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FINES wiII be charged if book is returned after the date stamped be10w. Q \‘ 8 007 BJUZ‘ 929 SURFACE SUBSTRATE EFFECTS ON KINETICS AND MECHANISMS OF ELECTRODE REACTIONS By Hsue-Yang Liu A DISSERTATION Submitted to Michigan State University in partial fquiIIment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 1982 ABSTRACT SURFACE SUBSTRATE EFFECTS ON KINETICS AND MECHANISMS OF ELECTRODE REACTIONS By Hsue-Yang Liu The double layer structure at the polycrystalline leadéaqueous interface has been studied by measuring the differential capacitance. The mixed electrolyte method was employed to study the specific ad- sorption of anions at the lead-aqueous interface from the measurement of the differential capacitance. The Hurwitz-Parsons analysis and other relative methods were employed to calculate the surface concen- trations of the specifically adsorbed anions. Furthermore, the Frum- kin isotherm was utilized to evaluate the free energy of specific adsorption and the interaction parameter 9. The effect of the elec- trode pretreatment on the adsorbabilities of anions at the polycrystal- line lead was also examined. The kinetics of a number of mechanistically simple transition- metal complexes have been examined at gallium, polycrystalline lead, and mercury surfaces in order to explore the dependence of electrode kinetics on the nature of the electrode material. Surprisingly, there were significant differences in the rate constants corrected for the ionic double layer effect between these surfaces. This indicated Hsue-Yang Liu the presence of "specific substrate" effects on electrode reactions. The enthalpies and entropies of activation for the electroreduc- tion of a number of Cr(III) complexes and Eu(III) at the lead-aqueous interface have been determined with a nonisothermal cell arrangement. The resulting small or even negative values of double layer corrected activation entropies at the lead surface suggest the occurrence of nonadiabatic electron-transfer processes. 0n the same grounds, the Marcus theory has been shown not to be adequate in the present case. A series of cobalt porphyrins were employed to examine the electrocatalysis of oxygen reduction at pyrolytic graphite surfaces. A rotating ring-disc electrode was extensively used to evaluate the reaction pathway and subsequent reaction mechanisms of oxygen reduc- tion at porphyrin-modified graphite surfaces. The "bulk" and “sur- face" redox properties of the Co(III/II) couple of the cobalt por- phyrins were also examined by using cyclic voltammetry. Unlike monomeric porphyrins, the dicobalt cofacial porphyrin linked by f0ur-atom bridge showed a remarkable enhancement of the electro- catalysis of the four-electron reduction of dioxygen to water. EDUCATIONAL GENEALOGY M. J. Weaver C. G. Enke D. Inman - H. Laitinen J. O. Bockris I. Kolthoff H. J. T. Ellingham N. Schoorl A. J. Allmand C. L. DeBruyn w. H. Nernst A. Franchimont N. Ostwald A. Hurtz C. Schmidt J. Dumas ' J. Lirbig - L. Thenard J. L. Gay-Lussac L. Vauquelin C. L. Berthollett A. F. de Fourcroy Jean Bucquet I A. Lavoisier ii To My Parents ' ACKNOWLEDGEMENTS The author wishes to expreSS his sincere appreciation to Professor M. J. Weaver for his inspiration, guidance, patience, and support during the course of this investigation and the preparation of this thesis. Helpfull suggestions by Professor C. G. Enke are deeply appreciated. The appreciation is also extended to Dr. D. Larkin for providing several essentially valuable suggestions. He is also grateful to Ed. Schindler, Jane Farmer, and Joe Hupp for their suggestions and friendship which were invaluable to the completion of this degree. Special thanks are given to his wife Huifen for her understanding and encouragement. Above all, he would like to thank his family for their faith and encouragement which made all of this possible. iv Chapter LIST OF LIST OF PART I CHAPTER CHAPTER '1. TABLE OF CONTENTS TABLES ......................... FIGURES ........................ I. INTRODUCTION .................... II. BACKGROUND .................... Thermodynamics and Kinetics of Electrode Reactions ....................... The Structure of the Electrical Double Layer ......................... Theoretical Treatment of Heterogeneous Electron-Transfer Reactions .............. Double Layer Effect on Electrode Kinetics ........................ Activation Parameters of Electrode Kinetics ........................ III. EXPERIMENTAL ................... General Apparatus ................... Reagents ............. _ ........... Electrochemical Techniques ............... Cyclic Voltammetry ................. DC and Pulse Polarography ............. Rotating-Disk Voltammetry ............. Capacitance Measurements .............. i. AC Bridge ................... ii. "Phase-Detection" Technique .......... D-OU'DI Page ix xi IO 19 27 3T 37 38 39 41 41 45 45 46 46 46 Chapter Page 4. Electrode Pretreatment ................. 47 CHAPTER IV. DOUBLE LAYER STRUCTURE AT THE LEAD- AQUEOUS INTERFACE .......... - ....... 49 1. Introduction ...................... 50 2. Characterization of the Electrode Surface ........................ El 3. Results ........................ 54 a. Capacitance Measurements in Non- specifically Adsorbing Electrolytes ........ 54 b. Time Dependence of the Measured Capacitance .................... 57 c. Specific Adsorption of Anions from Capacitance Measurements .............. 62 i. Iodide Adsorption in Fluoride- Based Electrolytes .............. 62 ii. Iodide Adsorption in Perchlorate- Based Electrolytes .............. 76 iii. Evaluation of the Free Energy of Specific Adsorption ............. 76 iv. Specific Adsorption of Thiocyanate, Bromide. Azide, and Chloride ......... 84 4. Discussion ....................... 84 CHAPTER V. ELECTRODE KINETICS AT THE LEAD- AND GALLIUM-AQUEOUS INTERFACES ............. 96 A. Rate Constants of Mechanistically Simple Transition-Metal Complexes ................. 97 l. Introduction ...................... 97 2. Results ........................ 99 The Pretreatment Dependence ............ 99 The Apparent Rate Constants of the One- Electron Electroreduction of Cr(III) Aquo and Ammine Complexes at the Lead-Aqueous Interface ..................... l02 vi Chapter Page c. Double Layer Corrected Rate Constants ........ 105 d. Rate Constants of Some Cr(III) Complexes Measured at a Hanging Gallium Drop Electrode ..................... ll2 3. Discussion ....................... ll3 a. Surface Contaminants ................ ll3 b. Reaction Mechanism ................. ll9 c. The Dependence of Outer-Sphere Electrode Kinetics on the Electrode Material ......... lZl B. Evaluation of Activation Parameters ............ 124 1. Results ........................ l24 2. Discussion ....................... l3l PART II CHAPTER VI. ELECTROCATALYSIS OF OXYGEN REDUCTION ....... 138 1. Introduction ...................... l39 2. Experimental ...................... 148 a Materials ..................... l48 b Rotating Ring-Disc Electrode (RRDE) ........ 149 c. Instrumentation .................. lSO d Porphyrin-Modified Graphite Surfaces ........ l55 3. Results ........................ l56 Characterization of the PG/Pt RRDE ......... 156 Oxygen Reduction at the "Blank" Pyrolytic Graphite Surface ............. 164 c. Redox Properties of the Cobalt Porphyrins ..................... 164 d. Oxygen Reduction at the Porphyrin- Modified Graphite Surfaces ............. l77 4. Discussion ..... . .................. l89 a. An Attempt to Assign the Surface Redox Waves of the Attached Cobalt Porphyrins ...... l89 vii Chapter Page b. Electrocatalysis of Oxygen Reduction at the Monomeric Porphyrin-Modified Surfaces ...................... 191 c. Electrocatalysis of Oxygen Reduction ' at the Dimeric Porphyrin- -Modified Surface ...................... 193 CHAPTER VII. CONCLUSION AND SUGGESTIONS FOR FUTURE WORK ....................... 201 1. Conclusion ....................... 202 2. Suggestions for Future Work .............. 204 REFERENCES ........................... 207 viii LIST OF TABLES Table Page 4.1 Standard Free Energy of Adsorption AG; for Several Anions at Lead, Mercury, and Silver Electrodes .................. 85 5.1 The Pretreatment Dependence of the Measured Rate Constants at Lead Electrodes for a .Number of Transition-Metal Complexes ......... 100 5.2 Summary of Rate Constants for the Electro— reduction of Several Transition-Metal Com- plexes at Lead and Mercury Electrodes ........ 106 5.3 Rate Constants for the Electroreduction of Some Cr(III) Complexes Measured at Lead and Mercury Electrodes in 0.5 M NaClO4 and 40 mM La(ClO4)3 ................. 110 5.4 Rate Constants for the Electroreduction of a Number of Cr(III) Complexes Measured at Mercury, Gallium, and Lead Electrodes ........ 114 5.5 Activation Parameters for the Electrore- duction of Various Trivalent Metal Complexes at Mercury- and Lead-Aqueous Interfaces ....... 125 ix Table Page 6.1 "Bulk" and "Surface" Redox Potentials for the 1302+”+ Couple of Cobalt Porphyrins. ....... 169 6.2 Kinetics Parameters for Oxygen Reduction at Porphyrin-Modified Surfaces ........... A. . 187 Figure 2.1 2.2 2.3 2.4 3.1 3.2 4.1 4.2 LIST OF FIGURES The electrode-solution interfacial struc- ture including the specifically adsorbed anions ...................... Equivalent electric circuit of polycrystalline electrode models: (a) Mode1.I; (b) Model II. . . Proposed reaction sites for Cr(III) aquo and ammine complexes at the electrode-aqueous interface .................... Free energy profile for simple electro- chemical reaction ............... ‘. Schematic diagram of an electrochemical cell ....................... Single amplifier potentiostat .......... Typical cyclic voltammogram for polycrystal- line lead electrode (prepared by method D) at 0.1 v sec'1 in 0.5 M NaClO Differential capacitance vs. electrode po- tential for polycrystalline lead in the following conditions: (a)--method (A) in 10 mM KF at 210 Hz extracted from Ref. 64;' 4 0000000000 Page 13 16 22 29 43 43 53 Figure 4.3 4.4 4.5 4.6 Page (b)--method (D) in 10 mM NaF at 200 Hz; (v) method (0) in 10 mM NaF at 50 Hz; ’ (A) method (D) in 10 mM NaF at 10 Hz; (A) method (D) in 0.2 M NaF at 200 Hz; (0) method (0) in 0.2 M NaF at 1000 Hz .......... 56 Differential capacitance at 1000 Hz vs. electrode potential for polycrystalline lead prepared by method (0) in the various -concentrations of NaClO4: (x) 10 mM, (0) 50 mM, (A) 0.5 M, (00 1.0 M, (v) 5.0 M ...... . . . 59 Time dependence of the differential capaci- tance at 1000 Hz for polycrystalline lead in 0.1 M NaClO4 ......... . .......... 61 Differential capacitance at 200 Hz vs. elec- trode potential fOr polycrystalline lead prepared by method (D) in mixed NaF/NaI electrolytes at an ionic strength of 0.2. Key to iodide concentrations: (x) O; (o) 2 mM; (A) 4 mM; (CM 10 mM; (V) 25 mM ......... 64 The concentration of specifically adsorbed iodide plotted against electrode charge for polycrystalline lead prepared by method (0) in mixed NaF/NaI electrolytes at an ionic strength of 0.2 (at 200 Hz). Key to iodide concentration: (0) 1 mM; (A) 10 mM; 000 25 mM; (V) 63 mM ................... 69 Figure 4.7 4.8 Page Differential capacitance at 210 Hz vs. electrode potential for polycrystalline lead prepared by method (A) in mixed KF/KI elec- trolytes at an ionic strength of 0.2. Key to iodide concentrations: (x) 0; (o) 1 mM; (A) 4 mM; (v) 10 mM; (0) 25 mM; (0) 70 mM. This figure was extracted from Reference 78 .......................... 71 The concentration of specifically adsorbed anions (bulk anion concentration 10 mM) plotted against electrode charge for poly- crystalline lead in fluoride electrolytes unless otherwise noted in the following conditions: (a)--method (A) for iodide at 210 Hz obtained by analyzing the corresponding capacitance curves in Ref. 78; (b)--method (B) for iodide at 1000 Hz; (c)--method (D) for iodide at 200 Hz; (d)--method (D) for iodide at 1000 Hz; (e)--method (D) for iodide (in perchlorate electrolytes) at 1000 Hz; (x) method (D) for chloride at 1000 Hz; (0) method (0) for azide at 1000 Hz; (V) method (0) for bromide at 1000 Hz; (A) method (0) for thiocyanate at 1000 Hz . . . . . . . . 73 xiii Figure 4.9 4.10 4.11 4.12 Page Differential capacitance at 1000 Hz vs. electrode potential for polycrystalline lead prepared by method (0) in mixed NaF/Nal electrolytes at an ionic strength of 0.2. Key to iodide concentrations: (x) 0; (o) 1 mM; (A) 10 mM; 000 25 mM; (V) 65 mM ...... 75 Differential capacitance at 1000 Hz vs. electrode potential for polycrystalline lead prepared by method (B) in mixed NaF/NaI electrolytes at an ionic strength of 0.2. Key to iodide concentrations: (x) 0; (o) 1 mM; (A) 10 mM; (C0 25 mM; (V) 65 mM ........ 78 Differential capacitance at 1000 Hz vs. electrode potential for polycrystalline lead prepared by method (0) in mixed NaClO4/NaI electrolytes at an ionic strength of 0.5. Key to iodide concentrations: (x) 0; (o) 1 mM; (A) 10 mM; 000 25 mM; (V) 65 mM ........ 80 Cb(1‘e) £n(-——6———J vs. a for specific adsorption of iodide for polycrystalline lead prepared by method (0) at 200 Hz in mixed NaF/NaI electrolytes at an ionic strength of 0.2. Key to various electrode charges (0) 1.0; (x) 0.0; (A) -l.O uC/cm2 ............... 83 xiv Figure 4.13 5.1 5.2 Page Differential capacitance at 1000 Hz vs. electrode potential for polycrystalline lead prepared by method (0) in (o) 0.5 NaF and (x) 0.5 Na C104 ................... 91 Log kapp’ where kapp is the measured rate constant, vs. electrode potential at mercury (closed symbols) and polycrystalline lead prepared by method (0) (open symbols) in 0.5 M NaCTo4 except for Cr(NH3)5ncs2+ in 40 mM La(ClO4)3 for a number of transition- metal complexes as fbllows: (o) Cr(OH2)3+; (V) 01mg);+ , (a) 2Cr(NH3)5c12+ ; (a) Cr(OH2)5SCN2+; (0) Cr(ouz)5c12+ ;(A) Cr(NH3)5 ncsz”; (a) Cr(NH3)50Hg+; (o) Cr(0H2)5N§+; (o) Cr(NH3)5N2+, (x) Cr(0H2)5F2+; (+) Cr(OH2)50503 . . . .' ...... 104 Differential electrode capacitance C against electrode potential E for (a) polycrystalline silver. (b) silver containing a monolayer of upd lead. (c) as in (b) but with addi- tional ca. two monolayers of bulk lead deposit. (d) polycrystalline lead. Lead layer prepared as indicated in Ref. 108. Electrolyte was 0.5 M NaClO4, pH 3.5; for (b) and (c) additionally contained 0.6 uM Pb+2 ................ m XV Figure 5.3 6.1 6.2 6.3 6.4 6.5 6.6 6.7 Differential capacitance at 1000 Hz vs. electrode potential for polycrystalline lead prepared by method (D) in 0.5 M NaClO4 at various temperatures: (x) 5.5°C; (o) 16.5°C; 600 25 5°C; (v) 36.2°C .......... .. . . . Structures of cobalt porphyrins ......... Diagram of a Rotating Ring-Disc Electrode (RRDE). .' .................... Schematic diagram for the connection of the "modified" bipotentiostat ..... . ..... Schematic diagram for the operation of the "modified" bipotentiostat .......... RRDE voltammogram for Fe(CN)E'53/-4 couple at the PG/Pt electrode. The potential of the Pt ring was held at 0.7 V vs. SCE. The scan rate of the cyclic voltammogram was Plot of the limiting disk current i2 vs. 1/2 the square root of rotation rate (w ) for the reduction of Fe(CN)g' (1.4 mM) on the PG/Pt electrode ................. Cyclic voltammogram at the "blank" graphite electrode of the RRDE at 0.1 V/sec in 0.5 M HTFA ....................... yvi Page . . 129 143 147 . . 152 154 161 163 ’ Figure 6.8 6.9 6.10-6.13 6.14-6.20 6.21 Page Cyclic voltammograms for the reduction of oxygen in 0.5 M HTFA at 0.1 V/sec on (a) the "blank" graphite disk electrode; (b) the platinum ring electrode; (c) the monomeric porphyrin-modified surfaCe; (d) the dimeric porphyrin-modified surface .............. 166 Cyclic voltammogram for the "bulk" redox reaction of C03“2+ of Co-Co-4 on the graphite disk electrode in 0.1 M TBAP dichloromethane at 0.2 V/sec ....... . ............ 168 Cyclic voltammograms for the "surface" re- dox reactions of Co3+l2+ (?) at the PG disk electrode in 0.5 M HTFA aqueous solution de- aerated with nitrogen at 0.2 V/sec. The por- phyrins under consideration are indicated in the corresponding figures ............ 173-176 Disc (upper-iD) and ring (lower-iR) currents for the reduction of oxygen in 0.5 M HTFA on the PG/Pt electrode (w = 600 rpm). Scan rate for the corresponding cyclic voltammogram for oxygen reduction at the PG disk electrode is at 0.1 V/sec except Figure 6.19 at 0.2 V/sec ...................... 180-186 Proposed mechanism for four-electron reduction of oxygen molecule at the dimeric porphyrin— modified graphite surface .............. 196 xvi-i Figure - Page 6.22 Proposed configuration for Co-O-O-Co complexes ...................... 199 xviii CHAPTER I INTRODUCTION The investigation of homogeneous electron-transfer reaction51'11 in terms of experimental measurements as well as theoretical inter- pretation has long been an interesting subject and has successfully progressed to a certain extent.' There are many ways with which the kinetics of electron-transfer reactions can be affected, such as Coulombic interactions, solvent reorganization energy, frequency factors, and electron and nuclear tunneling. Thus in order to in- vestigate the elementary electron-transfer processes, it is desirable to choose suitable chemical systems with which individual factors that control electrochemical reactivity can hopefully be separated. Such tactics have been extensively undertaken in the study of homo- geneous reactions.6’]0’11 Solid electrodes have successfully shown their usefulness in industrial practical applications, such as in the areas of batteries, fuel cells, or electrocatalysts. Thus, in order to improve their potentiality for the practical applications, it is essential to understand their fundamental properties, such as the electrode- solution interfacial structure and the thermodynamics and kinetics of electrode reactions. Although similar kinetic concepts apply to both homogeneous and heterogeneous redox reactions, the measurement and interpretation of heterogeneous electron-transfer reaction kinetics are still very scarce and incomplete. The application of electrochemical methods to the study of the energetics of electron-transfer reactions of- fers several advantages over the study of homogeneous processes. In homogeneous reactions, both of the reactants have to be activated 12’13 in order to allow elec- to reach the appropriate configuration tron-transfer to occur. With electrochemical reactions, however, only one reactant is required to be activated; the energy of the electrons within the electrode can be conveniently altered by an external source, the applied electrode potential. Therefore, the driving force for electrode reactions can be obtained by simply altering the applied electrode potential (i.e., overpotential). In contrast, the thermodynamics of homogeneous reactions can only be altered by changing the temperature or pressure. A fundamental question in electrochemical kinetics concerns the various ways in which the chemical nature of the electrode material may influence the energetics of electron-transfer reactions. This has been carefully examined at several solid electrodes14 (Au, Ag, and Pt) and liquid mercury electrodes for a number of mechanistically simple transition-metal complexes. In this work, the polycrystalline lead electrode was chosen for study, mainly because it possesses a fairly negative polarizable potential region compared with Au, Ag, or Pt. Therefore, the interference of the adsorption of anions on the study of electrode kinetics is insignificant compared with other well-studied solid electrodes. In addition, polycrystalline lead or lead oxide are the most common electrode materials being used in bat- tery technology. Galliun is another comonliquid metal other than mercury whose electrode-solution interfacial structure has been well studied and is shown to be markedly different from that at mercury. Therefore, it is interesting as well as important to compare elec- trode kinetics at gallium and mercury surfaces. First of all, it is obvious that the ionic double-layer struc- ture at the electrode-solution interface will be dependent on the chemical nature of the electrode material. Thus, it is important to understand the fundamental properties of this double-layer struc- ture at which electrochemical reactions occur. Valuable information of this type can be obtained from the measurements of differential I capacitance. In this work, the measurement of the differential double-layer capacitance was performed at the lead-aqueous inter- face in order to evaluate the effect of the ionic double-layer on the corresponding kinetics of electrode reactions. It has been shown that the ionic double-layer effect can account for the observed difference in the electroactivity between different electrode-solution interfaces. However, the comparison of electrode kinetics at polycrystalline lead, gallium, and mercury electrodes in this study indicates that the ionic double-layer effect cannot en- tirely explain the difference in the electroactivities. Contrary to homogeneous reactions, temperature is not usually employed as a variable for heterogeneous reactions. The experi- mental accessibility of electrochemical activation parameters from the measurements of the dependence of temperature upon the rate constants has been questioned.]5’16 Nevertheless, it has been 17 that the so-called "ideal" activation parameters determined shown at a constant Galvani potential can be obtained by utilizing a non- isothermal cell that is described in Chapter II. The evaluation of such activation parameters provides a means to examine enthalpic and entropic contributions to the energetics of heterogeneous electron transfer. CHAPTER II BACKGROUND The main purpose of this work is to examine to what extent the nature of the electrode material will affect electrode kinetics. It is essential to understand the thermodynamics of electrode inter- faces in order to pr0perly interpret the corresponding electrode kinetics. As mentioned in Chapter I, the electrode-solution inter- facial structure is expected to be different from one electrode to another. It is useful to understand some fundamental concepts of the double-layer theory in order to characterize the electrode- solution interfacial. At the same time, the measurement of specific adsorption of anions provides a means to investigate the intrinsic property of the interfacial structure. Then, the theoretical treat- ment of the elementary electron-transfer processes will be discussed. Since the ionic double-layer structure greatly depends on the chem- ical composition of the electrode, in order to compare electrode kinetics at different electrode surfaces, it is necessary to con- sider the corresponding ionic double-layer effect. Furthermore, the evaluation of activation enthalpy and entropy can provide in- sight into the properties of the transition state for the elementary electron-transfer reactions. 1. Thermodynamics and Kinetics of Electrode Reactions A simple electrode reaction can be expressed as 0x + ne' (electrode, ¢m) I Red . (2.1) 6 where Ox and Red are the oxidized and reduced species of a redox couple, n is the number of electrons involved, and am is the abso- lute potential difference (Galvani potential) between the electrode and solution. The thermodynamics of the redox couple can be des- cribed in terms of the overall electrochemical free energy of reac— tion AGb expressed as a? = AG° - nF¢m (2.2) where AG° and nF¢m are the chemical and electrical components of AGb respectively. Generally, the chemical reaction rates can be altered by the applied electrical driving force nF¢m. The Galvani ‘potential is experimentally inaccessible. However, by the use of a reference electrode which has a stable potential, the so-called electrode potential E, which is equal to the sum of the Galvani potential at the two electrode-solution interfaces, can be experi- mentally evaluated. The standard electrode potential E° is the fundamental thermo- dynamic parameter of a redox couple. It is the equilibrium value of E when both Ox and Red are in their standard states (i.e., their f is more activities equal to one). However, the formal potential E frequently used, which is evaluated for equal concentration of Ox and Red instead of equal activity. Since at the standard state AER = 0, then AGb for the reactions (2.1) at a given electrode potential E can be formulated as D ml 0 ll nF(¢m - ¢;) nF(E - E°) (2.3) where ¢$ corresponds to E°. Therefore, the overall driving force AGb of an electrochemical redox couple reaction can be evaluated from the measurement of (E - E°), even the individual values of o; and ¢m are unknown (or experimentally inaccessible). The general form of the net current of an electroreduction re- action at a given electrode potential can be written a518 i = i°{exp[-anfn] - exp[(l-a)nfn]}. (2.4) where f = RT/F (R is the gas constant, T is the absolute temperature, F is the Faraday constant), n'= (E - E°) is the so-called over- potential, i° is the exchange current at equilibrium state and a is the cathodic transfer coefficient. The transfer coefficient provides a measure of the symmetry of the energy barrier for the electrode reaction. For small values of n, i.e., Inl << l/nf, Equation 2.4 becomes i = i° (nfn) (2.5) and the resulting Equation 2.5 shows the linear relation between i and n- For large values of n, a Tafel relation can be obtained 1 = i°exp(-anfn) (2-6) 1.) or RT q, RT . - -fif-£n1 - EFF 2n1 (2-7) The plot of 0 vs. zni is termed a Tafel plot; the slope is frequently used to evaluate the apparent transfer coefficient. It is quite reasonable to assume first-order kinetics for simple electrode reactions such as the redox reaction 2.1. Then the measured rate constants are c c ' ‘ k = (208) ob nFCox and k3 = 13 (2 9) ob nFCred for the cathodic and anodic processes reSpectively. Therefore, the relationship between the observed rate constant and the applied elec- trode potential E (i.e., driving force) can be generated by substi- tuting Equation 2.8 into Equation 2.4 for the cathodic reaction kc = kS exp[-anf(E - E°)] (2 10) ob ob ' and Equation 2.9 into Equation 2.4 for the anodic reaction kgb = dab exp[(l-a)nf(E - E°)] (2-11) 10 where kgb is the standard rate constant for reaction 2.1. Then the transfer coefficient a can be calculated from _ -2.3RT 31°9 kob a - ( ) F SE (2.12) There are many ways in which the observed rate constant will be influenced, such as the temperature, the composition of the support- ing electrolyte solution, and the nature of the electrode material, and these influences will be discussed as follows. 2. The Structure of the Electrical Double Layer19 Since electrode reactions are expected to occur only within the so-called "electrical double layer" region, it is important to consider the structure and the behavior of the double layer before any further discussion of the theoretical treatment of the elemen- tary electron-transfer reaction. The first model describing the structure of the electrified electrode-solution interface was pro- posed by Helmholtz (1853) and Quincke (1861), which assumed the »double layer as a parallel plate capacitor. Then Gouy (1910) and Chapman (1913) independently modified this model by calculating the distribution of the electrode potential as a function of the electrolyte concentration by assuming a Boltzmann distribution of the ions between the double layer region and the bulk of solution. However, in the Gouy-Chapman model, ions are treated as point charges. Stern (1924) took account of the finite size of ions in the calculation of the distribution of the electrode potential, and 11 pointed out that the ions could not reach the electrode surface beyond some "plane of closest approach". The approximate validity of the Gouy-Chapman-Stern (GCS) model19 was experimentally demon- 20’2] This double layer model is currently used strated by Grahame. by electrochemists. According to the GCS model, the double layer can be divided into two regions (i) the compact (inner or Helmholtz) layer between the electrode and the plane of closest approach, (ii) the diffuse (outer). layer extending from the plane of closest approach to the bulk of solution. Figure 2.1 shows a schematic double layer. The measured double layer capacitance can be expressed as _ 1 f-cM-Z + E'— (2.13) where the subscript M and S denote the metal and solution respec- tively, and CM_2 and Cz_S are the capacitance of the compact and l,19 the elec- diffuse layer respectively. According to the GCS mode trode charge qm is related to the potential at the outer Helmholtz plane ¢2 (fbr convenience the potential in the bulk of solution ¢s is always set at zero) by -Zf¢ m [RTe 2C5 (e 2 q :3 7". i - 1)]1/2 (2.14) where e is the dielectric constant, 2 is the ionic charge of ions i, and C? is the bulk concentration of ions i. The differentiation of Equation 2.4 yields the diffuse layer capacitance Figure 2.1 12 The electrode—solution interfical struc- ture including the Specifically adsorbed anions MI: TA! NE TAL 0 9'0 0 13 VIAYA ‘I' VIV ‘II' VIA “Y1; ‘YAV Eb cation 69 09 G 6 G 0 in-- inner Helmholtz plane (p1 is the corresponding potential) oHp-- outer Helmholtz plane (p2 is the corresponding potential) ¢m-- potential at the electrode surface ¢s - ~potential at the bulk (set to zero) Figure 2.1 14 ' |Z|f¢2 . CZ-S = |Z|fA cosh ( 2 ) (2.15) However, the calculation of the compact layer Capacitance requires a much more complicated theoretical treatment. For a first approxi- mation, it is reasonable to assume CM-2 to be independent of the electrolyte concentration. Good agreement between the experimental 20’2] on the basis resultsand the GCS theory was obtained by Grahame of this assumption. HoweVer, this Simple double-layer model may only work for homo- geneous electrode surfaces, such as liquid electrodes and single crystals. The influence of the crystallographic structure of the polycrystalline electrode surface on the double-layer structure was 22,23 first considered theoretically by Grigoryev. Furthermore, the qualitative analysis of the models of electric double-layer struc- ture at polycrystalline electrodes has been studied by Damaskin.24 Figure 2.2 shows two possible equivalent circuits of the double- layer of a polycrystalline electrode consisting of two single crystal faces. In Figure 2.2a, each single crystal face has its own Helm- holtz and diffuse layers (Model I). In Figure 2.2b, each single crystal face possesses its own Helmholtz layer while the diffuse layer is common to the entire electrode surface (Model II). These models have been employed to study the effect of crystallographic inhomogeneity of a polycrystalline electrode surface on the result- ing "average" point of zero charge (pzc).24 They have also been . . . . . . 25 examined 1n connection with the electroreduction of several anions. 15 Figure 2.2 Equivalent electric circuit of polycrystalline electrode models: (a) Model I; (b) Model 11 16 (I) (I) C (.0 —. L—LZHc (a) H d Cél) and Cél) are the inner— and diffuse- layer capacitance of single-crystal face 1. (2) and 0:2) Ch of single-crystal face 2 are the inner- and diffuse- layer capacitance ( l) C H P¢ ‘4 m [—— (2) cu Cél) and Céz) are the inner-layer capacitances of single- crystal face 1 and 2 respectively. c” d is the common diffuse-layer capacitance. Figure 2.2 17 The measurement of the electrocapillary curve is a straight- fbrward way to examine the thermodynamics of an ideal polarizable electrode surface. The phenomena of the electrocapillary curve,19 surface tension as a function of electrode potential, can be des- cribed by utilizing the Gibbs adsorption isotherm26 Ill -dY = q ° dE + ZI‘i - du. (2.16) l where y is the surface tension, Pi is the surface excess of the ionic species i, and ui is the chemical potential. Then the elec- trode charge qm can be obtained from the corresponding Lippmann equation27 by differentiating Equation 2.16 q'" = - ( g} ) 11,- (2.17) at a constant temperature and pressure. At the electrocapillary maximum the electrode charge will equal zero as expected from Equa- tion 2.17, and the corresponding electrode potential E is termed the pzc.19 In general, the pzc coincides with the observed sharp minimum of the differential capacitance curve for a dilute solution consisting of nonspecifically adsorbing electrolytes.19 The oc- currence of the sharp minimum is a result of the parallel relation between the compact and diffuse layer capacitance. Since the diffuse 19 layer capacitance decreases with the square root of the electro- lyte concentration and the compact layer capacitance is independent 19 of the concentration, a minimum in the capacitance curve can therefore be expected when the electrolyte concentration is decreased. 18 For the study of specific adsorption of anions at the electrode- solution interface, mixed electrolytes28 consisting of a salt of the adsorbing anions and the nonspecifically adsorbing base electrolyte at constant total ionic strength have often been employed. The 28’29 method is used to determine the con- so-called Hurwitz-Parsons centration of the specifically adsorbed anions. In general, the Hurwitz-Parsons analysis is obtained from the Gibbs adsorption iso- therm. By assuming the amount of the diffuse layer adsorption is proportional to the bulk concentration, the Gibbs adsorption Equa- tion 2.16 can be reformulated as -dy = qm - dE + r;RT - dtnx (2.13) where P; is the component of PX present in the inner layer i.e., the surface concentration of specifically adsorbed anions, and x is the molar fraction of the adsorbing anions. Two cross-differen- tial equations can be obtained from Equation 2.18 3E alnx' (-—T) m = RT (———r) . (2.19) BI‘x q aqm I‘x and ‘ a m aRnx (5%TJE = - RT (“SE'lr' (2.20) x x Equation 2.19 was utilized by Dutkiewicz29 and Parsons28 and Equa- 30 tion 2.20 was employed by Weaver and Anson in their analysis of the specific adsorption of iodide from the mixed electrolytes 19 containing iodide and fluoride. Parsons, et al.28 found that the adsorption was well described by an isotherm congruent with respect to the electrode charge density qm. This implied that (aznx/aqm)r. was independent of the P;, then the Equation 2.19 could be integrated at constant am to give Equation 2.21 and from which the value of P; was calculated. . - '1' 33.2.01 - . rx - AEq /RT (aqm )1"); (2.21) In a similar way, r; can be evaluated from Equation 2.22 which is derived from Equation 2.20. (2.22) r = - Aqu/RT (——3‘""" ' ) . x 3E PX Details of the calculation of the surface concentration of the specifically adsorbed anions are discussed in Chapter IV. 3. Theoretical Treatment of Heterogeneous Electron-Transfer Kinetics 1 7-9 Most of the theories ’ of electron-transfer reactions were originally developed for homogeneous reactions. Heterogeneous re- 31 actions can be treated in a similar way to homogeneous reactions; the former is an especially simple type of electron-transfer process in which only one reactant needs to be activated for the reaction to occur. Analogous to homogeneous reactions, electrode reactions can 1 be divided into two broad classes, outer-sphere and inner-sphere 20 pathways. Figure 2.3 illustrates the essential differences between inner- and outer-sphere reactions. Outer-Sphere reactions can be defined as those where there is no direct interaction between the reacting ions and the electrode surface, i.e., the inner-shell sol- vent molecules adjacent to the electrode surface remain intact during the formation of the precursor state and transition state. If there is strong interaction between the reactants (to be more precise, the coordinated ligands) and the electrode surface, i.e., the reacting ions can penetrate through the inner-layer solvent molecules to form specifically adsorbed precursor and transition states, those reac- tions are labelled inner-sphere reactions. Two methods32 have been developed for distinguishing between inner- and outer-sphere electrode reaction mechanisms. These are (i) the response of the reaction rate to the addition of strongly adsorbed but chemically inactive anions and (ii) the difference in the potential dependence of the reaction rate, i.e., inferring mech- anisms from the values of a. The corresponding change of oz as a result of the change of the electrode charge by the addition of strongly adsorbed anions will result in the change of the observed reaction rate (Alogkgb) = (a1 - 2) ‘2—gR‘T' (A¢2)E (2.23) Since the adsorption of anions will produce negative values of (A¢2)E, for cationic reactants undergoing outer-sphere reactions their reaction rates will be enhanced by the addition of specifically 21 Figure'2.3 Pr0posed reaction sites for Cr(III) aquo and ammine complexes at the electrode-aqueous interface METAL 22 '3 5 49 Pa" Illmlllv Ill1 'llII» 90 QT '0 09 10 9 9T QT ‘ 06 0T 3%? AV co-ordinated anion <[[I) co-ordinated ammonia @ water molecule (iv) reactionsite for metal ions inner-sphere reaction (iii) proposed reaction site for Cr(III) ammine complexes. (ii) proposed outer Helmholtz plane, reaction site for highly 3+ 3+ hydrated cations, ie., La , Cr . (i) outer Helmholtz plane (according to Bockris, Devanathan & Muller). Figure 2.3 23 adsorbed anions. For inner-sphere reactions, however, the strongly repulsive interaction existing between the anionic bridging ligands of the reacting ions and the specifically adsorbed anions will diminish reaction rates as a result of repelling the reacting ions away from the electrode surface. A general form of the rate expression for both classes of reac- tion mechanisms was derived33 E _ b _ i _ 1 . . 1ogkalpp - logk + logy logy ”Helms” - AGAR + FE) + AGAP] (2.24) where Yb and y* are the activity coefficients of the bulk reactant and transition state respectively, and k is a potential-independent rate constant, E is the electrode potential, and AG;R and ASAP are the standard free energy of adsorption of the reactant and product respectively. Then from Equation 2.12, a can be expressed as aw a (AG° ) I-a (AG° ) _ 1 AP I AR 0‘app ‘ F 3E 1’ F SE 3 l 0‘1 (2°25) or alternately for outer-sphere reactions Bcbz Gapp = (II - (GI - Z) (-a-E-)u (2.26 where “app is distinguished from the intrinsic al. The typical values of (doz/BE)u in nonadsorbing electrolytes at ionic strengths 24 of 0.5-1 M are 0.02-0.05.30’35 For a simple electrode reaction, “I can be taken as 0.5. Therefore, for reactants (Z 3_l) undergoing outer-sphere reactions, the values of “app will be greater than 0.5 as predicted from Equation 2.26. For inner-sphere reactions, to the spontaneous adsorption of re- actants and products is too weak to measure, it is relatively dif- ficult to evaluate both 3(AGAP)/35 and 3(AGAR)/3E in Equation 2.26. However, a number of isothiocyanate complexes of chromium(III)36 have been found to be adsorbed in measurable quantities and the cor- 'responding values of 3(AGa)/aE were found to be negative. This is opposite to what is expected for cationic reactants whose free energy of adsorption will become more negative as the negative charge on the electrode surface increases. The resulting negative values of 3(AGR)/3Eofisothiocyanate metal complexes implies that the anionic ligand will retain at least part of their anionic character when holding the complexes at the electrode surface. Thus, it is reason- able to assume the values of 3(AGAP)/3E and A(aGKR)/3E to be nega- tive for anion-bridged inner-sphere reactions. Thus if a1 = 0.5 from Equation 2.25 the values of a for inner-sphere reactions aPP are expected to be less than 0.5. The mechanistic diagnoses based on these two methods have been found to be valid fOr distinguishing between a number of inner- and outer-sphere reactions at mercury electrodes.32 Similar to homogeneous reactions, heterogeneous electron-trans- fer processes are anticipated to proceed via two steps:4 (i) the formation of a precursor state by bringing the reacting ions from 25 the bulk to a suitable site within the double layer region where the electron-transfer reaction can occur (ii) the thermal activation of the precursor state enabling the electron to transfer and subsequent deactivation to form the product successor state. Thus, Reaction 2.1 can be rewritten as * Ox(solution) I Ox Ox* + nejZ Red* (2.27) * Red 12 Red 1: v: I where 0x and Red indicate the precursor and successor states, respectively. Assuming that the elementary electron-transfer step is rate determining, we can write the observed (overall) rate con- stant kob as (pre-equilibrium model)4 k = k ' K ob et P (2'28) where KP is the equilibrium formation constant of precursor states and ket is the first order rate constant for the elementary electron- transfer reaction within the precursor state. For the outer-sphere reaction KP can be expressed as .KP = K 0 ° exp(-WP/RT) (2.29) where K0 is the statistical value of KP when WP = 0, and WP is the 26 work required to bring the reacting ions to the reaction site. The value of K0 can be taken as the reactant radius r, indicating that all the reacting species within the distance r of the plane of closest approach will have a rough equal chanCe of undergoing elec- tron transfer. For a first approximation, the work term WP can be attributed to the Coulombic interaction, so that WP = ZForp, where Z is the net charge of the reacting ion, ¢rp is the average poten- tial at the reaction plane. This work term is mainly responsible for the double layer effect upon the observed rate constants. For the elementary electron-transfer step, k can be expressed . et utilizing a "semi-classical" model4 k = K - exp (-a0’*/ RT) (2.30) et ° F el n ° vP where Ke] is electron transmission (tunneling) coefficient, Fn is nuclear tunnelling factor (in general, Pn roughly equals unity), up is a nuclear frequency factor (~1013 sec"), and AGI is the electrochemical free energy of reorganization for the elementary reaction. Therefore the overall rate constant of Reaction 2.1 de- rived from the pre-equilibrium model is —4 kob = K0 - Kel ° Vp exp(-WP/RT) exp (-AG / RT) (2.31) However, a different model, a so-called "reactive-collision" model,3 is commonly used in the study of outer-sphere reactions. The ex- pression of the overall rate constant derived from the reactive- 27 collision model is kob = re12e exp(-WP/RT) exp(-AGl/RT) (2.32) 11 where Ze is the electrochemical collision frequency (~10 sec'1). For simplification Equation 2.31 and 2.32 can be written as kob = A - exp(-h6*/RT) (2.33) where A is the pre-exponential factor, which is 3x105 and 5x103 cm sec"1 for the pre-equilibrium and reactive-collision models, respec- tiVely. The comparison between these two models has been thoroughly discussed from theoretical as well as experimental points of view. 4. Double Layer Effect on Electrochemical Kinetics For the first approximation, the work term WP in the rate expres- sion Equation 2.32 can be assumed to be mainly due to the double- layer effect. Figure 2.4 shows the free energy profile for a simple electrochemical reaction 0x + e = Red plotted against the nuclear re- action coordinate. In Figure 2.4, P and S denote the precursor and successor states, respectively, and 0 and R denote the oxidized and reduced species, respectively. According to Figure 2.4 AG§_P = AGbrc + (WS - WP) and AG:C = F(E - E°) at a given electrode poten- tial E, then AG§_P = F(E - E°) + WS - WP). According to the relation _* . .Qié§_L_.. (2.34) o - “I < 654,) 28 Figure 2.4 Free energy profile for simple electro- chemical reaction free energy 29 nuclear reaction coordinate Figure 2.4 30 where AG* is the reorganization free energy and a1 is the intrinsic transfer coefficient, it denotes to what extent the reorganization free energy will change upon altering the electrochemical driving force A S-P' Therefore AGI can be correlated to AG?"t by afi* = hélnt + aI(WS - up) + aI(E - E°) (2.35) where Agint is the intrinsic barrier for electron-transfer reactions. Agint will be the free energy of the overall reaction when there are no thermodynamic driving forces, i.e., WS : WP = O and E = E°. By substituting Equation 2.35 into Equation 2.32 and taking the natural logarithm of both sides, it yields Equation 2.36. E _ -¢ - [wP + aI(NS - up)l - [aIF(E - E°)] (2.36) The last term of the right hand side of Equation 2.36 is the thermo- dynamic driving force and the second term is the intrinsic free energy barrier. It is useful to rewrite Equation 2.36 as E _ E RTtnkcorr - RTRnkob + [WP + aI(WS - WP)] (2.37) where kcorr is defined as the "double layer corrected" rate constant. As mentioned before, the work terms (WS and WP) can be treated as a result of the electrostatic interaction. Therefore, for the one 31 electron reduction reaction, WP==ZF¢rp and Ws=r(Z-1)F¢rp since the charge of the product is (Z-l). Then the Equation 2.37 will become E E sinkob = tnkcorr - (z - a1)f¢ (2.38) PP where (Z - aI)can be regarded as the effective charge on the reacting ion in the transition state. Then the term (Z - aI)f¢rp can be taken as the work term required to bring the reactants from the bulk to the transition state. This equation is also known as a form of the Frum- 37 kin relation, and is frequently used to correct the double layer' effect for outer-sphere reactions. 5. Activation Parameters of Electrode Kinetics The significance of electrochemical activation parameters has often been misunderstood. The energetics of the tranSition state of the electron-transfer reaction can be explored by the measurement 15 of the of activation parameters. There are different definitions electrochemical activation parameters which depend on which electrical state of the electrode reaction is controlled. The "ideal" and "real" activation parameters are the temperature dependence of reaction rate constants evaluated at constant Galvani potential am and constant overpotential (with respect to formal potential) respectively, and were first defined by Temkin.15 From the simplified rate constant expression Equation 2.34 and together with the Gibbs free energy relation 32 A61 = 1311* - T2353f (2.39) * and AS* are the activation enthalpy and entropy, respec- where AH tively, the rate constant can be related to the corresponding activa- tion parameters as kgb = A exp (R #) exp (% #) (2.40) Therefore, the reaction enthalpy and entropy of activation can be evaluated from the study of the temperature dependence of rate constants (Arrhenius relation). It has been critized about the experimental accessibility of the "ideal" activation parameters, because at least one component of the overall cell potential other than ¢m which is expected to be held constant will change when the temperature is varied. By the use of nonisothermal cells, however, may be a possible way to get around this cause for doubt. If the nonisothermal cell potential Eni is held constant, the temperature dependence of the metal-solution Gal- vani potential ¢m will be39’40 34> d¢ .. d¢ (3,3)“, = - (jail) + ( d—i—C) (2.41) where ¢tij is the Galvani potential difference across the thermal liquid junction between the "hot" and "cold" electrolyte, and ¢tc is the "thermocouple" potential difference between the hot and cold 33 regions of the working electrode. The value of (dotC/dT) has been shown to be very small (+ 15 uV/deg).4] The value of (d¢tij/dT) cannot be determined experimentally. However, it is probably also ).40b small (50 pV/deg Therefore, it is appr0priate to assume that (d¢m/dT)Eni 2 0. Therefore, holding Eni constant as the temperature is changed could also maintain the Galvani potential constant at least within these limits. The uncertainty of ASI, which results from the assumption (d¢m/dT)Eni = 0, can be estimated to be about 1 -1 17 i0.5 cal deg' mole From Equation 2.40 the "ideal" activation enthalpy can be ex- pressed as 1/2 AHidea] - ‘R (2.42) a“? It" 1/2 where the term tnT results from the temperature dependence of the 9 collision frequency Ze of the reactive-collision model. There- fore, the "ideal" activation enthalpy can be obtained from the slope of the plot of (tnk - RnTI/z) vs. T’]. Furthermore, the double- layer corrected activation enthalpy AHI can be gained by combin- corr ing Equation 2.42 with Equation 2.38 i _ i E a(pr AHcorr ' AHideal + F{(acorr ' Z)[;T:§J¢m} (2°43) T From Equation 2.43, it is necessary to evaluate the temperature de- pendence of the potential at the reaction plant ¢rp from the measure- ment of the temperature dependence of the pzc in order to evaluate 34 . . 1 the coeff1c1ent [aorp/3(T)]¢m. The relationship between the "ideal" and "real" entropies of ac- tivation can be written as follows i Si ASideal = A real + GASrc (2°44) where AS;c is the reaction entropy of a redox couple.39 The value of As;c is also obtained by the use of a nonisothermal cell from the measurement of the temperature dependence of the formal poten- tial of a redox couple. Thus, AS;c can be evaluated from the fol- lowing equation dEnl d3” d3 d¢ .. d¢"1 ”ti" = ”an * 71"?£ i will i F(Tai') = Asia (“5’ where (d¢tij/dT) and (ddtc/dl) are close to zero as discussed before. The "real" activation entropy Asteal can be correlated to the tem- perature dependence of the intrinsic reorganization barrier42 4e for the electron-transfer reaction as appears in Marcus theory8 by the relation 4 die ASreal = ' 43T' (2'46) where Ae/4 is equal to the value of A64l corr' By substituting the di- 8,9,26 electric continuum expression for 4e into Equation 2.46, the value of Asteal is estimated to be close to zero ( 0.25 e.u.). The 35 "real“ activation entropy is the mean of the entropic driving force of the forward and backward reactions 4 _ i,f i,b _ ASrea] - 0.5 (ascorr + Ascorr) (2.47) According to the Marcus theory, AS - - AS by assuming that corr corr the free energy curve is symmetrical, i.e., the transition state for the electron-transfer reaction has a similar environment to that for the reactants and products, then the value of Asteal is also equal to zero. The study of the activation entropy ASI provides a means to evaluate electron tunneling as well as the frequency factor for the kinetics of the elementary electron-transfer processes.‘ In addition, the validity of the application of the Marcus theory to the present study can also be tested. In the derivation of the Frumkin Equation 2.38, the work terms have been assumed to be totally due to Coulombic interaction. How- ever, other contributions to the work terms are still possible, such as the specific solvent interaction presented between the reacting ions and the electrode surface. Thus, it is worthwhile to formulate the activation parameters in a general form as follows. Another equivalent form of the rate expression Equation“-45 2.23 is RTtnkE = RTtnA-AGI -[AG° + (AG° - AG°)] - [ F(E - Ef)] ob int P “I 5 p “I (2.48) 36 where AG; and AG; represent the free energies required to form the precursor and successor states from the bulk reactant and product, respectively, and AGint is the so-called "intrinsic barrier". AGInt is the activation energy for the elementary electron-transfer step when the work terms AG; and AGE, and the overall driving force F(E - Ef) each equal zero. The "real“ activation enthalpy AHreal can then be expressed as E d(£nk ) ARI = -R [ °b ] = on* + (on; + aI(AH° dbl) int . s - 4118)] (2.49) where AH; and AH; are enthalpic components of the work terms of AG; and AGg, and AHint is the "intrinsic" activation enthalpy for the elementary electron-transfer step. In a similar way, the "real" activation entropy Asteal can be related to the "intrinsic" activa- ' tion entropy AS?"t by ’ 4 4 AS = ASint + [ASS + a1 (AS° - ASS)] (2.50) S where AS§ and AS3 are entr0pic components of the work term AG; and AGP. CHAPTER III EXPERIMENTAL 37 1. General Apparatus The three-electrode configuration was used in this study. For the measurements of electrode kinetics a conventional two-compart- ment electrochemical cell46 was usually employed, in which the ref- erence compartment was separated from the working compartment with a fine grade glass frit (Corning Co.). The glass frit was to prevent the mixing of the working solution with the electrolyte solution diffusing from the reference electrode and also to provide sufficient electrical conductivity for the operation of the potentiostat. A I three-compartment cell was used for bulk electrolysis, which utilized a mercury pool as the working electrode and had another glass frit to separate the counter electrode in order to prevent the mixing of products; For the temperature dependence measurements, a noniso- thermal cell was used, in which the temperature of the working com- partment was varied while keeping the temperature of the reference compartment constant. In order to vary the temperature of the work- ing solution, a water insulator jacket was also fabricated around the working compartment to maintain the temperature by a flow of thermostat water. A large counter electrode, either platinized gauze or spiraled platinum wire, was utilized for the measurement of the differential double layer capacitance. The large capacitance of the counter electrode minimizes its influence upon the measured double layer capacitance of the working electrode. The reference electrode employed in all of the measurements was 38 39 the saturated calomel electrode (SCE) (Sargent-Welch Corp.). The KCl filling solution of the SCE was changed to NaCl solution when measurements were performed in‘ClOi. This was done to prevent the precipitation of KC104 in the fiber junction. The potentials of reference electrodes were occasionally checked with a fresh home made "master" KSCE (potassium SCE). Since the electrochemical measure- ment was very sensitive to the presence of impurities, especially for solid electrodes, a relatively thorough, as well as tedious, pro- cedure was used in this laboratory to clean glassware. The glass- ware were first soaked in a 1:1 HNO3 and H2S04 solution for one day, then rinsed and soaked in a highly purified water for two days. 2. Reagents. The quality of water used to prepare all of the solutions was very critical to the electrochemical measurement. In this laboratory, a great deal of effort has been taken in the preparation of highly purified water. The water from a "Milli-Q" purification unit (Mil- lipore Corp.) was suitable for mercury electrodes. However, much more highly purified water was needed for solid electrodes and the measurement of double layer capacitance. Conway and coworkers48 proposed a relatively complicated method to purify water (pyro- distillation). The purification procedure involves passing water vapor through a column packed with platinum gauze and heated to 750° to 800° C in a stream of oxygen. In this way the organic materials could be catalytically combusted and entirely removed. The other way was to use a quartz subboiling still (Dida-Science Inc.) 40 which offered an efficient way to remove cationic impurities. In the subboiling distillation, infrared heaters vaporized liquid from the surface without boiling, thus minimizing the problem of entrain- ment associated with ordinary distillation. ‘The purity of prepared water could be evaluated from the reproducibility of electrode kin- etics and the stability of the measured differential double layer capacitance. Since oxygen is chemically active, the dissolved oxygen in the working solution was generally removed by purging solutions with a flow of purified inert gas (such as N2, Ar, or He). The purifica- tion of inert gas was accomplished either by bubbling through an aqueous solution containing vanadous ions and amalgamated zinc or a more efficient way by passing through a heated catalytic column packed with BASF R3-11 catalyst (Badische Aniline und Soda-Fabrik). Analytical grade reagents were used without further purification for mercury electrode studies. However, for solid electrode experi- ments they were recrystallized from highly purified water. Sodium perchlorate, which was used to prepare most of the solutions, was recrystallized from a solution prepared from 60% perchloric acid and sodium carbonate. A Cr(0H2)63+ stock solution was prepared by dissolving Cr203 in HC104 with the addition of H20. The syntheses of Cr(III) complexes followed standard published procedures. The 49 was used as the starting material for the preparation of Cr(NH3)50H3+,49 double salt aquopentaaminechromium(III) ammonium nitrate + + + + Cr(NH3)5N§ ,5‘ Cr(0M2)5N§ .53 Cr(NH3)5C12 .49 Cr(NH3)5scu2 .50 and + 49 Cr(0H2)5SCN2+.52 Cr(0H2)5F2+,49 Cr(0H2)5C12+, and 0r(0H2)50503. were also prepared as described in the literature. 41 3. Electrochemical Techniques Generally, the electrical response of an electrochemical cell is equivalent to the electrical circuit shown in Figure 3.1. R5 is the solution resistance, Rct is the frequency-dependent impedance, and C is the double layer capacitance. Due to the adsorption of ions or the heterogeneity of the electrode surface, Figure 3.1 could be modified by adding either resistors or capacitors. Most of the electrochemical techniques used in this study were performed with controlled potential methods by using a potentiostat. Figure 3.2 Shows a simple diagram of a single-amplifier potentiostat. The operation of the potentiostat is quite straightforward if two basic principles are kept in mind: (i) the amplifier input currents are assumed to be negligibly small, and (ii) if there is a closed feed- back loop from the output to the invert input, the amplifier will maintain the inverting input at the same potential as the noninvert- ing (+) input. Therefore, by means of the feedback loop through the counter electrode, the amplifier forces current through the work- ing electrode until EW = ES where Ew is the potential of the working electrode and ES is the potential of the signal generator (both are referred to the reference electrode). a. Cyclic Voltammetry A convention PAR (Princeton Applied Research) 174 or 174A polarographic analyzer, which would produce a triangular wave po- tential at a rate of 20 to 500 mV per second, together with Hewlett- Packard HP7045A X-Y recorder were employed in the measurement of 42 (upper) . Figure 3.1 Schematic diagram of an electrochemical cell (lower) Figure 3.2 Single amlifier potentiostat 43 C RS: solution resistance R : frequency-dependent impedance (:1: C: double layer capacitance Figure 3.1 CEJ: RE 5 +6} - we A r. A: operational amplifier 8: signal generator WE: working electrode RE: reference electrode CE: counter electrode Figure 3.2 44 cyclic voltammetry. A stationary electrode is required in this technique; either a hanging mercury drop electrode (HMDE) (Metrohm Model E441, Brinkman Instrum.), a hanging gallium drop electrode (HGDE), a metal foil electrode, or a rotating-disk electrode were used. The HGDE was prepared by replacing the mercury of a short capillary HMDE with gallium. All the experiments involving the HGDE were performed in a dry box which was heated to about 30°C by a thermostat in order to prevent freezing of the gallium. Cyclic voltammetry is a convenient technique with which to do an initial check of the purity of the solution and the potential region available to the working electrode employed. At the same time, electrode kin- etics could also be obtained from cyclic voltamograms by utilizing the equations derived by Nicholson and Shain55 (for quasi-reversible) or Galus62 (for totally irreversible). If the desirable potential sweep rate was above 500 mV/sec, a universal programmer PAR 175 coupled with PAR 173 served as a fast- potential ramp generator, and a Nicolet Explorer I digitized scope was used as a recorder. The PAR 175 could generate a potential sweep at rates up to 1000 V/sec. The advantage of employing the Nicolet explorer I is that it has an X-Y mode and also has a pen output option with an adjustable pen recording speed. Thus, an ordinary X-Y recorder could be coupled to the Nicolet Explorer I in order to ob- tain a quantitative record. The analysis of fast cyclic voltamo- grams was described elsewhere.56 45 b. DC and Pulse Polarography‘ The instruments employed in this technique were similar to those for the cyclic voltammetry. Usually, for the measurement of the polarography, the potential sweep rate was adjusted to between 2 to 10 mV/sec. A dropping mercury electrode (DME) was required to perform the polarography. The analysis of DC polarography was done by the 57 and equations derived by Oldham and 58 conventional Koutecky method, Parry were used to analyze pulse polarograms. c. Rotatigg:0isk Voltammetry_ For electrodes other than mercury, the rotating-disk electrode is the most convenient device. The theories as well as the derivation of equations of the rotating-disk voltammetry59 have already been thoroughly developed and discussed. The basic ideal of analyzing the voltammogram is to calculate the reactant concentra- tion just outside the double layer region which is Cr: 0b (1 - 113;) (3.1) where Cb is the bulk concentration and i is the diffuse limiting a current. Then the heterogeneous rate constant at an electrode po- tential E is given as kgb = i/FACr where A is the electrode area. The normal pulse technique was also employed at rotating-disk electrodes. 46 d. Cgpacitance Measurements (i) AC Bridge - The use of the ac bridge is the most common way to measure the differential double-layer capacitance. A Wien bridge61 was built in this department. The principle of the operation of the ac bridge is to match the adjustable pair of capacitor and resistor with the corresponding component of the electrochemical cell until a null point (when there is no phase difference) is detected by a scope. The advantage of the ac bridge is its simplicity, however, the disadvantage is the tedious procedure. (ii) "Phase-Detection" Technique - A PAR 175 was combined with a PAR 173 which also coupled with a PAR 174/50 ac polarographic ana- lyzer to scan the electrode potential as required, while a PAR 5204 lock-in amplifier was employed to measure the corresponding in- phase (resistive component) current iI and the quadrature (capacitor component) current iQ. The differential double layer capacitance, then, can be calculated as .2 .2 1 + 1 c = 01—17(ii—3) (3.2) I where w and V is the applied ac frequency and peak to peak potential, respectively. The constant term l/wV can be found from the calibra- tion of the lock-in amplifier with a dummy cell. 47 4. Electrode Pretreatments The purity of the lead rod used to fabricate the rotating-disk lead electrode was 99.9999% (Atomergic Chemical Co.). The rotating- disk electrodes were either obtained from Pine Co. or made in this department. The problem of air bubbles inside the lead rod caused difficulties in the electrode fabrication. The lead rod was first trimmed down to the suitable dimension (0.2 cm dia.) and glued on a stainless steel (5 cm) support with a special silver epoxy, silver- bond type 50 (Transene Company Inc.), then was pressed into a hot Teflon or Kel—F sheath. Thus the cooled sheath would assure the tight seal between the sheath and the lead. ' Several pretreatments were tested in order to evaluate the de- pendence of the measured capacitance upon the chemical and physical state of the electrode surface. The Russian school described a rela- tive complicated method (A).63 In method (A), the electrode was electrochemically polished in a solution of sodium acetate in acetic acid. As the cathode in the polishing bath, they used six rods made of spectrally pure graphite arranged symmetrically around the electrode to be polished at a distance of 5 cm. After polishing, the electrode was carefully washed with double distilled water and then placed in the measuring cell where, for two hours, it was cathodically polarized in an atmosphere of hydrogen at a potential of -l.34 vs. SCE. Bewick64 used method (B) to study the inner-layer water structure at lead electrodes using reflectance spectroscopy. In method (B) the electrode was initially mechanically polished and a freshly 48 prepared solution mixed from acetic acid, hydrogen peroxide, and methan- ol of the 2:3:5 ratio, was poured over the polished electrode 10 times. After rinsing the electrode with water, it was quickly transferred while wet to the degassing 0.5 M sodium perchlorate solution; then cathodically polarized at -l.5 V vs. SCE for thirty minutes. There is also an electrochemical method65 (C). The electrode was mechanically polished on roughened glass, electrochemically etched in perchloric acid (20%) and finally chemically etched in the perchloric acid for thirty minutes. Methods (B) and (C) as described above were employed in this work. We also used a relative simple mechanical polishing method (0), to pretreat the polycrystalline lead electrode. In the first part of the pretreatment, method (0) was similar to methods (B) and (C) in that the electrode was mechanically polished with lu alumina polish- ing powder (Buehler Ltd.) on a polishing wheel (Buehler 44-1502-160) using water as a lubricant. After a bright surface was obtained, the electrode was quickly transferred while wet to a degassing water solution to rinse it. Then the electrode was transferred immediately to a 0.5 M sodium perchlorate solution and the electrode potential was repeatedly scanned between -0.7 V and -l.6 V vs. SCE in order to stabilize this mechanically polished electrode surface. CHAPTER IV DOUBLE LAYER STRUCTURE AT THE LEAD-AQUEOUS INTERFACE 49 1. Introduction The study of the double layer structure and the accompanying phenomena of single-crystal and polycrystalline solid electrodes is 66 From currently a very active research area in electrochemistry. the measurement of the differential double-layer capacitance, a cor- rection for the ionic double-layer effect due to the Coulombic inter- action between the reacting ions and the electrode surface on the electrode reactions can be obtained. In this study, the specific adsorption of anions at the poly- crystalline lead-aqueous interface was examined as a means to investi- gate the intrinsic properties of the electrode-solution interface. The extent of the specific adsorption of anions was evaluated from the measurement of the differential double layer capacitance in solu- tions of mixed electrolytes having a general composition of (0.2 - x) M NaFi-xNaX, where X is the adsorbed anions examined. The so-called 28’29 was employed to calculate the surface Hurwitz-Parsons analysis concentration F; of the specifically adsorbed anions. The free energy of specific adsorption. AGE, was then obtained by utilizing 67 which includes an interaction parameter 9. the Frumkin isotherm Comparison of the values of AG; at lead and mercury electrodes was made in order to evaluate the dependence of the energies involved in specific adsorption of anions upon the nature of the electrode material. Several electrode pretreatments for the polycrystalline lead are 50 51 available in the literature.63'65 Thus, it is interesting to study the pretreatment dependence of the specific adsorption of anions at a lead surface. The difference in the values of A63 for various electrode pretreatments can be attributed to the difference in sur- face activities. Upon comparing the measured capacitance curves at the lead electrode in a 10 mM solution of sodium fluoride to that of sodium perchlorate, it seems that perchlorate ions are sig- nificantly adsorbed at the lead surface. Therefore, it is worth- while to perform the measurement of Specific adsorption of anions in perchlorate electrolytes with which to investigate the influence of 68-70 the adsorption of supporting electrolytes on the amount of the specifically adsorbed anions studied. 2. Characterization of the Electrode Surface The study of the double-layer structure at the electrode-solution interface is necessarily based on the possession of an ideally polariz- able electrode Surface. Figure 4.1 is a typical cyclic voltammogram for a solution of 0.5 M sodium perchlorate at the polycrystalline lead surface prepared by method (0). The lead pretreatment methods (A),63 (B),64 (C),65 and (D) have been described in Chapter III. As shown in Figure 4.1, the double-layer charging and discharging current-potential curves are smooth and symmetrical without any special features. This indicates that an ideally polarizable lead surface can be obtained by pretreatment method (0). Furthermore, 71 the values of the integral capacitance obtained from Figure 4.1 are comparable (115%) with the values of the measured differential 52 Figure 4.1 Typical cyclic voltammogram for polycrystal- line lead electrode (prepared by method 0) at 0.1 V sec"1 in 0.5 M NaClO4 . 53 ~.q ouzwfih \\ mom .m> >\m mo. .. mo- 1.[ VT’II 54 capacitance that will be presented below. 3. Results a. Cgpacitance Measurements in Non-SpecificallyyAdsorbing Electrolytes The differential capacitance of the lead-solution interface was measured with an ac bridge or "phase-detection" technique as des- cribed in Chapter II. Figure 4.2 shows the differential capacitance- potential curves for solutions of sodium fluoride at polycrystalline lead electrodes. This figure also includes literature data, curve (a) which was extracted from Reference 63, in order to illustrate the dependence of the differential capacitance upon the electrode pretreatment. The capacitance curves (a), and (b) which were ob- tained by the use of method (A),63 and (0), respectively, at 200 Hz, are compatible with each other. As described in Chapter II, the potential of zero charge (pzc) can be generally taken as the elec- trode potential at the minimum of the capacitance-potential curve for the dilute solution of non-specifically adsorbing electrolyte, for example, 10 mM sodium fluoride solution. However, this defini- tion may not be true for the polycrystalline electrode and will be 64 obtained the discussed later. By the use of method (B), Bewick same value of the pzc in fluoride electrolyte at the polycrystalline lead as reported by Leikis with method (A)63 (curve (a) of Figure 4.2). The curve (c) of Figure 4.2, which was obtained by the use of method (0) in this study, shows that the resulting pzc is also -0.8 V vs. SCE. Thus, all different pretreatment methods (A), (B), and (D) 55 Figure 4.2 Differential capacitance ys. electrode po- tential for polycrystalline lead in the following conditions: (a)--method (A) in 10 mM KP at 210 Hz extracted from Ref. 64; (b)—-method (D) in 10 mM NaF at 200 Hz; (7) method (0) in 10 mM NaF at 50 Hz; (4) method (0) in 10 11M NaF at 10 Hz; (A) method (0) in 0.2 M NaF at 200 Hz; (O) method (0) in 0.2 M NaF at 1000 Hz 56 25- mo 5 9. «Suki 85.8800 .2E2ot5 '15 ‘07 E/V vs. SCE Figure 4.2 57 yielded roughly the same pzc (see below). The Russian school reported63 that with method (A) the frequency dispersion of the measured capacitance at lead was relatively small (5 - 10% with variation of the frequency from 210 to 1000 Hz). According to Figure 4.2, for method (0) there is no significant fre- quency dependence for the 0.2 M sodium fluoride solution (5 - 15% with variation of the frequency from 200 to 1000 Hz) and for the 10 mM sodium fluoride solution (10 - 15% with variation of the frequency from 10 to 200 Hz). Figure 4.3 shows the differential capacitance-potential curves for solutions of sodium perchlorate with various concentrations 4 at lead electrodes prepared by method (0). Upon comparing curve (a) for Figure 4.3 with the curve (c) for Figure 4.2, it is seen that the electrode potential (-0.9 V vs. SCE) at the minimum of the capacitance curve of the 10 mM sodium perchlorate is more negative than that of the 10 mM sodium fluoride solution. This negative shift of the minimum of the capacitance curve may be attributed to the adsorption of perchlorate ions.72 b.) Time Dependence of the Measured Capacitance By the use of method (0), the measured capacitance values were found to vary (:10%) between consecutive pretreatments, which is probably due to fluctuations in the electrode area. Figure 4.4 shows an interesting result of the study of the time dependence of the differential capacitance at the lead electrode prepared by method (0) of 0.1 M sodium perchlorate solution at 1000 Hz. In Figure 4.4, 58 Figure 4.3 Differential capacitance at 1000 Hz vs. electrode potential for polycrystalline lead prepared method (0) in the various concentrations of NaC104: (x) 10 m, (o) 50 mM, (40 0.5 M, 60) 1.0 M, (V0 5.0 M 59 O 5 IO- NEoEi 62.2.8800 6:5th '|.5 E/V vs. SCE "0.7 Figure 4.3 60 Figure 4.4 Time dependence of the differential capacitance at 1000 Hz for polycrystalline lead in 0.1 M NaClO4 61 #—- E - ‘l.55V 5 \ “5. D n n #_ E- '1.5V 8 LV_V— E--I45v .5. '8 O 3 ..— 16.5 E W E"|.2V f.._:_155~ A A at) E--o.60v O \ u n + 5' -O.85v I45 _ x_X—_X-- E. ‘0.90V l A ' I l a 12 16 20 Time/hrs. ’ Figure 4.4 62 the capacitance is plotted against time for various electrode poten- tials, and the first reading was taken immediately after the mechanical polish. As seen in these plots, the capacitance values diminished substantially within the first hour, then they gradually reached some stable values. c. Specific Adsorption of Anions from Capacitance Measure- ments Mixed electrolyte solutions with constant ionic strengths having the composition of xM NaX + (0.2 - x) M NaF where X is 1‘, Br',_ Cl', SCN', or MS were used to study the specific adSorption of anions at lead surfaces from measurements of the differential double layer capacitance. Due to the time dependence of the measured capacitance, all the reported capacitance-potential curves were obtained by nor- malizing the corresponding measured capacitance curves to a constant value at -l.6 V vs. SCE. The capacitance values were found to be roughly independent of the NaX concentration at this and more nega- tive potentials. (i) Iodide Adsorption in Fluoride-Based Electrolyte - Figure 4.5 shows the capacitance-potential curves obtained by the use of method (0) at 200 Hz in solutions of xM NaI + (0.2 - x)M NaF where the con- centration of NaI varies from 1 mM to 100 mM. As described in Chapter II, the surface concentration r; due to the specifically ad- sorbed anions can be calculated by the so-called Hurwitz-Parsons 28,29 analysis at constant electrode charge utilizing the equation 63 Figure 4.5 Differential capacitance at 200 Hz vs. elec- trode potential for polycrystalline lead prepared by method (0) in mixed NaF/NaI electrolytes at an ionic strength of 0.2. Key to iodide concentrations: (x) 0; (o) 2 mM; (A) 4 11M; (0) 10 M; (V) 25 "M Differential Capacitance uF/cm2 5.5 N 01 N O l 64 '0.8 ’10 ‘12 '1.4 '1.6 E/V vs. SCE Figure 4.5 65 r' = AE RT (M) . 2.21 X qm/ aqm PX ( ) Alternatively, one can utilize a modification due to Weaver and 30 Anson at constant electrode potential involving the equation (de- rived from Equation 2°20) atnx ..__ m 1"x“ AQE/RT ( a—E_)I‘)'( (2.22) where (AE) m is the difference of the electrode potential between the base electgolyte and a given iodide-containing solution at a given electrode charge qm, and (Aqm)E is the difference of the electrode charge between the base electrolyte and a given iodide-containing solution at a given constant electrode potential E. These two quanti- m1 ties (atnx/aq P‘ and (atnx/GE)P. were obtained from the displace- x . ment of the corresponding chargeipotential curves, which were inte- grated from the corresponding capacitance-potential curves for various solution compositions. The quantity RT/F (atnx/aE)F. is the so-called "electrosorption valency"73 (EV). In an earlier :eport from this laboratory, the values of the electrosorption valency for specifically adsorbed an- ions at polycrystalline silver electrodes were found to decrease with decreasing negative electrode potential; for example, for the adsorption of chloride ions, at -0.9 V, EV = 0.25; at 0.3 V, EV = 0.15. In this study, the polycrystalline lead electrode exhibits relatively constant values of the electrosorption valency for iodide 66 ions over the entire electrode potential region examined. Thus, the values of EV vary only from 0.53 to 0.56 with variation of the elec- trode potential from -0.7 to -l.0 V. Furthermore, the EV values of lead electrodes are significantly larger than those of mercury elec- trodes (No.42). When the values of EV vary significantly with the electrode po- tential, an alternative way to calculate the surface concentration 75,76 P; is to utilize the equation E 2 m 1 _ 1 _§9__. . Pym] (alogx)E d5 (4") E _ 1 where all the symbols have the same meanings as those in Equation 2.21. In this method, qm - E curves were obtained by integrating the cor- responding C - E curves. The required coefficient (aqm/alogx)E was obtained by differentiating the set of qm - tnx curves at constant E. Thus, by integrating the resulting coefficient (aqm/alogx)E over the electrode potential interval, it yielded the desired surface concen- tration P;. On the other hand, F; can be also obtained by differen- tiating the y (relative surface tension) - 2nx curves that result from the double integration of C - E curves at constant E. In this method]7 there is no need to assume that the electrosorption valency is constant. There is, however, a limitation for the practical use of this method in that enough capacitance-potential curves of a number of concentrations of Max are required to calculate accurately the differential term (aqm/alogx)E. In this work, both methods were employed to calculate the surface 67 concentration of iodide ions, and yielded comparable results (:10%). Figure 4.6 shows the resulting plot of the surface concentration of the specifically adsorbed iodide ions against the electrode charge. The measurement of the specific adsorption of iodide, ions at lead prepared by method (A) has been studied by the Russian school; their data are shown in Figure 4.7. From a comparison of Figure 4.778 with Figure 4.5, it seems that with method (A) the Russian school obtained a relatively higher degree of specific adsorption of iodide ions at lead electrodes. The Hurwitz-Parsons method was also used to analyze the capacitance curves of Figure 4.7. The resulting surface concentration of the specifically adsorbed iodide for the mixed KF/KI electrolytes containing 10 mM KI is shown in Figure 4.8 curve (a). Measurements of the specific adsorption of iodide ions in the fluoride medium at the lead-aqueous interface prepared by method (0) were also performed at 1000 Hz in order to check the frequency de- pendence of the specific adsorption of iodide ions. The result is shown in Figure 4.9 and the corresponding plot of r; vs. qm for a solution containing 10 mM NaI is also shown in Figure 4.8 curve (d). The frequency dispersion of the specific adsorption of iodide ions at lead electrodes prepared by method (0) is small (10% between 200 Hz and 1000 Hz) by comparing curves (d) and (c) which was obtained in the same condition except at 200 Hz of Figure 4.8. Since method (B) was also used to pretreat lead electrodes to study electrode kinetics, it is of interest to examine the adsorb- abilities of various anions at lead electrodes pretreated in such a manner. The measured capacitance curves are shown in Figure 68 Figure 4.6 The concentraion of specifically adsorbed iodide plotted against electrode charge for polycrystalline lead prepared by method (0) in mixed NaF/NaI electrolytes at an ionic strength of 0.2 ( at 200 Hz). Key to iodide concentration: (0) 1 TIM; (A) 10 11M; (0) 25 1r"; (7) 63 M 69 xoWM/W/WWM .. O N -Eo.8_oE\..o_ x L _ 70 Figure 4.7 Differential capacitance at 210 Hz.vs. electrode potential for polycrystalline lead prepared by method (A) in mixed KF/KI elec- . trolytes at an ionic strength of 0.2. Key to iodide concentrations: (x) 0; 03) 1 mM; (4) 4 11M; (V) 10 rm); (0) 25 mM; (0) 70 11M. This figure was extracted from Reference 78 71 30" 5 0 I5- neoxui 85588 355:5 '15 E/ V vs. SCE ‘07 Figure 4 . 7 72 Figure 4.8 The concentration of specifically adsorbed anions (bulk anion concentration 10 mM) plotted against electrode charge for poly- crystalline lead in fluoride electrolytes unless otherwise noted in the following conditions: (a)——method (A) for iodide at 210 Hz obtained by analyzing the corresponding capacitance curves in Ref. 78; (b)--method (B) for iodide at 1000 Hz; (c)--method (D) for iodide at 200 Hz; (d)--method (D) for iodide at 1000 Hz; (e)--method (D) for iodie (in perchlorate electrolytes) at 1000 Hz; (x) method (0) for chloride at 1000 Hz; 03) method (0) for azide at 1000 Hz; (V) method (0) for bromide at 1000 Hz; 01) method (0) for thiocyanate at 1000 Hz 73 (b) (a) . . . . 4 3 2 I ~.Eo.mo_oE\..o_ x L Figure 4.8 l 74 Figure 4.9 Differential capacitance at 1000 Hz vs. electrode potential for polycrystalline lead prepared by method (0) in mixed NaF/NaI electrolytes at an ionic strength of 0.2. Key to iodide concentrations: (x) 0; (O) 1 "M; (A) 10 mM; (0) 25 mM; (V) 65 "N 75 «Euhioocozooaoo 825.830 " 1.5 "l.| '|.3 E/V vs. SCE ‘07 ‘09 Figure 4.9 76 4.10 and the corresponding plot of P; vs. qm for a solution contain- ing 10 mM NaI is also shown in Figure 4.8 curve (b). (ii) Iodide Adsorption in Perchlorate-Based Electrolytes - As mentioned above, the perchlorate ion has been shown72 to adsorb weakly at polycrystalline lead. Thus, it is useful to study in more detail how the weakly adsorbing supporting electrolyte, i.e., perchlorate ion, will influence the specific adsorption of iodide ions at lead surfaces. The effect of the adsorption of supporting electrolytes on the measurement of the specific adsorption of added anions has already been examined by some authors. In this work, the measure- ment of the specific adsorption of iodide ions was also performed in sodium perchlorate solutions and the results are shown in Figure 4.11. The corresponding F; vs. qm plot for the solution containing 10 mM NaI is shown in Figure 4.8 curve (e). In summary, curves (a), (b), and (c) of Figure 4.8 show the de- pendence of the surface concentration of the specifically adsorbed iodide ions F; at polycrystalline lead on the electrode pretreatments. However, curve (a) was obtained by analyzing the corresponding capacitance curves in Reference 78. Furthermore, curves (d) and (e) Show the dependence of F; at lead prepared by method (0) at 1000 Hz on electrolytes. (iii) Evaluation of the Free Energy of Specific Adsorption - The surface concentration F5 for a monolayer coverage of specifically ad- 2 sorbed iodide ions is estimated to be 102 uC/cm from the ionic radius of iodide ion (2.19 A).79 According to the F; vs. qm plots 77 Figure 4.10 Differential capacitance at 1000 Hz vs. electrode potential for polycrystalline lead prepared by method (B) in mixed NaF/NaI electrolytes at an ionic strength of 0.2. Key to iodide concentrations: (x) 0; «3) 1 m; (A) 10 m1; (0) 25 mM; (V) 65 mM 78 'l.6 ‘|.4 'I.O '12 E/V vs. SCE 'O.8 Aé o\\ \x\ 9||||l|1|1111|111 111111111111 \\w\\x . _ e _ O 5 0 5 3 2 2 «Soil 3:28.500 329.820 Figure 4.10 Figure 4.11 79 Differential capacitance at 1000 Hz vs. electrOde potential for polycrystalline lead prepared by method (0) in mixed NaC104/NaI electrolytes at an ionic strength of 0.5. Key to iodide concentrations: (x) 0; (O) 1 mM; (4) 10 mM; 00) 25 mM; (7) 65 mM 2: l\) [\J (I) (11 61' Differential Capacitance pF/cm 80 E/V vs. SCE Figure 4.11 \X o o /x \\ o \‘\v\ l}; ‘\x:::B:;E;§Iil"‘r’ '07 ’l. l ' | .5 II. ‘I ‘1- 81 of Figure 4.6, the average coverage (0 = F;/FS) of the specifically adsorbed iodide ions at lead surfaces is relatively low (5_7%) compared with that of other surfaces such as silver and mercury.75 However, Henry's law80 does not apply to the present systems, which is probably due to repulsive interactions between the specifically adsorbed ions. Thus, the analysis of the adsorption isotherm at the lead surface was performed using a Frumkin isotherm.74 The Frumkin isotherm can be expressed as = F- (.95) exp (9 '0) (H) where P5 is the surface concentration corresponding to a monolayer coverage, Co and P0 are the standard state concentrations for the ad- sorbing species in the bulk and at the electrode surface, reSpec- tively, 6 is the fractional coverage (= F;/rs), g is a surface inter- action parameter, and AG; is the standard free energy of adsorption. Plots of (zncb-£n (e/l-e)) against 6 were drawn in order to determine the interaction parameter 9 from the slope and the standard free energy of adsorption AG; from the intercept. The resulting plots of in [Cb(l-e)/e] vs. 0 are shown in Figure 4.12. From the slope and the intercept of the plots of Figure 4.12, the surface interaction parameter and standard free energy of adsorption at the pzc are 180 and 90 KJ mole'1 respectively. The large positive values of g in- dicate that a repulsive interaction exists between the specifically adsorbed iodide ions, and they are an electrode charge dependent parameter. The larger the negative electrode charge, the larger 82 Cb(1-o) Figure 4.12 2n( 0 ) vs. a for Specific adsorption of iodide for polycrystalline lead prepared by method (0) at 200 Hz in mixed Na/NaI electrolytes at an ionic strength of 0.2. Key to various electrode charges: (0) 1.0; (x) 0.0; (A) -1.0 uC/cmz 83 l 0.0 08 0.024 6 Figure 4.12 0.04 84 value of 9. (iv) Specific Adsorption of Thiocyanate, Bromide, Azide, and Chloride - The effect of the nature of the anion including chloride, bromide, and iodide on the differential capacitance at the poly- crystalline lead prepared by method (A) has been studied by Leikis. However, of these anions, only iodide was employed to study the specific adsorption by utilizing the mixed electrolyte method. The measurements and the analyses of the specific adsorption of thiocyanate, bromide, azide, and chloride at the polycrystalline lead prepared by method (0) at 1000 Hz were perfbrmed in a same manner as described above. Figure 4.8 summarizes the plots of the surface concentration as a function of the electrode charge for each of the anions examined. The summary of the standard free energy of adsorp- tion of these anions is given in Table 4.1 which also contains cor- responding data for mercury extracted from literature results.8]'83 4. Discussion From the study of the time dependence of the measured capacitance, the diminution of capacitance values with time is uniform over the whole polarizable potential region as shown in Figure 4.4. It seems likely that this diminution cannot be exclusively explained by the possible existence of trace impurities of organic materials in the test solution. It, however, could possibly be associated with the reconstruction of the electrode surface. In general, the adsorption of organic molecules will depress the measured capacitance to a great 85 Table 4.1. Standard Free Energy of Adsorption A62 for Several Anions at Lead, Mercury, and Silver Electrodes. o m- (Pb) Frequency "AGa(q '0)KJ/ Electrolyte Anion Method (Hz) molee gf 0.2M KF I" A 210 94 92* 50 0.2M NaF I' D 200 90 86* 90 0.2M NaF I' ' D 1000 90 86* 180 0.2M NaF I' B " 93 92* 117 0.2M NaF NCS' D " 86 80* 200 0.2M NaF Br' " " 79 76* 120 0.2M NaF N3' " " 80 76* 140 0.2M NaF Cl' " " ~74 0.5M NaClO4 I' " " 83 77* 180 0.5M NaClO4 NCS' " " 81 75* 200 0.5M Nac104 Br' " " 80 74* 350 1.0M KF Cl' Hg " 82 (b) 1.0M KF Br' " " 90 0.95M NaF N3' " " 86' 0.95M NaF NCS’ " " 0.95M NaF I' " ” 0.5M NaF Cl' Ag " 83 (c) 0.5M NaF Br' " " 96 0.5M NaF N3'_ " 4 " 93(d) 0.1M NaClO4 NCS " " 115 *Evaluated at 0 = 0.01. bThe g values at mercury are about 15 to 20. cThe g values at silver are about 10 to 15. dEvaluated at qm = 15 uC/cmz. 6Free energy of specific adsorption evaluated from the Frumkin isotherm. fInteraction parameter. 86 extent in the region of the pzc. This is due to the decrease of the dielectric constant within the compact layer as a result of the en- hancement of the dipole-dipole interaction between water and organic molecules in the pzc region. The pzc is a fundamental characteristic of an electrode, and some 84’85 the value of the studies have been done to try to correlate pzc of various electrode materials to the work function, electro- negativity, hydrophility, and heat of farmation of surface oxide. 85 was shown to follow this car- The polycrystalline lead electrode relation. As mentioned before, the pzc of the polycrystalline lead surface is the same for all three different pretreatment methods (A), (B), and (D). However, the distribution of individual single-crystal faces of the polycrystalline electrode can be significantly dependent on the way how the electrode surface is prepared. Since each Single-- .crystal face of a polycrystalline surface has its own pzc, then the pzc of the polycrystalline electrode might be a weighted average of the pzc's of individual single-crystal faces depending on their dis- 24 tribution. Therefore, the difference in the effective pzc of polycrystalline electrodes of different combinations of individual single-crystal faces can be expected due to the difference in the electrode pretreatments. It has been Shown that the pzc of the polycrystalline electrode is determined by the single-crystal face 86 a with the most negative value of pzc;74 for example, (1,1,1) t lead and (1,1,0)24 at silver. Therefore, it is possible that dif- ferent pretreatments can yield the same value of the pzc for the polycrystalline electrode, even though they may result in different 87 combinations of individual single-crystal faces. According to the curve (a) of Figure 4.2, with method (A) the Russian school reported63 a much sharper minimum in the capacitance curve at the pzc than that of curve (c) which was obtained by the use of method (0). It is likely that method (A) may preferentially etch the (1,1,1) single-crystal face of the polycrystalline lead electrode. In other words, this may imply that with method (A) the polycrystal- line lead electrode possesses a greater degree of homogeneity. Furthermore, from the study of cyclohexane adsorption on the indi- vidual faces of lead single-crystal electrodes,87 it shows that the property of the polycrystalline lead electrode pretreated by method (A) is similar to that of (1,1,1) lead single-crystal electrode. 0n contrast, the appearance of the broad minimum in the curve (c) at the pzc may indicate that with method (0) the polycrystalline lead electrode exhibits greater inhomogeneity. Another possible explanation for the broad minimum observed is related to the cause of the unexpected low value of the inner-layer capacitance. Figure 4.3 shows that for concentrated (3_l M) sodium perchlorate solutions the capacitance values decreased as the concentration in- creased. This was also noted for lead in Reference 88. This result may be associated with the pecularities of perchlorate adsorption,89'92 which is only slightly hydrated. They can squeeze onto the surface in a fashion similar to organic molecules. However, a further in- crease in the capacitance values at fairly negative electrode poten- tial is also observed, which can be explained by a reduction in the size of the hydration shell of cations Na+ in strongly concentrated 88 solutions.89"92 As seen in Figure 4.8, with method (A), curve (a),78 the poly- crystalline lead electrode shows a higher tendency to adsorb anions than that with methods (B) and (0), curves (b) and (c) respectively. This suggests that the (1,1,1) single-crystal face has higher ac- tivity for the adsorption of anions than other single-crystal faces. The high degree of inhomogeneity may be responsible for the relatively small adsorbabilities of anions at the polycrystalline lead electrode prepared by method (0). Furthermore, the difference in the capacitance values of curves (a), (b), and (c) of Figure 4.2 can also be at- tributed to the difference in the degree of homogeneities of the polycrystalline electrode. In general, the difference in the amount of the specifically adsorbed iodide ions at lead surfaces caused by the difference of the electrode pretreatments can be attributed to the difference in the availability of active sites on the lead sur- face for the specific adsorption of anions. The values of g of the Frumkin isotherm are shown in Table 4.1. The 9 values of all the anions examined at lead electrodes are sig- nificantly larger than those for the corresponding anions at mercury electrodes. These high 9 values at lead electrodes may be attributed to the limitation of the active sites for the specific adsorption of anions. The effect of the adsorption of perchlorate ions on the specific adsorption of interesting anions at lead electrodes is more sig- nificant in the case of weakly adsorbing anions. When the co- adsorption of supporting electrolytes is considered, the complete 89 28 ( Gibbs adsorption equation cf. Equation 2.18) for mixed electrolytes having a composition xM NaX + (0.5 - x)M NaClO4 will be -dy = qm - dE + [r; - {x/(0.5 - x)}r'c10 ]RTd£nx (4.3) 4 where Fx and FC104 are the components of TX and PC104 present in the inner layer, i.e., the surface concentration of specifically adsorbed anions. The derivation of Equation 4.3 assumes that the components d d of TX and r in the diffuse layer, TX and F , respectively, are C104 C104 present in the same ratio as the anion mole fractions, i. e. , P d/ P3104 = x/(0.5 - x). Figure 4.13 gives the differential capacitance curves for solutions of 0.5 M NaF and 0.5 M NaClO4 at l K Hz. By assuming the value of EV to be 0.25 for the adsorption of perchlorate ions, the surface concentration of the adsorbed perchlorate ions at the pzc can be roughly calculated to equal 0.7 x 10"] mole/cm2 from the Hurwitz-Parsons analysis. This surface concentration cor- responds to about 0.5% surface coverage. Therefore, the influence of the adsorption of perchlorate ions on the evaluation of the sur- face concentration of specifically adsorbed anions is negligible. The surface coverage of the adsorbed perchlorate ions (0.5 M) at the polycrystalline lead at the pzc is about 0.5% as described above. Due to the limited active sites at lead electrodes prepared by method (0), even this small amount of coverage of perchlorate ions could diminish the adsorption of other anions. This effect is more pronounced in the measurement of the specific adsorption of bromide, azide, and chloride. For example, the surface coverage of 90 Figure 4.13 Differential capacitance at 1000 Hz vs. electrode potential for polycrystalline lead prepared by method (0) in (o) 0.5 M NaF and (x) 0.5 M NaClO4 91 25" .m s «5&1 85588 Beaters - D ’15 EN vs. SCE '07 Figure 4.13 92 the Specifically adsorbed bromide ions in 0.1 M NaBr + 0.4 M NaClO4 solution is 0.56% at the pzc, which is quite compatible with the sur- face coverage of perchlorate ions for solution of 0.5 M NaClO4 (u0.5%). The 9 value for the specific adsorption of bromide ions changes from 120 to 350 as shown in Table 4.1 when the electrolyte is altered from fluoride to perchlorate. Thus, the effect of the competitive adsorption greatly influences the specific adsorption of anions at lead surfaces prepared by method (0), which is mainly due to the limited available active sites for the adsorption of anions. Furthermore, the 9 value is dependent on the electrode pre- treatment as shown in Table 4.1. This can be attributed to the dif- ference in the degree of homogeneity of the polycrystalline electrode. Because of the large variation of the values of g as shown in Table 4.1, the free energy of adsorption is also evaluated at 0 = 0.01. According to the values of the standard free energy of adsorption G; shown in Table 4.1, the order of the adsorbabilities of various anions examined at lead electrodes is I' > SCN' > Br'.: 81-83 and silver74 N3- > C1' which is similar to that of mercury electrodes. Furthermore, the variations in the adsorbabilities of the anions examined at lead surfaces are larger in fluoride than in per- chlorate electrolytes as judged from the difference in the values of A63. h(A6;)I'Br (= (AG;)I - (A6;)B”) is about 3 KJ/mole in the perchlorate solutions, while it is about 6 KJ/mole in the fluoride solutions. This difference can be attributed to the effect of the adsorption of perchlorate ions. According to Table 4.1, the extent of adsorption of all the anions examined at lead electrodes are lower than those of the corresponding 93 anions at mercury electrodes at a given electrode charge. The ener- gies involved in the specific adsorption of ions at metal-solution interfaces can be attributed to the interactions between ion-ion, ion-metal, ion-solvent, and solvent-metal, as have been discussed 93 in the literature.93 As pointed out by Trasatti, people tend to neglect the work connected with water desorption as an ion becomes 94-96 adsorbed. Thus, from the study of the effect of the nature of the electrode material upon the energies involved in the specific adsorption of ions, Trasatti85s97 85 emphasized the role of the solvent- metal interaction. He correlated the difference in the adsorbability of a certain anion at various metals to the difference in the surface potential of water 9:20 (dipole), which arises from the oriented water dipole, of various electrodes. The influence of the chemi- sorption of water upon the specific adsorption of ions was first 98 in the analysis of the double layer struc- brought out by Frumkin ture of gallium electrodes. The water molecules tend to orient preferentially their oxygen ends toward the electrode surface, so that the orientation of inner-layer water molecules is independent of the nature of the electrode material at very negative electrode surfaces.98 By the use of the above concepts, Trasatti85 has calculated the sur- face potential of water 9:20 at the polycrystalline lead to be -104 mV, 34 mV more negative than that of mercury electrodes (-70 mV). In other words, lead exhibits a higher affinity for water than mercury. Therefore, a straightforward explanation for the low ad- sorbabilities of anions at lead surfaces compared with those at mercury surfaces can be drawn on the basis of the difference in the values of 9:20. In addition, from the measurement of the differential 94 capacitance at lead-nonaqueous interfaces prepared by method (0), we found out that a trace of water will significantly influence the measured capacitance values. This, again, implies that lead surfaces have a strong affinity for water molecules. In this work, the value of the inner-layer capacitance at the pzc of lead electrodes prepared by method (0) was estimated to be 20 uC/cmz. This is relatively small compared to the literature value 40 pF/cm285 (by the use of method (A)). The small inner-layer capaci- tance might be due to the high degree of inhomogeneity of polycrystal- line lead electrodes prepared by method (0) or the existence of more than one water layer in the innerrlayer region. The increase of the thickness of the inner-layer will result in the decrease of the inner- 1ayer capacitance (= CM_2 = e/4nd). Therefore, the dielectric constant of water molecules adjacent to the electrode surface can be signific- antly dependent on the electrode pretreatment. Thus, the resulting thicker inner-layer of lead prepared by method (0) will prevent the incoming anions from specifically adsorbing at the electrode surface. However, with method (B) the adsorbabilities of anions at lead sur- faces are much higher than those with method (0), even though these two methods yield the same value of CM-Z' This difference can be explained by the difference in the availability of active sites for the adsorption of anions between these two methods as described above. As pointed out before, the values of EV for the specific adsorp- tion of anions at lead surfaces are relatively larger than those at mercury surfaces. Usually, the value of EV is employed as a means 100 of evaluating the partial charge transfer in specific adsorption of ions at the electrode surfaces. However, it can also be taken 95 as a geometric factor100 EV(g) which describes the position of the center of the adsorbed ions in the double layer in terms of potential and is defined as ¢ad ' ¢s W ‘4'“ EV(g) = where pad, 0m, and as are the potentials in the center of the ad- sorbed ion (i.e., in). the metal surface, and the bulk solution, respectively. The value of (0 - 05) is the same for both lead and m mercury electrodes at a given electrode charge. Therefore, ac- cording to Equation 4.4 the larger the values of EV, the larger the values of load - 051. To a first approximation, the position of the center of the adsorbed anions at lead surfaces is assumed to be the same as that at mercury surfaces. Then, the larger values of load - 051 are indicative of the smaller gradient of the potential profile in the double layer. Furthermore, the smaller gradient of the potential profile is indicative of the thicker inner-layer at the lead-aqueous interfaces compared with that at mercury surfaces. This is consistent with the estimated inner-layer capacitance at these Hg Pb . two surfaces, CM-Z > CM-Z as discussed above. CHAPTER V ELECTRODE KINETICS AT LEAD AND GALLIUM SURFACES 96 A. Rate Constants for Mechanistically Simple Transition-Metal Complexes 1. Introduction Even though the double-layer structure of polycrystalline lead electrodes has been relatively well studied by other authors,72’78’86’88 electrode kinetics at these surfaces have scarcely been investigated except for studies of the reduction of some anions. A number of electrode kinetics studies under well-defined conditions have been 35 silver,]4 14 Ireported at mercury, platinum, and gold14 electrodes. However, of these surfaces, only mercury has a double-layer structure which is understood in detail. In this study, measurements of the dif- ferential double-layer capacitance are combined with corresponding ‘kinetics measurements for simple transition-metal reactants at lead electrodes prepared by method (0) in order to ascertain if the re- activity difference between lead and other surfaces, notably mercury, are explicable in terms of the conventional double-layer model des- cribed in Chapter II. In this work, chromium(III) aquo and ammine complexes were chosen as reactants because of (i) the simplicity of electrode reactions involving these complexes which involve no bond breaking and formation during the electron-transfer process, (ii) the negative potential at which these reactants are reduced via an one-electron step is compatible with the negative polarizable potential region 97 98 characteristic of lead electrodes, (iii) the substitution inertness of chromium(III) complexes which eliminates the problem of ligand equilibrium yielding unknown reacting species, and (iv) the avail- ability of relatively straightforward syntheses of these reactants. The double-layer structure of the electrode-solution interface has been shown to play a very important role in the interpretation of electrochemical kinetics35 as discussed in Chapter II. The most common way to correct the double—layer effect is to utilize the Frumkin equation. Some unexpected results for the electroreduction of several mechanistically simple transition-metal complexes were ob- tained at polycrystalline lead electrodes in this work. The dif- ference of the rate constants observed between polycrystalline lead and mercury electrodes could not be simply explained by the convene tional GCS double-layer model. It has been shown that at the potential of zero charge (pzc) the structure of water molecules adjacent to the ‘gallium surface is drastically different from that at mercury.85 Therefore, in this work kinetics measurements were also done at a hanging liquid gallium drop electrode (HGDE). In this study, the dependence of electrode kinetics upon the nature of the electrode material was examined, and reasons for the observed significant dif- ference in rate constants remaining after the Frumkin correction are discussed. 99 2. Results a. The Pretreatment Dependence As shown in the last chapter, the amount of specifically adsorbed anions is greatly dependent upon the electrode pretreatment. Rate parameters were obtained on lead surfaces that were prepared by three different methods (B),64 (C),65 and (D), as described in Chapter III in order to examine to what extent the kinetics are sensitive to the history of the surface. Several chromium(III) complexes were chosen to examine this influence and typical results are shown in Table 5.1. From Table 5.1, it is evident that method (C) and (0) yield similar results for all the complexes examined, which is in accordance with the corresponding similarity of the differential double-layer capaci- tance obtained using these methods as described in Chapter II. On the other hand, method (B) yielded higher reaction rates for the com- plexes considered compared with methods (C) and (0). These three dif- ference pretreatment methods yielded similar values of aapp for all the complexes examined. However, the reaction rate constants ob- tained using method (B) were found to decrease with time. Eventually, the reaction rate constants approached the values obtained on sur- faces prepared using methods (C) and (0) within about twenty minutes. One possible reason for the decrease of reaction rates is that the lead surface is activated by the chemical polishing method (B) and is deactivated gradually. 2+ For Cr(0H2)5NCS the difference in the rate constants obtained on surfaces pretreated using method (B) with respect to methods (C) 100 Table 5.1. The Pretreatment Dependence of the Measured Rate Constants at Lead Electrode for a Number of Transition-Metal Com- plexes. Method Ba’f Method 03 Method 0a a e k b a e k b a e k b aPP aPP aPP aPP aPP aPP Reactant cm/sec cm/sec cm/sec C - - - M0112):+ 0.62 7.9x10 4 0.6 3.5x10 5 0.6 2.0x10 5 +° ' -3 -3 Cr(0H2)50503 0.44 5.0x10 0.48 1.1xlO C . Cr(MH3)5012+ 0.43 3.5x10‘3 0.35 2.0x10'3 0.35 2.0x10"3 2+C Cr(0H2)5NCS 0.44 1.7x10" 0.44 4.4x10‘3 aLead pretreatment methods B, C, and D are described in the Experimental Chapter. bApparent rate constant measured in 0.5 M NaClO4 (pH = 2). c kapp evaluated at 1000 mV vs. SCE. d kapp evaluated at 1200 mV vs. SCE. eDefined by a = -(2.3RT/F)(Alogk app app/AE)u' fSince rate constants measured at lead electrodes prepared by method B were very unstable and decreased with time, the kapp listed were measured immediately after pretreatment. 101 and (D) is much larger than those for other complexes. Furthermore, the rate constants for the electroreduction of Cr(0H2)5NCS2+ at sur- faces prepared by method (8) after stabilization with time was still larger than that at surfaces pretreated using methods (C) and (0). Since the potential region at which Cr(0H2)5NCS2+ is reduced is very close to the pzc of lead, the double-layer effect should be relatively small. Therefore, the large difference in the rate constants for 2+ may be due to the difference in the degree of adsorption Cr(OH2)5NCS of NCS’ at lead surfaces among different pretreatments. From measure- ments of specific adsorption of anions, method (B) has been shown to yield surfaces having a greater tendency to adsorb anions than that of method (0) as described in Chapter TV. Strictly speaking, the measured rate constant is a hybrid of those for competing inner-and outer-sphere reactions, and therefore dependent upon which reaction pathway will dominate. Due to the higher affinity for the adsorp- tion of thiocyanate ions at lead surfaces prepared by method (B), it seems that the reduction of Cr(0H2)5NCS2+ at lead electrodes pre- treated using method (B) is more likely to follow inner-sphere path- ways than that at lead surfaces prepared by other methods. As metnioned in Chapter IV, the degree of homogeneity of poly- crystalline electrodes may significantly depend on the electrode pretreatment, which may be responsible for the pretreatment dependence of electrode kinetics. Table 5.1 shows that the electrode reaction rate constants for a number of transition metal complexes measured at lead surfaces are dependent on the electrode pretreatments. In this work, method (0) was used to prepare lead surfaces to study 102 electrode kinetics because the procedure is straightforward and yielded reproducible electrode surfaces. b. The Apparent Rate Constants for the One-Electron Electro- reduction of Cr(III) Aguo andAmmine Cainflexes at the Lead- Aqgeous Interface Measurements of the electroreductions of several Cr(III) complexes were perf0rmed at lead-aqueous interfaces using normal as well as pulse rotating-disk voltammetric techniques that are described in the Experimental Chapter. The analysis of the voltammograms was performed by using a conventional method utilizing the Levich equation. Figure 5.1 summar1zes the resu1t1ng Tafel plots of log kapp’ where kapp is the measured rate constant at a certain electrode potential, 2+(+) against the electrode potential E for some Cr(0H2)5X and Cr(NH3)5X3+(2+) complexes where the ligand X is F’, C1", NCS', 50:, or 0H2, at both polycrystalline lead and mercury electrodes. The entire figure might look fairly complicated. However, it shows a very clear-cut trend. From the position of these Tafel plots, lead electrodes (open symbols) uniformly exhibit less electroactivity than mercury electrodes (closed symbols), i.e., at a given electrode po- tential the electroreduction rates of all the complexes examined are diminished when the electrode is changed from mercury to a polycrystal- line lead electrode. These differences may be due to the large difference in the pzc between these two electrodes (AE z 400 mV). pzc However, in spite of this significant difference in the observed rate constants, and in contrast to other solid electrodes such as 103 app’ where kapp is the measured rate constant, vs. electrode poltential at mercury (closed symbols) and polycrystalline lead prepared by method (0) (open symbolél in 0.5 M NaClO4 except for Cr(NH3)5NCS in 40 mM La(ClO4)3 for a number of transition- Figure 5.1 Log k metal complexes as follows: (o) Cr(OH2)g+ ; (v) Cr(MH3)g*“, (a) Cr(NH3)5C12+; (a) Cr(0H2)5NCSZ+; 2+, (0) Cr(OH2)501 . (4) Cr(NH3)5 Cr(NH3)50H23+; (0) Cr(0H2)5N32+; (a) Cr(NH3)5N32+; 2+. + (X) Cr(0H2)5F , (+) Cr(OH2)50S03 MCSZ“; (a) 104 N... . H.m unawam mom .9 >\m \ \ . eeoo_-x e.a>eooo.-x a>eooo_- oo _oeooo_m oeoeuoopm eeaooaom .mieopuvea ze oe eee eo_oez z m.o e_ aoeotpoo_m Assure: new new; on umcammoz mmxoPQEou Auuuvco meow we cowaoaumcogaoopu so; mucmumcou mama .m.m epoch 111 -agm coo. LLOU .oom\Eo cw ma acoumcou mama k. .ece ma N\~e merged s8 eoe_eeoeoo ecoox LL00 o .zgomsu mow as» sore umumpaopmo m? we mean: .qce me me mcwxmu An tweezemumo xo x mop soc» umcwecmumo .mempa cowuommg omego>m one am pmpucmuoa «nu we are econ: .ace.+wuwmm .uomwwm swamp o_n:ou o_:ow to» uoaomgtoo acmumcou opus mm are xn age .uum .m> >ecoop- um umamzpm>o ucmumcoo one; acogmaam m? xm .eo=e_peoo .m.m o_aae 112 105 to the discreteness-of—charge effect, the micropotential at the reaction site 5r may differ from the average (macro-) potential on the reaction plane ¢rp' The effect of the supporting electrolyte cation on the reaction site for the electroreduction of Cr(OH2)2+ and Cr(NH3)g+ has been well investigated at mercury electrodes.106 In Table 5.3, bath 02/2 and 02 were used to calculate k These corr‘ provide appropriately lower and upper limits, respectively, for the use of the GCS model in the calculation of kcorr' According to Table 5.3, the k of all the complexes measured corr in 0.5 M NaClO4 are similar to those measured in 40 mM La(ClO4)3, and this is true for both lead and mercury electrodes. The similarity of kcorr in different ionic strength solutions supports the appropri- ate validity of the application of the conventional GCS model in the calculation of ¢rp and hence the corrected rate constants. d. Rate Constants of Some Cr(III)Complexes Measured at a Hanging_Liquid Gallium Drop Electrode (HGDE) Damaskin and Frumkin103 introduced the concept of Chemisorbed water molecules with oxygen atom towards the metal as being respon- sible for the residual orientation of dipoles at the pzc. This concept has been successfully applied to explain the abnormally high inner- layer capacitance at pzc obtained at gallium-aqueous interfaces85 compared with that at mercury-aqueous interfaces, for example, in l M NaZSO4 solution Cugz = 30 uF/cm2 and C332 = 135 uF/cmz. Further- more, Trasatti used the same nation to calculate the surface po- H 0 tential of water due to oriented water dipoles 9M2 (dipole) as 113 discussed in Chapter IV. He found that at the pzc 9:30 = -0.07 V in 0.1 M NaF and 92:0 = -0.32 v in 0.1 M NaClO4. Since the water structure at the gallium-aqueous interface is remarkably different from those at lead- and mercury-aqueous inter- faces as described above. The study of electrode kinetics at the gallium-aqueous interface may provide insight into the observed "specific substrate" effect on outer-sphere electrode reactions between lead and mercury electrodes as mentioned before. A HGDE that is described in the Experimental Chapter was used to study electrode kinetics at gallium surfaces. Table 5.4 shows rate constants, k aPP and k for some Cr(III) complexes measured at mercury, lead, corr’ and gallium electrodes. The rate constants of gallium electrodes were evaluated from cyclic voltammograms. The analysis of cyclic voltammograms has already been described in Chapter III. As is ex— pected, there are still signifiCant differences in the rate constant I after double-layer correction between gallium and the other two sur- faces. This, again, is an indication of the presence of the "specific substrate" effect for the electrode reactions examined. Since at the gallium electrode the potential at which Cr(NH3)g+ is reduced is near the anodic limit of the electrode (-O.9 V vs. SCE), the rate constants of Cr(NH3)g+ measured at the gallium surface as listed in Table 5.4 may be questionable. .omm\5o :_ m? acmumcoo mac: .4. .m.o u stoop newssmmm x3 .omm\>eoop mumggcmmom um EnemoEEmupo> uppoxo mcwucoqmoccoo as“ mo pm_pcmuoa xmmq ago an accumcoo mums vmuomccou on» . a x soc» cmumpoamcuxm acmumcoo mums umuooggoum m .me u are e .xgowgu moo any ease umum_:opmu m_ we mean: .~\Ne u acem .m=m_a cowuommc omeem>e on» an —mwu:mpoa as» mw age mean: .ag hwiw.wuqamxmopugeooxmop soc» co=_eLmumo .uoowwo Loam, mpnaon tom umuooecoo acmumcou «Home .eopumz 2 mac cp mum .m> >eooo—u um uwumapm>o ocaumgoqsmu soot um acmumcoo one; acmgmaa o_Poxo sot; nonmapm>m mew: mucmumcoo_mumm .emuamzu qucme_coqu on» cw conweommu mm: was» moo: co mm: on» an no:_muno are: upon 114 a .mcocuomFNm . m-onN.m m-o.xe.e m-o_xN.m as e-o_xm.N m-opxm.P m-o_xN._ m-o_xe.. m-o_xm.N one m m N e-o_xN.m m-o.xe._ m-oPXN.N 5: +omo A recto e-o_XN.N e-opxe.e m-o_xm._ as 8-0.xm.~ m-oexe._ e-o_xm.N m-OPXN._ m-o_xm.e new N m m e-o_x_.N N-o_xm.m N-o_xN.m a: +m :o A :zveo N-o.xm.e e-o_xa._ e-o_xN.m ea m-o_xm a e-o_XN e m-o_XN.e m-o_xw.e e-o_xe.e ewe e m m-o_xN N m-o_xe _ N-opxm N I +mi Izveo e-o_xm.m m-o_xo._ m-o_x_.m ea N-OPXN.P e-o_xa.P N-o_XN.N e-onN._ e-o_xm.e new m N e-o.xm.. N-o_xm.N N-o_xe.e a: +mA Iovco Leoo ccoo ccoo Lgoo mam c.m>Eooo_-x o.a>eooo_-c d.e>eooo_-x o.o>eooo_-¥ o>ecoo_-x Aev peaooeoe .mouoguom_m new; new .e:___mw .zgaocmz um umczmmoz mmxmpaeoo AHHHVLQ co gossaz o co cowauauosotuom_m as» to» mucmumcou mama .¢.m mpnmp 115 3. Discussion a. Surface Contaminants Most of the solid electrodes, such as silver, platinum, and gold, exhibit substantial electrocatalyses of electrode reactions compared with mercury electrodes. However, Table 5.2 Shows that rate constants, measured as well as double-layer corrected, at polycrystalline lead electrodes are noticeably smaller than those at mercury electrodes. In this work, most of the experiments employed the mechanical pre- treatment method (0) to prepare the lead electrode before each measure- ment. One possible explanation for this "decatalysis" of electrode re- actions at polycrystalline lead surfaces is that the lead surface is grossly contaminated by impurities from polishing agents, an oxide film, or defects in the lead sample used to fabricate the working electrode. Therefore, it is desirable to do some experiments in order to characterize the polycrystalline lead surface after the pretreatment. The activity of electrode reactions is very sensitive to the electrode-solution interfacial structure which is highly dependent on the way in which the electrode is prepared. Any likelihood that the electrode surfaces used in this work are grossly contaminated can be largely precluded from the following experimental results. (i) Lead upd (underpotential deposition) on a polycrystalline Silver surface: Figure 5.2 presents the differential capacitance 116 Figure 5.2 Differential electrode capacitance C against electrode potential E for (a) polycrystalline silVer. (0) silver containing a monolayer of upd lead. (c) as in (b) but with addi- tional ca. two monolayers of bulk lead deposit. (d) polycrystalline lead. Lead layer prepared as indicated in Ref. 108. Electrolyte was 0.5 M NaClO4, pH 3.5; for ( b) and (c) additionally contained 0.6 uM Pb+2 117 25- 20" ' 15" eo .u 1N o N ‘1.4 “1.0 E/ V vs. SCE ‘02 '0.6 i’02 Figure 5.2 118 curves of 0.5 M NaClO4 solution at polycrystalline silver, poly- crystalline lead, and lead upd surfaces at l KHz. The lead upd has 108 to yield the same value of the pzc (in 10 mM NaF) been reported as that of polycrystalline lead electrodes (40.8 V vs. SCE). Ac- cording to Figure 5.2, it is surprising to see that the behaviors of lead upd on silver, curves (b) and (c), in the measurement of the differential double-layer capacitance are drastically different from those of polycrystalline silver, curve (a), but are Similar to those of polycrystalline lead curve (d). Since the deposition of the lead onto the Silver surface was done in a deaerated solution, the possible formation of the oxide film should be avoided. (ii) The addition of lead ions in the measurement of electrode 110 By the addition of lead ions, lead kinetics at lead surfaces: metal can be continuously deposited onto the working lead electrode surface. Since the rate of lead deposition (with [Pb2"] _>_ 100 mM) may be faster than the rate of diffusion-controlled surface contamina- tion, the lead surface can be replenished continuously during the measurement of electrode kinetics. Even though these two processes are in parallel, the surface coverage of the lead electrode is dominated by the process of the continuous lead deposition (>99%); because the concentration of the impurities should be very small (<1 uM). Therefore, in this study, the observed electrode kinetics at the lead surface must be associated with the major coverage of the electrode surface, 1ead. As is expected, there was no significant Change in the measured rate constants for Cr(0H2)g+, Cr(NH3)g+, and Cr(0H2)5NCS2+ with the addition of lead ions. 119 (iii) Electrode kinetics at the gallium-solution interface. As will be described later, electrode kinetics at the gallium-aqueous interface is similar to that at the lead surface. ‘07 Cyclic voltammetry has been shown (iv) Cyclic Voltammetry: to be a very convenient technique to monitor the electrode surface condition. Figure 4.1 is a typical cyclic voltammogram for 0.5 M NaClO4 solution at the polycrystalline lead pretreated using method (0), and different pretreatments yielded similar voltammograms. The resulting smooth voltammogram suggests that the electrode surface is ideally polarizable. b. Reaction Mechanisms 32 for the distinction of inner- from In Chapter II, two methods outer-sphere reactions are described; these involve measurements of (i) the response of the reaction rate to the addition of strongly adsorbed but Chemically inactive anions and (ii) the potential de- aPP)’ The effect of the specific adsorption of chemically inert anions pendence of the reaction rate (i.e., a such as Cl', Br’, or I' on the electrode reaction rates is recognized as a straightforward way to distinguish inner- from outer-Sphere reaction pathways.32 The reaction mechanisms of all the complexes used in this work at mercury electrodes have already been discussed in detail. Most of the polarizable potential range of lead in aqueous solutions at which the reactants are reduced is on the negative side of the pzc. From the measurement of the specific adsorption of anions as discussed in Chapter IV, it is evident that the adsorbability 120 of anions is relatively small. Therefore, in the case of lead elec- trodes, this method may not be applicable. Anyway, the addition of iodide ions resulted in the increase and decrease of reaction rates of Eu(III) and Cr(0H2)5C12+ respectively, and which is comparable to what was observed at mercury and outer- and inner-sphere path- 32 ways are assigned to the electroreduction of Eu(III) and Cr(OH2)5Cl2+ respectively. For other systems, due to the relatively negative po- tentials at which they are reduced, there are no significant changes in the observed reaction rates with the addition of iodide ions. As outlined in Chapter II, the reaction mechanisms can be assigned according to the value of the corresponding transfer coefficient. aapp’ i.e., “app < 0.5 aSSTgned for inner-sphere pathways and “app > 0.5 for outer-sphere pathways. In the case of mercury, for the reduc- tion of several Cr(III) complexes used in this work, it has been 32 shown that the assignment of the reaction mechanisms of these re- actants based on the values of app is consistent with that based the effect of the addition of strongly adsorbed but chemically inert anions. The Tafel slopes at lead in Figure 5.1 are close to those of the corresponding Tafel plots at mercury. Then, it is likely that the assignment of the reaction mechanisms of the reactants examined at lead surfaces can be done in a similar way. Thus, from Table 5.2, those complexes with a > 0.5, such as Cr(0H2)g+, Cr(NH3)g+, aPP and Cr(NH3)50Hg+ follow outer—sphere pathways, and those with 2+ 2 + < 0.5, such as Cr(0H2)5C1 , Cr(NH3)5C12+, Cr(0H2)5NCS , and “aPP Cr(NH3)5NCS2+ follow inner-sphere pathways. 121 c. The Dependence of Outer-Sphere Electrode Kinetics on the Nature of the Electrode Material To a first approximation, it is expected that for outer-sphere electrode reactions, in which there is no direct interaction between the metal surface and reacting ions in the transition state, the nature of the electrode material should have no specific influence on the measured rate constants after Frumkin correction.m’102 According ' to Table 5.2, the apparent rate constants, k , of all the complexes aPP examined at lead surfaces are two to three orders of magnitude smaller than those at mercury. As noted above, these differences may be due to the large difference of the pzc between lead and mercury electrodes which will result in different values of oz at a given electrode potential, i.e., these differences in ka are due to the PP double-layer effect. However, k double-layer corrected rate corr’ constants, in Table 5.2 at lead are still significantly smaller than those at mercury. This implies that the existence of a "specific substrate" effect on outer-sphere reactions. There is another way to illustrate the presence of the "specific substrate" effect as follows. Considering Equation 2.38 F app " corr ' (Z ‘ 5‘1) RT ¢rp (2.38) The difference in the observed rate constants between mercury and lead electrodes for the electroreduction of a given reactant can . be expressed as 122 Hg-Pb - -F(Z - GI) A Hg—Pb (5.2) Alogkapp ' 2.3RT rp Equation 5.2 is derived under the condition that there is no "specific ”g'Pb = 1ogkHg - 1ogkPb = 0. Since substrate effect, 1.e., Alogkcorr corr corr hg-Pb can be assumed to be the same for any reactant, aPP equal to the ratio of (Z - a1) where Z is the charge of the reactant. - the values of A0 the ratio of Alog for reactants with various charges shall be Note that this method does not require a knowledge of the diffuse- layer potential at either surface. Therefore, upon comparing the + + rate constants of Cr(0H2)g , Cr(0H2)5F2+, and Cr(OHz)SSO4 measured . . _ 3+ at mercury and lead surfaces, the expected ratio of (AlogkHg Pb)Cr(0H2)5 : aPP _ 2+ _ + (A1ogkggppb)5"(°“2)5F : (Alogkggppb)cr(0H2)5so4 = (3 - 0.5): (2 - 0.5) : (l - 0.5) = 5 : 3 : 1. However, according to Table 5.3 the ratio of Alongg‘"Pb for the three reactants considered is 1.87 : 1.14 : 1., 6P0 which is far from the expected ratio 5 : 3 : 1. This result strongly supports the presence of a "specific substrate" effect described as an extra term M to Equation 2.38, as in Equation 5.1. The variation in kcor r between these two surfaces examined are somewhat dependent upon the nature of the coordinated ligands of the metal complexes examined. This indicates the presence of a specific interaction between the coordinated ligands and the surrounding sol- vents within the transition state, and which depends on the nature of the electrode material. 46 As has been reported at mercury electrodes, electrode kinetics of the reduction of Cr(NH3)50Hg+, which is formed by simply replacing 123 one of the ammine ligands of Cr(NH3)g+ with an aquo ligand, are dif- ferent from that of Cr(NH3)g+, but are similar to those of Cr(0H2)g+. Furthermore, the difference in k between Cr(NH312+ 30d "(“3151)”;+ corr is probably due to an inner-shell effect whiCh depends on the bond length and bond strength between the center metal and its coordinate ligands. This observation was also found in this work. According to Table 5.2, k of Cr(NH3)50Hg+ at lead is close to that of corr Cr(OH2)g+, but much larger than that of Cr(NH3)g+. Because of the strong hydrogen bonding interactions between the aquo ligand and the surrounding water solvents, Cr(NH3)50Hg+ the aquo ligand may orient toward the electrode surface, i.e., the electrode would mostly ex- perience the aquo ligand during the electron-transfer process in spite- of the presence of the five ammine ligands. The study of electrode kinetics at the gallium-aqueous inter- faces not only provides strong evidence against the possible forma- tion of an oxide film at the lead surfaces used in this work but also emphasizes the importance of the role of the solvent molecules in the evaluation of the electron-transfer processes. According to Table 5.4, for Cr(0H2)g+ the order of the corrected rate constants for the . . Ga Pb Hg three metal examined is kcorr‘5kcorr < kcorr with the order of the values of 9320 of these electrodes. Gallium which is in accordance seems to influence greatly the extent of the interaction between the coordinated aquo ligand of metal complexes and the water molecules situated between the metal complexes and the electrode surface. The slow reaction rate of Cr(OH2)g+ observed at gallium can be partly explained by the change in the reaction Site due to the presence of 124 a strong solvent-surface interaction. For Cr(NH3)50Hg+ and Cr(OH2)5- ‘1' - Ga .. Pb Hg . $04, the order of rate constants lS also kcorr - kcorr < kcorr' Th1s trend also shows the dependence of electrode kinetics of the aquo complexes upon the water structure at the electrode surface. As stated above, due to the possible presence of the ligand orientation effect for the electroreduction of Cr(NH3)50Hg+, it is expected to Ga pb 3+ . . see kcorr < kcorr for Cr(NH3)50H2 . This 1s, however, contrary to what is observed kGa = kPb corr corr' These data seem to 1mp1y that the “specific substrate" effect is smaller for ammine as compared to .otherwise similar aquo complexes. Thus, for the reduction of G Cr(NH3)g+, k a is similar to k”9 001‘? COPY" B. Evaluation of Electrochemical Activation Parameters 1. Results Measurements of the temperature dependence of rate constants for a number of Cr(III) complexes and Eu(III) were performed at polycrystal- line lead electrodes utilizing a nonisothermal cell. In this work, a specially designed disk electrode that is described in Reference 56 was used. The procedure used to analyze the data obtained from the temperature dependence of the rate constants has been clearly i1- 1ustrated in Chapter II. Table 5.5 shows the rate constants, ka PP and kcorr’ and the corresponding activation parameters of a number 47 of Cr(III) complexes and Eu(III) at both mercury and lead electrodes. The corrected rate constants kcorr were obtained by utilizing the Frumkin equation. According to Equation 2.43, it is necessary to 125 .AA goaamcu :_ wonpcommu mm: =o_umcweLouou mu_ .Am—oEAAmoxv aooewo Loxmp m—nzou cow oouuoctoo :owum>_pom mo Aapmguco =AmmuA= ccoo .oom\eo coca" oN oeoez .AoNeN-ccooxeavee u cAaom mo Autoco macaw .uomewo coxep mpnaou upcoA soc umpomccoo accumcoo mama m u Amm\aamx:NNVAm\hmvu on peace .uopn pocmb do maopm sore um>ALmv acmAUAmwooo comment» peaceaa >eooopu mo Amwucmaoa muocuuwpm as am uw:AEEmaoo .uomN an accumcou mums newsmaaeooopux n>eooo_-x o Aev aceuommm .mmommsoacu muom=a< new; new uxeaocwz one up mmxmpaeou .Amuo: ucmpe>peh mzoptm> do copuoauogocuooAN asp to; memNQEmcma :o_am>.uo< .m.m open» 126 .omm\Eo ca ma acmamcoo mama .4. .oemmo 1 ccomm< n Ammsm< Sosa mmcaECmamm coaam>aaom ac Am—oe mmm\ammv Anomacm eammae .oe atom a memo x atom seem a m< a u we mcae=mmm An Aaax salvaxm Aa\ maaom we Aacmacm .umm\5m moaxo.m u mN mam A 0 Amy zm Emma mm>acmm .Amaoe mmm\_mov coaam>aamm ac Amocacm eammmae ; .am mocmemmma eoea :mama mama .maazoo AAAVZ\AAAsz mamacaocmam com Aone mmm\_mov Anomacm coaaommc =m_Em=AmoELm;a=a _ aaom_ .4. measummm An Nm.N :oaammcu acam: .moseaaeom .m.m o_ama 127 evaluate the temperature dependence of the potential at the reaction plane from the measurement of the temperature dependence of the dif- ferential double-layer capacitance in order to calculate the correct # activation enthalpy AHcorr' The temperature dependence of the dif- ferential capacitance curves over the temperature range 5°C to 40°C measured at lead surfaces are shown in Figure 5.3. It is evident that varying the temperature has only a minor effect on the measured capaci- tance at lead. Therefore, the value of [Born/3(l/T)]¢m of Equation 2.43 * corr at lead can be can be assumed to be zero. Then the value of AH * ideal’ complexes under consideration the corrected activation enthalpies * corr mercury electrodes. This implies that lead electrodes yield more a very close approximation to the value of AH For all the metal AH at lead are three to five Kcal/mole smaller than those at favorable enthalpic barriers for these reactants than mercury. The activation entropies were obtained from the relation TAS* = * corr * will be aH - AG+ where Ae* = RT(2nk - znA). The values of AS sensitive to the method used to compute kcorr and to the reaction model chosen to calculate the pre-exponential factor A. Although the un- ¢ idea] and As* shown in Table 5.5 certainty of the values of AS corr may be significant as described in Chapter II, only the comparison of values at mercury and lead surfaces will be emphasized in the Dis- cussion. The relationship between the "real" and "ideal" entropies of activation can be written as follows # # ASideal = ASreal +(1Asrc (2°44) where Asgc is the reaction entropy of a redox couple. The value of 128 Figure 5.3 Differential capacitance at 1000 Hz vs. electrode potential for polycrystalline lead prepared by method (D) in 0.5 M NaClO4 at various temperatures: (x) 5.5 C; (o) l6.5°C; (en 25.5?c; (v) 36.2°C _ 129 m.m ousmam mom .m> >\m m._.. m._.. 2.. m6... N20... 4 - d u - .~\J.\fl\LwauH.ll.ll \WH XV. ./ \..\_ /.. \. /. £9. 0 N zJU9' Ari/o aououdoo Iouuammo l30 AS* can be set equal to zero as described in Chapter II. For all real the metal complexes examined, the corrected activation entropies As* at lead are much more negative than those obtained at mercury corr * )Hg _ (AS* )Pb corr corr z 20 e.u. Also the values electrodes, i.e., (A5 of asteal in Table 5.5, which are obtained by substituting experi- mental values of ASfdeal into Equation 2.44, are quite different from 1 8’9 and other the value of zero that is predicted from the Marcus "weak overlap" outer-sphere theories. Since the activation entropy and the pre-exponential term A are unable to be independently determined, the values of Astorr in Table 5.5 were obtained by assuming the value of A. Therefore, it is of interest to evaluate the pre-exponential term by assuming the values of Asideal' The evaluation of the pre-exponential factor A provides insight into the collision frequency, electron tunneling, and the applicability of the Marcus theory. The values of AStdea] was set to aAS;c as predicted from the Marcus theory to obtain the values of A that are shown in Table 5.5. The resulting values of A for both mercury and lead electrodes are listed in Table 5.5. The values of A at lead for all the reactants examined are significantly smaller than those at mercury electrodes. Furthermore, the values of A at lead are up to eight orders of magnitude smaller than the theoretical values, 5 x lO3 and 3 x 105 cm/sec given by the reactive-collision8 4 and pre-equilibrium models . respectively. 131 2. Discussion Outer-sphere reactions, for which there is supposed to be no direct interaCtion between the metal complex and the electrode surface, the presence of the "specific substrate" effect as illustrated before is somewhat surprising. According to Table 5.5, compared with mercury surfaces lead surfaces exhibit favorable enthalpic and unfavorable entropic bar- riers for these electrode reactions examined. The relatively small activation enthalpies AHtorr correspondingly small or even negative values of the activation en- ¢ corr at lead are generally compensated by tropy AS¢ , i.e., smaller values corr resulting in large values of AG of kcorr at lead. It is surprising and unexpected to see that the values of Astorr at lead are relatively small or even negative. The reactants with +3 charge certainly have a higher tendency to order surrounding water structure than that of the corresponding products ¢ that have +2 charge. Therefore, the resulting Ascorr _ + + (- Asp - ASr) is expected to be positive and close to As;c. In other words, the 4 8 corr O + aASrc where AS violate the Marcus theory which pre- + real experimental values of AS dicts As* = A5* corr real 2 0. Table 5.5 also in- cludes the corresponding values of Asteal that were calculated from 4 4 0 =1: AS - aASrc. The values of Asreal at lead surface are ASreal = corr extremely negative. * 2 0 (or AS*’f ==-AS*’b ) is only true when The relation Asreal corr corr the transition state for heterogeneous outer-sphere electron-transfer reactions has the same environment as the reactant and product states. However, the transition state for electrode reactions is inevitably 132 within the double-layer region where the solvent structure can be expected to be significantly different from that in the bulk state. The adiabatic assumption is frequently used in the study of 4 corr shown in Table 5.5 were obtained under this assumption, i.e., the outer-sphere electron-transfer reactions, and the values of AS transmission coefficient for electron tunneling, Ke], was assumed to be unity. Equation 2.3l derived in Chapter II shows the relation between the rate constants and A§¢ -w 4 - P :Lii. kapp - KelKovpexp(Tfir0exp( RT (2.3l) However, the possibility that electron-transfer processes could be nonadiabatic has been already noticed by several authors.109 The g COVP Table 5.5 also suggest the possibility of nonadiabatic processes. relatively small (negative) values of AS found at lead shown in Therefore, the evaluation of the pre-exponential factor A by assum- z 1"9 AScorr found at lead shown in Table 5.5 also suggest the possi- bility of nonadiabatic processes. Therefore, the evaluation of the e GOV? a means to examine the observed "specific substrate" effect as well pre-exponential factor A by assuming AS = aAs;c provides us with as the experimentally small or even negative values of activation entropy at lead surfaces. Since there is no way to determine experi- mentally the activation entropy and frequency factor as mentioned above, in Table 5.5 both ASZorr and A were obtained under certain inevitable assumptions. Although there is a difference in the reactive- collision and pre-equilibrium models, for the present purpose it will 133 not make any difference to the values of A listed in Table 5.5 whether the former or latter model was used. Because the deviation of the values of A between calculated and theoretical values is so large (10‘5 to 10'9 fold smaller), the possibility of nonadiabatic pro- cesses at lead surfaces seems likely to be valid irrespective of the model that is employed. For a given reactant, the plane of closest approach to the elec- trode surface might be significantly different between polycrystalline lead and mercury electrodes. From the study of the double-layer structure at lead-aqueous interfaces, it shows that polycrystalline lead exhibits a higher affinity for water than mercury electrodes, which as noted above can be judged from the values of 9:20. The existence of strong interaction between the lead surface and water within the double-layer region results in constraining the reacting ions to be away from the electrode surface. The electron density associated with the orbitals at metal surfaces decreases exponentially 11‘ Therefore, the degree of with distance away from the surface. orbital overlap between the reacting ions and electrons of lead . electrode surfaces will be diminished resulting in the small value of Ke]. In addition, the value of KP’ the equilibrium formation constant of the precursor state in the pre-equilibrium model may decrease when the plane of closest approach is moved further away from the lead surfaces as a result of diminution of the concentration of reacting Species in the precursor state. Although the explanation given above to illustrate the observed small frequency factor at lead surfaces is quite plausible, the T34 values of AH:orr reported in Table 5.5 are surprising on the basis of this model. Since the corrected activation enthalpy is an intrin- sic barrier which shall be independent of the value of Kel' There- fore, the difference in the electroactivity between lead and mercury electrodes cannot be simply attributed to the effect of electron tun- neling. The enthalpic barrier, AH* , is the result of outer- and inner- corr shell reorganization energy for electron-transfer reactions. The 4 energy, which depends on the bond length . inner-shell reorganization and bond strength between the center metal cation and its coordinated ligands, of the reactions under consideration at both electrode sur- faces, mercury and lead, can be assumed with confidence to be the same. The outer-shell reorganization energy,3“)’d however, can be expected to be strongly dependent on the variation of the interaction between the electrode surface and solvent molecules surrounding the reacting ions in the transition state. In other words, the variation of AH* corr between lead and mercury is attributed to the existence of a specific solvent effect. From this study, it is evident that the solvent plays a very important role in electron-transfer processes. Even for outer-sphere reactions, the electrode still shows certain degree of influence on the solvent structure between the metal surface and the reacting ions within the transition state. The strong sol- vent interaction within the double-layer region may be responsible for the small enthalpic barrier of activation for electrode reactions at lead electrodes. This, however, is compensated for by the resulting * corr' Therefore, the negative low (unfavorable) entropic barrier TAS T35 entr0pic barrier obtained at lead surfaces, which more than compen- sates the favorably low enthalpic barrier, is responsible for the observed lower electroactivities of electrode reactions at lead com- pared with those at mercury. In addition, the strong solvent interaction with the electrode surface existing at lead-aqueous interfaces85 may influence the work term used in the calculation of the double-layer corrected rate * and AH* constants. The work term employed to calculate AGcorr corr is usually assumed to be purely Coulombic in origin. This assump- tion may be roughly true for the relatively hydrophobic mercury electrodes, however, it may not be valid for other electrodes with strong solvent interaction between the reacting ions and the electrode surface. When the reacting ions approach the reaction plane, they may experience strong interaction with the solvent molecules in the .double-layer region. Equation 2.49 presents a general expression for the relation between the "real" and “intrinsic" activation enthalpy e _ * o 0 AH - AHint + [AHP + aI(AH S — AH;)] (2.49) Therefore, if there are additional work terms other than electro- static work terms which can be included in the terms of AH; or AH°, ¢ corr' This then it may significantly influence the evaluation of AH notion can also be applied to the evaluation of the activation en- tropic barriers. In conclusion, the observed "specific substrate" effect is T36 attributed to the effect of electron tunneling and also to the effect of specific solvent interaction with the electrode surface. Furthermore, the influence of the specific solvent structure within the double layer region in the transition state for the electron- transfer step seems likely to dominate the observed "specific sub- strate" effect. PART I I 137 CHAPTER VI ELECTROCATALYSIS 0F OXYGEN REDUCTION I38 l. Introduction Oxygen reduction”2 has been well studied and has been success- fully employed as the cathodic reaction in some practical application of fuel cell technology. ‘However, only the relatively expensive material platinum is known to be an efficient catalyst for the desirable four-electron reduction of oxygen molecules to water. Thus, 113'118 of an electrode material at which oxygen re- the development duction can be significantly catalyzed is the focus of much current research. The pyrolytic graphite (PG) electrode has been extensively used in this study because it is cheap, has a wide polarizable poten- tial range, and also has a strong affinity for a number of macro- cyclic metal complexes which are anticipated to be able to catalyze oxygen reduction.]19 Recently, graphite electrodes chemically modified with macro- 113‘116 has been shown in several cases to cyclic metal complexes dramatically enhance the rate of oxygen reduction. At most modified graphite surfaces, oxygen molecules can only be reduced to hydrogen peroxide via two-electron reduction. Some iron(III) porphyrins148 can catalyze the four-electron reduction, however, the corresponding reaction potential of oxygen reduction are fairly negative (-0.05 V vs. SCE). The two-electron reduction is the first step for the stepwise reduction of oxygen molecules to water: Scheme I (in l M acidic solution) 139 T40 + - 02 + 2H + 2e 1 H202 E° 0.44 v vs. SCE (6.1) + - H202 + 2H + 2e :‘ZHZO E° l.54 V vs. SCE (6.2) However, it is the direct four-electron reduction of oxygen mole- cules to water that has the greatest practical application in fuel cell technology: Scheme II 02 + 4H+ + 4e- : 2H20 5° = 0.99 v vs. SCE (6.3) Since the equilibrium concentration of hydrogen peroxide at the desirable operational potential of an Oz/H2 fuel cell (+0.99 V vs. SCE) is relatively low (_<_ 1048 M),"7 an extremely high reaction rate (i.e., driving force) is required to subsequently reduce the hydrogen peroxide to water. This is why the "direct" four-electron pathway is preferred over the stepwise pathway. Metalloporphyrins, such as iron porphyrins are essential components 120 of cytochrome c oxidase which is the terminal enzyme in the respiratory redox chain that reduces dioxygen to water. Therefore, metalloporphyrins that are capable of binding oxygen moleculeslz} might be expected to constitute potent electrocatalysts for the four- electron reduction of dioxygen to water. (This concept has been il- 113'117 Recently, Collman and Anson”7 lustrated by several groups. demonstrated the remarkable enhancement of the electrocatalysis of the four-electron reduction of dioxygen to water through modification of the pyrolytic graphite surfaces with dicobalt face-to-face porphyrin. 141 However, the stability and reproducibility of these porphyrin- modified oxygen electrodes as well as the elucidation of the corres- ponding reaction mechanism still needs attention. In this work, a number of cobalt porphyrins including eight mono- mers and three dimers as shown in Figure 6.1 were used to examine the so-called "molecular engineering" of the chemically modified electrodes. The eight monomeric cobalt porphyrins have different substituents on the porphyrin rings, allowing substituent effect to be examined. Two of the three dimeric cobalt porphyrins, Co-Co-4123 124 and C8-C0- Co-S, that have similar structures to those used in Reference ll7 also yield similar results of the electrocatalysis of oxygen reduction. These two dimers are basically different in the length of the chains that connect the pairs of porphyrin rings. Thus, the effect of the distance between the cobalt centers on the electro- catalysis of oxygen reduction can also be examined. The other dimer, "slipped"-Co-Co-4,123 was prepared by connecting the meso-position of one porphyrin ring with the B-position of another porphyrin ring. Therefore, it will result in an offset in the relative position of the two cobalt atoms, i.e., will form a slipped configuration. It t"123 on the is of interest to inspect the influence of this "offse oxygen reduction kinetics. A rotating ring-disc electrode125 (RRDE), which has been demon- strated to be a useful tool for the investigation of the formation of the reaction intermediates during electrode reactions, was ex- tensively used in this study. Basically the RRDE consists of a disc and a concentric ring separated by a small Teflon gap as shown 142 Figure 6.1 Structures of cobalt porphyrins Co-OEP Co-Etio Co-TPP Co-TPP(p-0Me) Co-TPPF20 Co-OEP-Cl Co-OEP-Cl2 Co-OEP-Cl4 I43 R1 R2 R3 R4 R5 czn5 c235 H a a 0235 CH3 .H a H H H c635 c635 C635 3 H 634(p-0Me) c634(p-one) c634(p-oue) H H C6F5 C6F5 C6F5 c2115 “235 C1 H H c235 c235 c1 c1 H c235 c235 c1 c1 c1 Figure 6.1 144 Figure 6.1 (cont.) R R R' C8-Co-Co-5 C81117 -CHZCON(n-Bu)CHZCH2- Co-Co-4 C51111 -CH2CONHCH- R R' Slipped—Co—Co-4 -CH CONHCH- Csfin 2 145 in Figure 6.2. Therefore, the potential of both the disk and the ring can be controlled independently by a bipotentiostat. With the aid of the RRDE, the production of hydrogen peroxide at the disk can be detected at the ring by holding the potential of the ring at a value at which hydrogen peroxide will be oxidized. The result- ing ring-disk voltammograms for oxygen reduction at the porphyrin- modified graphite surfaces will be presented and discussed. Further- more, the corresponding formal potentials of the attached cobalt porphyrins at the graphite surfaces were also determined by conven- tional cyclic voltammetry. This measurement provides a way to dif- ferentiate the electroactivities of these cobalt porphyrins under consideration and allows the reaction mechanism of oxygen reduction to be determined. There are two possible pathways for oxygen reduction at the por- phyrin-modified surfaces, two-electron reduction of dioxygen to hydrogen peroxide and four-electron reduction of dioxygen to water as described. Thus, it is interesting to calculate the number of electrons involved in oxygen reduction which can be evaluated from the corresponding ring-disk voltammograms. There are a number of ways to calculate the number of electrons involved in electrode re- actions. The ring current is attributed to the oxidation of the hydrogen peroxide that is produced at the disk during oxygen reduction. Therefore, the ratio of (-iR/iDN), where iR and iD are diffusion-limited currents at the ring and the disk respectively, and N is the collection efficiency of the RRDE, can be treated as the -percentage of the over-reaction of oxygen reduction that follows 146 Figure 6.2 Diagram of a Rotating Ring-Disc Electrode (RRDE) 147 N.o muswfim $05: 3058:. omalozE 02:39. l48 two-electron reduction of dioxygen to hydrogen peroxide. Then, the average number of electrons involved in oxygen reduction at the disk can be extracted from the following relation 'iR nav = 4 - 2 (TEN) (6-4) If no ring current is detected, iR = 0, then, nav = 4. If oxygen reduction at the disk entirely follows two-electron pathway, -iR = iDN, then n = 2. The values of n can also be directly obtained from av 125 the limiting current using the Levich relation or the correspond- ing slope of the Levich plot (it vs. A: ). 2. Experimental a. Materials The cobalt porphyrins used in this work were kindly supplied by Professor C. K. Chang of this Department. Their structure are shown in Figure 6.l. Their syntheses and characterization have been dis- cussed in ReferenceleB and l24. Trifluoroacetic acid (HTFA) (MCB Co.) was used without further purification. Dichloromethane was purified by distillation. Highly purified water prepared as des- cribed in Chapter III was used to prepare the electrolyte solution (0.5 M HTFA). Tetrabutylammonium perchlorate (TBAP) was prepared by mixing tetrabutylammonium hydroxide and 70% perchloric acid. The addition of water gave a precipitate which was recrystallized from 95% ethanol. I49 b. RotatingRing-Disc Electrode (RRDE) A Pine Instrument Co. Model 0T6 rotating ring-disc electrode (RRDE) was extensively used in this work. The RRDE contains a pyro- lytic graphite (PG) disk and a platinum (Pt) ring as shown in Figure 6.2. The RRDE has been widely used to examine the formation of the intermediates during the electrode reaction. A certain portion of the materials produced at the disk will diffuse to the ring when the RRDE is rotated. The quantity of the intermediates produced at the disk that can be detected at the ring is dependent on the so-called "collection efficiency", N, of the RRDE. Therefore, the collection efficiency of the RRDE can be simply formulated as -l N ='WJ1 (6.5) where iR and iD are the diffusion-limited currents at the ring and the disk of the RRDE respectively. The collection efficiency is determined by the radii of the disk and the ring and the size of the 126,127 gap between them. The theoretical calculation of the collec- tion efficiency utilizes the following equation N = l-F(%)+82/3[l-F(a)]-(l+a+B)2/3{l-F(%)(l+a+B)]} (6.6) where a==(r2/rl)3-l, B = (r3/r])3-(r2/r1)3, and r1, r2, and r3 are defined in Figure 6.2. The function F(e) is defined as l/Z 3 1/3 F(e) = (gnniU—T—eg—Ll + 231; arctan(giE:-D + (5.7) l 4 150 and is tabulated in Reference l27. c. Instrumentation A bipotentiostat is required in the performance of the RRDE voltammetry in order to control the potentials of the disk and the ring independently. Generally, the potential of the ring is held constant while scanning the potential of the disk. In this work, a bipotentiostat was constructed by inter-connecting two PAR l74A polarographic analyzers together through their rear panel connectors as suggested by PAR Co. Figure 6.3 presents the diagram used to make the modification. The operation of this bipotentiostat is illustrated by a simplified circuit shown in Figure 6.4. The principle of the per- formance of this bipotentiostat follows: Working Electrode El (Wl): Since electrode El is in a voltage follower configuration, input equals the output E = - EA ' (6.8) ref Since the Working Electrode l is at virtual ground (not shown in this scheme) = 0 ' (6.9) (6.l0) Eref ' Ewl = ' EA therefore E1 = 'EA' Working Electrode 2 (W2): At the summing point 151 Figure 6.3 Schematic diagram for the connection of the "modified" bipotentiostat 152 REAR PANEL 7DDDUUDDI 160000008 CO 700000 c ,MDDUUD n1 [final 99 J37 DROP TIME/CELL J36 Access./Exy.rwa.’ M174A 10K (Blue) CONNECTOR T NORMAL Counter (Red) Electrode 9 working 'Electrode 1 (Blue) J (White) Reference Electrode Cell Working Electrode 2 Differential Input Recorder White B Y-AxisL Tilillrl T (Red) .___________________________ RL caoszn FOR IV FULL SCALE CURRENT AT W. E. 2 M174A REAR PANEL 7 00 J5 nouns. xuUDDU ounnnr vunuo m 00 [108 all 'J37 DROP TIME/CELL 336 ACCESS./EXT.PWR; SET CURRENT RANGE AI 0.1mA Figure 6.3 153 Figure 6.4 Schematic diagram for the operation of the "modified" bipotentiostat 154 (O) (v.g.) R / . E 5A1 A + \i'; R EEA’E“ (-E) (F1) A EEA’ t Etecrnomereni Ar) '8‘ . \ ti :2 w / w‘ ‘T‘vn 2 3w (E )L i we ~- we 'Wi if” (sz) ‘) e e) ( ”’2’ erec'mo- uerenz a I"‘l. l'RL (E M E SAZ % O)(v.g.) B 4. El SA: amplifier A: auxilliary electrode R f: reference electrode e W1(W2): working electrode Figure 6.4 155 of amplifier 5A2 sz = ‘EA ‘ EB therefore E2 = EB. Note that the relationship between the polarity of the applied potential and the polarity of the reference electrode vs. working electrode in the case of Working Electrode l is opposite that in the case of Working Electrode 2. A sodium saturated calomel electrode (SCE) (Sargent-Welch Corp.) was used as reference electrode. A platinum wire activated by means of a flame was used as the auxiliary electrode. A PAR Model ASRZ analytical rotator was employed to rotate the RRDE. The electro- chemical cell was as described in Chapter III except with larger dimensions in order to fit the larger RRDE. d. Porphyrin-Modified Electrodes 117 used to prepare the modified electrodes is rela- The procedure tively straightforward. The cobalt porphyrin can be irreversibly adsorbed on the pyrolytic graphite surface. First, the RRDE was carefully polished with 0.3 alumina on a polishing wheel as des- cribed in Chapter III. After polishing, the electrode was rinsed 156 with purified water and dichloromethane. Then it was soaked in a di- chloromethane solution containing a small amount of cobalt porphyrin (\m mVAV ”.0 ||\ VT’I! mount) 159 ii = 199 nADz/37'1/6m1/2CbF ' (6.13) where i2 is the diffusion-limited current (mA), n is the number of electrons involved in reaction, F is the Faraday, A is the electrode area (cmz), D is the diffusion coefficient (cmz/sec), y is the kine- matic viscosity (cmZ/sec), w is the rotation speed (rpm), and Cb is the bulk reactant concentration (moles/cm3). At 22°C, y = 9.57 x 139 10 cm/sec, the Levich equation can be simplified to i2 = 4.18 x 107 nADZ/3w1/2Cb (6.14) ‘According to Equation 6.l4, the limiting current is proportional to the square root of the rotation speed; the resulting Levich plot (11 vs AF) is shown in Figure 6.6. Furthermore, from the slope of the Levich plot, the number of electrons can be calculated. The value of n (l.05) evaluated from the Levich plot is close to the 3-/4- 6 0 Figure 6.7 shows the background cyclic voltamogram of the disk theoretical value (n = l) for Fe(CN) of the RRDE that was measured in 0.5 M HTFA deaerated solution. As has been reported,]30’131 the reduction wave (0.28 V vs. SCE) and the oxidation wave (0.37 V vs. SCE) seen in Figure 6.7 are probably due to the reduction of quinone-like group and oxidation of hydro- quinone-like group respectively. Those surface groups may be responsible for the irreversible adsorption of cobalt porphyrins at the graphite surface as a result of n-n electron interaction. 160 Figure 6.6 Plot of the limiting disk current i’. vs. 1/2 the square root of rotation rate (w ) for the reduction of Fe(CN)g' (1.4 mM) on the PG/Pt electrode 161 500— ' x 400 - /" < x {L ' / slope-IO.3 2'. 300 " /x ‘ 75 . t a 0 .5 200*- 3 g /" 100 r- " IO 20 30 I40 WIT/rpm,2 Figure 6 . 6 162 Figure 6.7 Cyclic voltammogram at the "blank" graphite electrode of the RRDE at 0.1 V/sec in 0.5 M HTFA 163 ~.m ouamem mom .m> >\w v.0 $6 0. O ’ ‘e d J V'rI/g wanna 164 b. Oxygen Reduction on the "Blank" Pyrolytic Graphite Surface Contrary to platinum which is known to be an efficient electro- catalyst for the four-electron reduction of dioxygen to water, the graphite electrode is a very poor catalyst for oxygen reduction. Figure 6.8 shows the voltammograms of oxygen reduction at the PG disk and the Pt ring of the RRDE in a 0.5 M HTFA solution saturated with oxygen. Compared with platinum, curve (b), the reduction po- tential of oxygen reduction at the graphite disk, curve (a), is rela- tively negative (-0.35 V vs. SCE). Furthermore, it has been shown131 that at the graphite surface the oxygen molecule is reduced via two- electron reduction to hydrogen peroxide. As discussed in the beginning of this chapter, the formation of hydrogen peroxide will block out the desirable four-electron reduction reaction. c. Redox Properties of the Cobalt Porphyrins Eleven cobalt porphyrins which are shown in Figure 6.l were em- ployed to prepare the porphyrin-modified graphite surfaces. The redox properties of some of these cobalt porphyrins have been ex- 134’135 in dichloromethane or benzonitrile solution. These amined are so-called "bulk" properties. In this work, the "bulk" redox potentials of these cobalt porphyrins were determined in 0.l M TBAP dichloromethane solution deaerated with nitrogen at the graphite disk of the RRDE. A typical voltammogram is shown in Figure 6.9. The derived data are listed in Table 6.1. The agreement of the redox III/II potentials of Co reaction between the reported data and the 165 Figure 6.8 Cyclic voltammograms for the reduction of oxygen in 0.5 M HTFA at 0.1 V/sec on (a) the "blank" graphite disk electrode; (b) the platinum ring electrode; (c) the monomeric porphyrin-modified surface; (d) the dimeric porphyrin-modified surface 166 Nd- w.o muswfim mum .m> >\m_ O NO v.0 . ’h- 3 . . . u . \\ \k'\ 410% «19% oo. 3 as vii/g iueun t 167 Figure 6.9 Cyclic voltammogram for the “bulk" redox reaction of Co(III/II) of Co-Co-4 on the graphite disk electrode in 0.1 M TBAP dichloromethane at 0.2 V/sec ' 168 ¢.o ouswfim V6 333m ,9, >\m od 169 Table 6.l. "Bulk" and "Surface" Redox PotentiaTs for the C02”3+ Couple of Cobalt Porphyrins. Cobalt . B + a S + b S c Porphyrln E1/2(vs Fc /Fc) E1/2(vs Fc /Fc) E1/2(vs SCan) Co-OEP 0.20 0.46 0.59 Co-Etio 0.20 0.30f - 0.45 0.58 Co-TPP 0.22 0.30f 0.29g 0.49h 0.53 0.66 Co-TPP(p-0Me) 0.280289 0.50 0.63 Co-TPPFZO ---- -—-- Co-OEP-Cl 0.23 0.56e 0.69e Co-OEP-Clz 0.23 0.55e 0.68e Co-DEP-Cl4 0.28 0.47e 0.60d’e C8-Co-Co-5 0.19 0.50 0.63 -0.06 0.17 0.30 SIipped- 0.18d 0.55 0.68 Co—Co-4 0.05 0.15 0.28 Co-Co-4 0.18 0.53 0.66 0.02 0.l8. . 0.31. Co-CZ-diester -0.05k 0.42"J 0.55‘ COZBFSN-H 0.15: -0.01 C028F4N-H 0.20: 0.15b’k 0.28‘3’k ' -0.01 ---- ---- 3+/2+ aBulk redox potential of Co measured in 0.1 M TBAP CHZClz at pyro- lytic graphite vs SCEa . The potentials were reported vs Fc+/Fc. Surface redox potential of Co3+/2+ measured in 0.5 M HFTA solution at porphyrin-modified surfaces. The potentials were reported vs. Fc+/Fc. CSame as b except the potentials were reported vs. SCE(aq). dOnly reduction wave was observed. eThese redox potentials were estimated from ill-defined cyclic voltam- mograms. fFrom reference l43 measured in 0.1 M TBAP benzonitrile vs.SCE(aq). gFrom reference l44 measured in 0.1 M TBAP dichloromethane. 170 Table 6.1. Continued. hFrom reference 134 measured in 0.l M TEAP benzonitrile. 1from reference l46 measured in 0.5 M HTFA vs. SCE (aq). jSame as i except vs. Fc+/Fc. kFrom reference 147 measured in 0.l M TBAP benzonitrile. 171 literature data is variable as shown in Table 6.1 which also includes the literature values. This variation may be due to the difference in the arrangement of the electrochemical cell which may cause the variation of the resulting junction potential. In this work, the arrangement of the electrochemical cell was clearly described in Chapter III. The electrode potential was measured with respect to an aqueous SCE, but the potentials listed in Table 6.1 are against the Ferricinium/Ferrocene redox potential (the "Ferrocene assumption").136 The Ferrocene assumption is that the absolute standard potential ¢; of the ferricinium-ferrocene (Fc+/Fc) redox couple is independent of the solvent. The investigation of the "surface" properties of the attached cobalt porphyrins in aqueous solution is very important in the evaluation of the reaction mechanism of oxygen reduction at the por- phyrin-modified surfaces. The "surface" redox potentials of the attached cobalt porphyrins were measured by cyclic voltammetry in 0.5 M HTFA deaerated solution. Figures 6.10 to 6.13 show some typi- cal surface cyclic voltammograms. The derived data of all the sur- face cyclic voltammograms are listed in Table 6.1. Due to the in- fluence from the twenty fluorine substituents which are strong electron-withdrawing groups on the porphyrin ring, Co-TPPF20 did not yield any detectable redox waves for both the bulk and the sur- face redox reactions. The assignment of these surface redox waves will be discussed later. It is difficult to determine quantitatively the surface concen- tration of the attached cobalt porphyrins by conventional cyclic voltammetry due to the interference of the relatively large 172 Figure 6.10-6.13 Cyclic voltammograms for the "surface" re- dox reactions of Co(III/II) (?) at the PG disk electrode in 0.5 M HTFA aqueous solution de- aerated with nitrogen at 0.2 V/sec. The pore phyrins under consideration are indicated in the corresponding figures 173 410$ o~.o muamam mu ¢.O _ m .m> >\m QC _emo-oo_ ¢ VT’I! luauno 174 Ha.m ousmnm ¢.O . mom .m> >\m m6 1J1 WicUloUbUL. —’ vii/l wanna ‘— 175 N~.m ousmee \ mom .9 >\m No ed - QC - 410$ 77818 Buojfl. . WI! luauno 176 m~.o ousmfim , D V‘H/l luaun ‘— 177 background current of the graphite electrode itself. Brown and Anson137 demonstrated that with modification of the time constant of the PAR 174 the differential pulse voltammetry yielded much better resolution of the surface concentration of weakly adSorbed molecules than with conventional cyclic voltammetry. Nevertheless, in this work the surface concentration of the attached cobalt porphyrins were esti- mated by integrating the corresponding cyclic voltammograms. The surface concentration of the quinone-like group at the "blank" 10 graphite surface is about 2.3 x 10' mole/cmz, close to a monolayer coverage. For the attached cobalt porphyrins, the values of surface '10 mole/cmz. Thus the concentration vary between 1.3 and 1.9 x 10 coverage of the attached cobalt porphyrins is between 60% and 80% of a monolayer (however, this will be smaller if the roughness factor is included). d. Oxygen Reduction at the Porphyrin-Modified Graphite Surface Figure 6.8 presents the cyclic voltammograms of oxygen reduction at the "blank", curve (a), and the porphyrin-modified, curves (c) and (d), graphite electrodes. Note the tremendous improvement of the electrocatalysis of oxygen reduction through modification of the "inert" graphite surface with cobalt porphyrins. Judging from the peak potential of these voltammograms, the cobalt porphyrin can sub- stantially lower the overpotential of oxygen reduction at the "blank" graphite surface. The PG/Pt RRDE with which the formation of hydrogen peroxide can be detected at the ring was used in this work. Representative 178 ring-disk voltammograms and the corresponding cyclic voltammograms for oxygen reduction measured in 0.5 M HTFA oxygen saturated solu- tion at the porphyrin-modified graphite surfaces are shown in Figure 6.14 to 6.20. These ring-disk voltammograms were obtained by scanning the disk potential between +700 mV and -50 mV vs. SCE to measure oxygen reduction and holding the ring potential constant at +1.0 V vs. SCE to monitor the formation of hydrogen peroxide. The derived data are listed in Table 6.2. Table 6.2 also includes the values of the transfer coefficient for oxygen reduction. The evaluation of the transfer coefficient was described in Chapter II. The values of n calculated using Equation 6.4 are listed in Table 6.2. There is a special feature of the rinngisk voltammogram of Co-Co-4, a maximum of the disk current i was observed as shown in Figure 6.20. m 117 There- A similar result was also obtained by Collman and Anson. fore, in Table 6.2 the values of n of Co-Co-4 were calculated accord- ing to the diffusion-limited i as well as maximum im currents. In 9. the case of Co-Co-4, the maximum current is much less stable than the limiting current, and the maximum current and the limiting currents decreased about 40% and 20% respectively after thirty minutes. Further- more, the maximum current would approach the limiting current within about thirty minutes. 0n the other hand, the limiting currents for oxygen reduction at the monomeric porphyrin-modified surfaces were relatively stable. Furthermore, upon comparing the surface redox potentials for oIII/II C and the half-wave potentials for oxygen reduction in the case of monomeric porphyrin-modified surfaces, it is seen that there 179 Figure 6.14-6.20 Disc (upper-i0) and ring (lower-iR) currents for the reduction of oxygen in 0.5 M HTFA on the PG/Pt electrode (w= 600 rpm). Scan rate for the corresponding cyclic voltammogram for oxygen reduction at the PG disk electrode is at 0.1 V/Sec except Figure 6.19 at 0.2 V/sec 180 ¢~.e unawah 718 . mom .m> >\m 0 _.0 N6 md 4100; VT’I! wanna 181 2 . 0 one»; «to; mom .m> >\m _.O.. O _.0 N6 171 Md Wedgié WW! 1081an 182 Ea -TPP IOOpAI l L i " 0.3 0.2 0.l o E/V vs. SCE Current i/pA 20 A Figure 6.16 1“ |——'I 1 183 . 419% nd. q 32% n~.o ouawum mum .a> >\w _..0.. _.O . .. d 718. hos-OIQQPIOUQ vim iuauna 184 3 .o unamwm <109H mom .2,>\u No r to no m.o, « ‘ — u d 71 oo. alooloolooL Vii/l memo Current i/pA #9" ‘7 185 [SLIPPED -Co-Co-4 ] POOFA 0.4 0.2 o -o.2 E/V vs. sce IZOpA Figure 6.19 186 <1OON c~.o wuawfim . 8m .2, >3 no .llnfllilill ¢.O a 1777/ ! 103.1an 187 Table 6.2. Kinetic Parameters for Oxygen Reduction at Porphyrin- Modified Surfaces. -0 o C a m 250mvb ( 1R/IDN) d Cobalt Porphyrin EU2 “app kapp 100% n "Blank" graphite” -0.35 «.10‘7 2.0 Co-DEP 0.17 0.53 3.6x10"3 - 67 2.6 Co-Etio 0.21 0.52 8800‘3 64 2.7 Co-TPP 0.27 0.67 32:00"2 72 2.5 Co-TPP(p-0Me) ' 0.11 0.42 2.3x10‘3 67 2.6 Co-TPPFZO 0.15 0.35 40le3 72 2.5 Co-OEP-Cl 0.14 0.46 1.7x10'3 62 2.7 Co-OEP-Clz 0.13- 0.55 9.6x10‘4 ' 67 2.6 Co-OEP-m4 0.16 0.60 2.55m"3 69 2.6 C8-Co-Co-5 0.16 0.47 mm“3 56 2.9 Slipped- _2 Co-Co-4 0.24 0.52 1.4x10 66 2.7 Co-Co-4 0.37 0.67 1.5 { 9: {3.8: 1 19 3.6 Co-Cz-diesterg 0.14 0.51 7.2x10‘3 75 2.5 0o2 FSN-Hg 0.36 0.51 1.8x10'2 40 3.2 Co2 F4N-Hg 0.48 0.751 3.81 1 6.7e 3.9e Co-Tsph 0.25 0.36 ~5x10'5 2.0 Fe-TAPP‘ -0.07 2.2J +5 -k 1 -6‘ j Fe(III)TMP 501 -0.11 0.56 ~6x10 2.0 aHalf-wave potential of oxygen reduction evaluated from the disk volt- ammogram (600 rpm). Potential vs. SCE (aq). bRate constant evaluated at 250 mV vs. SCE for oxygen reduction from the disk voltammogram (0.5 M HTFA). cRatio of the ring limiting current iR to the disk limiting current corrected for collection coefficiency iDN. The number of electrons involved in oxygen reduction evaluated from Equation 6.4. eEvaluated at the maximum current im. vaaluated at the limiting current i d 2. 188 Table 6.2. Continued. gFrom reference 117. Measured in 0.5 M HTFA. FFrom reference 113. Measured in 0.05 M H2504. TFrom reference 148. Measured in 0.05 M’HZSO4 at glassy carbon. JEvaluated from the corresponding cyclic voltammogram. kFrom reference 149 in which metal porphyrins employed are water- soluble. Measured in 0.05 M H2504 at glassy carbon. Estimated from the corresponding reference 117. ”The analysis of transfer coefficient was described in Chapter II. nEstimated from Figure 6.8 curve a. 1 189 is huge potential difference (300 - 400 mV) which is also observed by other authors.146 4. Discussion a. An Attempt to ASsigppthe Surface Redox Waves of the Attached Cobalt Porphyrins For all the monomeric cobalt porphyrins examined, there is‘a surface redox wave appearing between +0.5 V and +0.75 V vs. SCE as shown in Figure 6.10. As for the dimeric cobalt porphyrins, there are two distinguishable surface redox waves appearing between +0.5 V and +0.75 V and between +0.2 V and +0.4 V vs. SCE as shown in Figures 6.11 to 6.13. In addition, the free base porphyrin-modified graphite surfaces gave no surface redox waves in 0.5 M HTFA solution. This indicates that the wave observed at the monomeric porphyrin-modified surfaces is not due to the redox reaction of the porphyrin rings. Therefore, it seems reasonable that the surface wave between +0.5 III/II V and +0.75 V vs. SCE can be assigned to the Co redox reaction III/II of the monomers and the first Co redox reaction of the dimers. II/I The redox potential of Co redox reaction will clearly be more III/II negative compared with that of Co Then, the surface wave appearing between +0.2 V and +0.4 V vs. SCE can be attributed to the III/II 117 second Co redox reaction of the dimers. Collman and Anson also made a similar assignment, except they presumed that the first ,(ZoIII/II surface wave was beyond the limit of the graphite electrode. Thus, according to their presumption the first surface wave (between 190 +0.5 V and +0.75 V vs. SCE) observed in this work could be due to the oxidation of the porphyrin rings. However, from the measurement of the bulk redox potentials of these porphyrins, the oxidation po- tential of the porphyrin rings are more positive than those of COIII/II.]34’]35 This is true for both monomers and dimers. There- fore, the assignment of the surfaCe redox waves for the dimers as described above is still valid. The second surface redox wave of the dimers, however, lies at a similar potential region to that of the surface groups of the "blank" graphite surface. Nevertheless, the peak separation (AEP 2 125 mV) of the second surface redox wave of) the dimers is much larger than that of the surface groups (AEP : 75 mV) of the "blank" graphite surface. This can be attributed to the higher degree of the irreversibility of the second Con”II redox reaction of the dimer. Because of the difficulty in the investigation of the relatively small concentration of the attached cobalt porphyrins in the aqueous solution, the redox potentials of the attached cobalt porphyrins have been assumed to be equivalent to those of the bulk porphyrin in nonaqueous solution in the diagnosis of the reaction mechanism of oxygen reduction at the porphyrin-modified surfaces. Since the environment of the bulk cobalt porphyrins in benzonitrile or dichloro- methane solution is very different from that of the attached cobalt porphyrins in aqueous solution, the corresponding redox potentials of the bulk and the attached cobalt porphyrins can be expected to differ. Generally speaking, according to Table 6.1 surface attachment shifts the redox potential positive compared with that for the bulk com- plexes. This shift can be attributed to the difference in the 191 equilibrium constants of the precursor and successor states. How- ever, the interaction between the attached cobalt porphyrins and the surface groups at the graphite surface is not fully understood. Furthermore, on the contrary to the bulk'reactions, it is extremely difficult to characterize the intermediates of the surface reactions. Thus, the assignment of the surface redox waves as described could be ambiguous. b. Electrocatalysis of Oxygen Reduction at the Monomeric Por- phyrin-Modified Graphite Surface Figure 6.8 demonstrates that the electrocatalysis for oxygen reduction at the pyrolytic graphite surface can be improved tre- mendously by cobalt porphyrins. The improvement of the electro- catalysis can be most simply measured from the positive shift of the peak potential for oxygen reduction (AE = 500 m 600 mV) using cyclic voltammetry, as mentioned before. In the practical application of fuel cell technology,112 both the reaction potential (overpotential) and the corresponding current density are important factors determin- ing the efficiency of a fuel cell. As described earlier, two possible pathways for oxygen reduction were examined. Furthermore, it has been shown that the electrocatalysts that yield two-electron reduction of dioxygen to hydrogen peroxide has a less practical application. Therefore, it is of interest to know whether the reaction pathway of oxygen reduction at the graphite surface which is two-electron reduc- tion can be altered by the adsorbed cobalt porphyrins or not. Strictly speaking, the reaction pathway of oxygen reduction at the porphyrin- 192 modified surfaces can be a combination of the two possible pathways. The contribution of each pathway to the overall reaction can be evaluat- ed from the ratio of -iR/iDN as shown in Table 6.2. The values of -iR/iDN in Table 6.2 shows that for all the monomeric porphyrin- modified surfaces examined the percentage of the overall reaction of oxygen reduction at these surfaces that follows two-electron re- duction can be as high as 70%. This implies that monomers are unable to alter entirely the reaction mechanism of oxygen reduction at the graphite surface. The reaction mechanism of two-electron reduction of dioxygen to hydrogen peroxide at the monomeric porphyrin-modified surfaces has been proposed. The substantial improvement of the electrocatalysis of oxygen reduction can be attributed to the increase of active sites on the graphite surface by the adsorbed cobalt porphyrins that have great affinity for oxygen molecules. Oxygen reduction at the "blank" graphite surface has been shown to follow a similar mechanism to that of monomers.”9 However, the surface groups at the graphite may have less affinity for oxygen molecules. . It is interesting to evaluate the effect of varying the structure of the porphyrin rings on the electrocatalysis of oxygen reduction. In general, according to the values of -iR/iDN x 100% in Table 6.2, the reaction mechanism of oxygen reduction seems to be insensitive to the variation of the structure of the porphyrin rings. The electro- catalysis of oxygen reduction at these monomeric porphyrin-modified surfaces is not improved by the substitution of electron-withdrawing groups on the porphyrin rings. This is illustrated by the negative shift of the half-wave potential of oxygen reduction when the cobalt 193 porphyrin is changed from Co-OEP to Co-OEP-Cln where n = 1,2, or 4 or from Co-TPP to Co-TPPFZO. Because the affinity of the cobalt center for oxygen molecules could be diminished by the substitution of electron-withdrawing groups. Co-TPP-(p-OMe) that contains electron- donating substituents also yields less electrocatalysis of oxygen reddction than Co-TPP. This may be explained by.the presence of the steric effect arising from the four methoxy substituents of Co-TPP- (p-OMe). The difference in electrocatalysis for oxygen reduction between Co-OEP and Co-Etio can also be interpreted by the steric effect arising from the eight ethyl groups of Co-OEP. However, the electrocatalysis for oxygen reduction of Co-TPP which is comparable to that of Co-Etio. This is opposite from what is expected from the steric effect arising from the four phenyl groups of Co-TPP. Never- 111/11 of Co-TPP theless, the favorable surface redox potential of Co as shown in Table 6.1 may compensate for the steric effect. c. Electrocatalysis of Oxygen Reduction at Dimeric Porphyrin- Modified Graphite Surfaces In the previous section, the monomeric cobalt porphyrins show enormous enhancements of the electrocatalysis of oxygen reduction. However, the monomers can only catalyze two-electron reduction. In order to facilitate the desirable four-electron oxygen reduction, the electrocatalysts may need two nuclear centers (i.e., two cobalts) to bind oxygen molecules simultaneously. Thus, each cobalt might be expected to yield two-electron reductions. In this study, three dimers, C8-Co-Co-5, slipped-Co-Co-4, and Co-Co-4 were examined. 194 The ring-disk voltammograms of C8-Co-Co-5 and slipped-Co-Co-4, Figure 6.18 and 6.19, respectively, show significant ring current. Never- theless, C8-Co—Co-5 shows better electrocatalysis in terms of the value of -iR/iDN than slipped-Co-Co-4 and all the monomers as shown in Table 6.2. The value of -iR/iDN of C8-Co-Co-5 is around 56% which implies that two- and four-electron reduction pathways con- tribute about equally to the overall reaction of oxygen reduction. Therefore, the reaction mechanism of oxygen reduction at the graphite surface still cannot be significantly changed by C8-Co-Co-5 and slipped-Co-Co-4. Furthermore, it has been shown that four-electron reduction of dioxygen to water is not due to the concerted reduction of hydrogen peroxide.”7 In other words, C8-Co-Co-5 will not catalyze two-electron reduction of hydrogen peroxide to water. However, the behavior of Co-Co-4 is drastically different from those of CB-Co-Co-S and slipped-Co-Co-4. The ring current of the ring-disk voltammogram of oxygen reduction of C04Co-4 shown in Figure 6.20 is negligible compared with the disk current (< 10%). This strongly suggests that Co-Co-4 is able to catalyze greatly four- electron reduction of oxygen reduction of dioxygen to water. Similar ‘17 with a related di- results were reported by Collman and Anson cobalt porphyrin. However, they obtained slightly better electro- catalysis of oxygen reduction in terms of the reduction potential than ours, which may be due to the higher steric effect of the dimer used in this work. They also proposed the reaction mechanism117 for four- electron reduction of dioxygen to water at the dimeric porphyrin- modified surfaces, which is slightly modified and shown in Figure 6.21. The possibility of forming a stable u-superoxo Co-O-O-Co 195 Figure 6.21 Proposed mechanism for four-electron reduction of oxygen molecule at the dimeric porphyrin- modified graphite surface 196 2H0 Figure 6.21 197 complex, which is the required intermediate of the proposed mechan- 123 and Collman117 ism, has been illustrated by Chang from the study of EPR spectroscopy. Compared with C8-Co-Co-5, the C0-C0 distance of Co-Co-4 may be more suitable for binding oxygen molecules simultaneously. Then, this can be responsible for the higher electrocatalysis of Co-Co-4 for oxygen reduction. This is the same reason that slipped-Co-Co-4 has better electrocatalysis in terms of half-potential of oxygen reduction than C8-Co-Co-5. Of these three dimers examined, the EPR spectra of the u-superoxo 123’124 However, Co-O-O-Co complexes have been reported by Chang. a careful comparison of the u-superoxo EPR spectra indicates that there is slight difference between them. Chang suggests that the spectra difference, although small, is indicative of the variation of the cobalt-oxygen bonding in the dimer. Considering the structure of these dicobalt porphyrins, Chang has proposed that the superoxo bridging ligand is bound inai"trans"-configuration in C8-Co-Co-5 and slipped-Co-Co-4 but "cis" in Co-Co-4 which are shown in Figure 6.22. To explain the unique electrocatalytic activity of Co-Co-4, perhaps the "cis"-peroxide, being more exposed to solvent, is more accessible to protonation and thus facilitate the cleavage of the stable peroxide bond. This model is consistent with the experimental ‘38 as shown in Table 6.2. the electrocatalytic activity of results Co-Co-4 for oxygen reduction is relatively larger than those of C8-Co-Co-5 and slipped-Co-Co-4. Therefore, the cobalt-oxygen bond- ing is shown in the "cis“-configuration in Figure 6.21 instead of "trans"-configuration which was proposed by Collman and Anson. 198 Figure 6.22 Pr0posed configurations for Co-O-O-Co complexes 199 "trans H Figure 6.22 200 Furthermore, the small size of the cavity of slipped-Co-Co-4 make it difficult for oxygen molecules to enter, which may be responsible for the resulting small value of the ratio of -iR/iDN compared with that of C8-Co-Co-5. In addition, the proposed four-electron reduction mechanism presumes that the two cobalt centers need to be reduced before bind- ing oxygen molecules to form the u-superoxo Co-O-O-Co complex. In III/II of the attached this work, the surface redox potentials of Co dicobalt porphyrins as shown in Table 6.1 might provide important evidence for this presumption. CHAPTER VII CONCLUSIONS AND SUGGESTIONS FOR FUTURE WORK 201 1. Conclusions The measurement of the specific adsorption of various anions at the lead-aqueous interface showed that the amount of the specifically adsorbed anions depended significantly on the electrode pretreatment. This could be explained by variations in the degree of the surface inhomogeneity of the polycrystalline lead which resulted from dif- ferent pretreatments. Compared with mercury and polycrystalline silver surfaces, lead exhibited significantly less tendency to adsorb anions at a given electrode charge. This was probably due to the limitation of the active sites for the adsorption of anions at the lead surface. In addition, the values of the interaction parameter 9 evaluated from the Frumkin adsorption isotherm at lead surfaces were substantially higher (about one order of magnitude) than those at mercury surfaces. This difference was again attributed to the limitation of the active sites at the lead surface» The comparison of the values of ionic electrosorption valencies at lead and mercury surfaces suggests that the 1ead-aqueous interface had a thicker inner-layer than mercury, which was consistent with the estimated values of the inner-layer capacitance (Cu?2 > C592). The most significant finding of the present work was to demon- ' strate a "specific substrate" effect on the energetics of a number of outer—sphere electron-transfer processes involving transition- metal reactants. There were significant differences in the measured rate constants for the electroreduction of a number of mechanistically 202 203 simple transition-metal complexes at gallium, polycrystalline lead, and mercury surfaces. These differences could not be accounted for by the conventional ionic double layer effect. For outer-sphere electrode reactions, this discrepency was somewhat unexpected, be- cause there is no direct interaction betWeen the reactant and the electrode surface in the transition state. From the evaluation of the activation parameters for the electro- reduction of several metal complexes, the resulting small or even negative values of the double-layer corrected activation entropies at the lead surface indicated the possibility of nonadiabatic elec- tron-transfer processes. Furthermore, the Marcus theory was shown not to be adequate in the present case. On the other hand, the sig- nificant differences in the values of corrected activation enthalpies between lead and mercury surfaces suggested that there were non- electrostatic work terms involved in bringing the reactant from the bulk to the transition state. Compared with mercury, the gallium surface showed less electroactivity for the electroreduction of Cr(III) aquo complexes than for ammine complexes. Since the water structure in the double layer region at the gallium surface sig- nificantly differed from that at mercury and lead surfaces, the water seemed likely to play a very important role in the energetics of electron-transfer at these electrodes. Graphite is a very poor electrocatalyst for oxygen reduction. Monomeric porphyrin-modified graphite surfaces dramatically enhance the electrocatalysis. However, they are only moderate electro- catalysts for the four-electron reduction to water. Modification 204 of the porphyrin structure by adding electron-withdrawing or electron- donating groups on the porphyrin ring had no significant influence on the electrocatalysis. The dimeric porphyrins, with the exception of Co-Co-4, behaved similarly to the monomeric porphyrins. However Co-Co-4 is an ef- ficient electrocatalyst for the four-electron reduction of dioxygen to water. Since the electroactivitycn’C8-Co-Co-5 was no worse than that of slipped-Co-Co-4, the Co-Co distance of Co-Co-4 therefore, is not the only factor making it unique. From EPR spectra, the con- figuration of the u-superoxo Co-O-O-Co, which is the required inter- mediate of the proposed mechanism, of Co-Co-4 was shown to differ from those of C-Co-Co-S and slipped-Co-Co-4. The "cis" form of the Co-O-O-Co complex which is more exposed to solvent may be responsible for the better electrocatalysis by Co-Co-4. On the other hand,C8-Co-Co-5 and slipped-Co-Coé4 showed "trans" forms of the Co-O-O-Co complex. In addition, there was no direct correlation between the surface redox potentials of the attached cobalt por- 'phyrins and the electroactivities of the corresponding modified surfaces for oxygen reduction. 2. Suggestions for FUture Work Some preliminary results, not reported in this thesis, of elec- trode kinetics for a number of Cr(III) complexes were obtained at lead-nonaqueous interfaces. The rate constants at lead surfaces corrected for ionic double layer effect were close to those at mercury surfaces. This differs from that observed in aqueous solution 205 as reported in the present work. This provides additional evidence that the "specific substrate" effect observed here may be due to the specific structure of solvent water between the reacting ions and the electrode surface. Therefore, it is worthwhile to evaluate activation parameters at lead and especially gallium surfaces in nonaqueous solutions. At the same time, it also would be of interest to study the isotopic effect of water as the solvent on electrode kinetics at 1ead- and gallium-aqueous interfaces. . It would be useful to find a simple metal complex which can ad- sorb detectably at lead. vThen, the study of the corresponding electrode kinetics might provide insight regarding Franck-Condon barriers for elementary electron-transfer process at the lead surface. Since each single-crystal face of a polycrystalline electrode may possess significantly different electroactivities, it would be very interesting to extend the present study to the single-crystal 1ead surfaces. However, it has been noted that lead single-crystals are very unstable.86 Although cobalt porphyrins have been demonstrated to be remarkable electrocatalysts for oxygen reduction, their low stabilities at pyrolytic graphite surfaces in acidic solutions are the main drawback for their practical application. 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