t a : m a o : +m\+m m .o.o.n eem >Ee oN: .ws >2 ax . ou>_ocuuo.u :1:m — m acu>_0m o_n:ou xoooz N m .no_::o: osc< .ouoz .m oAnmh 99 Ammine and Ethylenediamine complexes The effects of separately deuterating the coordinated ligands and the solvent upon the irreversible electroreduction kinetics23 of various Co(III) ammine and ethylenediamine complexes are sum- marized in Table 6. Some corresponding kinetic data for several Cr(lll) ammine and ethylenediamine complexes are given in Table 7. Since essentially linear Tafel plots were obtained over the measurable overpotential range (ca. 300 mV) for each system, the kinetic parameters are again conveniently summarized as values of k3 PP at a selected electrode potential along with the corresponding values of G . The listed isotopic rate ratios (kNH/kND)E app corr O)E H00 and (k 2 /k 2 corr resulting from deuterating the ligands and the solvent, respectively, were obtained from the appropriate pair of apparent rate constants. As before, the latter ratios were corrected for the differences in double-layer structure between H20 and 020 using eqn (10), assuming that A¢rp - A¢d.23’33 Unfortunately, the values of Ef and hence ks for the ammine couples are unknown on account of the lability and thermodynamic instability of the reduced complexes. Inspection of Tables 5 and 7 reveals that separate deuteration of the solvent and the reactant's coordination sphere can both have substantial influences upon the electroreduction rates measured at a fixed electrode potential. The latter effects are largest for the reduction of Co(NH3)g+ and Cr(NH3)g+, where deuteration of the ammine ligands produced isotopic rate ratios (kNH/kND):orr that are around two in both H20 and 020 solvents. Values of ND)E corr Co(|ll) ammines and Co(en)§+ (Table 6). On the other (kNH/k considerably greater than unity are also seen for other 100 mm.c lo—xm.m : : ONO m.N e 1. _1 N m:.e m15.x...N .eem- :eg ze _+ex z . o z ee.e s-c.xm.e : : eNe mee.e N :o.: ::_xm.m : : : : me.— Nme.. ::.e m-e_xm_._ : : oNe eNN.e . e _1 N :m.. ::.e m-e_xe._ eem- meg z e.e e : Ne.e N-e.xm.N : : eNe me:.e N me.e 1e_xe.N : z e = m... N N hm¢.— Nm.o NIO—Xm.m : : O o .:.e . .1 : eme._ no.5 N-e_xm.N eem- eeex : 5.5 eN: :N.e :-e.x:.m : : eNe mse.e N eN.e -e.xm.N : z e : em._ 5 N . NO.N wh.o 1°—XN.N : : O a mN.e e m m .1 . N em.N eN.e e-e_xa.m eon- meg z a e o z 7100.... EU m0.u.m LLou eeou Leou new one o z n) >5 we ”AeNexxeNxx: “Aezxxzzx: x u uu>.e.uuu.m ueu>.om m a m N A _ .aoxo_o50u oc.5a_oocu_>zuu ocw oc_55< A.._Vou oEOn mo mu.uoc_x co_uu:ooeoLuuo_u ecu coo: muoomeu uncuOn. >Loocooom oco >co5_e: + NoomAmozv0u m m +N=e A zzvou m m +Nm A :zv0u m m +Nm A :zvoo N +m N +m N +m N +m eem.me2:oU :OmAmonOu eem.mzz:0e zomAmzzvou : m +mA :zvou +mAm=zveu acauuoux .: o.eae 101 onQEOo ooumeouaoo onQEOU oouo:0uoLeM eNe e.A eN: e. .ux0u ecu c. oocAAuso no AaAv coo :c_m: oamx mo mo:_m> ovumAA m:_ocoomoeeou 50ee ooc_munw .LcowA:x\:xv .QN: :— onQEOo ooumeouaoo go: away ou :N: c. onaeou pouncoAOLQ Lou Leoux no o_uo¢m .AaAv coo ::_m: coax 505m ooc_oun: .quA an «c52Aou c. ooumo_oc_ mou>AoLuquo :cAALoaeam c. ocm _m_ucouoa oooeuquQ an :N: c. umzu o: :N: e. moxaAQEOu ooumcouauo Lo ooumcouoLa Lo;u_o com Leoux mo o_um¢ one eeou : . mA:zx\:zxv I uA:zx\:zxv oa>AoLuquo ::_u50qa:m 05mm c. cam N N oUCAm x mo mo:_m> ovumAA chocoamoLLOU 50cm oocAmunc .ooumu_oc_ mm o : co 0 : eo:u_o c. oucamooE .umoA um mesa—cu :— oouou_oc_ mou>AOcuquo m:_ucoaaam :— ocm AmAACouoa oooLuquo um LLOU moonQEOo oouocouaoo oco ovum:0u0ea ac.oconmueeoo Lo» x nu:~um:0o can; oouuoeeou Lu>oA1oAaaoo mo o_um¢ m N A .5 tea c moAamh Lam mouoz .Amv coo 505A oo:_ouno .acoAuAmmoou commcoeu UAoOzuou ucocmoa< .u _o_ucouoa oooeuquO oououm an acoumeoo ouoe quozuau Aucoeoaaov oo>eomao :m.e s-c.x_.e : : eNe : m_A.e N m e mm.° A~Io—Xm.N : 2 O 3 +MA cavOU N... Am:.. :m.e e-e_xm.m : : oNe : :QA.e : .1 N m z e:.. :m.e e-e_xe.e eon- meg : 5.5 e 2 .mA euveu Alcoa EU mo.u.m O z a) >5 ccou Lcou ecou one can we uAeNex\eN=x: ”Aezxxzzx: x N uu>_e.uuo_m ueo>_om Nemuumue m a m N A AooacAucoov e vonh 102 me.e m.eAxNN : : o e : NS... A 1 N m m m:.e m-e_xe.. eem- .ouu :5 e: e z +Nmoz A zzvto A em.e m-e_xm.N : : eNe : a .: 1. : em.e m1.:xN.N eem- mAee_o:oo.ze e: eN= .mAzeuveu MN.O MIO—Xm.w 2 2 ONO +MANOOV:AM=vaOIU :NA.e m e .1 N N N a m AA.e m-e.xe.A eem- A e.uveu 2e e: o : +mA go: A zzveo-u NQ.O ANIO—XOom 2 2 ONO . 2 mam.e N o m N:.e e-e_xm.m : z e z +MA 52:.u a... . N A..N No.5 m-e_xm._ : : e e : Na... m .. 1 N e N me.N N:.e m-e_x_.. eem- A e.uveu :5 e: e : +mA 22:.9 AIUOm Eu m0.u.n Leou ecou ccou new one o z n> >5 we uAeNex\eNzx: mAezx\=zx: x N uu>.oeuuo.m ueu>.om uemuumue m a m N A .noonQEOU ocAEvouco_>:um oco oc_55< A.._veu 050m mo nuAuoe_x co.uu:ooeoLuquu osu coo: nuuoemm cacao». >caocooom oca >La5.cm .N oAnmA 103 hand, substitution of H20 by 020 solvent for a reactant with either protonated or deuterated ligands generally resulted in noticeable rate decreases, so that the listed values of (kHZO/kDZO):orr are uniformly less than unity (Tables 6 and 7). Also listed in Tables 5 and 7 are the net isotopic rate ratios (kH/kD)Eorr resulting from deuterating both the ligands and the surrounding solvent. It is seen that in every case (kH/kD)Eorr > 1. Nearly all the reactions listed in Tables 6 and 7 are believed to occur via outer-sphere mechanisms.23’33 The one exception is the reduction of Cr(NH3)5NCSZ+, which probably occurs via a thiocyanate-bridged pathway.33 It is interesting to note that there were virtually no variations in aapp observed for a given system as a result of deuteration of either the ligands or the solvent, at least within the experimental reproducibility of (lapp (+0.01-0.02). The notable exception is Co(NH3)50H2+ reduction, which exhibits significntly smaller values of (xapp in 020 than in H20. Unfortunately, basic solutions (pH 9) were required for this reactant in order to suppress the protonation of the hydroxo ligand; this prevented the separate study of primary and secondary effects since the ammine hydrogens are rapidly exchanged with the solvent under these conditions.105 The diffusion coefficients 0 obtained from the polarographic limiting currents were generally smaller for a given complex H O D O in D20 than in H20. The diffusion coefficient ratios 0 2 /D 2 3+ were typically 1.35:0.05 for Maq complexes and 1.2-1.25 for Co(lll) and Cr(Ill) ammine complexes. Deuterated ammine complexes also exhibited significantly (3-82) smaller diffusion coefficients 100 than the corresponding protonated complexes in both H20 and 020. The observed DHZOIDDZo ratios are roughly consistent with the higher viscosity of 020 (1.107 cP) compared to H20 (0.8903 cP):1°8 inserting this viscosity ratio into the Stokes-Einstein equation‘09 yields o"2°/o°2° - 1.243. DISCUSSION Interpretation of observed isotopic rate ratios In order to interpret the substantial kinetic isotope effects presented in Tables 0-7, it is useful at the outset to consider the fundamental significance of the isotopic rate ratios (kH/kD)E ”1 s corr‘ orr and (kg/k Consider the generalized electrochemical reaction ox + e-( ¢m) ' red . (15) We can express the free energies of the thermodynamic states prior to, and following, electron transfer (labeled states I and II, respectively) as”0 a? . 62x + u:- - F 1m (16) 671 ' (.;:ed (‘7) -o -o where Gox and Grad are the partial molal free energies of the oxidized and reduced species, respectively, and u:- is the chemical potential of the reacting electron. Since the overall free energy 0- II equal zero when ¢m - ¢; (the standard Galvani potential corre- of reaction .AG°( - c a? ) for eqn. (15) will by definition sponding to the experimental formal potential for the redox couple), then -o -o 0 red - Gox . -F¢1n (18) Although neither absolute nor even relative values of d>; in 105 different solvents are strictly thermodynamically accessible quantities, as noted above the electrochemical cell arrangement used here allows the measured differences in formal potentials in 020 and H20, 10E2-H, to be equated to a very good approximation (:1 mV.) with corresponding difference in 10;, ( A1 and AEg-H <:0 for each of these reactions (Table 5). The latter result indicates that A(§:ed - 6° )D'H ox 3+/2+ aq 9 is -l.3 kcal/mole ]. This finding has been interpreted in as (k:/ 0(60 _ 6° )D-H is negative (eqn. (19)) [8-9- f0“ Cr red ox 108 terms of the relative destabilization of the oxidized species M2; in 020 resulting not only from deuteration of inner-shell water molecules but also from the greater ”solvent-ordering" tendency11h of M2; in 020 compared to H20.10h Evidence supporting this latter contention includes the especially large values of 3+/2+ 11 aq couples; this result 3+ aq reaction entropies 05:6 for these M probably arises from hydrogen bonding between the M aquo ligands 2+ aq' is observed in 020 (05.0 e.u., u n0.2) than in H20 (03.2 e.u.)10h which is which is partly dissipated when the cation is reduced to M A significantly larger value of 05:: for Fei+l2+ consistent with the expected greater extent of hydrogen bonding 100 in 020 and H20. The observation that (kg/k0) >1 for each of the four 5 corr aquo couples given in Table 5 indicates that the intrinsic barriers for these reactions are significantly larger in 020 than in H20 1- (eqn (27)). In particular, for Cr3+l2+, [( AG )0 - (001' )H] aq ie ie is 0.7 kcal/mole. The intrinsic barrier is usually separated .1. into an "inner-shell" component (AG'e)ls arising from intra- molecular reactant reorganization (particularly from changes in metal-ligand bond lengths), and an "outer-shell" component 113 1- (08”)os arising from reorganization of the surrounding solvent. D ) The observed values of (kH/k may arise from either or both 5 s corr of these contributions. Thus the stretching of the metal-oxygen bonds that is required in order for the tripositive aquo cations M2: to accept an electron to form the corresponding Mg: species may well require significantly greater energy when the oxygen is bound to deuterium rather than to hydrogen as a result of 109 coupling between the vibrations of the M-0 and O-H (or 0-0) bonds. By taking such inner-shell contributions into account, Newtonns’116 has calculated that the ratio of the rate constants (k:/k:) for Z;/2+ self-exchange in H20 and D20 would be no greater than 1.15. Since the inner-shell contribution to the homogeneous Fe intrinsic barrier for homogeneous self-exchange is generally predicted to be twice that for the corresponding electrochemical exchange reaction113 (vide infra), it follows that the corresponding 3+/2+ D) . . H prediction for electrochemical Feaq exchange is (ks/ks corr is about (1.15)i or 1.07. It therefore seems quite likely that the markedly larger 3+/2+ aq (ca. 1.5, Table 5) observed value of (kg/k2) seen for Fe is at least partly due to contributions from water molecules beyond the primary coordination sphere. In view of the close similarity in the change in metal-oxygen bond distances A3 for Fe:: versus Fe::( 5-0.10 A) and Vi: versus VZ:(133-0.15 R)35 3+/2+ aq exchange reactions, it seems likely that such a calcula- together with the involvement of a t29 electron in both Fe and Vi+l2+ 3+/2+ . H D a _ _ tion for Vaq would also yield (ks/ks)corr 1.0 1.1, in con trast to the observed value of 1.5. The simplest approach to the estimation of the outer-shell contribution (150:8)05 involves treating the surrounding solvent 31 108 as a dielectric continuum. By inserting the known values of the optical and static dielectric constants anp and 85 for liquid H o [sop - (refractive index)2 - 1.777, 85" 78.3] 2 and liquid 02 .f. ship_for (AGie)°s derived by Marcus (eqn. (90) of ref. 113) O at 25°C ( Sop - 1.760, as - 77.95) into the relation- 110 H 0 leads via eqn. (27) to the prediction that (ks/ks)corr - 1.06 (using the typical reactant radius of 3.5 R and a reactant-elec- trode distance of 7 3). Consequently this dielectric-continuum model for the solvent is also unable to explain the observed values of (kH/kD) . s s corr However, it seems feasible that the substantial differences in short-range solvent polarization between the oxidized and reduced 3+/ 2+ aq couples could provide a much larger contribu- forms of the M tion to the increased intrinsic barriers in 020. Thus the forma- tion from Mi: of the transition state in 020 is expected to involve a greater increase in the extent of solvent ordering induced by hydrogen bonding compared with the corresponding process in 3+ aq will require a greater dissipation of this hydrogen-bonded solvent H20. Similarly, the formation of the transition state from M in 020 than in H20. These differences will not affect the intrin- sic barrier if .1. -o D-H -o -o D-H A(scorr Gox)c ' C’corr MGred - cox) (Cf‘ eqn. (26)) i.e., when the isotope influence upon the transition-state stabl- lity is that expected for a cation with a structure identical to that of the transition state but having the charge (3-ixcorr). However, in actuality the transition state is reached via the reorganization of nuclear coordinates while the reactant charge remains fixed, the electron transfer occurring rapidly (310"16 sec) once the transition state is formed.”3 The solvent reorienta- tion required for transition-state formation will therefore be unaided by concomitant variations in the cation charge so that the required solvent structural changes should involve an additional 111 component of the activation energy which will form part of the intrinsic barrier. Consequently, the larger structural differences between M3+ and M2+ aq aq in 020 compared with those in H20 are also expected to yield larger intrinsic barriers in 020, in harmony with the experimental results. However, it is difficult to estimate quantitatively the magnitude of this contribution. D ) H It is interesting to note that the magnitude of (ks/ks corr 3+/2+ 89 two hexacoordinate aquo couples Fe (2.8) is substantially larger than for the other 3+/2+ 3+/2+’ e aq and vaq [ 1.5 (Table 511 for Cr This difference parallels the markedly larger values of both A S and A ED-" observed for Cr3+l2+ ( rc f 39 3+/2+ an 50 e.u. and 55 mV, u - 0.1) compared with Fe 11,100 (03 e.u. and 03 mV.) and Viz/2+ (37 e.u., 33 mV.). These correlations are compatible with the notion that an important component of the observed values of (kg/k:)corr arises from specific solvent polarization. However, the intrinsic 3+/2+ aq barrier to Cr exchange should also contain the largest inner- shell contribution since in this case the electron is transferred into an eg orbital; at least part of the especially large value of (kg/kg)corr for this couple may arise from this source. It remains to rationalize the sizable isotope effects seen for the reduction of the Co(III) and Cr(III) amine complexes that are sunnarized in Tables 6 and 7. Since A E?" values for );+/2+), it Is not these reactions are unknown (except for Co(en possible to make a complete experimental separation of the observed ND)E and (k"2°/k°2°)E into Intrinsic and NH values of (k /k corr corr thermodynamic factors (eqn. (20)). Nevertheless, approximate ll2 limits can be placed on AEg-H which allow the intrinsic part to be estimated. The effects upon E1,. of deuterating separately the ligands 100 and the solvent have been examined for Ru(iII)/(II) amine couples that are structurally similar to the Co(III) and Cr(III) reactants considered here; the inertness of both Ru(II) and Ru(III) to substitution allows Ef to be evaluated accurately using cyclic voltammetry.10h Deuteration of the ligands was found to have ND-NH 100). only a very small effect upon Ef ( AEf ;:2 mV deuteration of the solvent also yielded small positive shifts In Ef (AEfDZO-HZo 100) is less than 10 mV . The net effect of deuterating both the ligands and the solvent, AEfD-Hfilo mV, is therefore typically 3+/ 2+ smaller than for M aq couples. This behavioral difference is probably due to the apparently smaller solvent "structure- making" ability of tripositive ammine complexes compared with 33 otherwise similar aquo species, presumably arising from the smaller tendency of the less acidic ammine hydrogens to engage in hydrogen bonding with surrounding water molecules.11 It is quite likely that the (experimentally inaccessible) behavior of the Co(III)/(II) and Cr(III)/(II) amine couples is not greatly different from that for the corresponding Ru(llI)/(II) couples. A clue to the probable values of AEgo-NH for (Co(III)/(II) ammines is given by the observation118 that the deuteration of the ammine ligands increases the equilibrium constant for the dissociation reaction 4. Co(NH on;+ + D o - Co(NH3)Soo2+ + D o 2 3 3’5 in 020 by a factor of 1.3. This finding can be rationalized 113 119 by the greater decrease in the zero-point vibrational energy of the N-D bonds compared with the weaker118 N-H bonds in the conjugate base resulting from its smaller cationic charge.120"21 A similar charge effect upon the redox thermodynamics of Co(III)/(II) ammine complexes is therefore expected; a corresponding change in the relative stability of the oxidized and reduced forms leads to the estimate .AEgo-NH = 7 mV. In any event, it seems very ND-NH likely that the values of lAEf for the Co(III)/(II) ammine and ethylenediamine couples and probably also the Cr(III)/(II) couples are small and positive. Therefore from eqn (18), the E ND) NH values of (k /k corr greater than unity observed for these reactions are probably associated with still larger values of NH ND E ND-NH (k s/k s)corr' For example, if iAEf - 7 mV 3+/ 2+ NH ND E z for c°(NH3)6 , then since (k /k )corr 2.0 in both H20 _ 13 H D g and 020 (Table 6) and acorr 0.5 , from eqn (19) (ks/ks)corr 2.3. It therefore appears that deuteration of amine ligands yields noticeable increases in the intrinsic electrochemical barrier for Co(lII)/(II) and Cr(III)/(Ii). This effect probably is at least in part an inner-shell effect arising from coupling between the symmetrical M-N stretching vibration and the stretching and 116 bending modes of the N-H (or N-D) bonds. (Such coupling has been estimated theoretically to be much stronger than that between M-0 and O-H bonds in aqua complexes‘16) ”i S COI’T’ . Additionally, there may be a contribution to (kg/k from the expected greater interaction between the ammine hydrogens and solvatlng water molecules when the former are deuterated (see below). However, this latter contribution is likely to be less significant than 110 for aquo couples in view of the apparently weaker ligand-solvent interactions for the ammine complexes.10h Since the effect of separate deuteration of the solvent upon the Co(III) and Cr(IlI) amine reduction rates yields values of (kHZO/kDZO)E that are less than unity (Tables 6 and 7), given corr that the values of AEfDZO-HZo are probably small and positive it is quite possible that this thermodynamic factor could account partly or even entirely for the observed isotope effect (eqn. (18)). O/k020)E is about 0.7 for Co(NH3)g+ and Co(ND3lg+ corr reduction (Table 6), if for example AEfDZO-HZo is 20 mV, then 0 D 0 g /k52 )corr Thus since (kHZ from eqn. (19) (kgz 1.0. Although there are several factors that could produce larger intrinsic barriers in D20 compared with H20 solvent [(k:2°/k:2°) > 1] , the opposite situation corr is unexpected and would be without an obvious explanation. It therefore seems most likely that the values of liEfDZO-HZO for the (Co(III)/(II) and Cr(III)/(II) amine couples are sufficiently large (ca. 10-20 mV) so to offset the observed values of (kH20/k020):orr yielding (kgzolkgzo) = 1 (eqn. (18)). In any case, the corr observation of non-unit values of (kHzo/kozo):orr is intriguing. Since the interactions between the ammine hydrogens and the oxygen of the solvatlng water molecules should be very similar in H20 and 020, this result suggests that there are significant differences in the long-range solvent polarization induced by the ammine reactants in H20 and 020. These differences are likely due to "specific” (hydrogen-bonding) differences between these solvents; the Born model predicts only negligible (‘<0.5 mV) values of A EfDZO-HZO since the dielectric constants of liquid H20 and 020 are almost identical (78.3 and 77.95, respectively, at 250C108). 115 The equal value of “app observed in H20 and 020 for each of the electrode reactions, except for Co(NH3)SOH2+ reduction, indicates that the position of the reaction site in the interphase‘h is normally unaffected by isotOpic substitution. The origin of the smaller value of “app observed for Co(NH3)50H2+ reduction in 020 compared to that in H20 (Table 6) may well be the same as that responsible for the anomolously small values of a app for this reaction in H O which have been found to increase with 2 increasing temperature. This latter result has been attributed to stabilizing hydrogen bonding between the oxygen of the hydroxo ligand and the inner-layer water molecules which diminishes as the electrode potential becomes more negative due to the tendency of the inner-layer water to become polarized with the hydrogens pointing towards the metal under these conditions.89 This effect ls expected to diminish with increasing temperature since the extent of hydrogen bonding should then decrease. 0n the other hand, the substitution of D O for H20 should increase the extent 2 of hydrogen bonding at a given temperature, in harmony with the observed smaller value of “app in 020 at 25°C. Comparisons between isotope effects for correspondingelectrochemical and homogeneous reactions. The foregoing suggests that a substantial part of the rate changes observed upon replacing hydrogen with deuterium in the reactant's coordination sphere as well as the surrounding solvent can arise from the influence of water molecules beyond the coordina- tion sphere, i.e., from secondary as well as primary isotope effects. Additional evidence favoring such an interpretation 116 is obtained by comparing the isotope effects for corresponding electrochemical and homogeneous reactions. By assuming that the reorganizational barriers consist of independent, additive contributions from each reactant, it has been shown thatHB’122 e h h i (ks/2°) - (kox/Z ) (28) h ox are the (work-corrected) rate constants for where k: and k the electrochemical and homogeneous exchange reactions involving a given redox couple, and Z'1 is the homogeneous collision frequency. 123,1211 It has recently been shown that eqn. (28) can be generalized to include heteronuclear (cross-) reactions, expressed by (k°/2°) = (kh /z“)* (29) s 12 where k?2 is the rate constant for the homogeneous cross-reaction, and where ke is the rate constant at the intersection of the 12 (double-layer corrected) cathodic and anodic Tafel plots for the two constituent electrochemical reactions. Eqn. (29) has been found to be in approximate accordance with experimental rate data for various ammine and aquo couples, although significant behavioral differences between these two reactant types were observed.12h From eqn. (29), the following predicted relationship between the isotope effects for corresponding electrochemical and homogeneous reactions is obtained: HDe Huhi (k12/k12)corr ' [:(kIZ/k12)corr*] (30) D )h H D e H Table 8 contains comparisons between (k12/k ) and (k12/k12 corr 12 corr resulting from solvent deuteration for four redox reactions involving Co(III) ammines and aquo complexes. The electrochemical rate ratios were obtained from the rate constants at the intersection 117 Table 8. Comparison of Solvent Isotope Effects for Corresponding Electrochemical and Homogeneous Reactions. 1 2 Reactant Pair (szlk?2)sorr (k?2/k?2)20rr Co(NH3)g+- Criz 1.9 1.33 Co(NH3)g+ - vi: 3.0 1.73 Co(NH3)SOHg+ - vi: 2.0 2.63 Fez; - Fe:; 1.6 2 3 1Ratio of rate constants at the intersection of the (cathodic and anodic) Tafel plots for the constituent electrochemical half-reactions obtained in H20 and 020 using acidified 0.0 M_KPF6 as supporting electrolyte (see text and refs. 123 and 120), after correction for double-layer effects using eqn (5) as indicated in the text. 2Ratio of rate constants for listed homogeneous rection in H20 to that in 020 in same supporting electrolyte, from literature source indicated. 3ref. 103. href. 101. 118 in 0.0 !.KPF53 the (small) double-layer corrections were applied as outlined above. The homogeneous rate ratios were taken from the literature as indicated (note that the work terms are expected to cancel in such homogeneous rate ratios if the same supporting electrolyte is used in 020 and H20). Contributions to these rate ratios arise from differences in thermodynamic as well as intrinsic factors in H20 and 020.10 In contrast to the prediction 0 )e ) (kH IkD )h . H of eqn (30), it is seen from Table 8 that (k12/k12 corr __ 12 12 corr' It is expected that eqn (30) would apply if the solvent isotope effect arises solely from changes in the inner-shell reorganization energy since this contribution should be insensitive to the sur- rounding environment. The unexpectedly larger electrochemical rate ratios implicate the involvement of surrounding (outer-shell) water molecules. Given that the cationic complexes in Table 8 undoubtedly exert a substantial influence on the structure of the surrounding solvent, it would be expected that Viz, for example, would experience a significantly different solvent environment when involved in a homogeneous electron-transfer reaction with Co(NH3)g+ compared with its environment at the mercury-aqueous interface. This difference could account for the markedly larger D e H value of (kn/k12 corr H D h (3.0) compared with (k12/k12)corr (1.7) for this reaction (Table 8) inasmuch as the surrounding solvent structure (the extent of hydrogen bonding, etc.) could be quite different in the two environments. It has been pointed out that no significant solvent isotope effect has been observed upon the rates of homogeneous outer- 119 sphere processes for reactants that do not contain coordinated 96 water. This finding has been used to support the contention that the often large isotope effects observed for reactions involving aquo complexes are chiefly or even entirely due to deuteration of the aquo ligands.96 However, only two homogeneous reactions involving reactants not containing replaceable protons appear to have been studied: Co(NH3)g+ + Cr(bpy)§+, and Co(phen)g+/2+ 96 self-exchange. The significant solvent isotope effects observed for the electrochemical kinetics of ammine and ethylenediamine complexes (Tables 6 and 7), illustrate the more general occur- rence of this effect beyond aquo complexes. It is interesting to note that deuteration of the ammine ligands yields sizable decreases in the rates of electrochemical and homogeneous processes involving Co(NH3)g+ or Co(NH3)SOHg+ in either H20 or D20. Thus Co(NH3)g+ reacts a factor of 2.3 times slower than Co(NH3lg+ at a given electrode potential (Table 6) and a factor of 1.35 times slower for its homogeneous reduction 02 However, again the relative electrochemical + 1 by Cr(bpY)§ . and homogeneous isotope effects differ from expectations since egual rate decreases are predicted theoretically under those 113 This discrepancy between theory 80d experiment conditions. may again be due to an environmental solvent effect arising from the difference in the interactions between NH3 and N03 ligands and surrounding water molecules. 120 CONCLUSIONS Taken together, the foregoing results provide fairly convincing of the Tafel plots for the constituent half-reactions obtained evidence that the deuteration of solvatlng water molecules can induce substantial changes in the electrochemical kinetics as well as thermodynamics of transition-metal aquo, ammine, and ethylenediamine redox couples. As such, they furnish an illustra- tion of the limitations of the conventional dielectric-continuum model in describing the role of the surrounding solvent in the activation process leading to electron transfer and suggest that an additional component of the activation barrier may arise from extensive changes in short-range solvent polarization associated with the formation and fission of hydrogen bonds. Since there is reason to believe that 0...D hydrogen bonds in 020 are signifi- cantly (==0.25 kcal/mole), stronger as well as more extensive than O...H bonds16’125 in H20, larger intrinsic barriers in 020 would generally be expected for redox couples whenever the electron transfer entails an alteration in the hydrogen-bonded structure of the surrounding solvent. The present approach of employing electrochemical cells where both the kinetic and thermodynamic parameters in 020 and H20 can be compared at a constant Galvani potential (constant free energy of the reacting electron) provides additional experimental information beyond that which is accessible to homogeneous redox systems, and illustrates the virtues of electrochemical systems in exploring the fundamental influences of the solvent upon redox processes. CHAPTER VI. THE UTILITY OF PULSE-POLAROGRAPHIC ANALYSIS TECHNIQUES IN THE ASSESSMENT OF ELECTROCHEMICAL KINETIC PARAMETERS FROM TOTALLY IRREVERSIBLE CHRONOAMPEROMETRIC TRANSIENTS 121 122 INTRODUCTION The analysis of the current transients which result from potential-step perturbations is a well-established route to the determination of heterogeneous charge-transfer rate parameters. Both chronoamperometric126 301127 and normal pulse-polarographic data-analysis methods have been utilized. The former analysis considers the dependence at a fixed potential of current upon the time following the application of the potential step (i-t plane), whereas the latter analysis is concerned with the variation with potential-step amplitude of the current at a constant time into the pulse (i-E plane). Figure 21 illustrates the baiiiwick of each analysis technique on the current-time-potential surface. These large-amplitude methods are particularly suitable for assessing rate information as a function of overpotential, including that for reactions which are totally irreversible from a chemical as well as electrochemical standpoint. A major preoccupation in our laboratory is the acquisition of quantitative rate data, often for irreversible electrode reactions, at solid and mercury electrodes over wide ranges of overpotential and hence rate constants. These studies are performed in order to probe correlations between electrochemical reactivity and surface structure. Since we frequently utilize potential-step techniques for this purpose, we have been concerned with establishing clearly the experimental upper limits to the magnitude of the rate constant that can be reliably evaluated. Although the question of the measurability of large standard rate constants (i.e. for chemically reversible redox couples at small overpotentials) has been extensively considered, the 123 Aoum .m> >E v 44:23.05 .AeAgoemoEoocoEUlii Aoom E: NEE. \ 2.3959201 mast \ \ N o As: Enema Current-time-potential surface for the reduction Figure 21. of Cr(0H2)g+ in 1 M_NaCl04 (pH 2). 120 equally important question of the measurability of rapid rate constants when the reverse reaction rate is negligible (i.e. at large overpotentials) has been relatively neglected. Regardless of the analysis method employed, it is neccessary for this purpose to ascertain from empirical evidence a minimum time following the potential step for which the mathematical analysis used is valid inasmuch as the extent of kinetic information will generally 80,126 be greater at shorter times. Although the analysis of individual current-time curves has been most commonly employed, we have preferred to employ a pulse-polarographic readout, i.e. to display the current at a fixed time following the potential step as a function of the step size. The immediate advantage of this approach is that the simple explicit mathematical analysis due to Oldham and ParrySh can be utilized. In contrast, the mathematical analysis of chronoamperometric transients is complicated when the rate constants become large.126 Moreover, chronoamperometric transients demonstrate an essentially featureless decay of current. One is less likely to observe consequences of nonidealities of the experimental potential-control and current-measurement equipment In a collection of current-time curves measured in response to various potential steps than in the ensemble of pulse polarograms which can be generated from the same data. Although some attempts have recently been made to account for the effect of potentiostat 128,129 nonidealities upon chronoamperometric transients, they are approximate at best. Quantitative calculations have apparently been limited to small-amplitude steps.128 125 we have utilized a microcomputer-based electrochemical data acquisition and analysis system to gather extensive current-time- potential data for irreversible electrode reactions in order to make a direct comparison of the effectiveness of pulse-polarographic and chronoamperometric data analysis methods for reliably evaluating rapid rate constants. In this chapter experimental results are reported for the one-electron reductions of Cr(OH2)2+ and Co(NH3)5F2+ at the mercury-aqueous interface. These reactions were chosen since they are mechanistically simple, following outer-sphere pathways in concentrated fluoride of perchlorate electrolytes. In these solutions, the reactant is either not adsorbed or only slightly adsorbed at the reaction plane gig the influence of the diffuse layer.22’23’32 He also compare the experimental data with the results of digital simulations of the distortion in current-potential-time data arising both from reactant adsorption and from nonidealities in the potential-step waveform. These results illustrate the Importance of such effects in determining the upper limit to the rate constants that can be reliably evaluated and demonstrate the important advantages of pulse-polarographic readout for diagnosing, by simple means, the presence of these effects. EXPERIMENTAL Reagents All solutions were prepared in distilled water which was 'deionized by_a "Milli-Q9 water-purification system (Mlllipore Corporation). Solutions of I‘M KF supporting electrolyte were prepared by dissolution of recrystallized salt; solutions of 126 1 M_NaCth were made by diluting a stock solution which resulted from neutralizing concentrated perchloric acid with solid sodium carbonate. Solid [Co(NH3)5F](Cth)2 was synthesized as described 130 previously. Stock solutions of acidified Cr(lII) perchlorate were obtained by reducing CrO3 with excess hydrogen peroxide in perchloric acid.32 All potentials are quoted relative to a NaCl-saturated calomel reference electrode. This electrode has a potential in contact with 1 M electrolytes which is 5 mV more negative than the conventional s.c.e. The flow rate of the dropping mercury electrode (dme) employed for these measurements was 1.3 mg/sec. Measurement System The electrochemical measurements were performed with a 131 whose conventionally designed three-electrode potentiostat control amplifier is capable of providing :100 V at 1 A. For the more sensitive ranges (cell current below 1 mA), the current- to-voltage converter (IEC) is a low-bias, high-speed (18 MHz gain-bandwidth product) operational amplifier. A slightly slower (0 MHz) amplifier is used in conjunction with an emitter-follower Darlington buffer for larger cell currents. The stability of the IEC in response to the charging-current transient was improved considerably by the simple expedient of placing in the feedback loop of the IEC back-to-back low-leakage zener diodes the sum of whose reverse-breakdown voltage (V2) and forward-bias voltage (Vf) were less than the supply voltage.133 This IEC is represented schematically in Figure 22. Whereas a large potential step applied to the cell could cause the basic IEC to oscillate for as much 127 FWi n1C) r321 -4:K ”— :12 car: 1'1 (WE) E0 = "cctth Figure 22. Transient stabilization of current-to-voltage converter . 128 as a millisecond, the transient-stabillized IEC avoids oscillation by providing a feedback current through the diodes whenever the cell current was large enough to drive the IEC output toli (Vf + V2). Figure 23 shows the first hundred microseconds of representative current-time responses to potential-step perturbations of various magnitudes. The measurements were made a 50-nsec intervals by a Biomation Model 820 transient recorder (Gould-Biomation Inc.). (For clarity, not all data are shown.) The potentiostat system was placed under the control of a laboratory microcomputer which performed the functions of potential control, measurement timing, data acquisition and management, and real-time graphic display of averaged signals. Several chrono- amperometric transients were sampled and digitized for each potential- step value, averaged, and plotted in pulse-polarographic format. Background currents were measured for solutions of supporting electrolyte alone under identical conditions. Of some significance in this regard is the use of the same IEC sensitivity for solutions with and without depolarizer because of disparities at different sensitivities in amplifier offsets which result from the sight leakage current through the zener diodes. Positive-feedback iR compensation was used; its effect was slight because of the substantial (1 molar) supporting-electrolyte concentration. RESULTS Plots in pulse-polarographic format of background-corrected chronoamperometric transients at a dme in response to potential steps from -600 mV applied to cells containing 2 W! Cr(OH2)2+ and 2 mflH+ in 1 M NaCth are shown for multiples of 2 milliseconds Current (microamperes) o. -7500 Figure 23. 129 FIGURE 23 I T I I l T T l I 1 I 1 l T I I I l .I—I-I—a r- ...n .- o .0—0 — 0 ~ M. I- nn- —. 0 can .a .- 0. - a- n on we .0 as — O. - o -0 o .1 e a -- no- I- 000 d -0. 000 o 0000 - .0. .00 J O O. O O- o o a 0 0. “1 fi - o “a 0 fl 0 a da- .I 1—00 0 e on“ so all—- a II. 0 * o o o - 1- on up —( O O. - o n o o .0 O 0 ~ .A o o o n -1 a o o o a O f— 0. - .4 o a a a o la a o o I. a oo o o oo o .1 a so so -0 as o o a. o O O. - 1. a .- n o o. - _I 1— cu I. .. J 1 J I J 1 1 I. 1 1 1 l 1 1 1 l 1 1 80. 120. Time (microseconds) Current-time transient responses to potential 4. steps for Cr(OH2)g reduction. 130 and 100 microseconds in Figures 20 and 25 respectively. While the expected sigmoidal shape is observedau for the longer time values, as the sampling time decreases below 2 msec the polarograms develop a progressively more peaked shape ("maximum"), even to the extent that a limiting-current region Is not observed prior to the onset of proton reduction. 0n the other hand, dc polarograms for this solution at identical drop times do not show maxima. Similar observations were made for the reduction of Co(NH3)SF2+ in neutral 1 M KF. Figures 26 and 27 show the background-corrected normal pulse polarograms derived from the chronoamperometric data obtained for the electroreduction of this complex. These polarograms differ from those for Cr(OH2)g+ reduction in that at a given sampling time, the size of the peak is smaller for Co(NH3)5F2+ reduction. Again, maxima are absent from dc polarograms for Co(NH F2+ reduction. 3’5 Limiting-current values (ilim) obtained from pulse polarograms from which maxima are absent agree quite well with the Cottrell equation. Plots of ilim vs. t.i (Where t is the time following the potential step) are linear without a systematic pattern of residuals from the regression line. The intercept of the line is not statisitcally different from zero. Extrapolation of this plot to the sampling times where the polarograms exhibit maxima produces estimates of the limiting current which are substantially less (by as much as 202) than the experimental values. Rate constants determined from the monotonic polarograms by the pulse-polarographic techniques“ agree well with published 22,23,32 values and are internally consistent in that polarograms 131 FIGURE 24 1.0.0 IITIIIIIIIIIIIIIIIIIIIIIIIII'1111'1111'11176111T O 1 .0 msec - 0W0 A 1.5 msec C) p. :0; o orig 11111111111[11.111111111111111111 CI 2.0 msec 0 O 2.5 msec AGED m duo :noooc'ooooonooow" Cunant(hfluoenwanu0 I'I'I'I'I'I'I'I‘ITIII'I'I'I'I' 1 OK) i- 1111l1111lJlllllllllllL1[1111'1111111111111111111 .006 -‘ .5 FNNanfiel<>vw°°'a 1111111111111111111111111111111111111111111111111111111111111111 TITIIIIIIII'llTTllIII'IIIIIIITI'IIIIIIIIIIITIIIIIIIIIITIIITIIIII 3 0.0 11111111111111'L111111111!I1111111111111111111111 0.0 I .a Potential (V) Figure 26. Pulse polarograms for Co(NH3)5F2+ reduction at 2 msec intervals. 130 HGURE 27 7000 rillljllllIT—I—TIIIIIITIIIlIIIrlelIIITITlllIITITTT O 200 usec A 400 ec #3 0000 C] 600 psec o 00 C) 0 800 psec 000% V 1000 psec O C) (AAMMA AA AMAAAAAAAAAA Cunent(nflaoonmeum) ‘Defi;goimrOiwtggmgmggugpgwhmg VVYVVVvvavvv'vvvv W888 11L11111111 L1111111111111 L1111 11 1 114111 I 1 1 1 11 ngL“| -001 . -101 Pohuflkfl 00 0.0 T1'1111rTlll—IIIITIFNTIIIIIIIIIIIIIIIT 1111111111J11111111111114111111111111 Figure 27. Pulse polarograms for Co(NH3)5F2+ reduction at 0.2 msec intervals. 135 sampled at different times in the pulse yield essentially identical rate constants . DISCUSSION A Comparison of Chronoamperometric and Pulse-Polarographic Data Analyses It could be argued that potential-step chronoamperometry and pulse polarography should produce identical rate constants because they are derived from the same set of data. However, a crucial difference between the two techniques is that they employ different groupings of the data. Chronoamperometric analysis makes use of any current-time (l-t) curve for which the currents are less than their counterparts measured at potentials where the reaction is diffusion-limited. As noted above, the essentially featureless morphology of the i-t curves provides no obvious clue of unexpected behavior. A pulse polarogram, on the other hand, offers a built-in diagnostic capability because the electrode behavior at a fixed time following the potential steps is shown as the reaction passes from activation control to the diffusion limit. For electrochemical systems such as Co(NH3)5F2+ reduction whose polarograms should have a predictably simple shape, then, the pulse polarogram shows at a glance whether the boundary conditions of simple theory have been satisfied when the i-t transient does not. The factors which produce the anomalous pulse-polarographic currents (i > ilim) can presumably also operate in the potential region where i < ilim' The shape of the polarogram suggests to the experimenter that simple theory should not be used on 136 these data, but no such admonition is inherent in the chronoamperometric curve. It is of interest, therefore, to compare the rate parameters derived by both techniques from the identical set of current- time-potential data for those circumstances where the data indicate that both analyses are possible. Some attention must be paid to the details of the chronoamperometric analysis. Rather than risk introducing artifacts into the kinetic parameters through the use of approximations to the exact equation,126"27 130 we attempted a nonlinear regression analysis based upon the explicit formalism.126 The analysis could not be conducted successfully in large part due to difficulties in evaluation of the function y(x) - exp(x2)erfc(x) (31) A numerical integration technique for calculating the error-function complement 2 " 2 erfc(x) - 1 - erf(x) - 1 - n] exp(-u )du (32) o is of no avail for large values of the argument because a computer maintains a floating-point representation of a real number with a finite precision characteristic of the size of the number. As x increases, erf(x) approaches 1; even when multiple-precision arithmetic is employed, the significance of the digits supplied by the computer in calculating [1 - erf(x)] consequently becomes vanishingly small. The failure of this numerical-integration calculation of y(x) to agree with approximate values of y(x) determined for large x by series approximation36’126 (which can actually be shown to be divergent for large values of the argument) renders impossible the task of fine-tuning the rate parameters to minimize the residuals in the nonlinear regression. 137 37 Analysis can be performed in Laplace space without such a calculational difficulty. Exponential interpolation37 between data points was used in determining the Laplace transform of the experimental current-time curve. That this approximation itself produced no spurious results was evidenced by its rendering within 22 the anticipated rate constant from a set of test data which were generated by a digital simulation.26’135 The results of a Laplace analysis of Cr(OH2)g+ reduction data, shown in Table 9, demonstrate the effect on the derived rate constants of the short- time current enhancements. The values of kf agree well at -975 and -1000 mV with those obtained from pulse-polarographic analysis of monotonic polarograms; but as the potential becomes more negative, the disparity becomes greater. (The procedure of extrapolating the pulse-polarographic Tafel plot (log kf vs. E) beyond -1075 mV is justified in the light of the observation that the apparent electrochemical transfer coefficient (Clapp) is independent of the potential in this region.)1h The distortion produced in the Laplace-analysis plot for -1175 mV can be seen in Figure 28, where the curvature at low abscissa values is pronounced. The derived rate constants for potentials beyond -1000 mV are too small, in keeping with the notion that the exponential nature of the Laplace transform emphasizes the currents at the beginning of the pulse,37 which are abnormally enhanced. The Maximum Reliable Rate Constant That the reduction of Co(NH3)5F2+ proceeds gig a simple mechanism without specific adsorption of the reactant has been established.22’23 The theory of irreversible pulse polarographyah predicts that 138 Table 9. Laplace analysis of chronoamperometric data obtained for reduction of 2 mM'Cr3+ in 1 M NaCth/Z mM_H+. a,b a,c d E, mV Slope Inteafept kcalc’ kex vs. Na s.c.e. sec/coul sec /coul cm/sec cm/sec - 975 25730 151000 .0122 .0109e -1000 18030 68610 .0170 .0180e -1025 11090 55280 .0273 .03558 -1050 7100 60010 .0000 .05338 -1075 0720 66510 .0665 .0907e -1100 3360 60800 .0935 .161f -1125 2020 60070 .130 .279f -1150 2700 00520 .115 .081f -1175 1900 57360 .162 .831f -1200 1050 63110 .217 1.001: a Linear-regression parameters for a plot of 1/(T(p) x pi) vs. pi, where p is the Laplace-transform variable and T(p) is the Laplace transform of the time-dependent cell current i(t). b Slope - i/(nFAkcalcC), where F is the Faraday, A the electrode area, kcalc the calculated heterogeneous charge-transfer rate constant, and C the bulk concentration of reactant (ref. 37). Here, A - .0165 cm2 and C - 2 x 10"6 moles/cm3. c Intercept - l/nFA03C), where D is the diffusion coefficient, and other symbols as in Note b. (ref. 37). Here, D - 5.9 x 10"6 cm2/sec. d Rate constant derived either from monotonic pulse polarograms according to the method in ref. 17 or from extrapolation of the experimental Tafel plot (see text). e Denotes experimental value. f Denotes extrapolated value. 139 Figure 28. Laplace-space analysis of current-time transient for Crag reduction (-1200 mV). 100 FIGURE 28 { q q—H—u—Afiq—Jfiq—Ji—d—A—d—q—q—di—J 1000. 1 p0.5 ._.r._r_._._Ll_.Au_.r._._._._b. . 1 600000. mole—13. 101 for such kinetically uncomplicated electrode reactions the faradaic current sampled at a fixed time following the application of potential steps should vary monotonically with the overpotential. The reliability of rate parameters for Co(NH3)5F2+ reduction should therefore be called into question if the voltammetric data from which they are derived show peaks when displayed as pulse polarograms. The shortest sampling time for which the pulse polarograms for this system are monotonic is 000 microseconds. How many of the pulse-polarographic data are to be used for rate-constant calculations depends on the precision desired for the results. One can derive by standard propagation-of-error mathematics the effects that the rational function for R1: has on the uncertainty in the rate constant:8l"'32 Ak /k -| -20x3 +16x2 - 21x +10 I Ax f f 2 x (33) 2(7 + 0x )(1 - x) where Akf/kf and Ax/x are the respective relative uncertainties in the rate constant and in x (the ratio of the current to the limiting value). Assuming that one can measure x to within 12, the relative uncertainty in the calculated rate constant will be below 52 for x it 0.92. The use of a diffusion coefficient of 8.3 x 10-6cm2/sec (refs. 22 and 23) suggests that rate constants as large as 0.33 cm/sec can be considered reliably evaluated. For Cr(OH2)g+ reduction, however, this limit is only 0.10 cm/sec because the diffusion coefficient of Cr(OH2)g+ is only 5.9 X 6 32 10 cm2/sec, and because pulse polarograms for Cr(OH2)g+ reduction show maxima for sampling times below 1.5 msec. 102 Chemical Causes of the Polarogggphic Peaks It remains to determine the causes of the peaks in the pulse polarograms. It is tempting to consider that the shape of the curves, which is strongly reminiscent of conventional polarographic maxima, is ascrlbable to the same causes. However, tangential motion of the mercury surface introduced by differences in surface tension at various points of the cathode figures prominently 136 in the explanation of such maxima. Such conditions are unlikely to exist in the Cr(OH2)g+ solution inasmuch as Cr(OH2)g+ is not 32 and as the rest potential (~600 mV) specifically adsorbed at Hg is close to the potential of zero charge (pzc), which is about -520 mV. The contribution of the reactant to the surface tension is therefore negligible, and electrolysis of the Cr(OH2)g+ during the first millisecond of the pulse should affect the surface tension imperceptibly. In addition, the extent of electrolysis increases with the sampling time and is its greatest in the dc polarograms. In these cases, however, no peaks are seen. Peaked shapes have been observed previously for pulse polargrams in two different circumstances: reactant depletion at an unrenewed 137 (solid) surface and adsorption of electroactive species where 138 the electrode reaction is reversible. One feature which distinguishes depletedereactant polarograms from those in Figures 20-27 is that the plateau currents are less than the "true" limiting currents. These "true" values are ascertained by increasing the wait time 137 Neither between pulses to alleviate concentration polarization. the theory nor the experimental results from studies of reactant depletion suggest the incidence of currents greater than the 103 "true" limiting values. Furthermore, the peak in the polarogram is both predicted and observed in the case of reactant depletion to disappear as the wait time between pulses is increased or the pulse width decreased.137 The behaviour shown in Figures 20-27 is seen regardless of the drop time or the duration of the pulse, albeit that in the former instance a greater current is produced as a result of the larger electrode area. The digital simulation of reversible pulse polarograms of adsorbed reactants also predicts plateau currents less than the 135.138 ”true" limiting values. Empirical observations bear this out when the "true" limiting currents are determined by deliberately ‘38 It excluding adsorption-inducing anions from the solution. should be pointed out that a difficulty with this adsorption calculation is that the size of the Henry's-Law adsorption coeffecient necessary to produce pulse polarograms of the shape seen here and in the reversible-reaction study is quite large--about 0.05 cm.20 This implies for the conditions employed in that study (100-micromolar iodide concentration) the surface charge of Iodide ions is 500 microcoulombs/cmz, about 1.5 monolayers. This value is unrealistically large and certainly beyond the realm where Henry's Law could be expected to apply. Nonetheless, digital simulation can be used to expose the. role of adsorption in irreversible pulse-polarographic phenomena. 32,85 Values of ‘02 obtained from double-layer data produce estimates of the diffuse-layer adsorption coefficients (cf. Equation 0) 3+ _ a -6 - . -5 . from Cr(OH2)6 at 600 mV (Kads 10 cm) and 1200 mV (Kads 10 cm) for a reactant radius of 3.5 angstroms. A simulation performed 100 with reactant adsorption of this magnitude yields polarograms with peaks 102 or less above the limiting current and a shape which agrees qualitatively with the experimential results here.26 The simulation predicts even larger peaks (252 above the limiting current at 100 microseconds) if the adsorption is strong (Kads - 1.0 x 10"5 cm) throughout the wave. This prediction is borne out by the time-resolved pulse-polarograms for Cr(NH3)5(NCS)2+, a complex whose adsorption constants exceed 2 x 10.5 cm over much of its polarographic wave.18 The polarograms have peaks 002 in excess of the limiting current at a sampling time of 300 microseconds, and the peaks persist until 5 msec into the pulse. A more sophisticated weak-adsorption calculation using diffuse- Iayer profiles and 102 values for 1 M_KF electrolytes and rate- potential parameters characteristic of Co(NH3)5F2+, however, shows no maxima.26 The simulation results are nevertheless valuable in that they suggest that experimental conditions which tend to produce or keep the reactant near the electrode longer than simple theory assumes can be responsible for producing peak-shaped polarograms. The Effect of Instrument Performance on Pulse Polarograms The causes of peaks in pulse polarograms can be electronic as well as chemical. Examination of the simple electronic schematic representations of an electrochemical cell and the potentiostat (Figures 29 and 30, respectively) indicates that the dynamic characteristics of both the control amplifier (CA) and the IEC will have an effect on the shape of the applied-potential waveform. The system must be considered lg toto because the electronic 105 (:0110‘19 r “(Ol’k irig Electrode Electrode (CE) (WE) (RE,) I. I selutien resistance compensated by potentiostat Iu - uncompensated saluticn resistance 0" - castle-layer capacitance I, - resistance at charge-transfer reaction Figure 29. Schematic representation of an electrochemical cell. 106 I III-CIIIIIIIIIIIIIIIIIIIIIIIIIII .«ssuo.1uou uumuuou ............................n...j... _! Schematic representation of the potentiostat circuity. Figure 30. 107 information fed back to the CA from the reference electrode is on a potential-difference scale which depends crucially on the maintenance of the working electrode at virtual ground by the IEC. To the extent that the latter is incapable of performing this task in the face of the charging-current transient produced by a potential step, the actual applied cell potential--that is, the voltage difference between the summing point of the IEC and the output of the reference-electrode buffer amplifier--will be at variance with the theoretical (instantaneous) ideal. The customary criterion of potentiostat performance is the rise time of the reference buffer, but a condition necessary for this to reflect the applied potential is that the IEC feedback to the working electrode at its input a current of identical magnitude but opposite in sign to the cell current provided by the CA. If an Integrated-circuit operational amplifier forms the IEC, a situation commonly encountered in electrochemical instrumentation, it can provide only 10 to 20 mA to its summing point. To match the charge produced by the CA for a l-V step into a one-microfarad double-layer capacitance would require 50 to 100 microseconds. Indeed, without a nonlinear feedback element such as in Figure 22, the maximum output current is never reached for IEC sensitivities above 1 mA/V, protracting system response time even further. It is possible to characterize the IEC summing-point and reference-buffer behavior and determine the actual applied potential. Additional buffering (shown inside the dashed lines in Figure 30) was installed since it was observed that the potentiostat could oscillate if a probe from a voltage-measuring device were attached 108 to the reference buffer and that the magnitude of the noise in the IEC output depended critically upon the length of the cable connecting it to the microcomputer's analog-to-digital converter. (This is understandable in view of the fact that the cables present capacitive loads to these amplifiers, which will unintentionally contribute to their output characteristics and thereby affect the behavior of the entire cell-potential control loop.) To provide a quantitative description of the time-dependence of the applied potential, one needs data taken at rates greater than the computer system is capable; the Biomation transient recorder was employed to sample circuit voltages with 8-bit (1 part in 256) resolution at intervals as small as 50 nsec. Measurements were made of both the IEC summing-point and- the reference-electrode voltages during potential steps for the reduction at Hg of 2 mM’Cr(OH2)g+ in 1 M_NaCth. The former, an example of which is shown in Figure 31, are triangular in shape, ranging from 10 to 00 mV at maximum excursion. The situation can be much worse for solid electrodes; Figure 32 shows the behavior for a polycrystalline silver electrode of large area (0.5 sq cm). The reference potentials were approximately exponentially damped square waves with time constats of eight to ten microseconds. 130 Nonlinear regression applied to the reference signals using a single time-constant produced residuals of the same sign in a cluster at the beginning of the step, suggesting that the signal rises less quickly than exponential damping predicts. Use of two time constants in the model reduced the chi-squared value considerably, with essentially random distribution of residual 109 Summing-point behaviour 40.0 TIIIIIIITIIIIIIIIIIIIIIIIII'IrITIIIIT 30.0 :- .5, .5 I 1' : A _. .— 3 20.0 E- .: v : : é : ,5... + : 351- +1 : .3 ‘- + + + + I . iu++- + +» ‘+ - 0.0 :- 4; £— .1 -1000 1 l l 1 1 1 1 1 1 1 1 1 l 1 1 1 1 l 1 1 1 1 1 l 1 1 1 l 1 1 1 l 1 1 I 1 1 1 J: 40. (NO ‘flnw1(nficnxumondc) Figure 31. Summing—point deviations for Griz reduction at Hg. 150 FIGURE 32 .I TIIIIIIITIIIIIIIIIIIIIIIIIIITTTTIIII 111111111 30 O O O .. l. e. . .8 e .e e .: 1111111111111111111111111111 O. .0. .0 C O . Summing-point deviation (mV) #11111III'IIIIIII‘IonIIIIIIIIIIIIITTITIII 11111111I1111111111 o 1111111111111111111111111L111111111111 O ,8 Time (microseconds) Figure 32. Summing-point deviations for Co(NH3)5F2+ reduction at Ag. 151 signs for data at short times. There is a trend to the two time constants: one remains fixed at about 3.5 microseconds irrespective of potential-step size, while the other varies from 0.1 nanosecond for a 125-mV step to about 1.2 microseconds for a 750-mV step. This is encouraging in that the slew rates of potentiostat amplifiers should provide an exponential damping more or less without regard to step size, while the time constant of the load (the cell) should increase, mainly as a manifestation of integral capacitance. However, the value of the varying time constant at low overpotentials seems unrealistically small. The maximum summing-point excursions increase with step size, again in harmony with larger electrode capacitances. The results of the foregoing analysis allowed the mathematical description of the time dependence of the applied potential throughout the polarographic wave, the results of which are summarized in Figure 33. When the effect of a time-dependent heterogeneous charge-transfer rate constant derived from the substitution of the potential-time curve into the Tafel equation was simulated digitally, peak-shape polarograms resulted (Figure 30) which were in qualitative agreement with the experimental data. The use of slightly larger deviations from instantaneous potential application gave results closer to experimental performance. This is not surprising inasmuch as the calculation does not allow for iR drop. Simulations demonstrate that peaks a few percent above the limiting current can be introduced into the short-time pulse polarograms by an uncompensated solution resistance as low as 50 ohms. 152 Applied potential waveforms 1.600 I l l l I T1 1 I I l T T l I I Fl I I III I l I I TIT I I I T T I I I I F- -i — d — - I— / - .. , .i — e— .2 f 3; - 2' .. C -i .3 O _ a. — .d - - om 1 11L1 1111 11114 1 1|J11 l I II I 1111 1 1 1 1 1 1 1 1 0 04) 4N10 ‘nnui(nficnxneonde) 3+ aq Figure 33. Applied-potential waveforms for Cr reduction at Hg. 153 FIGURE 34 1e1 I I I 7 I IN T I l I I T T] I I T I I I T I$$$$;l I r1 T r " VV — vZAAAAAAAXXXX- I" A 1'4 — A ideal potential step X - (TV potential step as in Figure 33 X — L. .1 _ X - 1' - . s — x - . A .. h x d P — - g: - .— 3 '2 .A It _ A n! -( 0.0 - can!!! -i -PL1 1 J_1 l 1 1 1 1 1 1 l 1 1 1 1 111 1 1 1 1 l 1 1 l 1 1 L1 1‘ FRHanfiaI 1,0) “i E X+ VODUDDDDDDDQD 2 : X 5 : 0a AAAAAAAA‘ce : E ggéh 0000000000 3 1....111 11111113 0.0- 11111111111111111111L11J '°'5 -1.3 I%hmM(m 3+ Figure 00. Natural-drop dc polarograms for Craq reduction (1.8 mg/sec). 171 FIGURE 41 BOOEIIII1IIII IIIIIIIIIIIIIIFIIIIITII‘T‘UIII O 100 msec A 200 msec El 300 msec u § 0 4-00 msec fi" V 500 msec ”(*gfxxxxxx + 1.00 sec *Xx X 1.50 sec Xx 3K 2.00 sec XX 4.. x +++ +++++ + * + x+ * vvvvav' X+ VOOOOOOOW * VOUDDDD *X+XOD“ D *+ ::AA §X GA GA AAAAA Cunnut(nflunanmnnu0 lllllll'lIlIIIIII'IllIIIIIIIIIIIIIIII'IIIIIIIII'IIIIIIIII'IIIIIIIIIIIIIIIII lllllllllllllllililllllllllllllljllllllllllllll|lllllIllllllllllllllllllllj WE'SE éggoooo ° °°o DOMIEE gng;llJllolllllllllllLlllllLLLJ -O.5 -1.3 PotontialM 3+ Figure h1. Natural-drop dc polarograms for Craq reduction (3 mg/sec). 172 FIGURE 42 ‘i‘t’ :l I I I I I I I I I I I I I [II III I III I I II I I I I 7 I T I 1 I4] 1 ‘I’TII A O 100 msec ‘§ A 200 msec ***‘ Cl 300 msec * 0 400 msec V 500 msec fifi§xxxxxxx + 1.00 sec x x 1.50 sac 3;: 3K 2.00 sec * + + in... as + *4- Curnnt (miaoomperu) IIIII'IIIIIIIIIIIIIIIIIIIIIIIIIIIII'IIIIIIIIIIIIIIIIIIIIIIIIIIIII'IIIIIIIIIIIIIIIII X + d 4 4 d I 33g xgggo 00 0000000 0.0 Era—EL‘JiEEELII[$1110111141111ILlLLnnlllnL Potential (V) 1.3 Figure #2. Natural-drop dc polarograms for Crgz reduction (4 lug/sec). 173 produced by the drop knocker and consequently show currents that are always less than the values for knocked drops at all potentials. However, the peak-shaped polarogram results from the depletion being larger for potentials at the top of the wave, where the cell current is not dependent on the rate of the electrode reaction, than it is at the foot of the wave, where the extent of concentration polarization created by the previous drop is substantially smaller as a consequence of kinetic control of the current.137 That the peaks are more pronounced for larger flow rates is additional corroboration of this point. The cell current, and hence concentration depletion, will be larger for a greater flow rate even though the smaller drop time which accompanies a larger flow rate opposes this depletion increase somewhat. Since the mass of the falling drop at a given potential is essentially 1&9 independent of the flow rate, the amount of stirring due to the fall of the drop is roughly the same regardless of the flow rate. More depletion remains uncompensated by solution movement at the higher flow rates, and the size of the peak is therefore expected to be larger for a larger rate of Hg flow. The data obtained at 1.8 mg/sec (Figures 37 and #0) are encouraging in that they show the anticipated monotonic polarograms for knocked drops and potential-dependent deletion effects which seem just barely unaccepatable for naturally falling drops. These results suggest that some electrochemical reactions may produce natural- drop polarograms of a shape appropriate to Koutecky analysis for flow-rate values around 2 mg/sec. This point will be examined in further detail later in this chapter. 17h The Effect of Small Flow Rates It is also interesting to determine the accessibiltiy of rate information from polarographic data obtained at a flow rate of around 1 mg/sec. Figure #3 shows time-resolved polarographic data obtained for forcibly dislodged drops from a dme whose flow rate was 0.97 mg/sec. The corresponding natural-drop data were of poor quality owing to a low signal-to-noise ratio, predominantly because of concentration depletion. The extent of this depletion at this small flow rate can be appreciated by considering the limiting-current behavior for the knocked drops shown in Figure #4 along with the Ilkovic-equation prediction. Only for sampling times around 2 seconds do the experimental values approach the calculated ones. Despite the depletion the short sampling times may yet yield kinetic information because the Koutecky analysis is sensitive to the ratio of a current to its limiting value for fixed sampling time. Indeed, if one compares rate constants derived from the 50- msec polarogram with those from the Z-second polarogram (Figure #5), one can see that the two values agree where the two analyses overlap and that the former values lie on a linear extrapolation of the Tafel plot for the latter rate constants. This behavior is consistent with that previously derived from conventional pulse-polarographic data (Chapter VI). Dc-polarographic data taken at sampling times two orders of magnitude lower than conventional times can indeed extend the accessible rate information by a factor of ten under these capillary conditions, in keeping with the prediction of Koutecky's equations. These results show that 175' FIGURE 43 ‘00 I I T I I I I I I I I I I I I I'I I I I I I l I I I I I I I I r I I I I 1 I I 4 E O 50 msec xxxxxxxxn I E A 100 msec W 1 I C] 150 msec x I - x>°<>0000t - 3.0 :- 0 200 msec xfix XX 1 I V 250 msec w I : + 500 msec +++HW : " : )<.100 N9< +- - .. . sec .1 2.0 E- X 1.50 sec §( + W -_ I X 2.00 sec + 0 vi W Z : xx VVZVXOOOOOOO : E : at + 0 j V _ d E 1.0 :- J C I 0.0 :— -] hi I I I l I I I I.l I l L I l I 1 LI I I I I I l I I L I ILLLL 1 LJ 1 : -O.5 -1.3 Fannnfiol(N9 Figure #3. Knocked-drop dc polarograms for Cr3+ reduction aq (0.97 mg/sec). 176 HGURE 44 ‘0” I I I I I I I I I I T I I I I I T I I Cunnnt . IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII 0 IIIIIIIIIIIIIIIIIIIIlIIIIIIIIIlIIIIIIIIIIIIIIIIIIIIIIIIIIIII 5.0 0 El Knocked 0 O Knocked (first) 0 AM A 4.0 0.0 IIIIII IIIIIIJI I :- PIIIIIIIIIILHIIIIILIIIIIIIIIIIILIIILIIIIIJIIIAIIJIIIII 00° -‘ O1 lflnnnfiaICV) Figure 46. Comparison of polarographic techniques for Co(NH3)5F2+I reduction (50 msec). 181 FIGURE 47 76° IITIIIIIIIIIIIIIIjI’IjIIIIIIIIIIIIIIIIIrIIIIlIIIITIrII A Natural 0 Natural (first) II [II Knocked 0 Knocked (first) Omani (microa'nporoo) . IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII 0.0 IIIIIIIIIIIIIIIIIIIIIIIIIJIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII IIILIIIIIIIIIIIIIIIIILIIIIIIIlIIIIIIIIIIIIILIIUJJJJII‘ 0.0 ' -1.1 Potential (V) Figure 47. Comparison'of polarographic techniques for Co(NH3)5F2+ reduction (0.5 msec). 182 Table 10. Values of i/ilim for four polarographic techniques for the reduction of Co(NH3)5F2+ in i‘fi KF. a Denotes natural drops. b Denotes natural first drops. c Denotes knocked drops. d Denotes knocked first drops. 183 a b c d a b c d .05 sec .1 sec 200 225 0.012 250 0.002 0.014 0.012 0.0047 0.001 0.014 275 0.006 0.009 0.018 0.019 0.016 0.010 0.025 300 0.041 0.017 0.014 0.027 0.029 0.024 0.017 0.034 325 0.073 0.031 0.025 0.033 0.035 0.044 0.026 0.057 350 0.13 0.059 0.046 0.054 0.063 0.078 0.046 0.095 375 0.18 0.11 0.075 0.090 0.11 0.15 0.083 0.17 400 0.27 0.20 0.13 0.15 0.18 0.26 0.15 0.28 425 0.38 0.33 0.22 0.25 0.29 0.41 0.45 0.44 450 0.54 0.50 0.38 0.39 0.44 0.59 0.40 0.62 475 0.71 0.68 0.50 0.55 0.62 0.74 0.59 0.78 500 0.88 0.83 0.68 0.72 0.81 0.81 0.72 0.90 525 0.92 0.92 0.81 0.84 0.96 0.93 , 0.86 0.94 550 0.97 0.96 0.87 0.92 1.00 0.97 0.91 0.97 .15 sec .2 sec 200 0.006 0.004 0.005 225 0.017 0.004 0.004 0.017 0.011 0.005 0.006 250 0.022 0.005 0.009 0.018 0.019 0.013 0.014 0.014 275 0.035 0.019 0.021 0.030 0.025 0.024 0.028 0.032 300 0.061 0.031 0.034 0.036 0.039 0.036 0.036 0.037 325 0.11 0.055 0.059 0.063 0.065 0.064 0.058 0.069 350 0.20 0.10 0.097 0.12 0.13 0.12 0.12 0.13 375 0.32 0.18 0.18 0.20 0.22 0.20 0.20 0.23 400 0.50 0.30 0.29 0.33 0.35 0.34 0.34 0.36 425 0.67 0.47 0.46 0.47 0.52 0.51 0.51 0.54 450 0.84 0.65 0.63 0.68 0.69 0.69 0.67 0.71 475 0.95 0.79 0.77 0.82 0.84 0.82 0.80 0.84 500 0.90 0.88 0.91 0.93 0.91 0.90 0.92 .25 sec .3 sec 200 0.0087 225 0.006 0.005 0.0099 0.0081 0.0066 0.018 250 0.019 0.014 0.016 0.017 0.022 0.013 0.013 0.025 275 0.027 0.024 0.023 0.025 0.031 0.030 0.025 0.030 300 0.041 0.045 0.045 0.046 0.038 0.041 0.042 0.044 325 0.074 0.072 0.073 0.079 0.079 0.084 0.071 0.081 350 0.13 0.13 0.13 0.14 0.15 0.14 0.14 0.15 375 0.24 0.23. 0.22 0.25 0.25 0.24 0.24 0.26 400 0.37 0.37 0.36 0.39 0.40 0.40 0.39 0.41 425 0.55 0.54 0.54 0.56 0.58 0.58 0.56 0.59 450 0.71 0.73 0.70 0.73 0.72 0.75 0.73 0.74 475 0.84 0.85 0.83 0.80 0.84 0.86 0.84 0.86 500 0.92 0.92 0.92 0.92 0.91 0.94 0.92 0.94 184 FIGURE 48 1.00 III! 1111 lIII llll lle lllI llIT IllI 1W7 IIfi _ l l T l l l I l l _ L .. — -i o p on. '1 I- 0 fi l- .. d e n- e u e V - ‘ an A — .0 Cd 00 b .e- cue-o '- 0. e y— . C! e .. - 4 O r- . n—I e i— .0 .1 E 1. . .4 V L- o _ “ Q e-e-‘ce I— . - o -I Q a. i— . - .e wan-e _ -0 - e e o- — - 0‘ o 00 I. -0 1— - c. -- o... o q m 0 .0. .0. - - e- e a u- .— - ‘1 b q i- u l— e- L. .1 I— .1 _2.m LIIIIILIIIIIIIII_IIllIIIIIIILIIIJIJIIIIIJJIIIJLIII 0.0 o. 1 Time (eeconds) Figure 48. Effect of drop-knocker solenoid response time and displacement on polarographic current-time curves (large displacement). 185 HGURE 49 10W I I I I I I I I I I I II I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I b u q 1 . '-. 1 g _ a... —J 8 _ “z.?%. : é — “can. -I * - 0... d r ~ .m 1- —I I. -1 .2m I I I I I I I I I I I I I L I I I I I I l I I I I J I I I I J I I I I I I J I I I I I I I I I I I:- OJ) OJ Thne Gumnhde) Figure 49. Effect of drop-knocker solenoid response time and displacement on polarographic current-time curves (small displacement). 186 by a smaller travel, but at the expense of more than doubling the delay due to the response time of the solenoid. The complications caused by the experimentally convenient drop knocker impose a lower limit at this flow rate of about 150 msec for artifact-free current-time data. Nevertheless, this represents access to a two-fold larger rate constant than can be measured at half a second, the fastest available sampling time on conventional instruments in our laboratory. Comparison of Limiting Currents With Reported Behavior The limiting-current data described above stand in sharp contrast to published reports of high-speed polarographic behavior.36 The results of Bond and O'Halloran show limiting currents 1533. than those predicted by the Ilkovic equation for end-of-drop measurements at freely flowing capillaries with flow rates above 36 10 mg/sec. These authors, however, show no distortion of the shapes of polarographic waves for the reversible reduction of Cd24- in l fl_HCl. It is possible that the response time of their current-measuring equipment may be responsible for the disparity between their results and those of the present study. Their 36 currents were measured with an x-y recorder, a device which typically has a slewing speed less than 30 in/sec. Since the pen takes at least 30 msec to travel an inch, it is likely that the subsecond currents are not accurately represented by the recorder trace. Not suprisingly, the reported measurements36 show a larger negative deviation from Ilkovic behavior as the flow rate is increased (sampling time decreased). The measurement system used in the present study is fully capable of representing 187 the currents at short times because the amplifiers used have 131 As a consequence, the power bandwidths in excess of 10 kHz. limiting-current data reported here are far less likely to have been distorted by the speed of the measurement equipment. The previous study made no measurements at short times and small 36 flow rates, so there is no basis for comparison of such results. The Effect of Sampling Time of Polarographic Maxima Figure 50 shows two sampled-current polarograms for the reduction of Cr(NCS)g-, dissolved in l n NaCth at pH 2.7, at a dme with a flow rate of 2.0 mg/sec. The explanation of the polarographic shapes lies in the interactions between the redox center and the electrode. Complexes of Cr(lll) containing isothiocyanate ligands have been shown to exhibit strong adsorption at Hg electrodes.18 The hexaisothiocyanate complex in particular has a Henry's-Law adsorption constant of about 0.03 cm.18 Because of this strong adsorption, the reduction of the complex at the growing drop can produce uneven concentration distributions at the surface, leading to additional drop movement and producing a maximum.136 Currents sampled shortly into drop life thus have a better chance of "outrunning" the drOp movement, and the results in Figure 50 clearly indicate this. The current peak is six times as large as the limiting current at #00 msec, but just over twice as large at 50 msec. The feature of greatest importance in the SO-msec polarogram, however, is the definition of a limiting- current region for potentials gositive of those where the maximum appears. All of the current-potential data between -400 and 188 FIGURE 50 2°00 '- I I I I I I I I I I T I I I I I I T I I I I I I I I I I I I I I I I I I I I IJ .— AA .. :- O 50 msec A -: _. a, .: -- A 400 msec -: L. A. A. - r. A .: '— A A .1 :' a, :3 fr -_ A .2 g '— A .1 8 3- A .1 :- 000A '3 :' 4 0° 03“ ‘2 :‘ A 00000 '3 .. A .— I— A o d 0.0 "- W - I I I I l I I I I I l I I L 14 I I I I I I I I I I I I I I I I I I I I — -O.3 -1.1 Pohuflkn 00 'Figure 50. Dc polarograms for the reduction of Cr(NCS)g- in 15 NaCth (pH 2) 189 -700 mV can be taken with justifiable confidence as being uncomplicated by the maximum, and this renders the rate information accessible. The lack of an inflection makes the same assessment unreliable for the IOU-msec polarogram. 0n the other hand, high-speed current sampling presents no such advantages to the study of the reduction of [cis-Co(en)2(N3)2]+ in neutral 1 fl KF. While an inflection is seen in the polarograms (Figure Si), complications presumably due to the adsorption of released azide ions preclude determination of the requisite limiting current. The Effect of Sampling Time on Kineticallprontrolled Waves The determination of a limiting current for the reduction of perbromate in concentratied nitrate or mixed nitrate/fluoride electrolytes is virtually impossible at conventional times because of the onset of kinetically controlled bromate reduction at extremely negative potentials.26 Figure 52 shows the effect of diminishing the sampling time from 900 msec to 100 msec in the reduction of perbromate in l flNaNO3 at a 2 mg/sec flow rate. Kinetic parameters derived from the polarograms obtained at conventional times would be of questionable reliability because of the uncertainty in the limiting-current value. The most rapidly sampled polarogram, however, does not suffer from this limitation. The benefits of time resolution do not always accrue to the study of kinetically controlled polarograms. The reduction of perbromate in l n NHhF produced the time-resolved polarograms shown in Figure 53. The rapid current sampling is not fast enough 190 FIGURE 51 200 I I I III I I I I IT I I1 I I I I I I I I I I I I I I I I III TTI I I I - O 50 msec a : A 100 msec 1 V V - El 150 msec VV V W V A - VOOOOOOOVV Vvvo . O 200 msec OMV 0 ’ v.33 gowzo" '3 ‘ A - V 250 msec 0 -* L- on :AAAAAAAA DO A b VDAA o A '33 A _ 000 00 A AA .i! _ A 0° 00 A o '— 5 +- o 0 W -I no- ” o " g ~ A: ° 4 l- 0 all - ? q .. 5‘ .. I I I IJI I IJ I I IILi [J L I I I I I I I II I I I I I I I4 I I I II 0.2 -O.6 ‘ FernfiolCV) Figure Si. Dc polarograms for the reduction of cis-Co(en)2(N3); in i flKF. 191 FIGURE 52. 1300EII1IITjIII1TIII—IIIIIIIIIIIIIIII I-OIOOmsec LIJ E-A 300 msec [—0 500 msec I msec Ing <1 (O \I O O O O msec Current (microomperes) I I IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIILIIIIIIIIIIIIIIIIIIIIIIIIIIII ITII'IIFIIIIIIITIIIIIIIIIIIIIIIIIIfIrIrITII IIIJ IIIIJIIIIIIIXIIIIIIJILJIJIIIII P 0.2 I .4 Potential (V) Figure 52. Dc polarograms for the reduction of KBrOh in l n NaN03. I92 FIGURE 53 400 [VI fl I I I IT Ij ITF‘I I I I I I I I I I I I I I I IIj I Tq Z O 100 msec j E A 300 msec j E- El 500 msec VVVV'VVVV .3 t o 700 msec ngvoOOOOgOO : 21;? C V 900 msec V 3000:3000 DD 1 3 3 V300 D AAAAAAA : g : VooDuDAAAA 1 3 E V800 A 00 E 5 E 0 AAA 0000000 E E 2. DA 000 .2- E C A 0 : 8 I 0000 Z ; é o : 2 A° 3 0.0 :— 0 '3 E Z -1 I I I I I I I I I I I I I I I I I I I I I I I I I I I LII I I I: 0.3 -O.4 Fknanfiol(y) Figure 53. Dc polarograms for the reduction of KBrOh In I n NHl‘Fo 193 to shift the perbromate wave far enough negative of the reversible Hg-oxidation wave to provide a region of potential where the electrode is ideally polarizable. Therefore, the data measured at positive potentials always contains some current-diminishing contribution from the oxidation reaction. It remains a question of judgment, then, how far negative the potential must be so that the currents in l !_NHhF result only from perbromate reduction. CONCLUSIONS Rapidly sampled polarographic data have been shown to be capable under appropriate circumstances of producing clear advantages, over data measured at conventional times, for the assessment of electrochemical-reaction rates. The complications due to polarographic maxima or to interference waves can sometimes be eliminated through the use of short sampling times. Not all flow rates can be used for such studies, nor can all technique variations and sampling times be utilized at a given flow rate. Specifically, flow rates above 3 mg/sec produce severe depletion effects or undesirable tangential mercury-drop velocity components. For flow rates around 2 mg/sec, sampling times below 150 msec produce spurious results for knocked drops as a consequence of mechanical response times and stirring complications. Below 1 mg/sec, natural drops cannot be used reliably, whereas knocked-drop polarograms allow the determination of rate constants as large as 0.07 cm/sec which agree with values measured by normal pulse polarography. CHAPTER VI I l. SUGGESTIONS FOR FURTHER STUDY 1914 195 Research endeavors can be rewarded not only with answers to questions posed as the research was conceived but also with the additional problems which emanate from those answers. This section presents suggestions for further investigation which are based upon the conclusions of the previous chapters. MEASUREMENT-SYSTEM IMPROVEMENTS There are several ways in which the measurement system described in Chapter II could be enhanced, based upon the experience of this study. First, the signal-to-noise ratio can be improved both in general and for specific types of experiments. While the electronic noise present in the laboratory environment, particularly within the computer itself, does not completely vitiate the use of the mainframe A/D converter, there is little doubt that digitization of the measured signals as close as possible to their sources would improve the signal-to-noise ratio of the measurements, particularly for low-level voltages. A battery-powered, remote sampling head containing the sample-and-hold amplifier and A/D converter would permit information transmission in the digital domain.h7 Optical isolation of the domain converter from the (digital) DNA interface would decrease the noise induced by high- speed logic-gate transitions. In addition, the potentiostat circuitry was optimized more for speed than for sensitivity, the best performance being obtained for currents in the 0.i to 10 mA range. For the dc-polarographic studies, which occur on more protracted time scale than the pulse experiments and in which the currents are smaller, a programmable gain stage in the analog-measurement subsystem would enable current 196 sampling even closer to drop birth than the measurements described in Chapter VII. Finally, greater computational throughput could be realized by interfacing the data-acquisition timing with the operating system's resident-monitor code through pseudo-device handler programs. In this way, the real-time, dual-task capability of RT-llh2 could be utilized, allowing the use of the computer by two operators: one who performs time-critical measurements without compromise in timing integrity and one who executes data-analysis or software-development programs with nearly imperceptible delays. The results of Chapter VI show that the speed of the potential- control circuitry clearly establishes upper limits to the electrochemical rate measurements which can be made reliably with the use of simple models. Several changes can be made to improve the response time of the potentiostat. One method is to inject charge of a sign opposite to the control-amplifier current into the summing point of the current-to-voltage converter. This charge could come either from an amplifier which differentiates electronically the output of the control amplifier or from a current source which is switched on momentarily when the cell potential is stepped. Alternatively, one could eliminate the need for a current-to- voltage converter by designing a control amplifier which contains 150 a linear transconductance stage. This portion would provide a voltage output which is proportional to the output current of the amplifier. There is also the intriguing prospect of controlling the cell potential solely by programmed charge injection.”1 This technique is considerably more complicated to implement 197 than conventional (completely analog) control, and its original '51 is probably too slow for most electrode-kinetics configuration measurements. Nonetheless, the method is capable of producing potential changes in cells containing concentrated aqueous electrolytes much faster than voltage-control amplifiers. The versatility of the measurement system will be increased through the creation of additional applications software. Conventional charge-based experiments such as chronocoulometry are now in progress, not only for the customary mercury-electrode studies but also for those at solid electrodes. A novel automated differential- capacitance technique based upon small potential-step chronocoulometry is also currently under development. STUDIES or SOLVENT STRUCTURING Chapters IV and V presented results which demonstrate further the applicability of a model which includes secondary solvent structuring engendered by reactant ions in solution. It would be interesting to expand the study of the potential dependence of the electrochemical transfer coefficient to include the reductions of substituted Co(lll) ammine complexes in electrolytes such as 0.h ! KPF6 where the requisite double-layer corrections are small. In particular, the transfer-coefficient variations of the Co(lll) analogs of the Ru(lll) amine complexes scrutinized in the half-cell reaction entropy study11 could shed additional light on the role of hydrogen bonding between solvent molecules and reactant ligands in electron-transfer processes. In addition, the isotope-substitution studies suggest that larger intrinsic energy barriers would generally be expected 198 in 020 whenever the electron transfer entails an alteration in the hydrogen-bonded structure of the surrounding solvent. To explore this prediction further, it would be desirable to select chemically reversible redox couples which exhibit significant values of ABE-H and yet do not contain replaceable protons so that the secondary isotope effect upon the electrochemical kinetics would provide the sole contribution to (kg/k0) . Exa les 5 corr mp include hexachloroiridate (IV/ll) and hexacyanatoferrate (Ill/ll), as well as oxalato complexes. Furthermore, it would be interesting to determine A62-" for the Co(lll) amine complexes studied in Chapter V in order to scrutinize changes in the intrinsic barrier heights for electron transfer to these complexes, similar to the treatment of the aquo-complex results. The use of very high-speed, double-pulse coulostatics to determine formal potentials by the Tafel-plot intersection method (see Chapter lV) is possible for those complexes whose reduced forms aquate slowly enough to be seen on the reverse pulse. An added benefit of these formal-potential measurements is that their temperature dependence would provide the half-cell ll entropy changes which attend the electron-transfer reaction. DC-POLAROGRAPHIC MEASUREMENTS Chapter VII demonstrated the limits to the accessibility of electrochemical rate information derived from rapidly sampled dc polarograms. The application of this method to kinetic-probe experiments involving perbromate reduction would provide information to complement that produced by the outer-sphere, cationic Co(lll) ammine probes. It would also be of interest to determine the 199 effect of a variable forced drop time on the polarographic limiting currents at a fixed flow rate and sampling time to see what additional complications are introduced by the added stirring. REFERENCES (I) (2) (3) (I) (5) (6) (7) (8) (9) (10) (11) (12) (13) (1h) (15) (16) (17) (18) (19) (20) (21) REFERENCES For a recent review, see W. R. Heinemann, P. T. Kissinger, Anal. Chem. 52, 138R (1980). See, for example, H. Taube, Electron Transfer Reactions of Complex Ions in_$olution (Academic Press, New York: 1970). v. R. Grove, 91111. Mag. (Series _3_) 15, 127 (1839). W. Ostwald, g; Elektrochem. l, 122 (189A). Chemical and Engineering News §§_(1l), 6 (1978). J. O'M. Bockris, A. K. N. 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