MSU LIBRARIES n. RETURNING MATERIALS: Place in book drop to remove this checkout from your record. FINES wi11 be charged if book is returned after the date stamped below. 19"“. CORRELATIONS BETWEEN MOLECULAR STRUCTURE AND ELECTROCHEMICAL REACTIVITY By Joseph Thomas Hupp A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 1983 ABSTRACT CORRELATIONS BETWEEN MOLECULAR STRUCTURE AND ELEC'EOCHEHICAL REACTIVITY BY Joseph Thomas Hupp Differential capacitance measurements indicate that several simple anions are adsorbed extensively at the silver-aqueous interface. Electrochemical roughening which is required in order to observe Surface Enhanced Raman Scattering (8338) from adsorbed ions was found to yield only small changes in the average surface concentrations of such ions. Correlations were established between the intensities of SEES signals and the surface concentrations of the Raman scatterers. Modification of the silver-aqueous interface via underpotential deposition (UPD) of a single atomic layer of lead or thallium alters the interfacial properties such that adsorption is inhibited and the solvent inner-layer is restructured. Electron-transfer reactivity for several chromium complexes at silver is markedly decreased following UPD of lead or thallium. The decrease in reactivity was traced to a change of reaction mechanism from inner- to outer-sphere. Reactions following outer-sphere mechanisms at mercury, UPD lead/silver and UPD thallium/silver exhibit similar rates at each surface (after correcting for diffuse double-layer effects), but markedly different activation parameters. The differences for the latter are speculatively attributed to solvent-related work terms. An encounter preequilibrium treatment of electrochemical kinetics is pr0posed. It is utilized to examine the nonadiabaticy question for outer-sphere electrochemical reductions. The treatment is also employed to correlate homogeneous and heterogeneous electron-transfer reactivity, particularly for aquo complexes of transition metals. It is concluded from such correlations that the Fe(H20)g+/2+ homogeneous self-exchange follows an anomalous, possibly inner-sphere, reaction pathway. Correlations of reaction entropies with molecular parameters suggest that a molecular rather than a continuum treatment of the solvent is required in order to describe ionic salvation adequately. Absolute calculations of electron-transfer rate constants for homogeneous cross reactions and electrochemical reactions show tolerable agreement with experiment. The residual differences are attributed to ligand-specific work terms as well as specific reactant-solvent interactions. A method for incorporating the entropic component of such interactions into theoretical treatments of electron transfer is proposed. All glory to the Father of Lights and to his son Christ Jesus. ii ACKNOWLEDGMENTS I wish to thank several people who helped me along the road to the Ph.D. degree. From the beginning Professor Michael Weaver shared his enthusiasm for research, encouraged genuine collaboration and sought to develop the scientific interests and abilities of this student. Each of these factors made research in his group an enjoyable exper- ience and for this I sincerely thank him. Dr. George Leroi is gratefully acknowledged for filling in as the major professor at Michigan State. The assistance and interest of the members of the Weaver group both at Michigan State and Purdue is appreciated. Special mention must be made of Dr. Ned Larkin who imparted to the author the secrets of solid electrodes and who helped initiate the studies of UPD metal sur- faces. Thanks are due also to H.Y. Liu who tenaciously pursued parallel experimental work and willingly shared his findings and insights. Thanks also to Dr. Tomi Li for producing some ruthenium.compounds on short notice. The Postal Service is expressly acknowledged for attempting to deliver the degree several weeks late. I am grateful to Liz, Mike and Janet Sarault for their special efforts in helping to overcome this obstacle. My appreciation is expressed to my family - especially my wife Liz, my parents, and Mary and Madelyn - for supporting and encouraging my efforts. iii LIST OF LIST OF CHAPTER A. B. C. TABLE OF CONTENTS IABLESOOOOOOOOO0.00.00...IOOOOOOOOOOOOOOOI0.00.0000... FIGURES...OOOOOOOOOOOOOOOOCOOOOOOOOOOOOOOOO00.0.00...O I - INTRODUCTIONOOOOOOOOOOOOOOOOOOOOOOOO00.0.0000...O. overViEVOOOOOC00.0.0000....0...OOOOOOOOOOOOOOIOOO...O. 1. EIECtrOde ChemistryOOOOOOOOOOOOOOOOOOOOOOOOOOOOO 2. Electron-transfer Chemistry..................... Structure of Electrochemical Interfaces............... 1. TherEOdyn‘miCSOOOOOOOOCCOOOOOOOOOOOOOOOO00...... 2. A “Odel 0f the Double L‘yer.OOIOOOOOOOOOOOOOOOOO Electrochemical Kinetics.............................. Electron Transfer Theory.............................. II - EXPERIMENTAL..................................... Materials............................................. 1. sclvents.00....O...0......OOOOOOOOOOOOCOOOOCOOOO 2. BlCCttOlytessaasoaeoooesaeaeaeaoeseasaaasosseeoe 3. Metal complexes.000......OOOOCOOOOOOOOOOOOOOOOOO 4. BlECtrodeso00000000000000aasaoaaeoesoasaooeoaeaa Apparatu‘OOOOOOOOOOOOOOOOOOOOOOOCOOOOOOOOOOOOOO0.0.0.0 EICCtrOChemical MeasurementBOOOOOOOOOOOCOOOOOOOOOOOOOO 1. Differential caPCCitanceeaoaosaasaooaaeassesses. 2. EICCtIOde KineticsOOOOOOOOOOOOOOOO0.0.0.0...O... 3. Formal Potentials.00......OOOOOOOOOOOOOOOOOOOOO. iv Page ix xiii 13 19 26 34 34 34 36 37 39 42 42 45 CHAPTER III - DOUBLE-LAYER STRUCTURE AND IONIC ABSORPTION AT SOLID METAL ELECTRODE-AQUEOUS INTEREACES.............. A. E. Specific Adsorption of Halide and Pseudohalide Ions at Electrochemically Roughened Versus Smooth Silver- Aqueou‘ Interfaces.00......OOOOOOOOOOOOOOOOOOO0......O. lo Introduction.nu..."........................... 20 R33u1t8 and Discussionaaesaeasaaaaasaaoaasasoosso a. Determination of Roughness Factors for Silver surface“.OOOOOOOOOOOOOOOOOOOOOOOCOOOO b. Determination of Anion Specific Adsorption.. 3. Surface Crystallographic Changes Induced by Electrochemical Roughening....................... 4. Implications for Surface-Enhanced Raman scatterinSOOCO00.00.0000...0......00.0.0.0...O... Specific Adsorption of Transition-Metal Complexes at SilverOOOOOOOOOOIO0.0.0...0.00.000000000000000000000000 The Influence of Lead Underpotential Deposition on the Capacitance of the Silver-Aqueous Interface............ 1. IntIOduCtion.00......OOOOOOOOOOOOOOOOOOOOO0....O. 2. Electrode Preparation............................ 3. Result‘.OOOOOOOOOOOOOOOOOIOOOOOOOOOOCOOOOOOOOOOO. 4. DiscussionOOOOOOOOOOOOOOOOOOOOOOOOOOOCCOOOOOOOOOO The Influence of Lead Underpotential Deposition on Anion Adsorption at the Silver-Aqueous Interface....... 1. IntrOduCtion.O...COO...0.0000000000000000000000CO 2. ResultBOOOOOOOOOOOIIIOOOCOOCOOOOOIOOOOOOOOCOOO... 3. DiscuasionOOOOOOOOOOCOOO.COOOOOOOCOCOOOOOOOCOOOOO The Influence of Thallium Underpotential Deposition on Anion Adsorption and the Double Layer Structure at the Silver-Aqueous Interface............................... 1. Intruduction.0.00.00...0.0.0.0....IOOOOIOOOOOOOO. 2. Electrode Preparation............................ 3. Results.0.0.0.000....0.0000000000000000000COIO... a. Capacitance Measurements in Single Electrolytes................................ b. Capacitance Measurements and Anion Specific Adsorption in Mixed E1ectrolytes............ 4. DiscusSionOOOOO00......0.0.0.0000...0.0.0.0000... 5. conCIuaionBOOOOOOOOOOOOOOOOOOOOOOOCOOOOOOOOOOOOO. 46 46 46 48 48 54 81 86 92 97 97 103 106 111 111 123 131 136 136 136 138 138 140 154 155 F. The Role of the Surface Metal Composition in Deter- mining Anion Ad‘orption.OOOOOOOOOOOOOO0.0.0.000....0... 155 1. IntrOduCtionaoaaeoaoeaaasaaoooeaaaaeooaoaoeeeoaao 155 2. Results and Discussion........................... 155 3. conc1u‘10n‘.0.000000000000000000.000000000000000. 162 G. A Method for Evaluating the Surface Concentrations of Two Like-Charged Ions Simultaneously Adsorbed at an Electrode-Solution Interface........................... 163 CHAPTER Iv - ELECTROCHEMICAL KINETICSOOOOOOOOOOOO000.......0... 171 A. The Frequency Factor for Electrochemical Reactions..... 171 1. Introduction..................................... 171 2. The Collisional Model............................ 172 3. The Encounter Preequilibrium Model............... 175 4. Comparisons of Models............................ 182 5. Relation Between Electrochemical and Homogeneous Rate Constanta..........o...............ou...... 185 6. Comparison Between the Kinetics of Corresponding Inner?" and Outer-Sphere Pathways.sesseaaasoaaasao 188 7. The Apparent Frequency Factor from the Temper- ature Dependence of Electrochemical Kinetics..... 190 8. More Sophisticated Treatments.................... 192 9. Conclusions...................................... 194 B. The Significance of Electrochemical Activation Para- meters for Surface-Attached Reactants.................. 195 1. Introduction..................................... 195 2. Relationship between Activation Parameters for Surface-Attached and Bulk Solution Reactants..... 197 3. Significance of the Frequency Factor for Attached Reactants............................... 206 C. An Experimental Estimate of the Electron-Tunneling Dis- tance for Some Outer-Sphere Electrochemical Reactions.. 211 1. Introduction.OOOOOOCOOOOOOCOOOOOOOOOOOOOOOOOOOOOO 211 2. DiscussionOOOOOOOOOOOOOOOOOOOOOOOOIO0.0.0....O... 219 3. conclusionBOOOOOOOOOOOO0.00.00.00.000.0.0.0000... 228 D. The Influence of the Electrode Surface Composition on Redox Reaction Pathways and Electrochemical Kinetics... 230 1. IntrOduction.OOOOOOOOOOOOOIOOOOOOOOOOOOOOOOOOOOOI 230 2. Results and Discussion.OOOOOOOOOOOOOOOOO000...... 231 a. Rate.Formulations.0.00.00.00.00.0.0.0.000... 231 b. Reduction Kinetics of Complexes Containing Potential Bridging Ligands.................. 232 vi c. Reduction Kinetics for Complexes Lacking Bridging Ligands............................ d. Activation Parameters for Outer-Sphere Reductions at UPD Lead/Silver............... 3. conCIusions.0.0.0.0000...OOOOOOOOOOOOO0.0.0000... CHAPTER V - INFLUENCES 0F SPECIFIC REACTANT-SOLVENT INTER- ACTIONS ON ELECTRON-TRANSFER KINETICS AND THERMODYNAMICS.. A. The Influence of Specific Reactant-Solvent Interactions on Intrinsic Activation Entropies for Outer-Sphere Electron Transfer Reactions............................ 1. 2. 3. 4. IntrOduction.OOOOOOOIOOOOOOOOOOOOOOOO0.0.0.0....O Origin of the Intrinsic Activation Entropy....... Real Chemical Environments. Incorporating Spe- cific Reactant-Solvent Interactions in Activation Entropy Calculations............................. Comparisons with Experiment...................... B. Utility of Surface Reaction Entropies for Examining Reactant-Solvent Interactions at Electrochemical Inter- faces. Ferricinium-Ferrocene Attached to Platinum BlQCtrOdesseaseoeaccesses.seas-00000000000ceases.aaeaao 1. 2. 3. C. Size, IntrOduCtionaa...0000000000.00000000000000.0000. Measurement of Surface Reaction Entropies....... Interpretation of Surface Reaction Entropy values.0.00.0.0...OOOOOOOOOOOOOOO00.00.00.000... Charge, Solvent and Ligand Effects on Reaction Entropie'.OOOOOOOOOCOOCOCOOOOOOOOOOIOOOOOOOOOOO0.0.0... 1. 2. 3. 4. IntrOduction.0......OOOOOOOOOOOOOOCOIO0.00.0.0... Results.OOOOOOOOOOIOOCCOOOOOCOOOOOOOOCOOOOOOOOOOO Discussion.OOOCOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO conCIuaion800000000.000000...COOOOOOOOOCCCOOOOOOO CHAPTER VI - APPLICATIONS OF THE RELATIVE ELECTRON-TRANSFER THEORYOOOOOOOOOIOO000......0.0.0.0....OOOOOOOOOOOOOOOOOOO. A. Electrochemical and Homogeneous Exchange Kinetics for Transition-metal Aquo Couples: Anomalous Behavior..... 1. 2. 3. 4. Introduction..................................... Rate Constants for Electrochemical Exchange...... Rate Constants for Electron Exchange from Homo- geneous Cross-Reaction Kinetics.................. Comparison Between Electrochemical and Homo- geneous Exchange Kinetics........................ Correlation of Intrinsic Barriers with Reactant Structure.0.000.000.0000...IOOCOOOOIOOOOOOOOOI... Conclusions and Mechanistic Implications......... vii 248 250 256 258 258 258 261 267 270 276 276 279 283 289 289 290 294 303 304 305 305 309 313 327 329 334 B. Some Comparisons between the Energetics of Electro- chemical and Homogeneous Electron-Transfer Reactions... 1. 2. 3. 4. 5. 6. Introduction..................................... Electrochemical Rate Formulations................ Relation Between Electrochemical and Homogeneous Reaction Energetics.............................. Electron Exchange................................ Influence of Thermodynamic Driving Force......... conCIu‘ion‘.0......0.0.0.0....OOOOOOOOOOOOOOOOOOO C. Entropic Driving Force Effects Upon Preexponential Factors for Intramolecular Electron Transfer: Implica- tions for the Assessment of Nonadiabaticity............ CHAPTER VII - COMPARISONS BETWEEN EXPERIMENTAL KINETICS PARA? METERS AND THE ABSOLUTE PREDICTIONS OF ELECTRON-TRANSFER mEORY...OOOOOOOOOOOOIOOOOOOOOOO0.000.000.0000...000...... A. C. D. IntrOduCtion..0.I.OOOOOOOOOOOIOOOOOOOOOO0.0.0.0.0000... Calculation of Kinetics Parameters..................... 1. 2. 3. Pre-exponential Terms............................ FtflflCkflond-on Barrier8........................... Kinetics Formulations and Work Corrections for Experimental Parameters.......................... ResultBOOOOOOOOOCCOOOOOCO0......OOOOOIOOOOOOOOOOOOOOOCO Discussion.0..0.00....OOOOOOOOCCOOIOOOOOOI0.0.0.0000... conCIusions.OOOCOOOOOOOOOOOOO...OOOCOOOOOOOOOOOOOOOOOO. CHAPTER VIII - CONCLUSIONS AND SUGGESTIONS FOR FURTHER WORK.... A. canCIuSionBOCOOOOCOOOOOOOOOOOOOOOCOOOCOOOOOOOOOCOOCOOOO B. Suggestions for Further work........................... APPENDIX I - REACTION ENTROPIES FOR TRANSIT ION-METAL REDOX COUPLES INVMIOUS SOLVENTSOOOOOOCOOOOOOOOOOIO...0.0.0.... APPENDIX II - NEGATIVE ACTIVATION ENTHALPIES................... REFHMCESOOO0.00...OOOOOOCOOOOOOOOOOCOCOOOO00.000.00.000....0. viii 337 337 338 341 345 346 359 360 373 373 375 376 380 390 392 414 424 425 425 428 431 434 437 LIST OF TABLES Table Page 3.1 Coverage of Roughened Silver (RF-1.9) by Bromide Ions at the Capacitance Peak Potential in Mixed Electrolytes........ 68 3.2 Standard Free Energies of AdsorptionIAG:(kJ mole-1) for Anions at Various Silver Surfaces............................ 82 3.3 Standard Free Energies of Adsorption AG:(kJ mol-l) and Inter- action Parameters g for Anions at UPD Lead/Silver............ 132 3.4 Standard Free Energies of AdsorptionflAG:(kJ mol-l) of Anions at a Polycrystalline Lead Electrode.a........................ 133 3.5 Standard Free Energies of Adsorption AGgOu 301-1) and Inter- action Parameters g for Anions at Several Surfaces........... 156 b 3.6 Enthalpies of Desolvation for Anions in Waters............... 158 3.7 Heats of Formation of Metal Oxidesa.......................... 161 ix 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 Kinetic and Themmodynamic Data for the One-Electron Reduction of Cr(III) Complexes at the Mercury-Aqueous Interface at 25°C Apparent Rate Constants for the Reduction of Complexes Containing Potential Bridging Ligands. E - -700 mV........... Effects of Iodide Addition on Rate Constants at UPD Lead/ SilverOIOOO0.0.000....0.0.000000000000IOOOOOIOOOO0....0...... Formal Equilibrium Constants for Anion Adsorption at Solid Electrode/Aqueous Interfaces................................. Estimated Values of Rate Constants for the Elementary Electron-Transfer Step of Several Reactions. E I -700 mV..... Ratios of Estimated ket Values for Reactions at UPD Thallium/ Silver and MercuryOOOOOOOO0.00000000000000000000000IOOOOOOOOO Rate Constants for Outer-Sphere Reactions. E - -1000 mV..... Ideal Activation Enthalpies (kJ mol-l) for Reductions of Metal Complexes at UPD Lead/Silver, Mercury and Lead Surfaces 1 Ideal Activation Entropies (J deg- mol-l) for Reductions of Metal Complexes at UPD Lead/Silver, Mercury and Lead Surfaces 217 234 238 241 243 247 249 254 255 5.1 5.2 6.1 6.2 6.3 7.1 Intrinsic Activation Entropies for Selected Homogeneous Self- 1 mol-1), calculated without a - Exchange Reactions, ASint (J deg (Equation 5.12) and with (Equation 5.13) Consideration of Specific Reactant-Solvent Interactions, and Comparison with merinentIOOOOOOOOOOOOOOOOOOOOCOOOOOOCOOOOOOOOOOOOOOOOOOO... 272 1 1 Formal Potentials (mV) and Reaction Entropies (J deg- mol- ) for Surface-Attached and Bulk-Solution FerriciniumrFerrocene couple‘OOOOOO...OOOOOOOOO...0.0.0.0000...OOOOOOOOOOOOOOOOOOOO 284 Kinetics and Related Thermodynamics Parameters for the Elec- trochemical Exchange of some M(III)/(II) Aquo Redox Couples at the Mercury-Aqueous Interface at 25°C..................... 310 Estimation of work-Corrected Rate Constants kgxtgfl sec-1) at 25°C for Fea+l2+, V3+l2+, Eu3+l2+, and Cr3+l2+ Self-Exchange 84 8Q 84 8Q from Selected Cross-Reaction Data............................ 314 Summary of Rate Constants for Electron Exchange at 25°C, and Comparison with Theoretical Predictions...................... 325 1 Reaction Entropies,AS§c (J deg- mol-l) for Various Redox cou9193 in Aqueous salutionoaoseaoaoaaaoaasasaaaosoaoaoaaoaoa Thermodynamic and Structural Parameters for Redox Couples.... 378 xi 7.2 7.4 7.5 7.6 7.7 7.8 A.1 Observed and Calculated Rate Constants (M-ls-1) for Homo- geneous Electron-Transfer Reactions.......................... 381 Observed and Calculated Rate Constants for Electrochemical Electron-Transfer Reactions.................................. 395 Observed and Calculated Electron Transfer Parameters......... 397 Observed and Calculated Activation Entropies and Entropy 1 Driving Forces (J’ deg- mol-l) for Homogeneous Electron TransferOOOOOOOOOOOOOO0......OOOOOOOOOOOOOOOOCOOOOOOOC0...... 406 Observed and Calculated Activation Entropies and Thermo- dynamic Driving Forces for Electrochemical Electron-Transfer Reaction.........0....I0.0...OOOOOOOOOOOOCOOOOOOOOOOOOOOOOOOO 408 Observed and Calculated Activation Enthalpies and Thermodyna- ‘mic Enthalpy Driving Forces (kJ' mol-1) for Homogeneous ElQCtron-Tran’fer ReaCtions.OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO 409 Observed and Calculated Activation Enthalpies and Thermodyna- mic Enthalpy Driving Forces (kJ mold) for Electrochemical Electron-Transfer Reactions.................................. 412 1 Reaction Entropies (J deg- mol-l) for Transition-Metal REdox couples in various salventso0.000000000000000...0...... 432 xii Figure 1.1 1.2 3.1 3.2 LIST OF FIGURES Model of the interface between an electrode and an electrolyte solution showing the decay of potential from the metal surface (on) to the outer Helmholtz plane (¢2) to the bulk electrolyte solution (¢8)......... Schematic representation of overlapping vibrational states superimposed on classical potential energy sur- faces. The magnitude of the splitting of potential energy curves in the intersection region corresponds to twice the value of the electronic coupling matrix clue“: RAB.0.0...00......OOOOOOOOOOOOCOOOOOOO.0...O...O. Differential capacitance of polycrystalline silver in 0.5 M NaC104 plotted against electrode potential for various roughness factors (RF)indicated.................. Differential capacitance for polycrystalline silver at -550 mV versus roughness factor as determined using UPD nethOd (see text).....OOOOOOOOOOOCOOOOOOOOOOOOOOOOOOOOOOO xiii Page 16 28 49 52 3.3A 3.33 3.4 3.5A 3.58 3.5C Differential capacitance versus electrode potential for electropolished polycrystalline silver (RF 1.2) in NaCloé- NaCl mixtures at ionic strength 0.5. Keys to chloride concentrations: 1, 0 mg: 2, 1 mg; 3, 2.5 mg; 4, 6 mg: 5. 15 w; 7, 100 m; 8’ 200 mOOOOOOOOOOOOOOOOOO0.0.0.... 58 As in Figure 3.3A, but for electrochemically roughened silver (RP1.9)00....OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO 59 Surface concentration of specifically adsorbed chloride (per cm2 real area) at electropolished (solid curves) and roughened silver (dashed curves) versus electrode potential for bulk chloride concentrations of 0.015 M and 0.10 g, analyzed from.Figures 3A and B as outlined in text ........ 6O Differential capacitance vesus electrode potential for electropolished polycrystalline silver in NaClOa-NaBr mix- tures of ionic strength 0.5. Key to bromide concentration (solid curves): 1, 0 mg; 2, 0.6 mg; 3, 2 mg; 4, 5 mg; 5, 15 mg; 6, 40 mg; 7, 100 mg. The dashed curve is the cell resistance for 100 mM_bromide plotted on the same ”tenti‘l scale.00......OOOCOCOOOOCOOOOOOOCO00.0.0.0....0. 61 As in Figure 3.5A, but for roughened silver (RF-1.9)...... 62 As in Figure 3.5A, but for roughened silver (RF-4.2)...... 63 xiv 3.6A 3.6B 3.7A 3.7B 3.8A 3.8B 3.9 Surface concentration of specifically adsorbed bromide (per on? real area) at electropolished (solid curve) and rough- ened silver (dashed, dotted-dashed curves) for bulk concen- tration x at 15 m§,obtained from Figures 3.5A and B........ As in Figure 306A but for x-loo wOOOOOOOOOOOOOOOC000...... Differential capacitance versus electrode potential for electropolished silver in NaCIOA-NaI mixtures of ionic strength 0.5. Key to iodide concentrations: 1,0 m!; 2, 0.2 an; 3, 0.5 mg; 4, 1.2 mg; 5. 2.2 mg; 6, 5 ma; 7, 10 mg. As in Figure 3.7A but for roughened silver (RF 4.6)........ Differential capacitance versus electrode potential for electropolished silver in NaCIO4-NaNCS mixtures of ionic strength 0.5. Key to thiocyanate concentrations: 1, 0 mg; 2, 0.3 mg: 3, 1 mg; 4, 3 mg; 5, 10 mg; 6, 30 mg; 7, 100 my, As in Figure 3.8A but for roughened silver (RF-2.1)........ Differential capacitance versus electrode potential for roughened silver in KCl-KSCN mixtures of ionic strength 0.1. Key to thiocyanate concentrations: 1, 0 mg; 2, 5 mg; 3, 10 mg; 4, 23 m; 5, 50 messesssessseessseessessssseesss 64 65 70 71 72 73 74 3.10A 3.103 3.11 3.12 3.13 3.14 Differential capacitance versus electrode potential for electropolished silver in NaCloa-NaN3 mixtures of ionic strength 0.5. Key to azide concentrations: 1, 0 mg; 2, 1 mg: 3, 3 mg: 4, 10 mg: 5, 30 mg: 6, 100 mg.............. 77 As in Figure 3.10A, but for roughened silver (RF-2.3)..... 78 Surface concentration of specifically adsorbed azide (per cm2 real area) at electropolished (solid curves) and roughened silver (dashed curves) versus electrode potential for bulk azide concentrations of 0.01 M and 0.1 _M_ analyzed from Figures 3.10A, 3.10B as outlined in the text.......... 79 Atomic positions of the (100). (110), and (111) faces in the fcc structure (after Hamelin, et a1., reference 1)..... 85 Fractional coverage, a, of chloride anions (solid curve) and normalized Raman peak intensity (dashed curve) for Ag-Cl- stretching mode, both plotted against electrode potential. Electrolyte is 0.4511an4 + 0.1 §_NaCl. Rmman d‘t‘ frat reference 102.000.000.000000000000000000000000'OO. 89 Fractional coverage, 6, of bromide anions (solid curve) and normalized Raman peak intensity (dashed curve) for Ag-Br- 3.15 3.16 3.17 stretching mode, both plotted against electrode potential. Electrolyte is 0.45 M Na0104 + 0.05 M HaBr. Raman data from reference 102.000.000.000000000000...OIOOCOOOOCOOOOOOOOOOOO 90 Cathodic-anodic cyclic voltammogram for adsorbed 08(NH3)5pyIII/II interface in 0.1 M NaBr + 0.08 M NaCl + 0.02 M HCl. redox couple at roughened silver-aqueous Electrode roughened by means of an oxidation-reduction cycle in this supporting electrolyte; (roughness factor ca. 1.8 on 1110.33) spy concentration - 50 uM; sweep rate - 100 V sec-1............ 94 basis of capacitance measurements). Bulk Os Cyclic voltammetry of surface bound Os(NH3)5pan/u in 80 mM NaCl + 20 mM HCl. Silver electrode was roughened by means of an oxidation-reduction cycle. Initial potentials for each sweep are indicated. Sweep rate - 50 V s-l. Bulk 08111 (“3)5py conc'entr‘tion . so “EOOOOOOOOOOOOOCOO0.00... 96 Linear sweep current-potential curves for anodic removal of lead layer deposited on silver. Sweep rate was 5 mV sec-1, electrode rotated at 600 r.p.m. Electrolyte was 0.5 M RaClO4 adjusted to pH 3.5 with H0104, containing 0.6 uM Pb2+. Lead deposits corresponding to anodic stripping curves (a)-(c) formed as follows: (a) Electrode rotated at xvii 3.18 3.19 3.20 600 r.p.m., held at -0.585 V for 10 mins. (b) As (a), but held at -l.20 V: for additional 20 mins. with no rotation. (c) Electrode rotated at 600 r.p.m., held at -0.65 v for 10 minute‘ 101......OOIOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO0.0... 10]- Differential electrode capacitance c versus electrode potential E for: (a) polycrystalline silver; (b) silver containing a monolayer of UPD lead; (c) as in (b) but with additional ca. 2. monolayers of bulk lead. deposit; (d) polycrystalline lead. Lead layer prepared as indicated in caption to Figure 3.17 and the text. Electrolyte was 0.5 M HaClO4 pH - 3.5; for (b) and (c) additionally contained 0.6 uM Pb2+ ............................................... 104 Differential electrode capacitance C versus electrode potential E for a mono layer of UPD lead on polycrystalline silver (curves a-d) and for polycrystalline bulk lead (curves a’-d’) as a function of ionic strength of sodium perchlorate, adjusted to pH 3 .5 . Concentrations of NaClOa: (8,8’) 005 E; (b) 0.1 g; (C) 0.05 A; (d,d’) 0.01 Eeeesssssslos Differential electrode capacitance C versus electrode potential E for UPD lead layer on polycrystalline silver having various coverages of lead. Electrolyte was 0.5 M xviii 3.21 3.22 3.23 3.24 3.25 NaClO4, pH 3.5, with 0.6 pM Pb2+. Lead coverages (percentage of monolayer): (a) 02; (b) 221; (c) 352; (d) 61X; (E) 931; (f) 1001..............o..................107 Differential capacitance vs. electrode potential for UPD lead/silver in NaCl + NaF mixed electrolytes at an ionic strength of 0.5 M. Key to chloride concentrations: (0) 0 mM: (0) 8 mM: (v) 20 mM; (A) 60 mM; (I) 200 mM..........ll3 Differential capacitance vs. electrode potential for UPD lead/silver in NaBr + NaF mixed electrolytes at an ionic strength of 0.5 M. Key to bromide concentrations: (0) am; (.)3w—; (‘)10w_; (V) 30 “-OOOOOCCOCOOIOO0......114 Differential capacitance vs. electrode potential for UPD lead/silver in NaI + NaF mixed electrolytes at an ionic strength of 0.5 M. Key to iodide concentrations: (0) 0 mM; (0) 0.3 mM; (V) 1 mM; (A) 3 IBM; (A) 10 “313 (CI) 30 13!; (.)100 m-COOOOOOOOOOOOOO00......0.00.00.00.000.00.00.00.00115 Surface concentration of chloride vs. electrode potential for UPD lead/silver. Conditions as in Figure 3.21.........ll6 Surface concentration of bromide vs. electrode potential for UPD lead/silver. Conditions as in Figure 3.22.........ll7 xix 3.26 3.27 3.28 3.29 3.30 3.31 Surface concentration of iodide vs. electrode potential for UPD lead/silver. Solid line: NaI + NaF. Dashed line: HaI + NaClO4. Concentrations as in Figure 3.23............ll8 Surface concentration of chloride vs. electrode charge density for UPD lead/silver. Conditions as in Figure 3.21.0.0...OOOOOOOOOOOOOCOOOOCCOOOOOOOOOOOOOOOOOOOOOO0.0.0.119 Surface concentration of bromide vs. electrode charge density for UPD lead/silver. Conditions as in Figure 3.22....O00.0.00...OOOOOOOOOOOOOCOOOOOO...0.0.0.00000000000122 Surface concentration of iodide vs. electrode charge density for UPD lead/silver. Conditions as in Figure 3.26.00.00.00.0.00.000.00.00...OOOOOOOOOOOOCOIOOOOOOOOO0.0.0121 Differential capacitance vs. electrode potential for UPD lead/silver in NaBr + NaC104 mixed electrolytes at an ionic strength of 0.5 M. Key to bromide concentrations: (0) 0 mM, (0) 1 mM, (0) 3 mM, (A) 10 mM, (v) 30 mM, (D) 100 m-OCOOOOOOOOOI...00.0.00...OOOOOOOOOOOOOOOOO0.0.0.00.00.00.0120 Surface concentration of thiocyanate vs. electrode potential for UPD lead/silver in NaNCS + NaF mixed electrolytes at an ionic strength of 0.5 M. Key to thiocyanate concentrations: (A) 1 mM, (0) 3 mM, (0)10 mM, (I) 30 mM, (:1) 100 mM........124 XX 3.32 3.33 3.34 3.35 3.36 3.37 Surface concentration of azide vs. electrode potential for UPD lead/silver in NaN3 + NaF mixed electrolytes at an ionic strength of 0.5 M. Key to azide concentrations: (D) 3 mM, (-)10 '5, (A) 30 an, (A) 121 “fleessessssssesssssesesseseeselzs Surface concentration of perchlorate vs. electrode potential for UPD lead/silver in NaClO4 + NaF at an ionic strength of 0.5 M. Key to perchlorate concentrations: (I) 10 mM, (0) 30 IBM, (0) 80 mM, (A) 200 mM, (4) 500 mM (data at 500 mM were extraWIated)OOOOOOOOOOOOOOOOOOOO0.0.00.00.00.00...0.0.126 Surface concentration of thiocyanate vs. electrode charge density for UPD lead/silver. Conditions as in Figure 3.31..127 Surface concentration of azide vs. electrode charge density for UPD lead/silver. Conditions as in Figure 3.32..........128 Surface concentration of perchlorate vs. electrode charge density for UPD lead/silver. Conditions as in Figure 3.33..129 Linear sweep current-potential curves for anodic of thallium layer deposited on silver. Sweep rate was 20 mV/s. Electro- lyte was 0.5‘M_NaF, containing 0.8 uM TlClOa. Curve (a): 3.38 3.39 3.41 electrode held at -960 mV for 12 minutes while rotating at 600 RPM; (h) electrode held at -960 mV for 12 minutes at 600 RPM and then held for 15 minutes at -l300 1“ without rot‘tionOOOOOOOOOOOOOOOCOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO0.0137 Differential capacitance versus electrode potential for: (a) a monolayer of underpotentially deposited thallium on poly- crystalline silver in 0.05 g NaClO4; (b) the equivalent of circa. 3 monolayers of thallium on polycrystalline silver in 0.05 g Na0104; (c) as in (a), except in 0.2 g Na0104........l39 Differential capacitance vs. electrode potential for UPD thallium/silver in NaCl+RaF nixed electrolytes at an ionic strength of 0.5 .11. Key to chloride concentrations: (0) 0 mg; (0) 1 all; (A) 10 mg; (v) 50 III! (I) 100 m4: (0) 200 m-OOOOOOOOOOOOOOOOOOOCOCOOOOOOOOOOOOOOOCOOOOOOCOOOOCOCOOO0.0141 Differential capacitance vs. electrode potential for UPD thallium/silver in NaBr + Na? mixed electrolytes at an ionic strength of 0.5 11. Key to bromide concentrations: (0) 0 mg; (l) 20 “-3 (A) 50 “‘3 (V) 100 “-3 (.) 200g00000000000000000142 Differential capacitance vs. electrode potential for UPD thallium/silver in NaI + Na? nixed electrolytes at an ionic strength of 0.5 5. Key to iodide concentrations: (A) 0 m5; (0)1 mg: (0)5 mg: (I) 10 mg: ([3) 20 1115(0) 50 mg...........143 xxii 3.42 3.43 3.44 3.45 3.46 3.47 3.48 3.49 Surface concentration of chloride vs. electrode potential for UPD thallium/silver. Conditions as in Figure 3.38...........l44 Surface concentration of bromide vs. electrode potential for UPD thallium/silver. Conditions as in Figure 3.39...........l45 Surface concentration of iodide vs. electrode potential for UPD thallium/silver. Conditions as in Figure 3.40...........146 Surface concentration of chloride vs. electrode charge density for UPD thallium/silver. Conditions as in Figure 3.38.......l47 Surface concentration of bromide vs. electrode charge density for UPD thallium/silver. Conditions as in Figure 3.39.......l48 Surface concentration of iodide vs. electrode charge density for UPD thallium/silver. Conditions as in Figure 3.40.......149 Surface concentration of perchlorate vs. electrode potential for UPD thallium/silver in NaClO4 + NaF mixed electrolytes at an ionic strength of 0.5 fl. Key to perchlorate concentra- tions: (0)10 mg; (A) 60 mg; (a) 200 Msssosssssossssososssolso Surface concentration of thiocyanate vs. electrode potential for UPD thallium/silver in NaNCs + NaF mixed electrolytes at an ionic strength of 0.5 a. Key to thiocyanate concentra- tions: (0) 1 mg, (I) 5 mg, (4) 20 mg, (C) 50 m, (D) 100 mg..151 xxiii 3.50 3.51 4.1 4.2 4.3 Surface concentration of perchlorate vs. electrode charge density for UPD thallium/silver. Conditions as in Figure 3.80....0.00000IOOOOCOOOOOI00......0.00.0.0...0.0.0000152 Surface concentration of thiocyanate vs. electrode charge density for UPD thallium at silver. Conditions as in Figure 3.9.0.0000000000000000000000000000000COCOOOOOOCOO...0.153 Schematic potential-energy surfaces for a single step elec- trode reaction, illustrating the distinction between "real" and "ideal" activation enthalpies for attached reactants (see tE‘t for detai18).........0.00.00.00.00COO...0.0.0.0000000000205 Schematic plot of electronic transmission coefficient Kel for an outer-sphere electrochemical reaction against the reactant-electrode separation distance r. A’A" and B’B" represent anticipated planes of closest approach for Cr(III) amine and aquo, reactants, respectively. The shaded and cross-hatched areas represent the corresponding values of the 0 "effective reaction zone thickness" Kel Gre for these tenetantsOCOOOIOOOOOOCOOOOOOOOOOOOOOO0....0.0.0.0000000000000224 Log of apparent rate constant for Cr(NH3)5Cl2+ versus elec- trode potential at UPD lead/silver and at silver.............235 4.4 4.5 4.6 5.1 5.2 5.3 Log of apparent rate constant at UPD lead/silver or UPD thallium/silver versus log of apparent rate constant at silver. Key to reactants: (1) Cr(NH NC82+; (2) 2+ 2+ 3’s + Cr(H20)5NCS ; (3) Cr(NH3)5N3 . 2 . s (4) CI(H20)5N3 a (5) cr(na3)5c12*; (a) cr(uzo>5c12*; <7) cr(un3)53r2* 00.0.000000236 Diffuse layer potential $2 versus electrode potential at UPD lead/silver. Electrolytes: (a) 0.5 g NaF; (b) 0.5 g nac104;(C) 0.47ENaCI04'.’0.03aN‘Ioossssosssoosoossssooszl‘o Estimated value (outer-sphere assumption) for log ket at UPD lead/silver versus log ket at silver. Reactants as in Figure 4.40.0000...OOOCOCOIOOCOOOOOOO0.00....0......0.0.0.0000000000244 Schematic representation of the ionic entropy of an individual redox center as a function of its effective ionic charge during the electron transfer step. See text for details.....266 Plot of relative ionic entropy of Ru(bpy)§ (bpy-2,2’ -bipyridine) in acetonitrile as a function of the square of the ionic charge :1. The solid line is the best fit line through the experimental points; the dashed line is the slope of this plot predicted by the Born model...............275 Mode of attachment of ferrocene to platinum.surface..........281 5.4 5.5 5.6 5.7 Ferrocene derivative (n-ferrocenemethylene-p-toluidine) used as as solution analog of surface-attached ferrocene in Figure 5.3.0...0.000.000.0000...0.00.00.00.00.0000IOOOOOOOO0.0.0....281 Representative plot of formal potential for surface-attached ferriciniumrferrocene couple, 3:, versus temperature in aqueous 0.1 g TRAP. Potentials versus saturated calomel electrode at 24 C, using nonisothermsl cell arrangement......282 Plot of reaction entropies for surface-attached and solutions phase ferricinium-ferrocene couples in various solvents versus solvent Acceptor Number, taken from reference 277. Filled triangles: surface-attached ferrocene (Figure 5.3); open triangles: bulk-solution derivatized ferrocene (Figure 5.4); open circles: bulk-solution ferrocene. Key to solvents: l, acetone; 2, dimethylformamide; 3, propylene carbonate; 4, acetonitrile; 5, dimmthylsulfoxide; 6, nitromethane; 7, firmethylformamide; 8, formamide; 9, ”than01;10, water.0.00.00.00.00...OOOOOOOOOOOOOOOOOO0......287 Reaction entropy versus effective radius of reactant. Key to solvents: (0) water; (A) dimethylsulfoxide; (D) acetonitrile. Key to reactants:(l) Cr(bpy)33+; (2) Fe(bpy)33+; <3) nu(bpy)33*; (4) c-au63*............3oz h h 2 Plot of (2 log “12 - log kzz) vs. [log K12 + (log K 12) /4 log (kglkgzlzifl for homogeneous cross reactions involving Fer/2+, calculated as Fe: oxidations. kg: for low spin H(III)/(II) polypyridines taken as l x 109 ail sec.1 (see 3+/2+ text). k1]?1 refers to Feaq self exchange; kh to self 22 exchange for coreactant couples. zh assumed to equal 12,!T1 sec-1; value of kgl required for plot obtained by iteration: kgl - 10.3 H-1 sec-1. Data sources given in l x 10 Table 6.2 or reference 311 unless othewise stated. Closed points refer to cross reactions; open point to "observed" Fei+l2+ 3+, self exchange. Key to oxidants: l. Ru‘q, 3+. 3+. 4+. + 3+. 3+. 2. Euaq, 3. Crag, 4. an, 5. Viq 6. Ru(Nn3)6 , 7. Ru(en) , 8. Ru(NR3)5py3+; 9. Ru(bpy)g+; 10. Ru(NB3)5nic3+, reference 3 320; ll. Ru(NR3)5isn +; 12. Ru(NB3)4bpy3+, reference 310; 13. 0s(bpy)§+, reference 334; 14. Fe(bpy)§+, reference 335; I 15. Fe(phen)g+, reference 336; 16. Co(phen)g+, reference 337; [17-19 from.reference 330]; 17. Ru(terpy)§+; l8. Ru(phen)3+; 19. Ru(bpy)2(py)g+; [20-23 from reference 3381 20. 0s[5,5’-(Cna)szy]§+; 21. Os(phen)3+; 22. 0s(5-C1-phen)g+; 23. Ru[5,5’-(CH3)2 bpy]§+; [24-31 from reference 339]; 24. Ru[3,4,7,8-(CH3)4 phenlg+3 25. 6.2 6.3 Ru[3,5,6,8-(CH3)4 phen]§+; 26. Ru[4,7--(Cl13)2 phen]§+; 27. . 3+ 3+ Ru [4,4 ---((3E3)2bpy]3 ; 28. Ru [5,6'(Cfia)zphen] 3 3 29. Ru(S-CH3 phen)3+; 30. Ru(5-C6H5phen)§+; 3+ 2+ 3 ; 32. FeaqOOOOCOOOOIOOOOO0.00.00.00.00000321 31. Ru(S-Cl-phen) As for Figure 6.1 but for cross reactions involving Viz/2+, + . . , h +/2+ expressed as Viq oxidations. kll refers to Viq self exchange. Data sources from Table 6.2 or reference 311 4+ unless otherwise stated. Key to oxidants: 1. an; 3*. 3+. 3*. 3+. 2. Ruaq, 3o 311(m3)6 , 4s RU(NH3)5PY D 50 00(en) D 6. Co(bpy)§+; 7. Ru(NH3)5isn3+, reference 321; 8. co2 '%3 sinh 1 [om/(8RTEEOCb) / ] (1.10) 18 where z is the charge number of the ions in a charge symetric electrolyte, e is the electronic charge, k is Boltzmann’s constant, R is the gas law constant,€: is the dielectric constant of the medium and so is the permittivity of free space. Evidently the absolute magnitude of ¢2 is smallest when <5" is small and the electrolyte concentration is large. In order to minimize work corrections such conditions are often intentionally chosen in electrode kinetics studies. (Note the parallel between ¢2 values and diffuse-layer capacitances with regard to the influences of Cb andon on the magnitude of each). A modification to Equation 1.10 is needed if specific adsorption occurs. Since additional charge FI“ will be accumulated on the electrode side of the interface in the form of adsorbed ions, we must rewrite Equation 1.10 as: ZkT . -l m 3 ¢ . 2;— sinh [(0 +FI'1/(8RTeeoCb) 1/2 2 1 (1.11) In calculating <92 values from interfacial compositional data via Equation 1.11 one must be fairly careful since the presence of adsorbed ionic charge generally will produce compensating changes in the electrode metal charge. An important implication of Equation 1.11 is that specific adsorption, by inducing variations inwbz, can be expected to influence the kinetics of electrode processes. In contrast to the diffuse layer potential, the potential drop across the inner layer is not easily calculable. Nor is it amenable to experimental investigation. What can be said is that it likely does_ 19 not change with alterations in electrode charge at a fixed electrode potential or with changes in electrolyte concentration.38 C. Electrochemical Kinetics In Chapter IV the kinetics of several reactions of the type ox + e- (electrode)+-red (1.12) are discussed. The intent here is to outline a largely pheno- menological view of electrochemical kinetics.46 A description of the microscopic quantum representation of reactions such as Equation 1.12 is delayed until the next section. The rates of electrochemical reactions are most often deter- mined, as might be expected, by measuring currents. (All of the kinetics data reported in this dissertation were determined by measuring currents). The current which flows as a consequence of a reaction such as 1.12 is governed by two factors: the kinetics of electron transfer and the rate of transport of the reactant from the bulk solution to the surface. As long as the electron transfer rate is comparable to or slower than the mass transport rate we can separate the two, since the latter is independently calculable. Many electrochemical analysis techniques are specifically designed to maximize the rate of mass transport in order to facilitate the rate separation and allow fast electron-transfer reactions to be studied. Once a “mass transport corrected" rate (i.e. current) is obtained it can be directly translated into a rate constant, provided that the 20 reaction follows kinetics which are first order with respect to the reactant in solution. This is the case for the reactions studied here. The relation between the current i and the electron-transfer rate constant k is: k - i/nFCbA (1.13) where n is the number of electrons transferred, F is the Faraday, Cb is the bulk concentration of the reactant in mole cm"3 and A is the electrode area in cmz. The rate constant obtained from Equation 1.13 has the unusual units of cm s-l, reflecting the fact that a solute in a three-dimensional solution is reacting at a two-dimensional surface. One factor that can complicate rate measurements is the occurrence of a significant back reaction (red going to ox). In this case the result from Equation 1.13 must be adjusted in order to obtain the rate constant for the forward (reduction) reaction alone. In the present study this problem was avoided in two ways. First, some reactions were monitored under conditions sufficiently removed from equilibrium that the reverse reaction occurred to a negligible extent in comparison to the forward process. For other reactions, notably reductions of chromium(III) amine complexes, electron transfer is followed by a very rapid aquation of the product, rendering a direct back reaction impossible. Reactions of this type are said to be chemically irreversible. (Of course, one must check that the aquation product itself is not readily oxidizable, lest errors result from this process). 21 An essentially universal feature of rate constants for simple electrochemical reactions is that they respond to the electrode potential E in the manner indicated by Equations 1.14 and 1.15: 1f - u“ expl-aF(E-Ef)/RT] (1.14) 1h - k8 exp[(l-a)(F)(E-Ef)/RT] (1.15) The parameters in the equations are the forward (reduction) and backward (oxidation) rate constants kf and kb’ respectively, the transfer coefficient , the electrode potential E, and the standard rate constant k8 which is defined as the value of k at the formal potential Ef. The transfer coefficient can be viewed as an electrochemical analog of the Bronstead coefficient and similar parameters which relate reactivity to thermodynamic driving force.“6 The value of a is typically close to 0.5. For chemically irreversible reactions, measurements of formal potentials, and necessarily k8 values, are often precluded. Nevertheless, the rate-potential relationship can still be expressed by noting how the value of k is related to the rate constant at some arbitrary fixed potential E’, as in Equation 1.16: k - 13' expl-aF(E-E’)/RT] (1.16) All of the rate constants discussed thus far can be termed "apparent rate constants." What is meant by this is that the measured 22 k values reflect not only the intrinsic reactivity of the reactant, the thermodynamic driving force, and the degree of coupling between the reactant and the electrode, but also the work required to bring the reactant to a reaction site close to the electrode surface and to transport the product back into the bulk solution. It is desirable to separate out these last factors in order to gain some idea of the "true" reactivity of a molecule at an electrode. While there are numerous factors that might contribute to work terms for electrode reactions, electrostatic interactions between a charged electrode surface and charged reactant and product molecules definitely are known to be important.45 For outer-sphere reactions, defined here as reactions taking place in the diffuse double layer rather than in the inner layer, the Frumkin equation can be used to estimate the magnitude of nonspecific electrostatic effects on rate constants. According to Frumkin47 1n k I In kcorr-(IIRT)[(z-nacorr) For] (1.16) where 1 -z(d¢r/dE)l/[l-(d¢r/dE)l (1.17) - acorr The parameters in Equations 1.16 and 1.17 are the apparent rate constant k, the work-corrected rate constant k the work-corrected corr’ transfer coefficient acorr’ the reactant charge 2, the diffuse-layer 23 potential ¢r at the reaction site, and the number of electrons, n, which are transferred. In the absence of detailed information ¢r is often assumed to equal 1.0. " ’ *n-l & n+1... ’ ’ n-l 5 14(1): 11 (L )y 11(1.)x M (L )y m+l ’ 2 n-l M(L): + a (L )y (1.22) The first step is the formation of a precursor state consisting of a pair of weakly interacting reactants in a bimolecular complex. Except in the case of diffusion-controlled reactions, precursor formation can be viewed as an equilibrium step. Step 5 is essentially the reverse of step 1, and exerts (via the work term We) only a minor influence on the overall energetics. The crux of the electron transfer problem is contained in steps 2 through 4. Although early in the development of electron-transfer theory Marcus demonstrated that the central problem could be treated fairly 13,62 successfully via statistical mechanics, it has since become evident that the detailed dynamics can best be understood in terms of 21,25 the quantum. mechanics of radiationless transitions. In particular, the latter approach is able to rationalize various peculiarities associated with extreme exothermicity,63 low ENERGY 28 REACTION COORDINATE Figure 1.2. Schematic representation of overlapping vibrational states superimposed on classical potential energy surfaces. The magnitude of the splitting of potential energy curves in the intersection region corresponds to twice the value of the electronic coupling matrix element HAB' 29 58,64 65,66 temperatures as well as account and isotOpic substitution, for rate behavior under more normal conditions. The basic idea of the quantum mechanical treatment is that charge transfer constitutes a radiationless transition between weakly coupled electronic states, namely, the oxidized and reduced states of each reactant.25 In the parlance of theoretical chemistry the precursor states of reaction 1.22 are said to be "vibronically coupled."58 What is meant is that the actual radiationless transition (electron transfer, step 3) is greatly facilitated by prior vibrational excitation of the metal-ligand and intra-ligand bonds of the reactants together with solvent repolarization. [Strictly speaking, solvent repolarization evidently involves librational (restricted rotational) rather than vibrational motion].56b Figure 1.2 is a schematic representation of selected vibrational states superimposed on classical reactant and product potential energy surfaces. According to the Franck-Condon principle,67 "the probability of an electronically allowed transition is proportional to the absolute' square of the overlap integral of the vibrational wavefunctiona of the initial and final states."68 The square of the overlap integral or "Franck-Condom factor“ will be maximized in the intersection region of the classical potential energy surfaces. In this region the positions of the nuclei in a classical sense are identical in the initial and final excited vibrational states. Nevertheless, electronic transitions can also take place outside of the intersection region, albeit with less probability since the overlap of vibrational wavefunctiona is diminished.68 This yields the peculiar result that the "positions" of 30 the nuclei, as specified by the maxima in the vibrational wavefunctiona, change in the course of the electron transfer. In the semi-classical theory of electron transfer (popularized by Sutin) this 23 An illuminating discussion of is referred to as "nuclear tunneling." the Franck-Condon principle in connection with electronic transitions can be found in reference 68. An additional requirement for a radiationless transition is that the initial and final vibronic states be isoenergetic, at least to the extent specified by the uncertainty principle. However, energy conservation for the inner-shell and solvent modes separately is not required.23 Evidently energy sharing between nodes can occur, although as yet a thoroughly consistent theoretical description of this process is lacking.96 The Franck-Condon principle indicates that electronic transitions will occur from a range of excited initial vibronic states centered around the classical intersection region. However, the transition probabilities are weighted not only by the vibrational overlap integrals but also by the Boltzmann factors describing the relative population of each vibrational level (both initial and final).21’23 Typically, the Boltzmann factors will tend to favor transitions from vibrational states lying below the intersection region, and increasing- ly so as the temperature is lowered. In consequence, such "nuclear tunneling“ becomes more important at lower temperatures.23 If the actual electronic transition (step 3, Equation 1.22) is the slow process in the overall reaction scheme, the reaction is termed nonadiabatic and the rate constant is given by: 31 k IJKPH) ve1(r) ZF.C.(r) dr (1.23) where Kp is the precursor formation constant and incorporates work terms, steric factors, etc.,'ve1 is the frequency of passage between activated reactant and product states, and Z F.C. is the Boltzmann and Franck-Condon weighted sum of the transition probabilities between the initial and final states. Each of these factors depends on the reactant separation distance r.17 The frequencyve1 is determined chiefly by the square of the matrix element RAB describing the degree 14,15 of coupling between donor and acceptor electronic orbitals. In terms of classical potential energy surfaces ZHAB is represented as a "resonance splitting" of the diabatic reactant and product surfaces into upper and lower adiabatic surfaces (Figure 1.2).15’57‘ In the case of strong coupling of electronic orbitals, \’el may become sufficiently large that vibrational activation becomes the slow step. In this circumstance the electron transfer reaction is described as "adiabatic“. (The term evidently originates from the idea that the reaction system when strongly coupled will follow the lower adiabatic potential energy surface rather than one of the diabatic surfaces of Figure 1.2). Quantumvmechanical treatments of electronrtranafer have tended to emphasize nonadiabatic rather than adiabatic reaction mechanisms because of calculational difficulties with the latter. One of these centers on the applicability of Boltzmann statistics given that the populations of the higher energy vibrational states will be rapidly and continuously depleted by rapid electron transfer.17’24'6O 32 Nevertheless, the rate constant for adiabatic electron transfer can be formulated to a good approximation as in Equation 1.23, except with a nuclear activation frequency Vn in place of V el' Although Equation 1.23 represents an adequate description of the overall rate process it is often convenient for computational purposes to formulate rate expressions somewhat differently. It is useful to imagine that reactions proceed by a classical transition state mechanism.13’23 The pre-equilibrium formulation is retained. However, the reactants are assumed to surmount a fixed activation barrier and to decay to products at a frequency vn' The activated state is defined as the unique nonequilibrium solvent and bond configuration for which reactant and product free energy curves intersect. This is equivalent to assuming a Franck-Condon factor of unity in the intersection region and zero elsewhere. Forbidden transitions are taken into account by 19,20,23 introducing a nuclear tunneling correction I‘ n' In essence this lowers the ‘barrier from. its classical value to a 'value representing the best compromise between the Boltzmann distribution terms and Franck-Condom factors. Additionally, an electron tunneling term 1:91 is introduced to reflect the possibility that electron transfer may not occur every time a transitionrstate configuration is reached. If HAB is known, K e1 evidently can be estimated with tolerable accuracy from the Landau-Zener theory. (An enlightening “mechanical" derivation of this theory in terms of timescales for traversing different portions of the classical potential energy surfaces is given by Kauzmannég). 33 According to the classical theory with quantum corrections,23 the overall electron transfer rate constant is given by: e k I Kp Vn Tn Kelexp(-AG IRT) (1.24) where AG* is the activation free energy corresponding to the height of the classical Franck-Condon barrier. The primary virtue of the classical approach is that the most significant element, namely the Franck-Condon barrier, can be calculated in a straightforward manner. According to Marcus,13A1G* is usefully divided into intrinsic and thermodynamic elements. The latter is determined largely by the energy gap between the wells of the reactant and product free energy curves. The former is calculated from the changes in metal-ligand and intraligand bond distances accompanying electron transfer and also from solvent dielectric properties. The detailed aspects of such calculations for reactions of transition metal complexes are described in Chapter VII. Although Equation 1.24 is a somewhat artificial formulation which may well misrepresent the detailed dynamics of electron transfer reactions, nonetheless it provides a surprisingly accurate numerical description of the (theoretical) rate constant formulated in Equation 1-23-23 Therefore the use of this semi-classical approach23 (i.e. transition state theory plus quantum corrections) to calculate rate constants for comparison with experiment appears to be justified. CHAPTER II EXPERIMENTAL MM 1. Solyents Formamide was purchased from Eastman. Sulfolane (tetramethylene sulfone) and H-methylformamide, both 992 pure, were purchased from Aldrich. The remaining nonaqueous solvents were either Aldrich "Gold Label" grade or Burdick and Jackson doubly-distilled materials. Containers of each solvent were opened and subsequently stored inside an inert atmosphere box. Each solvent was dried over activated 48 molecular seives. Although electrochemical experiments were performed outside of the box, the nonaqueous solutions were prepared and added to sealed electrochemical cells under inert atmosphere conditions. Solvent preparation and purification efforts were considerably more involved for aqueous experiments. The chief reason for this is the sensitivity of surface electrochemistry work, e.g. electrode kinetics and double-layer capacitance measurements, to small amounts of both organic and inorganic impurities. In the laboratory at Michigan State, water was distilled twice from alkaline permanganate (0.01M KOH, 0.01 M KMnOA) to oxidize organic impurities and eliminate other nonvolatile 34 35 organic and inorganic contaminents. Remaining ionic impurities were eliminated by distillation through a quartz nonboiling still (Dida Sciences). At Purdue it was discovered, largely through the efforts of David Milner, that sufficiently pure water could not be obtained from the available feed water using these methods. However, it was found that water of surprisingly high purity could be obtained by circulating house distilled water through a Milli-Q Reagent Grade Water System (Millipore Corp.) equipped with a Twin-9O output particulate filter. A key to obtaining pure water is to avoid contact with Tygon or other plastic tubing. Water purity was monitored chiefly through capacitance and stripping voltammetry experiments at a hanging mercury drop electrode, the former being sensitive to organic impurities and the latter to heavy metals. 2. Electrolytes Where possible, salts of reagent grade or better were used. Otherwise, these were recrystallized two or three times from water and dried in a vacuum oven before use. Doubly distilled 702 HClO4 from G.F. Smith Chemical Co. was used without further purification. Lanthanum perchlorate solutions were prepared by dissolving high purity La203 in HC104. In nonaqueous experiments similar results were ob- tained with and without drying the supporting electrolyte in a vacuum oven immediately prior to solution preparation. Certain experiments involved controlled formation of an under- potentially deposited monolayer of lead or thallium. This was achieved by rotating a disk electrode for several minutes in solutions that were 36 submicromolar in lead or thallium ions (see Chapter III D). As such, it was absolutely essential that the concentrations of other reducible 6 metal ions be maintained orders of magnitude below lO-‘g_in order to avoid also depositing these on the electrode surface. The presence of unwanted metal ions was signaled by extraneous peaks on stripping voltammograms. Satisfactory results were obtained only by using rigorously purified electrolytes, namely, triply recrystallized reagent grade ”80104 from G.F. Smith Chemical Co. or "ultra pure" NaF from Alfa Products. To avoid contamination, carefully cleaned glass (rather than metal) spatulas were used for transferring chemicals for solution pre- paration. Since silver readily adsorbs common impurities such as Cl-, Br- and I- to a much greater extent than either F- or 0104-, the same precautions were taken before attempting capacitance measurements at this surface in HaClO4 or NaF solutions. 3- MM Samples of Os(NH3)5pyrazine oCla, Os(NH3)5pyridine- 013, Os(NH3)54,4’rbipyridine-H ' (CF3SO3)4, Ru(NH3)5pyridine ° (PF6)3, Ru(NH3)5pyrazine-(PF6)3 and Ru(NH3)6°(CF3COO)3 were kindly supplied by Dr. Peter Lay and Dr. Roy Magnuson. Samples of Ru(en)3- Br3 and Ru(NH3)2(bpy)2'(C104)2 were provided by Dr. Gilbert Brown, while Ru(NH3)4 phen'(CF3000)2°3H20 was supplied by Professor Larry Bennett (phen-l,lO-O-phenanthroline). Samples of Ru(bpy)3°Cl3 and Ru(NHB)6°Cl3 were purchased from G.F. Smith Chemical Co. and Matthey-Bishop, respectively. Ferrocene was purchased from Aldrich and N-ferrocenemethylene-para-toluidine from the Alfred Bader Library of 37 Rare Chemicals. A surface-attached ferrocene derivative was prepared from ferrocene carboxaldehyde (Aldrich) as outlined in reference 70. . 3+ 71 3+ 72 2+ 73 2+ Solutions of Eu(H20)n , Cr(nzo)6 , Cr(H20)5Cl , Cr(H20)5F 73,74 + 73,75 2+ 73,76 2+ 73,77 , Cr(H20)5 so4 , Cr(H20)5N3 and Cr(H20)5NCS were prepared (mainly by Ken Guyer and H.Y. Liu) according to literature methods. Samples of Cr(NH 7 8 3)Sazo-(c104)3, Cr(nu3)501- (c104)2, 78 Cr(NH3)SBr-(0104)2, 78 Cr(RH3)SN3-(0104) 79 Cr(NH ) 2’ 3 5 80 81,82 , 83 (6104)2, , Co(bpy)3 ((3104)2 and Ru(NHs) NCS ' , Cr(bpy)3'(0104)3. 4 bpy-(0104)3 84 were prepared in the Weaver group according to literature procedures. Samples of Cr(en)3- (0104)3 were unwittingly donated by Dr. F.C. Anson. 4. Electrodes Platinum flag, gold flag, glassy carbon disk and hanging mercury drop electrodes were all used in measuring formal potentials and reaction entropies. The choice of electrode was dictated by the formal potential of the complex and the region of ideal polarizability of the electrode material. High purity silver disk electrodes (4 mm or 2.5 m diameter) encased in teflon were used for most surface electrochemistry experiments. A specially designed silver disk electrode85 exhibiting minimal thermal conduction between the electrode surface and the stainless steel lead‘ was employed in variable temperature kinetics experiments. Careful attention was given to surface preparation in kinetics and capacitance experiments. The object was to insure that each 38 experiment was begun with a clean, smooth metal surface. To achieve this a silver electrode was first mechanically polished with 1.0 micron and then 0.3 micron alumina (Beuhler, Ltd.) on Beuhler Microcloth. A two-speed polishing wheel (Buehler 44-1502-160) was employed. After thorough rinsing with water the electrode was immersed in an electro- polishins solution of 41 s 1"1 NaCH, 44 g 1'1 131103 and 38 g 1'"1 1<2co3 and held at +0.2 V versus an SCE reference for two minutes.“ The electropolishing step exerts a smoothing and cleaning effect by continuously dissolving and redepositing the cold-worked layer of silver which is formed by mechanical polishing. Electrochemical surface area measurements indicated that the true area of the electropolished silver typically was only about 1.2 times greater than 86 the geometric area. Although most contaminants are removed by electropolishing, some cyanide, possibly in the form of silver complexes , retains . 87 This was removed by rinsing the electrode, followed by soaking in 2! HClO4 for fifteen minutes, further rinsing, and immersion under potentiostatic control (-0.7 V versus SCE) in 0.U! NaF. Once immersed the potential was switched to -l.7 V where hydrogen evolved on the silver surface. After one minute the potential was returned to -0.7 V. Hydrogen bubbles on the silver disk were removed by bubbling the solution with purified nitrogen. The hydrogen evolution and nitrogen bubbling steps were then repeated. The importance of the overall electrochemical pretreatment is evident in comparative differential capacitance experiments. Electro- polished surfaces yield -capacitance-potential curves which are un- changed in repeated scans and exhibit sharp features in adsorbing 39 electrolytes. Capacitance-potential curves obtained with electrodes which are subjected to mechanical polishing and rinsing only, although resembling those for electropolished surfaces, lack detailed features. Also, the capacitance increases slightly with each successive potential scan, with a significant hysteresis between forward and reverse poten- tial scans. The differences in behavior between the mechanically pol- ished and electropolished electrodes can be attributed to the presence of surface contaminants at the former which apparently are gradually removed by repeated adsorption and desorption of the electrolyte. For SEES-related work, electrodes were roughened by immersing in 0.1‘MiKCl at -l4O mV, switching the potential to +210 mV until 20-40 mC cm_2 of anodic charge had passed, and then stepping the potential back to -l40 mV until an essentially equal amount of cathodic charge had passed. For the experiments reported in Section III A (anion adsorp- tion) the roughened electrodes were soaked in 2,!._H.C104 for fifteen minutes to remove adsorbed chloride. Interestingly, electrochemical toughening alone was insufficient to clean mechanically polished electrodes as evidenced again by comparative capacitance studies with electrodes which had been electropolished prior to roughening. The preparation of underpotentially deposited metal surfaces is described in Section III C. Lemmas; Two-compartment cells of various designs were used. The come partment in which the reference electrode was immersed was separated from the section containing the working and counter electrodes by two 40 "fine" or "very fine" porosity glass frits (Corning, Inc.). For activation parameter and reaction entropy measurements a nonisothermal cell was employed in which the temperature of the working compartment was adjusted by circulating water through a surrounding jacket.55 A Braun Melsungen circulating thermostat was used for this purpose. Cells for rotating disk voltammetry held approximately 10 ml and were constructed such that the working compartment diameter was roughly three times greater than the diameter of the working electrode. A teflon collar was fitted to the top of each cell as that the solution could be isolated, at least partially, from the outside atmosphere. Cells for capacitance experiments held 30 to 50 ml and were equipped with a port for adding solutions during an experiment. The cells were constructed such that contact with the external atmosphere was possible only through an opening of circa 1/8” diameter in the top of each cell. A platinum wire was used as a counter electrode in all experi- ments. In capacitance experiments the counter electrode was at least one hundred times larger in area than the working electrode, and at least three hundred times larger than the geometric area of roughened electrodes. This insures that the measured cell capacitance is essentially that of the working electrode alone. Saturated calomel electrodes were employed as reference elec- trodes. In perchlorate electrolytes an SCE filled with HaCl rather KCl was used in order to avoid spurious liquid junction potentials which might arise from precipitation of [(0104 in the teference electrode frit. The potential of each reference electrode was routinely checked against the potential of a master SCE filled with KCl. Due to the 41 differing mobilities of 118+ and Cl- in water a liquid junction potential which varies significantly with the ionic strength of the experimental solution is introduced between this solution and the reference electrode.88 Therefore, potentials measured against the NaSCE were corrected to equal those which would be obtained versus the KSCE, since the K61 filled reference more nearly maintains a constant electrode-solution potential difference as the electrolyte composition is varied. In nonaqueous work the reference compartment was filled with an aqueous solution. The thermal junction between the working and reference compartments was filled with the nonaqueous solvent in order to minimize contamination of the working compartment by water. In reference 55,srguments were outlined which supported the notion that thermal liquid junction potentials are negligible in non-isothermal cells when the reference compartment and thermal junction are filled with 3 g KCl. Although there are no reasons g m to expect negligible thermal liquid junction potentials when low ionic strength nonaqueous solvents are used in place of aqueous 3 M KCl, Saeed Sahami has verified that this is indeed the case for a number of solvents.89 Since oxygen is potentially electroactive, all solutions were deoxygenated by bubbling with nitrogen or argon and then maintained under a stream of either gas. Argon was preferred when ruthenium complexes were examined since ruthenium (II) is capable of binding dinitrogen. Before being introduced into a cell, nitrogen or argon was passed through a column packed with BASF R3-ll catalyst (Chemical Dynamics Corp., Plainfield, NJ) heated to 140°C in order to remove 42 residual traces of oxygen and then saturated by bubbling through the appropriate solvent. C. Electrochemical Measurements 1- WW Initially double layer capacitance measurements were made by using a null-balance method. A small amplitude 1000 Hz AC signal was applied to the cell. The output was then matched against an external resistance and capacitance through a Wein bridge configuration. The measured cell resistance and capacitance were assumed to correspond to the resistance of the solution and the double layer capacitance of the working electrode. This method is sufficiently tedious and time consuming that only a limited number of data could be gathered in each set of measurements. (Typically, one capacitance measurement was made over each 50 mV interval of electrode potential). Very low signal-to-noise ratios were encountered in dilute solutions, thereby limiting the applicability of the technique to solutions which were 10 n! or greater in electrolyte concentration. Due to instability of the oscillator, measurements below 500 Hz were not feasible. In later experiments a phase-detection technique was employed.90 An AC signal (typically 4 mV peak-to-peak, 100 Hz) from a signal generator contained in a PAR 5204 lock-in analyzer was applied to the cell. At the same time the electrode potential was slowly varied using a PAR 175 Universal Programmer and a PAR 173 potentiostat. The output current from the cell was then resolved into quadrature and in—phase 43 currents, iQ and i1, respectively. These were simultaneously recorded versus the electrode potential by using a pair of Houston 2000 Omnigraphic K-Y recorders. The cell capacitance C was calculated from '2 02 s 1 WI(1 + 1. i 2.1 I 1 Q)/Q ( ) where nais the AC frequency (radian s-l) and V is the root-mean-square potential of the AC signal. The cell resistance R was calculated from __ . .2 .2 R - VII/(II + 1Q) (2.2) At very low frequencies C is essentially proportional to iQ thus simplifying the analysis. For adsorption studies at silver, scan rates of 5 -10 IN a"1 were sufficient to insure that identical capacitance-potential curves were obtained in forward and reverse scans in most electrolytes. However, in thiocyanate solutions scan rates of 2 mV a"1 or less were required. 2. Electrode M A major goal of the electrode kinetics studies at underpotentially deposited electrodes was to obtain electron-transfer rate data at surfaces having a fixed metal composition over a range of potentials beyond the UPD region. Conventional kinetics measurement techniques such as rotating disk voltammetry yield changes in surface composition as the electrode potential is changed, with significant bulk deposition of metal atoms occuring during excursions to potentials 44 negative of the UPD region. However this problem can be avoided by employing normal pulse polarography. By selecting an initial potential just positive of the bulk deposition potential for lead or thallium, changes in surface composition due to additional metal deposition can occur only during the 50 maec pulses to more negative potentials. In dilute solutions of PbF2 or T1C104, metal deposition during the pulses proved to be negligible. The pulse polarography technique produced satisfactory results provided that the electrode was rotated at a rate between 600 and 1500 RPM. Moderate rotation replenishes the reactant in the diffusion layer during the 2 or 5 second interval between pulses.91 In comparative kinetics studies with other solid electrodes for which cyclic voltammetry, rotating disk voltammetry, and pulse polarography could all be used, rate constants for electronrtransfer reactions determined by the three methods agreed within experimental error.” Current-potential curves were obtained using a PAR 174A polarographic analyzer (Princeton applied Research Corp.), a Hewlett- Packard 7045A X-Y recorder and a Pine Instrument ASR2 electrode rotator. Rate constant-potential data were extracted from the curves by using the OldhamrParry analysis.93 In a few cases rate constants were detenmined from irreversible cyclic voltammetry waves by using the analysis devised by Galus.94 Potential sweeps at rates of 50 to 500 mV s.1 were generated with a PAR 174 or 174A polarographic analyzer. 45 3- MW Formal potentials were estimated by averaging the oxidation and reduction peak potentials of reversible or quasi-reversible (peak separations of 60 to 100 mV) cyclic voltammograms. Typically, scan rates of 100 IVS-1 were used. Strictly speaking, the half-wave potential obtained from a reversible cyclic voltammogram will differ slightly from the formal potential if the diffusion coefficients of the oxidized and reduced halves of the redox couple are inequivalent. Since this complication yields errors of perhaps 2 or 3 mV the distin- ction between half-wave and formal potentials was ignored. Surface formal potentials E: for adsorbed osmium redox couples were obtained from fast cyclic voltammetry measurements in dilute solu- tions (circa 50 ‘5) of the reactant of interest. The strategy here was to “outrun" the diffusion of the ommium complex to the surface. Current due to a solution species increases with the square root of the poten- tial scan rate, while current due to an adsorbed reactant increases linearly. Scan rates of 10 to 200 V s-1 were sufficient to generate cyclic voltammograms which reflected the electrochemistry of the adsor- bed, rather than solution, reactant. Measurements were performed using a PAR 175 potentiostat and a PAR 173 potential programmer capable of providing sweep rates of 1000 V s-l. At high scan rates voltammograms are distorted by the iR drop associated with the solution resistance. Complications due to iR drop can be fairly well eliminated by using an adjustable feedback circuit built into the PAR 173. Vbltammograms were recorded on a Nicolet Explorer digital storage oscilloscope. The stored data were then transmitted to a conventional X-Y recorder. CHAPTER III DOUBLE-LAYER STRUCTURE AND IONIC ABSORPTION AT SOLID METAL ELECTRODE-AQUEOUS INTEREACES A. Specific Adsorption g; Halide and Pseudohalide Ionsuat Electrochemically Roughened Versus Smooth SilvereAgueous Interfaces [Originally published in Surface Science, 12:, 429 (1983)] 1. Introduction The discovery of Surface-Enhanced Raman Scattering (SERS) from adsorbates at silver electrodes that have been roughened by means of a prior “oxidationrreduction cycle" (ORC)8 has generated intense interest in characterizing the nature of the physical phenomena involved. The effect shows promise of providing a valuable.§g.gitg spectroscopic tool for elucidating the microscopic structure of metal-electrolyte inter- faces. A central question to be addressed for this purpose is the relationship between the nature and intensity of the SERS signals and the structure and composition of the metal-electrolyte interfaces, especially the surface concentration of the adsorbate acting as the Raman scatterer. However, little progress on this matter has been made to date; the required studies of the interfacial composition under conditions where SERS are observed have largely been absent. 46 47 Halide and pseudohalide anions form an especially interesting series of model adsorbates for fundamental SERS studies in view of their simple structure and tendency to adsorb strongly at a number of solid metals, including the silver-aqueous interface which has been utilized in most Raman investigations so far. Most importantly, the anionic surface concentrations can be determined quantitatively from measurements of the differential double-layer capacitance C d against the electrode potential E for varying bulk concentrations of the adsorbing anions,86’95 35,36 using the so-called "Hurwitz-Parsons" analysis. Silver is an especially tractable metal for this purpose since surprisingly reproducible values of C d that are largely independent of the applied a.c. frequency can be obtained at smooth 44,86,95 electropolished surfaces. Nevertheless, this simple yet powerful method for extracting the surface compositional data needed for the quantitative interpretation of SERS has received scant attention by practitioners in this area. We have recently obtained specific adsorption data for chloride, bromide, iodide, azide, and thiocyanate at a polycrystalline silver-aqueous interface from C d-E data and also using a "kinetic probe" technique.86 Although these anions are very strongly adsorbed, especially at more positive potentials, these surfaces exhibit no detectable Raman scattering. However, mild ORC toughening, corres- ponding to the redeposition of only a few silver layers, can yield surfaces displaying measurable Raman scattering for these and other 96,97 inorganic adsorbates. It is therefore of interest to explore the influence of electrochemical roughening on the double-layer structure 48 of the silver-aqueous interface, in particular on the surface concentration of such structurally simple adsorbates. Fleischmann et al. have recently noted the effect of extensive electrochemical roughening upon the capacitance of a silver electrode in chloride media, although no thermodynamic analysis of the data was undertaken.98 We report here specific adsorption measurements for chloride, bromide, iodide, azide, and thiocyanate obtained from Cd-E data at electrochemically roughened silver electrodes. These are compared with corresponding data gathered at a smooth polycrystalline surface. The results indicate that the surface roughening procedure that is crucial to SERS has a relatively small influence on the average surface concentration of these anions, although noticeable changes occur in the morphology of the capacitance-potential curves. The data enable quantitative comparisons to be made between the appearance of SERS and the average surface concentration of the Raman scatters. 2. Results and Discussion a. Determination 2f, Roughness Factors fo_r 333113; Surfaces Figure 3.1 shows three representative C d-E curves obtained for polycrystalline silver in contact with 0.5 M NaClOA. This medium was chosen as the "inert" background electrolyte for the present studies in view of the relatively weak adsorption of perchlorate. Although we previously used 0.5 M NaF for this purpose,86 fluoride anions appear to be more strongly adsorbed than perchlorate on silver,99 so that 0.5 g NaC104 is preferred here. The lowest curve in Figure 3.1 was obtained 49 '60! I I T r l 1 I _ RF-4 - RFI 2.5 .. (:dl,}LF:CH712! a) O 4O -_/\ .AM\'- L o -480 £60 4200 6. mV. vs a.c.e. Figure 3.1. Differential capacitance of polycrystalline silver in 0.5 ggNaClOA plotted against electrode potential for various roughness factors (RF) indicated. 50 after electropolishing the electrode in a cyanide medium,86 whereas the upper two curves were measured following oxidation-reduction cycles in 0.1 M_mCl as described above. Both these ORCs involved passing greater amounts of anodic charge, (ca. 50 and 120 mC cm.2 for the middle and upper curves, respectively), than are normally required in order to induce SERS for adsorbed anions such as chloride. Nevertheless, no marked changes in the shape of the C d-E curves are seen, the capacitance increasing monotonically with increasing roughness brought about by passing larger quantities of anodic charge,<3oac, during the ORC. This suggests that approximate estimates of the roughness factor RF (i.e., the ratio of the actual to geometric surface area) can be obtained simply from the ratio of measured capacitances at a given electrode potential with respect to that for a smooth surface. This method for determining RF was checked against an alternative approach which involved measuring the faradaic charge consumed for the deposition or redissolution of a monolayer of underpotential deposited (UPD) lead.3’100’101 The procedure entailed measuring the charge under the cathodic-anodic cyclic voltsmmetric peaks obtained in the potential region -300 to -400 mV for a solution containing 5 mg Pb2+. Essen- tially symmetrical cyclic voltammograms were obtained using slow sweep rates (cs. 5 mV s-l. The roughness factor was calculated by assuming that the charge required for deposition (or redissolution) of a monolayer of lead atoms on a perfectly smooth silver surface equals 310 HO cm-z.3 (In performing this calculation the contribution due to double layer charging was neglected. Since the capacitance of a smooth silver electrode is about 35 uF cm-2 over the 250 mV interval where 51 underpotential deposition occurs, double layer charging would require about 9 HC Suez. This yields an error of perhaps 32 in the estimates of electrode area). Three voltsmmetric peaks could be resolved, at about -300, -320, and -350 mV. Roughening the electrode produced little change in the appearance of the cyclic voltammograms besides enhancing the current. This together with the similar form of the C -E d curves seen in Figure 3.1, indicates that no major changes are occurring in the average microscopic properties of the silver surface beyond an increase in the overall surface area. Generally, the values of the RF obtained from the double-layer capacitances agree quite well (within ca. 10-202) with those found using the lead UPD method (Figure 3.2). Electrodes roughened 2 sufficiently to yield intense SERS signals, say 0' - 10 mC emf , ORC exhibited only moderate roughness factors; thus typically RF=1.5-2 for OORC I 20 mC cmfz. For electropolished silver it was found that RF 1.2 from the lead UPD method. The values of RF for the roughened elec- trodes were somewhat irreproducible, depending upon the exact manner of the washing and soaking steps following the ORC. An examination of these factors was made by recording C -E curves in the 0.1 M;K01 d electrolyte used for the ORC. A Cd-E curve obtained immediately after an ORC by scanning the potential from -100 mV to and from various more negative potentials out to -1200 mV exhibited negligible hysteresis even after several potential scans over 15-20 minutes. Interestingly, this reversibility is in complete contrast to the behavior of the SERS 1 240 cmf ,mode (silver-chloride stretching) for adsorbed chloride which is almost entirely and irreversibly quenched upon scanning more 52 . 120 ~ . ,3 - .. E 9 1L. £3<>" . 3. «3 o - . . 0 4o. . 1’ .. I 2 8 «i Roughness Factor Figure 3.2. Differential capacitance for polycrystalline silver at -550 mV versus roughness factor as determined using lead UPD method (see text). 53 102 negative than ca. -500 mV under these conditions. Washing and soaking the roughened electrode in perchloric acid yielded significant decreases in the capacitance in 0.1 M KCl, corresponding to RF decreases of up to ca. 302, depending on the vigor of the washing procedure and the soaking time (up to ca. 30 minutes). Nevertheless, the individual Cd-E curves obtained after returning the electrode to the cell consistently exhibited little or no hysteresis. Although most capacitance data were obtained using an a.c. frequency of 100 Hz, the frequency dependence of Cd was also examined. Over the frequency range 20-1500 Hz in 0.5 M NaC104, the apparent values of Cd generally increased with decreasing frequency, although only of the order of ca. 102 for every lO-fold frequency change. The extent of this frequency dispersion was similar on roughened and electropolished surfaces, and largely independent of the electrode potential. This behavior is somewhat more ideal than found for electropolished silver in 0.5 M NaF, where noticeably greater frequency dispersions were found at potentials positive of ca. -700 mV.86 However, in solutions containing small amounts (<10 mM) of strongly adsorbing anions such as chloride or bromide the frequency dispersion problem may well be more serious, judging from the differences in capacitance values obtained at 1000 Hz in 0.5 M_NaF and at 100 Hz in 0.5 M NaClOa. The results of our earlier study86 quite possibly are somewhat in error, the reported surface concentrations being smaller than the true surface concentrations. 54 b. Dgtermination pg Anion Specific Adsorption These results indicate that the electrochemically roughened silver surfaces exhibit sufficiently well-behaved and reproducible behavior to allow quantitative estimates of specific anion adsorption to be obtained from C d-E data using the Hurwitz-Parsons approach. Following our earlier measurements,86 C d-E curves were recorded in a series of mixed electrolytes having the general composition (0.5-x)M NaClO + xM NaK, where X is the adsorbing anion, either Cl-, Br-, 1-, 4 ms. , or N 3. previously roughened or electropolished silver electrode in 0.5 M The general procedure was to record a Cd-E curve for a NaClO4, and then obtain C d-E curves following successive additions of Max using the same electrode. The surface concentrations of specifically adsorbed anions were calculated from each family of C d-E curves using two variants of the Hurwitz-Parsons analysis, as follows. The electrocapillary equation for the mixed electrolytes employed here can be written as36 -d Y-gm dB «1» [Ix-{XKOJ-XHI‘ lRlenx (3.1) c1o, where I‘ is the surface tension, c:Ill is the excess electronic charge density on the metal surface, E is the electrode potential, andI‘ X and P are the surface excesses of the added anion X and the perchlorate Cloh anion. Provided that the components of 1‘ K and C101, in the diffuse respectively, are present in the same ratio as the a c101 Equation (3.1) can be rewritten as layer, 1‘ g and I’ 310 1, anion mole fractions, i.e. 1‘ 2/1‘ - x/(O.5-x). as expected,36 then 55 m I I I -d 1' o dE + [PX-{x/(0.5-x)}Fc10thlenx (3.2) where F' and r ' is small (vide infra), we can write X 0101* -dY'Iode - F'Rlenx (3.3) X I Equation (3.3) suggests that the desired values of PX can be obtained simply from I PX I -(l/RT)(3Y/31nx)E I -(l/RT)(3AY/3lnx)E (3.4) The required coefficients (BY/Blnx)E were obtained from the Cd-E curves by noting that the observed coincidence of these curves at negative potentials will also be associated with values of oIll and that are both independent of x. Therefore the Cd-E curves can be integrated twice to yield a corresponding set of AY-E curves, where M is the surface tension with respect to the (unknown) value at some suitably negative potential. [Since the Cd-E curves were often not quite coincident at the most negative potentials (ca. -1300 to -l400 mV) at which Cd could be accurately evaluated due to the onset of hydrogen evolution, a short extrapolation of these curves to more negative potentials was re- quired]. The required values of OY'I lnx)E were obtained for various values of x and E from the family of M -E curves, yielding plots ofI‘ K against E for various values of x. We shall denote this approach as Method I. It has been recently employed, for example, to determine chloride specific adsorption at single-crystal silver surfaces.95 56 We have previously used a related approach, denoted here as 86 , 103 , 104 Method 11, based on the following "cross-differential" relation which can be obtained from Equation (3.3):103 m ,'_ (30 / x) E Ia-RT( lnx/aE)F" (3.5) Provided that the coefficient (3C5m/31'x)E is essentially independent of coverage, I‘ x‘ can be found from I 1" x - -(A°’)E/sr(31nxlas)r. (3.6) where (A0 “)3 is the change in electrode charge density at a given electrode potential brought about by the addition of the adsorbing anion X. This quantity can easily be found by back-integrating the Cd-E curves as before, but only once to yield a family of relative m o E curves. The required coefficient (alnx/aEhv, can be evaluated from the relative shape of these on-E curves as described in reference 103. [Note that Methods I and II require only information on the chapges in am (orY ) brought about by altering the anion concentration, x, so that a knowledge of the potential of zero charge or absolute values of on is not required]. Although Method II provides a particularly direct route to 1‘ 1;, its use, at least as outlined above, proved impossible with the present systems. The chief difficulty is that the coefficient (aux/311),. in each case varied with both the surface anion concentration and electrode potential, and therefore could not be assessed from the 57 relative shapes of omLE curves. When such variations are minor the coefficient can still be evaluated via an iterative analysis. However, the iterative approach, when tried here, yielded divergent results. Figure 3.3A shows a typical set of Cd-E curves for electro- polished silver (RF21.2) in a series of mixed NaClO4-NaCl electrolytes with x I 0 to 0.2 M. Figure 3.38 gives a corresponding set gathered 2 for a roughened silver electrode (a I 40 mC cm- , RF I 1.9). ORC Comparisons of Figures 3.3A and 3.3B shows that the general features of the Cd-E curves are similar on the smooth and roughened electrodes (yigp‘ppppp). The latter curves have values of Cd that are about 501 higher in accordance with the measured roughness factor. [Here and elsewhere Cd is reported in terms of the geometrical (apparent) surface area.] At potentials more negative than ca. -1300 mV, the capacitance is almost independent of the bulk chloride concentration, indicating that here chloride specific adsorption is negligible. As the potential becomes less negative, progressive increases in Cd are seen for the chloride-containing solutions which become larger with increasing bulk concentration as a consequence of greater chloride specific adsorption. The resulting values ofI‘éi as a function of potential for two chloride concentrations, 0.015 and 0.1 M are shown in Figure 3.4 for both electropolished (solid curves) and roughened surfaces (dashed curves). (The surface concentrations here and below are reported in terms of the actual surface area, i.e. by taking into account the measured roughness factors RF 1.2 and 1.9 for the electropolished and roughened surfaces, respectively). It is seen that the corresponding I PCl values are somewhat smaller on the roughened compared to the 58 l— O 6 ‘ -4éo -e‘oo 4260 E, mV. vs. a.c.e Figure 3.3A. Differential capacitance versus electrode potential for electropolished polycrystalline silver (RF = 1.2) in NaClOa-NaCl mixtures at ionic strength 0.5. Keys to chloride concentrations: 1, OmM: 2, 1 mM: 3, 2.5 mM; 4, 6 mM; 5, 15 mM; 6, 40mg; 7, 100 mM; 8, 200 mM. 59 20C r r 1 t . 1 1 l IGO U 0 o ' «160 -800 4200 E , mV. vs. see. Figure 3.38. As in Figure 3.3A, but for electrochemically roughened silver (RF = 1.9). 6O 100 I I r I l I I 80 . O) O T mole - cm'2 40L 1‘): IO “3 O I -200 -600 '1000 ~1460 E, mV. vs. s.c.e. Figure 3.4. Surface concentration of specifically adsorbed chloride (per cm2 real area) at electropolished (solid curves) and roughened silver (dashed curves) versus electrode potential for bulk chloride concentrations of 0.015 M and 0.10 M, analyzed from Figures 3.3A and 3.33 as outlined in text. 61 9- -|OO .5 u. :1. . R, 13 arm ‘9 -5o ~2oo ‘ -660 1 40100 -|4oo E, M! vs. see Figure 3.5A. Differential capacitance versus electrode potential for electropolished polycrystalline silver in NaClOa7NaBr mixtures of ionic strength 0.5. Key to bromide concentration (solid curves): 1, 0 mM5 2, 0.6 QM; 3, 2 mM: 4, 5 mM: 5, 15 mM; 6, 40 mM: 7, 100 mM, The dashed curve is the cell resistance for 100 mM bromide plotted on the same potential scale. 62 250 . 200 ~100 (v R. 'E '50 - ohm. 9 LI. 1100 5 " - 0 3 50 . J I I I L g 41 0 200 -600 ~1000 ~1400 0 E. mV. vs. a.c.e. Figure 3.58. As in Figure 3.5A, but for roughened silver (RF-1.9). 63 Figure 3.50. As in Figure 3.5A, but for roughened silver (RF=4.2). 64 '50 I I I r I PxIO', mole-cm: 0| 0 I -400 £00 4200 E, mV. vs. s.c.e. ’ Figure 3.6A. Surface concentration of specifically adsorbed bromide (per cm2 real area) as electropolished (solid curve) and roughened silver (dashed, dotted curves) for bulk concentration x at 15 mM. obtained from Figures 3.5A and B. 65 '50 l l l r 1 ‘1" S 100 - _79 O E ‘0 it t... . 501- t \s O l j J l L -400 -800 -IZOO E, mv vs. see Figure 3.68. As in Figure 3.6A, but for x I 100 mg, 66 electropolished surface, and only increase marginally with increasing bulk chloride concentration. Although the decrease in 1‘81 upon surface roughening is relatively mild (up to ca. 301) it is considered to be greater than the experimental uncertainty in X’ which under favorable conditions is estimated to be no larger than 10-152. Figures 3.5A-C show representative C d-E curves gathered for bromide electrolytes, (0.5 M NaClOA + 1M NaBr with xI0 to 0.1 M). using electropolished (Figure 3.5A) and roughened silver having RF values of 1.9 (Figure 3.53) and 4.2 (Figure 3.56). Again, the shapes of the Cd-E curves on the roughened surfaces largely resemble those at the smooth electrode, the values of C being greater on the former to d an extent that is approximately in accordance with the measured rough- I Br electrode potential for 0.015 M bromide at these three surfaces, and mess factor. Figure 6A shows the resulting plots of 1‘ against Figure 3.6B shows the corresponding plot for 0.1 M bromide. As for chloride, the values of Pg: are marginally smaller on the roughened compared to the electropolished surface, and to an extent which increases with increasing roughness. Figures 3.5A-C also show representative plots of the resistive component R of the measured impedance against potential for 0.1 M bromide, shown as dashed curves. Although R is approximately constant beyond -700 mV, it exhibits sharp variations at potentials positive of the major Cd peak where high coverages of bromide are obtained. Similar behavior was observed for the other adsorbates studied here (cf. reference 86). Such variations are inconsistent with the usual representation of the interface as a pure "RC" circuit. The reason for 67 this behavior is unclear, but may be associated with a sluggish restructuring of the adsorbate layer at high coverages. In any event, the derived 1’ 1; values are clearly less trustworthy under these conditions. Nevertheless, the shape of the Cd-E curves in the high coverage region can still yield useful information. The measured capacitance can be considered to consist of two components, one reflecting the dielectric properties of the particular’ interfacial. composition ("constant coverage" capacitance) and an additional part arising from the variation in the adsorbate concentration with electrode poten- tial.105 This latter component will be greatest when the fractional surface coverage 6 is about 0.5 because (ar’x/aE)x and hence (son/38)x are anticipated to reach maximum values at this point and will vanish in the limits of low and saturation coverage since then (8F£/33)x4>o, Therefore the major capacitance peak will occur at a surface coverage around 0.5. This is borne out in Table 3.1 for Br- adsorption at roughened silver. The onset of concentrationsindependent and relatively potential-independent capacitances at more negative and positive potentials signals that the anion coverages approach zero and unity, respectively. For chloride, the Cd-E curves converge only at positive potentials close to the onset of surface oxidation, ca. 0 mV. Bromide adsorption is sufficiently stronger so that the major capacitance peak occurs at more negative potentials and the Cd-E curves converge to a plateau at potentials positive of ca. -300 mV, indicating that a monolayer of adsorbed bromide is formed in this region. The surface 68 Table 3.1 Coverage of Roughened Silver (RF-1.9) by Bromide Ions at the Capacitance Peak Potential in Mixed Electrolytes l§£:l_ Coverage 0.002 M 0.45 0.005 0.40 0.015 0.47 0.040 0.53 0.100 0.52 69 concentration corresponding to a close-packed monolayer is estimated to be 1.6 x 10.9 and 1.35 x 10"9 moles cm.-2 for chloride and bromide, respectively.86 Figures 3.7A and 3.7B show Cd-E curves for iodide-containing electrolytes obtained on electropolished and roughened electrodes, respectively, and Figures 3.8A and 3.8B show the same for thiocyanate. Both these anions are sufficiently strongly adsorbed to yield large increases in Cd upon their addition to 0.5MNaClO4 even at the most negative potential (ca. -l300 mV) at which measurements could be made without interference from hydrogen evolution. This precludes a quantitative adsorption analysis since sizeable extra- polations to more negative potentials are required to a value where anion adsorption is negligible from which the Cd-E curves can be integrated. Nevertheless, once again the shapes of the C -E curves on d the electropolished and roughened electrodes are similar, the latter merely exhibiting larger Cd values to an extent consistent with the roughness factor determined in 0.5 MpNaCloa. Both iodide and this- cyanate are tenaciously adsorbed, apparently saturating the surface at potentials positive of ca. -900 mV for bulk anion concentrations of a few millimolar and above on the basis of the plateaus observed in the Cd-E curves under these conditions (Figures 3.7, 3.8). However, the Cd-E curves for thiocyanate exhibit a pronounced structure in the more positive potential region, most notably yielding a large capacitance peak at ca. -250 mV which grows sharply as the bulk thiocyanate concentration is increased above 1 mM. The magnitude of this peak is noticeably dependent on the a.c. frequency, being markedly smaller at 7O 250 I I I I I I .. 1 4 \\\ 5 '50)- “ - 7 e. . E 9 UL =L - . 1'5 L) 50 - 4 o 1 1 1 4 1 1 '200 '600 'IOOO - I400 Figure 3.7A. Differential capacitance versus electrode potential for electropolished silver in NaClOa-NaI mixtures of ionic strength 0.5. Key to iodide concentrations: 1, 0 mg: 2, 0.2 mM: 3, 0.5 mM: 4, 1.2 mM; 5, 2.2 mM: 6, 5 mg; 7, 10 mg. 71 ‘mo I I r I f I 800 _ 7 an 600 P " /6 9‘5 - - 1L 5 3: 400 ' ‘ m . / 0 w 4 3 200- I, 2 1 D ‘/ 1 a -200 I -600 l -|000 L -1400 E , mV. vs. s.c.e. Figure 3.73. As in Figure 3.7A, but for roughened silver (RF 2 4.6). 72 150 ' -cm'2 5 O N o- m 0’s) 6,. [LP “‘-e // “f"— (\ 50 ,4 J'hyv“ - '. 0 «100 -300 -|200 E, mV.vs. s.c.e. Figure 3.8A. Differential capacitance versus electrode potential for electropolished silver in NaClOa-NaSCN mixtures of ionic strength 0.5. Key to thiocyanate concentrations: 1, 0 mM: 2, 0.3 mM: 3, 1 mM: 4, 3 QM; 5, 10 mM: 6, 30 mM: 7, 100 mM, 73 6 300- I] . 5 I J 2001- 4 .. on IE 7 e: 6 u. ' ’ ‘ =1: 5 m 4 ° IOO- I . I 3 4 2 ' an“ 2 2 "I. - ‘ Q‘ - 7 \y . 3 6 5 0L 1 l 1 4 l I O '400 “800 '1200 E. mV. vs. see. Figure 3.88. As in Figure 3.8A, but for roughened silver (RF = 2.1). 74 r I l r l T l - 4 200- 1 -* 'E 0 )- .- “i . 3‘ 1' :3 100 I 5/ 1' l l j l l 1 -400 -800 -4200 E. mV vs. ace 0r Figure 3.9. Differential capacitance versus electrode potential for roughened silver in KCl-KSCN mixtures of ionic strength 0.1. Key to thiocyanate concentrations: 1, 0 mM; 2, 5 mM; 3, 10 mM; 4, 23 111M; 5, 50 mM. 75 1000 Hz than at 100 Hz; the latter was used to obtain the data in Figure 3.8. (No faradaic current was detected at these potentials.) In contrast, the Cd-E curves for iodide are featureless and essentially independent of the bulk iodide concentration in this region. It seems feasible that these additional features observed for thiocyanate are due to potential-dependent rearrangements of the adsorbate layer associated with alterations in the surface bonding geometry. Although thiocyanate very likely binds to metal surfaces preferentially via the sulfur atom,97 the nitrogen atom should also have some affinity for the silver surface which could result in a relatively flat or bent orientation. At more positive potentials, the enhanced electrostatic field at the silver surface resulting from larger positive electronic charge densities95 and greater packing densities may increasingly favor a more perpendicular orientation with the NCS— ion bound only via the sulfur where most of the anionic charge is located. Since the most comprehensive SERS study of thiocyanate employed 97 it is of interest to examine thio- chloride-thiocyanate mixtures, cyanate adsorption at roughened silver under these conditions. Figure 3.9 shows Cd-E curves for KCl-KSCN mixed electrolytes. Although a quantitative analysis is again precluded, it is evident that only small bulk concentrations of NOS. are needed in order to produce curves which are characteristic of NCS- adsorption and completely lacking the features associated with Cl- adsorption. These data are most rea- sonably interpreted in terms of strong preferential adsorption of thiocyanate at the expense of chloride. This conclusion is consistent 76 with the finding in the SERS study that the usually intense Ag-Cl stretching mode at 240 cm”1 is completely eliminated when millimolar amounts of NOS. are added to the bulk solution.97 The C d-E curves for azide at electropolished (Figure 3.10A) and roughened silver (Figure 3.108) form an interesting comparison with the behavior of thiocyanate in view of the structural similarities of the two anions. Azide is sufficiently weakly adsorbed at the most I negative potentials to allow values of FK to be determined. The resulting plots of 1‘;3vs. E for azide concentrations of 0.01 and 0.1 M at electropolished and roughened silver are shown in Figure 3.11. In contrast to chloride and bromide, azide yields significantly larger values of I”; on the roughened compared to the electropolished surfaces. Although the extent of azide adsorption is comparable to that of bro- mide at relatively negative potentials, ca. -900 to -1200 mV, the I increases in PN as the potential becomes less negative are less 3 I pronounced than those for bromide (Figure 3.6). Therefore values of I‘ N 3 close to that expected for a monolayer of azide adsorbed "end on", ca. 9 mole cm-z, are barely attained even at the most positive 1.6 x 10- potentials (ca. 0 mV), and at x I 0.1 M (Figure 3.11). This feature can also be deduced from the shape of the Cd-E plots for azide (Figure 3.10); instead of the single major capacitance peak and a decrease to much smaller values at more positive potentials as seen for the halides, the azide curves exhibit two relatively shallow peaks. One possible reason for this more complicated behavior is that there is a change in orientation of the adsorbed azide with increasing coverage. A relatively flat orientation of the linear N; ion which may be 77 80 y I I I I I I I 601- - ‘1" E I- ‘4 9 .3540 P - J 20 " "1 1 I 1 ' l I 1 L l 200 -200 -600 -1000 -I400 E. mV. vs a.c.e. Figure 3.10A. Differential capacitance versus electrode potential for electropolished silver in NaClOa-NaN3 mixtures of ionic strength 0.5. Key to azide concentrations: 1, 0 mM: 2, 1 mM; 3, 3 mM; 4, 10 mM; 5, 30 mM. 78 Cd, 7“: ~cm'2 I I 40 200 Figure 3.108. “600 fl000 4400 'E. mV. vs. see. ‘200 As in Figure 3.10A, but for roughened silver (RF I 2.3). 79 [50- l" x lO".mols_-_.(:m"2 5.3 (I C) L 1 _ -400 '800 -1200 E,mV. vs. a.c.e. 0)- Figure 3.11. Surface concentration of specifically adsorbed azide (per cm2 real area) at electropolished (solid curves) and roughened silver (dashed curves) versus electrode potential for bulk azide concentrations of 0.01 M and 0.1 M, analyzed from Figures 3.10A and B as outlined in the text. 80 preferred at low coverages as a result of ligand-metal overlap would need to give way to a more compact "end on" orientation in order to achieve surface concentrations above ca. 7 x 10"10 moles cmfz Support for this interpretation is also obtained from the related observation that the so-called “electrosorption valency", -(RT/F)G§1nx/ 106 3E) F" for azide depends markedly on the adsorbate coverage and elecfiode potential, changing from about 0.3 at the most negative potentials to about 0.15 in the potential region positive of the major Cd peak at ca. -900 mV. This is nicely consistent with a change in azide orientation from flat to vertical in that this transformation would place the anionic charge further from the electrode. The latter orientation would yield a smaller value of EV since this quantity depends in part on the fraction of the double-layer potential drop 106,107 traversed by the anionic charge upon adsorption. Since the surface concentration data in Figures 3.4, 3.6 and 3.11 I X Approximate estimates of their mag- were obtained by using Equation 3.3, significant errors in F 108 may arise from perchlorate coadsorption. nitude can be estimated by inspecting Equation 3.2 which takes this factor into account. ‘nn general Equation 3.3 will tend to under- estimate P; since the second term in brackets in Equation 3.2, which is neglected in Equation 3.3, will always be positive. The error is most likely to be significant for the least strongly adsorbing anion, chloride, for which the largest bulk anion concentrations, and hence x. AlthougthCIOu is not known quantitatively, kinetic probe measurements x/(0.5-x), are required in order to induce a given value of I indicate that in pure perchlorate media F 1‘ C10 2 0III over a range of u 81 positive electrode charges,86’109’110, yielding r010 : 2.5 to 3.5 x u 10-10 mol cm.2 in the potential region ca. -200 to -400 mV. For high chloride concentrations, say x I 0.1 so that [x/(0.5-x)] I 0.25, the apparent values ofI‘x from Equation 3.3 are about 8 to 10 x 10"10 mol (:111-2 in this potential region, so that the magnitude of the correction term [at/(0.5-x)11‘c10 , ca. 1 x 10"10 mol cm'z, is small yet sig- u I nificant. However, the actual error in I‘x is almost undoubtedly smaller than this since strong chloride adsorption will inevitably diminish I 010 substantially. The errors in r; are likely to be negligible for smaller values of x and with the other adsorbing anions. Admittedly, the presence of the perchlorate may still influence the values 0f 1‘; from Equation 3.3 but the analysis errors themselves appear to be minor. Interaction parameters and standard free energies of adsorption at 0Ill I 0 were calculated for each ion by fitting surface concentration data to the Frumkin isotherm (Equation 1.9) with standard states of l 2 molecule cm- for the adsorbate and 1 mole liter.1 for the anion in bulk solution. The effective potential of zero charge in 0.5MNaClO4 was taken as -930 mV. The results for electropolished and roughened polycrystalline silver are listed in Table 3.2 together with Valetteis 95,111 and bromide111,112 findings for chloride at single crystals. C. Surface Crystallographic Changes Induced My Electrochemical Roughening In addition to yielding quantitative information on the extent of specific ionic adsorption, the Cd-E curves can also provide useful 82 Table 3.2 Standard Free Energies of Adsorption llG:(kJ mole-1) for Anions at Various Silver Surfaces Electrode Adsorbatea . G: ‘g polycrystalline silver (smooth) Cl-(0.5.M_Na0104) -95 90 polycrystalline silver (smooth) Br-(0.5,M,NaClO4) 7-101 50 polycrystalline silver (smooth) N3-(0'5 M Na0104) - 95 70 roughened silver (RF 2) Cl-(0.5,M_Na0104) - 92 90 roughened silver (RF 2) Br-(0.5,M,NaC104) -100 40 roughened silver (RF 2) N;(0.5 M NaClOA) - 94 14 (111) silver 01"(o.o4 a NaF) -1oob — (110) silver c1'(o.04 a, 11.1?) - 95b — (100) silver c1"(o.04 a NaF) - 93b — (110) silver c1"(o.04 a 10296) - 93.5c 160 (110) silver Br‘(0.04 M NaF) - 98d 40 (110) silver 131-"(0.04 a 10:36) - 99c 45 a. Base electrolyte listed in parentheses. b. From reference 95, based on a virial isotherm. c. Calculated from data given in reference 111. d. Calculated from data given in reference 112. 83 clues to the crystallographic nature of the metal surface. Thus the shapes of the Cd-E curves obtained at single-crystal silver electrodes can be diagnostic of the particular crystallographic orientation ex- posed at the surface.“"95998 Moreover, a number of well defined capacitance peaks are obtained in chloride and bromide electrolytes whose shape and potential are characteristic of the surface crystallo- graphic orientation.95.98 This suggests that comparisons of Cd-E curves obtained for polycrystalline and various single-crystal surfaces in a given electrolyte could provide information on the crystallo- graphic components of the former surface, and shed light on the structural changes induced by electrochemical roughening. The major featurs of the Cd-E curves in, for example 0.1 M chloride at electropolished silver in Figure 3A, are a shoulder at -1000 mV (feature I), a major peak with a sharp summit at -550 mV (II), and a sharp peak at -lOO mV (III). Upon roughening the electrode (Figure 3.3B), features I and II become more pronounced, and III is diminished. A Cd-E curve with similar features to those in Figure 3.3B was also obtained by Fleischmann et al. for highly roughened silver (RFZZ 98 15) in 0.1 M NaCl. Comparisons with the Cd-E curves obtained for comparable chloride concentrations at silver surfaces having (111). (100), and (110) orientationsgs’98 reveal that feature I closely resembles that found for (110) crystallites, feature II with (100), and feature III with (111) crystallites. Sketches of surfaces possessing (111), (100) and (110) orientations are shown in Figure 3.12. The Miller index notation for face centered cubic crystals is used. It appears that electrochemical roughening in chloride media results in an 84 increase in the proportion of facets resembling (100) and (110), and a decrease in those resembling (111) crystallites. The Cd-E curves for bromide electrolytes are consistent with this interpretation. The two main features at electropolished poly- crystalline silver in 0.1‘M_bromide (Figure 3.5A) are a shoulder at ca. -1150 mV (I) and a major broad peak at -800 mV (II). Roughening the electrode (Figures 3.SB,C) results in little change in II but yields a significant increase in I. Comparison with corresponding single 95 crystal data suggests that feature II is probably formed from a composite of closely overlapping peaks from several low-index faces, whereas I is predominantly associated with the (110) and (100) faces. These and possibly other higher index planes therefore seem to be more prevalent on the roughened surfaces. This finding seems reasonable since metal oxidation and rapid redeposition would be expected to produce a relatively “loose" and somewhat disordered surface, with a smaller proportion of the most densely packed (111) plane. Nevertheless it should be noted that the overall changes, both in the shapes of the Cd-E curves themselves and in the surface anion concentrations induced by even quite extensive surface toughening are surprisingly mild, the major effect being simply to enhance the effective surface area. Thus, although the morphology of the surface at the 1 micron level that is probed by scanning electron microscopy is strikingly altered by electrochemical roughening113 it appears that such large-scale surface reconstruction gives rise to only relatively minor alterations in the average crystallographic structure as well as in the average double-layer composition. 85 Figure 3.12. Atomic positions of the (100), (110) and (111) faces in the fee structure (after Hamelin, et a1., reference 1). 86 d. Ipplications for Surface-Enhancgd Rappn Scattpripg The enormous increases in the intensity of SERS brought about by electrochemical roughening of the type and magnitude employed here114 stand in sharp contrast to the relatively moderate (1.5-to 4-fold) increases in the actual surface areas and the minor changes in the surface concentration of adsorbed anions. This implies that the role of surface roughness in promoting SERS is to enhance greatly the inelastic scattering efficiency of the adsorbate scattering centers, in harmony with commonly held views.8’114 Nevertheless, it is of consid- erable interest to ascertain the functional relationships, if any, between the intensity and nature (frequency, bandshape) of the Raman scattering and the average surface concentration of the Ramanractive adsorbate. The adsorption data presented here show that substantial specific adsorption of a number of anions occurs even at strongly negative potentials. Thus in the range of adsorbate concentrations 0.01-0.1 M, bromide, iodide, and thiocyanate are adsorbed with coverages above half a monolayer at potentials positive of about -800, -1150, and -1100 mV, judging by the position of the major peaks in the Cd-E curves (Figures 3.5-3.8). Although stable SERS signals are observed for these anions at potentials close to the anodic limit, ca. 0 to -250 mV, the scattering intensity is found to diminish to small or even imper- ceptible levels upon shifting the potential to these more negative 97,115-117 values. Moreover, as noted above for chloride, scanning the potential to such negative values and returning yields negligible hysteresis in the Cd-E curves and hence the rx-E plots, yet the SERS 87 signals are almost entirely irreversibly quenched upon the return 97,116,117 scan. Further, comparisons between the present adsorption data and SERS spectra obtained under comparable conditions as a function of electrode potential for chloride, bromide, iodide,115 95,117 118 and azide indicate that in each case the Raman thiocyanate, signals at a previously roughened silver electrode become markedly and irreversibly weaker as the potential is shifted negative only to the point where the anion coverage falls significantly below a monolayer, as signaled by an increase in C towards the major C -E peak. This d d result holds for Raman signals associated with both metal surface- ligand and internal vibrational modes. From Figures 3.3B, 3.5B and C, 3.78, 3.8B, and 3.10B these potentials for x 0.01 M are ca. ~200, -500, I900, -900, and +100 mV for chloride, bromide, iodide, thiocyanate, and aside, respectively. For azide, a monolayer is only formed close to the onset of metal dissolution at ca. 150 mN; indeed stable SERS spectra for this anion are not seen at more negative potentials117 even though extensive azide adsorption occurs as far negative as ca. -800 mV (Figure 3.11). .A likely explanation for this surprising behavior is that the most efficient Raman scattering occurs from specific surface sites associated with particular morphologies, probably small metal clusters which are metastable with respect to incorporation into the metal lattice.119 At adsorbate coverages close to a monolayer, anions will bind to these sites giving rise to SERS and will also occupy the large majority of nearby metal lattice sites. Although not contributing to the observed Raman signal, the latter adsorbate can stabilize the 88 Hanan-active clusters by preventing their dissipation into the sur- rounding lattice. Altering the potential to sufficiently negative values so that a fraction of this adsorbate is desorbed will provide lattice positions into which the least stable clusters can rearrange, leading to an irreversible decrease in the Raman intensity. However, judging by the essentially reversible nature of the Cd'E curves, this rearrangement process appears to involve only a small fraction of the metal surface. These considerations provoke the desirability of examining the potential dependence of SERS on time scales that are sufficiently short that the irreversible decay of the Raman signal does not occur. Data gathered under such conditions, largely using a spectrograph optical multichannel analyzer arrangement for rapid time resolution, are 97,102,119 starting to appear. In Figure 3.13 electrochemically deter- mined surface coverages (a value of 1.0 corresponds to a monolayer) and relative Raman scattering intensities for chloride at silver are plotted against electrode potential. The SERS data were gathered by Weaver, et al. at the IBM Research Laboratory in San Jose, CA.102 The intensities are normalized such that a value of 1.0 is obtained at the most positive potentials. A similar plot for bromide at silver is shown in Figure 3.14. Both figures indicate that there is indeed an approximate proportionality between the surface concentration and the Raman intensity for chloride and bromide. However, thiocyanate ex- hibits somewhat different behavior inasmuch as marked (ca. 3-fold) decreases in Raman intensity for the C-N stretching mode (VON) occur under reversible conditions when the potential is made more negative in 89 I - \ 0.4114. N000, + 0.1M NoCl SURFACE COVERAGE or NORMALIZED RAMAN INTENSITY 8 Figure 3.13. Fractional coverage, 0, of chloride anions (solid curve) and normalized Raman peak intensity (dashed curve) for Ag-Cl- stretching mode, both plotted against electrode potential. Electrolyte is 0.4 M NaClO + 0.1 M NaCl. Raman data from.reference 102. l. 9O SURFACE COVERAGE or NORMALIZED RAMAN INTENSITY Figure 3.14. Fractional coverage, 0, of bromide anions (solid curve) and normalized Raman peak intensity (dashed curve) for Ag-Br- stretching mode,both plotted against electrode potential. Electrolyte is 0.45 M NaClO4 + 0.05 M NaBr. Raman data from reference 102. 91 the region ca. -150 to -750 mV120 even though the thiocyanate coverage 97 This behavior may be is maintained near a monolayer throughout. associated with the potential dependence of thiocyanate orientation that was suggested above.97 Thus a change in adsorbate surface bonding to a less perpendicular orientation as the potential is made more negative would be expected to yield a decrease in the Raman scattering efficiency of the ch mode since the component of the polarization vector normal to the surface would thereby be diminished.121 Finally, it should be noted that considerably (ca. lO-fold) more intense Raman scattering can be obtained for several adsorbed anions such as chloride, bromide, and thiocyanate if the electrode surface is 122’123 Nevertheless, illuminated by the laser beam during the ORC. preliminary measurements indicate that such laser illumination has only a small influence upon the Cd-E curves recorded in the presence of such anions, indicating that only minor changes in both the effective surface area and the anion surface concentrations occur under these conditons.124 The observations reported here suggest that there are two main requirements for the observation of stable SERS signals for anions at silver. First, active sites must be generated. Dissolution and redeposition of silver in complexing media evidently accomplishes this. Second, the active sites must be stabilized, e.g. by anion adsorption to the extent of saturation as suggested above. The inability to meet one or both of these requirements may account for the absence of SERS 125 126 from most other metal electrodes. Thus, lead , thallium and other white metals may be SERS-inactive because only small coverages of 92 anionic adsorbates can be obtained even at the most positive available potentials. Mercury is another SERS-inactive metal exhibiting only weak tendencies to adsorb ions.127 On the other hand, the difficulty of forming active sites may account for the lack of SERS at noble metals. Although anions are adsorbed extensively at platinum, for example, this material resists dissolution. At gold, SERS is observed 128 only under extreme conditions where metal dissolution (and active site formation?) become possible. In contrast, the SERS effect is well established at copper129 which, like silver adsorbs anions readily and is easily dissolved and redeposited. Nevertheless, there are indi- cations that other factors such as optical properties of surfaces may contribute to the electrode selectivity of the effect.8 Although preliminary, the observations at silver point to the desirability of correlating the nature and intensity of SERS signals with the interfacial composition, both from the standpoint of under- standing the nature of the SERS effect itself and its utilization as a microscopic probe of electrochemical surface structure. It will clearly be important to study structurally simple adsorbates having known surface concentrations and well-defined bonding geometries in order to unravel the importance of such basic factors as surface concentration, surface bonding and stereochemistry to SERS. B. Specific Adsorption pg Transition-Metal Cogplexps.gp Silver In addition to simple anions, the adsorption of some transition- metal complexes at silver was examined. The study was undertaken 93 within the context of the overall group effort to explore the physical phenomena associated with Surface-Enhanced Raman Scattering (SERS) and use the effect to examine electron transfer reactions at surfaces. Such electrochemical measurements provide independent information concerning the surface concentration and redox reactivity of SERS- active molecules. In particular, fast cyclic voltammetry in dilute solutions (50 to 100 11;!) of strongly adsorbing complexes represents a powerful and convenient electrochemical means of acquiring such information.85 ' 13° The molecules studied were Os(NH3)5pyridine3+, Os(NH3)5pyrazine3+ and Os(NH3)5bipyridine3+. All three are substitutionally inert and undergo reversible electron transfer at convenient potentials. Shown in Figure 3.15 is a surface cyclic voltammogram (200 V s-l) for Os(NH3)5 py3+ reduction and reoxidation at roughened silver in 0.1 M NaBr + 0.08 M NaCl + 0.02 M HCl. The almost symmetrical shape and near coincidence of the anodic and cathodic peaks, together with the linear dependence of the peak current upon potential (not shown), indicate that the waves arise from adsorbed reactant. From the area mderneath the current peaks the surface concentration of the complex is calculated to be about 3 x 10.11 mole cm-z. A monolayer would require about 15 to 20 x 10-11 mole cm"2 for a "vertical" orientation with adsorption via the pyridine ring. The peak width at half height is 125 mV. This is greater than the value of 90 mV expected for Langmuir adsorption and indicates that repulsive interactions exist between adsorbed molecules.33 50- I I I' -450 -550 -550 -7so -850 E,mV vs see Figure 3.15. Cathodic-anodic voltammogram for adsorbed 03(1‘11-13)5pynl/II redox couple at roughened silver-aqueous interface in 0.1 M NaBr + 0.08 M NaCl + 0.02 M HCl. Electrode roughened by means of an oxidation-reduction cycle in this supporting electrolyte; (roughness factor ca. 1.8 on basis of capacitance measurements). Bulk OsIII(NH3)5py concentration I 50 uM; sweep rate I 100 V sec-1. 95 From the average peak potential a surface formal potential, Bi, of -705 mV is inferred. This is significantly negative of the bulk solution formal potential of -650 m.V131 and indicates that the complex is bound more strongly in the Os(III) than in the Os(II) state. Interestingly, in 0.1 M NaCl + 0.1,MIHCl the surface formal potential is shifted to -670 mV (Figure 3.16). The 35 mV difference in E: values may well represent the influence of the double layer on the surface redox thermodynamics. Thus, the presence of the electrical double layer subjects the adsorbed reactant to an electrostatic interaction with the charge at the electrode surface. Addition of an electron to the reactant reduces its charge and therefore its interaction with the electrode charge. For a one-electron reduction of an adsorbed cationic complex the difference in electrostatic interactions for the oxidized versus the reduced state should yield a change in surface formal poten- tial of ¢r' Recall that ¢r is determined to a first approximation by the total charge, on + F1:, at the surface (see Equation 1.11). In both chloride and bromide electrolytes the total charge, and therefore ¢r’ should be negative (see Section III. A), but or should be more negative in the latter, thereby yielding a shift of E: in the observed direction. The influence of electrode potential on the amount of adsorption of Os(NH3)5py3+ was investigated by selecting different initial potentials for the fast cyclic voltammetry measurements, as shown in Figure 3.16. (With dilute solutions of the reactant and fast sweeps the potential perturbation will "outrun" the adsorption-desorption equilibrium and provide a measure of the extent of adsorption at the 96 ~ ‘- i! MA C i\~\ 7) 1.. i8 Rho (use Lao nuuoae 21./.11) \ 1.. 1’171/ mwmcno u.—o. awnwuo <0Hnuaamnnw om anemone cocoa OmAzzuvmowHHH\HH u: we 33.2moH + No 38 map. mkwBr->Cl-. This is confirmed by the F’ versus E curves shown in Figures 3.24 through 3.26 and theI" versus on curves shown in Figures 3.27 through 3.29. (The surface concen- trations are corrected in each case for the residual electrode roughness of 1.2, while the capacitance-potential curves are uncorrected.) 4 at least, by comparing the C-8 curves in Figure 3.30 for NaBr + Na0104 The effects of 010 co-adsorption can be gauged qualitatively, with those in Figure 3.22. Particularly at more negative potentials perchlorate adsorption seems to diminish the adsorption of bromide. More quantitative comparisons are made in Figures 3.26 and 3.29 using I- as an example. Here data obtained from NaI + Na0104 mixtures are shown as dashed lines. The PI values are uncorrected for the error due I 010 ,1. perchlorate adsorption occurs (r 010., >0) (see Section III.G). However, to the extra term -[1/(l-x)] I‘ which is present when significant 124 I I I T I 6 _1 N IE 4 _J U 2 o E s :2 .x r— 2 .1 \D -1000 E. mV vs. see Figure 3.31. Surface concentration of thiocyanate vs. electrode potential for UPD lead/silver in NaNCS + NaF mixed electrolytes at an ionic strength of 0.5 5, Key to thiocyanate concentrations: (A) 1mg. (0) 3 mg, (0) 10 mg, (I) 30 mg, (a) 100 mg. 125 1 - ', mole cm 2 d I / /p D I‘>’< 10 \1 () l l -600 -800 -1000 -1200 E. mV vs. see Figure 3.32. Surface concentration of azide vs. electrode potential for UPD lead/silver in NaN3 + NaF mixed electrolytes at an ionic strength of 0.5 fl. Key to azide concentrations: (0) 3 mg, (I) 10 mg, (A) 30 mg, (a) 121m. 126 1 I ' 6 - A " \ \ \ N . \ 'E 4}- \A "" ° \ 2 . \ O E \ :1" \A 2 2 . \ .x " ° \ '- p.. \ o \\ . \ . \‘\ o . \ ‘ , -600 -800, 4000 4200 E. mV vs. sce Figure 3.33. Surface concentration of perchlorate vs. electrode potential for UPD lead/silver in NaClO4 + NaF at an ionic strength of 0.5 21. Key to perchlorate concentrations: (I) 10 mg, (0) 30 mg, (0) 80 mg, (A) 200 mg, (L) 500 mg (data at 500 mg were extrapolated). 127 J; I I"): 10", mole cm"2 NJ I A ____-Al ! 1 -2 o 2 0’... , p0 cm“2 Figure 3.34. Surface concentration of thiocyanate vs. electrode charge density for UPD lead/silver. Conditions as in Figure 3.31. 128 I I I T r 2 ._ -. 75 " ‘ 2 A O E . 79:1 + A - ~’( I 1.. . / //-/ b /7:/ _ 4%“ O /1 /L 1 l 1 -2 o _2 2 0"", 11C cm Figure 3.35. Surface concentration of azide vs. electrode charge density for UPD lead/silver. Conditions as in Figure 3.32. mole cm"2 II : 1‘ho 129 F'- / . .1 / /// y '/ 8/0 -/ L—éé’T/M' 1 1 1 1 '2 0 2 0"“, 11.0 cm'2 Figure 3.36. Surface concentration of perchlorate vs. electrode charge density for UPD lead/silver. Conditions as in Figure 3.33. 130 the F; -oIn curves do take account of the shift of the pzc from -800 mV in NaF solutions to -886 mv in 0.5 g NaClOA. (The latter value was calculated by back integrating capacitance-potential curves for various NaF-NaClo4 mixtures). Standard free energies of adsorption, as well as interaction coefficients, were calculated at various electrode charges by fitting the data in Figures 3.27 through 3.29 to the Frumkin isotherm (Equation 1.9). These parameters are listed in Table 3.3. Also included are AG: and g values for 1. adsorption from solutions of lower ionic strength. The values of P; (the surface coverage at saturation) which were used 9, 1.35 x 10"9 and 1.07 x 10"9 86 in calculating AG: values are 1.6 x 10- mole cm._2 for chloride, bromide and iodide, respectively. From capacitance-potential curves (not shown), plots of F versus E were constructed for NCS-, N3- and 0104- adsorption from NaF solu- tions (Figures 3.31, 3.32, and 3.33 respectively). The corresponding P - m curves are presented in Figures 3.34, 3.35 and 3.36. values of I AG: and g are listed in Table 3.3. The values of r8 are less certain for these ions than for the small spherical ions. Based on a "radius" 141 10 mole cm.-2 was calculated for 9 a value of 9.3 x 10- 9 of 2.36 X 2 -. mole cum--2 and 1.86 x 10- mole emf 142 010 Estimates of 1.65 x 10’ 4 were used for azide86 and thiocyanate anions, respectively. This assumes that a "vertical" orientation and hexagonal packing is preferred by each ion. 131 3.1m By comparing the results presented here with those in Section III. A, it can be seen that anion adsorption (with the exception of perchlorate) is substantially diminished at silver when the surface is modified by underpotential deposition of lead. This is true even if the results are compared at a fixed electrode potential rather than charge, despite the 130 mV "advantage" for UPD lead due to the shift of the effective pzc. Similar observations concerning the inhibiting effects of lead UPD on halide adsorption were noted earlier by Stucki and Schmidt based on thin-layer electrochemistry experiments.146 It may be instructive to compare the adsorption capabilities of UPD lead/silver with those of bulk lead.136 Listed in Table 3.4 are data obtained by H.Y. Lin for anion adsorption at polycrystalline lead m 136 at 0 - 0. the values onSG: generally are less negative for bulk lead indicating less adsorption at this surface, at least in the limit of infinite dilution. (The value in Table 3.4 for Br- apparently was miscalculated and probably is actually more negative, judging from sur- face excess data also reported by Liu). A comparison of r’ versusom curves from Dr. Liu’s dissertation with those presented here indicates that adsorption also is less at bulk lead compared with UPD Pb/Ag for finite bulk solution concentrations (10 mg!) of adsorbing anions. Nevertheless, given the sensitivity of adsorption at bulk lead to the electrode pretreatment method,136’147 the differences between bulk and UPD surfaces may well represent artifacts rather than differences in chemistry. Overall, the adsorption capabilities of UPD lead/silver and 132 SN mam- SN 98.. 08 mi. Emz E18 -8 on new- 2 CS. ofl em- SN 2.. fiaz mnémoa own 3. o8 S- Emz made mz 23 9%.. 2m 9%.. o2 mm- 83 as. $2.2 m3: 1am 8H 8.. SK 8- 8m 5.. o3 £1 Emz ”@8182 on? 3... $392 made 1H 02 mam- 2: No- 2: $1 , :32 m2: 1H 2 921 3 9:..- o: om- mm 8.. Emz made 1H m MU< w ”cc w MU< w wwq Adamaouuomam mmmnv mofim< 180 on when Huao oafio aria o N m um>HHm\vmmA am: an m:0fim< mow w mumumemumm mofiuommmuaH was AH Hoe fixv oo< :ofiuauomv< wo mmwwummm swam cumvcmum .m.m manna 133 Table 3.4 Standard Free Energies of AdsorptionAGao (kJ mol-1) of Anions at a Polycrystalline Lead Electrode.a Anionb AGO a 1' -9o nos" -86 Br- -79 us -80 c1' -74 a From H.Y. Liu, Ph.D. Dissertation, Michigan State University, 1982. b Base electrolyte was 0.2 g NaF in each case. 134 bulk lead can be regarded as fairly similar. The central conclusion from this study is that the deposition of a single atomic layer of lead is sufficient to transform the silver surface into one resembling lead, at least with regard to adsorption properties. It may be worthwhile to discuss briefly a few details of the results. One peculiar aspect of anion adsorption at UPD lead/ silver is the magnitude of the g values. These are greatest when adsorption is weak, when the electrode charge is sero or negative, and when perchlorate is used as the base electrolyte. The most extreme values (e.g., g ' 1500 for Dr.) are very unlikely to result from lateral interactions between adsorbed ions. Such large g values might be indicative of the existence of a limited number of active surface sites which are capable of adsorbing ions more strongly than are the majority of sites. Another idea is suggested by Paynefs observation that the second virial coefficient (analogous to the g parameter) for chloride adsorption at mercury increases as much as ten-fold when water is replaced by a solvent which binds more strongly to the surface.148 In changing from mercury to lead, solvent-metal interactions are likewise increased, as are the g values. One could speculate that metal-solvent and adsorbate-adsorbate interactions are somehow interrelated. Another explanation is that these results are simply due to systematic analysis errors. When surface coverages by anions approach a few tenths of a percent or less the capacitance method has nearly reached its limit as a surface concentration measurement technique. Given the form of the Frumkin isotherm, errors in estimating very small 135 I values of F can yield substantial errors in the value of the inter- action parameter. The difference in g values between fluoride and perchlorate electrolytes (see also reference 136) evidently reflects the complications due to 0104- co-adsorption. Perchlorate can influence the g parameter either by distorting the iodide adsorption isotherm via competition for surface sites or by introducing an extra term, -[8/(1-X)]I£iou, which has been neglected. It is evident from both the charge-based (Figure 3.26) and potential-based (Figure 3.29) comparisons that perchlorate co- adsorption causes a substantial diminution of the extent of iodide adsorption. At higher iodide coverages at least, this diminution must be regarded as a real chemical effect rather than an artifact due to the term "IX/(1"!)Il‘éml+ . The extent to which perchlorate co- adsorption diminishes iodide adsorption is much larger than one would anticipate from a simple "blockage" of sites by a small amount of adsorbed 0104-. Evidently in addition to blocking a small portion of the electrode surface, adsorbed 0104- also exerts a repulsive force on surrounding ions thereby inhibiting I- adsorption. Such an interpre- tation is consistent with observation of positive g values for both iodide and perchlorate adsorption from flax-NaF mixtures. 136 E. The Influence eg Thallium Underpotential Deposition ee_Anign Adsorption and the Double Leger Structure,e§ the Silveg-Agueous Maniac:- l. Ingreduction We have found that lead underpotential deposition has a profound influence on the double layer structure and ionic adsorption capa- bilities of the silver-aqueous interface. Clearly it is desirable to investigate additional systems. Thallium underpotential deposition on silver is a logical choice, since this combination has already been employed in a number of studies aimed at characterizinga’4 or applying 8,125,126 the UPD phenomenon. Nevertheless the interfacial properties of UPD as well as bulk thallium have scarcely been examined pre- 149 An additional motivation for gathering data at this viously. particular surface is the desire to understand more satisfactorily the results of electronrtransfer kinetics at UPD thallium/silver. 2. Electrode Preearatign The underpotentially desposited thallium surface was prepared in essentially the same manner as the UPD lead surface. To summarize briefly, a pretreated silver electrode was held at about -960 mV and rotated for several minutes in a dilute solution (~5 x 10..7 L!) of TlClO4 until a monolayer of thallium atoms had been deposited. According to Bewick and Thomas, two monolayers of thallium can be underpotentially deposited on carefully pretreated silver single crystals:3 Curves a and b of Figure 3.37 are linear-sweep voltam- 137 “b -900 —700 -550 -300 E. mV vs. as e. Figure 3.37 Linear sweep current-potential curves for anodic of thallium layer deposited on silver. Sweep rate was 20 mV/s. Electrolyte was 0.5 fl NaF, conyaining 0.8/1 11 TlClO Curve (a): electrode held at 40 -960 mV for 12 minutes while rotating at 600 RPM; (b) electrode held at -960 mV for 12 minutes at 600 RPM and then held for 15 minutes at -1300 mV without rotation. 138 mograms showing the removal of UPD thallium from polycrystalline silver. The area under each curve is 200 110 cm"2 which is essentially exactly the amount expected for the removal of one atomic layer of thallium3 from an electrode having a roughness factor of 1.2, given 4 If the that the electrosorption valency for Tl+lTl is unity. potential is adjusted to a value negative of the UPD region and maintained for 15 minutes without rotating the electrode, only a small additional amount of thallium is deposited as evidenced by the addi- tional peak on curve b of figure 3.37. Whether this represents the start of a second UPD layer or instead bulk deposition, is not clear since this was not investigated further. 3-.&=;w_1u1 a. Capacieance Measurmnts is, Single glectgelytes Figure 3.38 summarizes the results obtained in sodium perchlorate electrolytes. The thallium-modified electrode is approximately ideally polarizable to about -1600 or -1700 mV versus sce, compared with -l300 mv for pure silver. As the potential is made more positive than about -900 mV, as in curve a, thallium is removed and the capacitance gra- dually inereases until it attains values characteristic of silver. Curve b shows the effect of depositing the equivalent of about three atomic layers of thallium on silver. Curve c illustrates the effect on the capacitance of increasing the concentration of NaCloa. Difficulty was encountered in performing measurements with electrolyte concen- trations below 50 mg. Nevertheless, capacitance-potential curves 139 § § E 1 Figure 3.38. Differential capacitance versus electrode potential for: (a) a monolayer of underpotentially deposited thallium on polycrystalline silver in 0.05 g NaClOA; (b) the equivalent of circa. 3 monolayers of thallium on polycrystalline silver in 0.05 11. NaClO (c) as in (a), 4; except in 0.2 _11 NaClO4. 140 consistently exhibited minima at about -1020 mV in 10 mgNaClo4 and -960 mV in 10 mg NaF. The latter value can be identified as the effective potential of zero charge if it is assumed that fluoride adsorption is negligible. b. Capacitance Measurements eeg_eeieg_82ecific Adsorption.ge gggeg,zlectrolytes Capacitance-potential curves for chloride, bromide and iodide adsorption from constant ionic strength (0.5 g) NaX + NaF mixtures are shown in Figures 3.39, 3.40 and 3.41, respectively. Surface concen- trations of specifically adsorbed anions were ascertained by applying the Hurwitz-Parsons 8031731335’36 to the C-E curves. The resulting surface concentration-potential data are plotted in Figures 3.42, 3.43 and 3.44 for 01-, Dr. and 1-, respectively. Surface concentration- charge curves are shown in Figures 3.45, 3.46 and 3.47. Capacitance values for UPD thallium/silver were measured in perchlorate-containing and also in thiocyanate-containing ‘mixed electrolytes. The F ’ versus E and 1" versus on data which were calculated from these measurements are shown in Figures 3.48 through 3.51. Capacitance measurements were also attempted in NaN + NaF 3 electrolytes, but the results were insufficiently reproducible to yield azide surface concentration data. Free energies of adsorption were calculated for the five anions at \o P210“. mole cm‘2 “1000 -1100 42100 E. mV vs. see Figure 3.42. Surface concentration of chloride vs. electrode potential for UPD thallium/silver. Conditions as in Figure 3.39. 145 ‘1 T 1 31- . N 9 IE 2_ .1 o 2 O E :é‘ ‘ .. ~>< L1 1_ ‘ , . \_ \ O l l 1.1 l -1000 -1200 -1400 E. mV vs. see Figure 3.43. Surface concentration of bromide vs. electrode potential for UPD thallium/silver. Conditions as in Figure 3.40. 146 I _I I I 1 8. - ‘r 6 .. S F 2 o D d E .9 41- '1 .x F-n 2’ " 0 E. mV vs. sce Figure 3.44. Surface concentration of iodide versus electrode potential for UPD thallium/silver. Conditions as in Figure 3.41. 147 0.4 1 I l 1 N O l LE) 0.3? .... 2 E _- o.2- ° .. "s V 0.1-- / , Ir/II/I;F’////;://///A~ W // A o p 1 1 1 3 2 1 0 0‘": 51.0 cm"2 Figure 3.45. Surface concentration of chloride vs. electrode charge density for UPD thallium/silver. Conditions as in Figure 3.39- 148 I If I I I I I :3.— TE (5 <0 .2 21- O E :52.~ e ' .x ‘ L. 1— /’/ , 0 v / ./.4/ / //./ 24"» O 4éé';dr’. 1 1 1 Figure 3.46. Surface concentration of bromide vs. electrode charge density for UPD thallium/silver. Conditions as in Figure 3.40. 149 I r I I f 8- a - n ‘7‘ a 5' ~ 0 o o I ~ 5 e '2 4- . .x L. r d 2- .1 1- d O l l Figure 3.47. Surface concentration of iodide versus electrode charge density for UPD thallium/silver. Conditions as in Figure 3.41. 150 0.4 1 1 T . T 2 m /. / 0.2 - A o .. I‘$< Io". // / / .A 0 °\ \kgta . . . 1 °§ -1000 -1200 -1400 E. mV vs. see Figure 3.48. Surface concentration of perchlorate vs. electrode potential for UPD thallium/ silver in NaClOa + NaF mixed electrolytes at an ionic strength of 0.5 g. Key to perchlorate concentrations: (0) 10 mg; (a) 60 mg; (a) 200 mg. 151 .: n _ FxIO . mole cm2 D’z/I”/”/’/’DCI II’//”/”””' (J IJ’I/I/ll”’f’ \Ohofis o \ . O\O\. A§ E. mV vs. sce Figure 3.49. Surface concentration of thiocyanate vs. electrode potential for UPD thallium/silver in NaNCS + NaF mixed electrolytes at an ionic strength of 0.33, Key to thiocyanate concentrations: 1 mg, (I) 5 mg, (A) 20 m1_4_, (s) 50 mg, (m) 100 mg. -1000 -1200 152 0.4 . n PXIO . mole cm"2 .0 N Figure 3.50. charge density for UPD thallium/silver. Surface concentration of perchlorate versus electrode Conditions as in Figure 3.48. 153 mole cm"2 I 2 .A I 132 10‘ Figure 3.51. Surface concentration of thiocyanate versus electrode charge density for UPD thallium at silver. Conditions as in Figure 3.49. 154 4. Discussion The pzc estimate of -960 mV for underpotentially deposited thallium is the same as the value reported by Leikis for bulk thallium. 149 This agreement, together with the observation that the capacitance for UPD TllAg is influenced only marginally by further deposition of thallium, suggests that UPD Tl/Ag and bulk thallium surfaces possess similar chemical properties. The capacitance values obtained here are perhaps 25! lower than those found for bulk thallium. However, larger values are obtained if the silver electropolishing step is omitted in preparing the surfaces. This suggests that differences in surface roughness may well account for the differences ~. in capacitance between bulk and UPD thallium. The shift of the capacitance minimum potential in substituting fluoride by perchlorate is good evidence for specific adsorption of the latter. The ionic strength dependence of the capacitance points to the increasing influence of the diffuse layer as the electrolyte concen- tration is lowered. Evidently no data exist regarding anion adsorption at bulk thallium. There is one report concerning the electrocapillary properties of a 0.022 thallium + 99.982 gallium alloy in contact with 150 adsorbing electrolytes. Thallium.apparently is the major component 150 The of the electrode surface, despite its small bulk concentration. basic finding is that the alloy, in comparison to most other metals is able to adsorb halide ions only weakly. This is consistent with the findings for UPD thallium/silver. 155 5. 92mg. Clearly. underpotential deposition of thallium. alters the thermodynamic properties of the silver-aqueous interface. The differential double-layer capacitance is lowered and anion adsorption is diminished considerably. Such behavior is similar to that found with underpotential deposition of lead. Anion Adsorption 1. Introduction In order to examine the question of how the thermodynamics of anion adsorption are influenced by the composition of the electrode surface, results for silver, UPD lead/silver, UPD thallium/silver and mercury electrodes will be compared. Since the same substrate electrode is used for each of the solid surfaces, differences ascribable to electrode pretreatment, surface roughness and so forth should be eliminated. Although not part of the same series as the three other surfaces, mercury is included since data gathered at this electrode generally are trustworthy. 2. gesults and Discussion values of AG: and g atom - 0 are assembled in Table 3.5. the results for mercury were calculated in each case from data given in the 103,145,148,151-153 literature. Parsons’ surface concentration data for 145 thiocyanate adsorption at mercury from single electrolytes could not 156 .ouzaouuomam omen «Odomz.m_n.o .mea moomummmu ow mo>fiw sumo aouw noumasoamu a .omH mucouowmu ow oo>ww some some nonmasoamo .h .mu Houuomao moon mmz.m.ma.o « .HmH monouomou ow o>qw sumo aomm vmumasoamo : .mumaouuooam ammo memz 2 H w .Nma oommuouou ma mo>fiw sumo aoum mommasoamom .mumaomuomam omen mM_m.H o .mqa mommummmm ow oo>Hm zummz mom sumo aouu .uxou ma oomfiauso mm commawumm v .moH oomoummmu ma mo>fim_mumo aomm mommasoamu o .oumaouuomam omen «aflomz_m.a A .omuo: omasuomuo mamas: .ouzaouuooam omen mmz z m.om so“- ans 1 x.mme- 3.0Hm- ooN n om- com a“- lag m ao2 ems n.acq fi.a~m cam am 1 z . 1 s 111 -1- a.wos s.mmm1 owe can cos n mm 1 oau I I I . l H ace- «Hoe «.mos «.0oa oua mm as n mm 1 m 11- 11- 1-1 ex~auv oom aw- own m.om1 -moz 11- 11- o.no¢ u.n~oa1 cam om- mam om- 1H m m m m m ooq w ooa m cue w owe «mumpsomv< um>aam Nassau: m¢\om am: m<\Ha mm: m mmUMMufim Hmum>wm um mmoam< How w mmmumammmm mowuommmumH was Aa Hoe may ow< cowummomm< mo mmfiwmocm womb vmmvcmum .m.m manna 157 be fitted to a Frumkin isotherm. The difficulty most likely can be traced to changes in diffuse layer (i.e., 01- > F- 2 0. At silver the order is I- > NCS- > Br- > 010 N3- > 01- > F- > ClOu- 2 0. For most ions, adsorption is greatest at silver, followed by mercury, UPD lead/silver and finally, UPD thallium/silver. In order to understand these trends it is useful to consider each of the factors controlling the energetics of adsorption. These are: the partial desolvation of the anion upon adsorption, desolvation of the electrode at the adsorption site, and the bonding interaction between the anion and the metal surface.154’155 For adsorption of different anions at the same surface only the first and third factors will vary. Thble 3.6 lists values of "anion desolvation enthalpies" taken from Table l of reference 155. Inter- estingly, these follow the same order as the adsorption equilibria for anions at mercury, UPD thallium/silver and UPD lead/silver, suggesting that partial desolvation. of anions is of central importance. Evidently. ionrmetal bonding interactions at each of these electrodes are similar for different anions or else vary in exactly the same 158 Table 3.6 Enthalpies of Desolvation for Anions in Water8 1m; Sr 010 cf Taken from reference 155. 159 manner as the desolvation enthalpy. Since the ordering of adsorption strength is somewhat different at silver, variations in the anion- silver bond strength evidently must be significant, at least for perchlorate in comparison to the other anions. Surprisingly, there is little consensus concerning the nature of the bond between an ion and an electrode surface. Levine has con- sidered the adsorption bond to be little more than an image interaction 156 between the ionic charge and the metal. Vijh has tried to represent the anion adsorption process as the formation of surface compounds of 155 the type 11+ X-. However, this hardly seems reasonable when the electrode carries no charge. Barclay,157’158 159 as well as Conway, claim that adsorption is analogous to metal complex formation. Barclay, in particular, has elaborated on this idea and attempted to apply the nebulous Hard-Soft Acid-Base approach160 to adsorption. Although some success is claimed, one finds equally good agreement with experiment by ignoring completely the anion-electrode bond and focusing instead on ionic salvation. Trasatti dismisses both the Vijh and Barclay approaches on the grounds that they do not account for differences in the strength of adsorption as the electrode material is varied.154 unfortunately, the present results do not seem to provide many new clues concerning the merits of these different approaches to anion-electrode bonding. Trassatti has popularized the idea that differences in metal- solvent interactions are the chief factor contributing to differences 154 in the adsorption capabilities between various electrodes. The most "hydrophilic" surfaces are expected to adsorb ions only weakly, while 160 the less hydrophilic surfaces should induce stronger adsorption. Un- fortunately, Trassatti’s attempts at testing these ideas are flawed because he chose as a quantitative measure of adsorption the shift of the pzc in nonadsorbing electrolytes following the addition of 15" This measure is biased against the electrode-solution iodide. interfaces exhibiting large capacitance values since these will require large amounts of adsorbed charge in order to displace the pzc by a given amount. Similarly, the proposed correlation of the potential 154 shift with the magnitude of the inner-layer capacitance or its 154 is hardly useful since a correspondence is expected in reciprocal the absence of any sensitivity of adsorption strength to the electrode composition. A comparison of AG: and g values for anions at different metals should provide a more objective test than a comparison of shifts of zero-charge potentials. An accurate knowledge of at least the relative strengths of interaction of the solvent with different metals is required in order to evaluate these ideas. A measure of such interactions is given by the difference between the work function of a metal and the potential of zero charge of the same metal in contact with a nonadsorbing 133b’ 161 The two will differ on an absolute scale by the electrolyte. amount of the potential drop across the inner layer of solvent dipoles. This potential drop will be nonzero if the dipolar solvent molecules are preferentially oriented. A problem however is the lack of suf- ficiently accurate values of the work function for most metals. A more approximate approach to evaluating hydrophilicity is based on the notion that water molecules, if preferentially oriented, will 161 Table 3.7 Heats of Formation of Metal 8.1222222 Pb(c) + 1/2 02 (g)->Pb0(c) 2T1(c) + 112 02 (g)+T120(c) 238(1) + 1/2 02 (8)+3820(c) H8(1) + 1/2 02 (8)+380(c) 2A3(c) + 1/2 02 (g)+Ag20(c) a Taken from reference 165, pp. D45-47. Oxidesa 162 154,161 bind to an electrode via the oxygen end since metal surfaces 158 should behave as Lewis acids. If this is true (as seems to be the case) the enthalpy of metal oxide formation may provide an indication 161 of the affinity of a surface for water. A direct check of this hypothesis is possible by considering some recent work on the chemistry of oxygen-bound adducts of water with single metal atoms.162-164 From matrix isolation spectroscopy, Margrave and co-workers162 found that shifts of the v2 bending mode of water which accompany adduct formation with Group III‘A metal atoms are indeed paralleled by decreases in the heats of formation of HHOH compounds as well as the corresponding metal oxides. Also, v is shifted more for Tl---0&2 than for Pb---0H indi- 2 2 cating greater sigma bonding between water and thallium than between 162,163 water and lead. Silver and mercury have not been studied. 165 Although Table 3.7 lists AH; values for several metal oxides. comparisons are hampered because the oxide stoichiometry is not the same in every case, the overall indication is that oxygen affinity increases in the order: AgRh then from Equations 4.17 C>0; this is responsible for the inequality sign in Equation 4.15. Commonly, however, an equality sign is employed in Equations 4.15 and the frequency factors are presumed to be given by Equations 4.2 and 4.3. In view of the above discussion, it is deemed more appropriate to employ Equation 4.18 with A: and A: estimated using the encounter preequilibrium formulation [Equations 4.9 and 4.10] rather than Equation 4.15. Noticeably different numerical relationships between kg: and kl;x are predicted by Equations 4.15 and 4.18. In the limiting case where C * e I 0 (i.e. ZAGex e I AG ), using the typical numerical values Hm I 3 ex,h 200, Nmr 100, T 298K, r1) 7 x 10 cm, (Ere 5th 1 x 10 cm, Kel IK :1 I 1, yields from Equation 4.15 e 2 _ -5 h (kex) 8.5 x 10 kex (4.19) whereas from Equation 4.18 e 2 _ -3 h (kex) 2.5 x 10 kex (4.20) with kzx in cm s"1 and kg: in Mil 3.1. The common observation181 that e2 -4h (kex) < 10 he x therefore indicates that the inequality 188 Aczx,e> A0.5 62x,h is rather larger than previously suspected on the basis of the collisional formulation [Equation 4.19]. However, taking into account the likely magnitude of the inequality 2Ac:x,e> Asz’h by estimating C as in Equation 4.17s leads to very good agreement between Equation 4.18 and experimental rate data for a number of transition- metal couples.182 One recent discussion of the relationship between electrochemical and homogeneous rate constants also employs a preequilibrium model for the frequency factors. A relation was derived that is numerically the same as that conventionally obtained using the collisional treatment, resulting from an apparent identity of vn are with 2e. However, this numerical agreement is fortuitous, resulting from the assumptions are I -7 11 'I1.183 10 cm and “11 I 10 183 The latter choice was prompted by the presumption that Vn approximates the frequency of solvent reorienr tation when AG:s provides the major part of AG*. As noted above, typically v =V- " 1013 an1 even when AG* >AG? . n is os is 6. Qegparison Between _§e_Kieetics e; Correspendieg IEEQIZHEES Qeter-Sehere Pathweys Besides the inherent virtues of the preequilibrium model, it is clearly also applicable to inner-sphere electrode reactions since these involve the formation of a specifically adsorbed intermediate of well- defined structure, analogous to the binuclear "precursor complexes" formed with homogeneous inner-sphere pathways, it can be measured directly for reactions for which the precursor intermediates are sufficiently stable to be analytically detected. Thus K: I Pp/Cb, 189 where Pp is the concentration of the (adsorbed) precursor intermediate and Ch is the bulk reactant concentration.30 values of ket can there- fore be determined from kob and K: using Equation 4.5, or directly from the current required to reduce or oxidize a known concentration of adsorbed reactant.107 Since Equation 2.23 is expected to apply equally well to pre- cursor states involving surface-attached or unattached rectants, the comparison between corresponding values of ket for a given electrode reaction proceeding via inner- and outer-sphere pathways provides fun- damental information on the influence of reactant-surface binding upon the energetics of the elementary electronrtransfer step.30 We have made such a comparison for a number of reactions involving transition- metal complexes at both mercury and solid electrodes; the results are described in detail elsewhere.3°’109’184 In particular, it appears that the overall catalyses (i.e. larger values of kob) often observed for inner-sphere rections, especially at solid metal surfaces, are fre- quently influenced by larger values of KP brought about by surface at- tachment.109’184 In the context of the present discussion, it is ime portant to note that AG* for outer- as well as inner-sphere electron transfer should be estimated using Equations 4.5, 4.6 and 2.23 rather than the conventional use of Equations 4.1 and 4.9 assuming that An equals Ze [Equation 4.2]. 190 7. The Apparent Frequency Factor from the Temperature Dependence pf Electrochemical Kinetics In principle, direct information on the magnitude of the frequency factor for electrochemical reactions can be obtained from measurements of the dependence of electrochemical rate constants upon temperature. Despite the early seminal work of Randlessz’185 rela- tively few measurements of electrochemical Arrhenius parameters have been reported, at least under well-defined conditions. This is due in part to a widespread doubt as to their theoretical significance arising from an apparent ambiguity in how to control the electrical variable as the temperature is altered. The matter has recently been discussed in detail for mechanistically simple electrode processes involving both solution-phasess-55 and surface-attached reactants.186 (following section). Conventionally: k - 1’ exp(-AH#IRT) (4 21) corr ' where 411* and A’ are the activation enthalpy and apparent frequency factor, respectively, obtained from an Arrhenius plot. Two different types of activation enthalpies should be distinguished.53-55 The so- called "ideal" activation enthalpies AHzi are derived from the temr perature dependence of the rate constant measured at a constant metal- solution (Galvani) potential difference. So-called "real" activation enthalpies, AHzi are obtained from the temperature dependence of the standard rate constant; i.e., of the rate constant measured at the 191 standard potential at each temperature. The former approximate the actual enthalpic barrier at the electrode potential at which it is measured,53-55 whereas the latter equal the enthalpic barrier that remains in the absence of an enthalpic driving force, i.e. under “thermoneutral” conditionmsz’53 The frequency factor Ai obtained from AH: and kcorr will differ markedly from the "true“ frequency factor A.n [Equation 4.1] since Ai will contain a contribution from the entropic driving force.53-'55 ,4 However, the frequency factor Ar extracted from AH: and k is corr closely related to An since”-55 : 1‘ kcorr - Ar exp(”Liar/RT) 2‘ ,5 mtla) exp(-AHr/RT) (4.22) _ e e K elAueprSS ,1 where ASint is the "intrinsic“ activation entropy, i.e. the activation entrapy that remains after correction for the entropic driving force (see Section V.A). Providing that the outer-sphere transition state is formed in a sflmilar solvent environment to that experienced by the bulk reactant and product, (see Section V C), AS" will be close to zero int 1 186 (:10 J deg- mol-1), so that Ar=An providing that Ke e1 appropriate double-layer corrections upon the rate constants have been ~l and the made 0 Experimental values 0f Ar (or equivalently, apparent activation entropies obtained assuming a value of An) are not abundant, especially for conditions where the electrostatic double-layer corrections are 192 known with confidence. At metal-aqueous interfaces, it appears that A;<103 cm sec”1 for most transitionemetal redox couples.53-55’185’187 Since these values are closer to that predicted from the collisional than from the encounter preequilibrium formulation (vide supra) it might be argued that the former model is more appropriate. However, it seems likely that these disparities arise in part from a breakdown in ,1 the assumption ASint I 0 as a result of differences in the solvating environment at the electrode surface and in the bulk solution. Smaller (ca. 5- to lO-fold) values of Ar relative to An can also result for reactions having large inner-shell barriers since thenl.‘n and there- 23 In fore An will decrease significantly with increasing temperature. addition, the observation Ar<11) to the overall reorganization energy. This result is num- erically similar to the conventional frequency factor kT/h at ambient temperatures. The nuclear tunneling factor 1‘u in Equation 4.37 is close to unity for small values of ACE. Although Fn>l, it generally increases with decreasing temperature, thereby decreasing the measured values of * AH and hence yielding smaller apparent values of A3. However, the 208 effect is calculated to be negligible at ambient temperatures for . * -l 23 reactions where.AGi< 40 kJ mol . The only other contributor to Aa is the electron tunneling term K21, which is unity for an adiabatic reaction. Therefore any discre- pancies between experimental values of A.a and the corresponding cal- culated values ofvn may normally be attributed to a small value of 197,198 K21. Thus contrary to some recent statements, the observation that Aa<<1013 s"1 or, equivalently, of large negative activation 13 e _ entropies obtained from AHr a by assuming that Aa”lO s 1 (Equations 8 4.33 and 4.34) can be taken as evidence that Ke (<1. 1 Objections that the Marcus and other electronetransfer models based on "absolute reaction rate" theory do not apply to surface- attached reactants”7 are incorrect; no extra assumptions are made in applying contemporary theories to these reactions besides the choice of an appropriate statistical formalism for the frequency factor. In fact, redox processes involving surface-attached reactants are in some respects better model reactions for testing electron-transfer theories than are outer-sphere electrochemical reactions. Since the surface- attached reactant and product can be identified with the precursor and successor states, both the thermodynamics and kinetics of the elemen- tary electron-transfer step are susceptible to direct experimental determination. As noted above, this is strictly not the case for outer-sphere reactions, so that the intrinsic barrier Anint and fre- quency factor A801 can only be obtained from the experimental kinetics parameters by estimating the enthalpic and entropic work terms (Equations 4.24-4.27). 209 In addition, for outer-sphere reactions there is a substantial uncertainty regarding the theoretical formulation of A801 and its relation to the frequency factor for the elementary step. The con- ventional collisional model predicts a typical value of A80 of ~5 x l 103 cm {1.54 The alternative "preequilibrium" (Equation 4.27)54 describes the frequency factor as a product of an equilibrium constant KP for the formation of a precursor state from the bulk reactant, and a frequency on for solvent reorganization and bond vibrations as in Equation 4.8. Significantly larger values of A801, around 5 x 105 cm s-l, can be derived using this model.31’zoo’210 However. there is a significant uncertainty in RP and hence A801, arising from the lack of information on the effective thickness of the precursor state "reaction zone“ within which the reactant is required to reside so that electron tunneling can occur with sufficient probability to contribute to the reaction rate.200’210 (However, see Section V. C). These uncertainties regarding the theoretically expected values of A80 lead to diffi- 1 culties in separating out the various other contributions to the experimental frequency factors. Such difficulties are absent for reactions of surface-attached molecules. It is interesting to note that the advantages that are expected in the study of attached molecule reactions as compared to solution electrochemical reactions have close parallels in studies of homo- geneous electron transfer. Thus, rate data and activation parameters for intramolecular electron-transfer reactions in ridgid binuclear complexes are more easily interpreted than are the corresponding re- 205 sults for the usual second order outer-sphere reactions. The 210 problems associated with the choice of an appropriate theoretical formalism for the frequency factor, and the uncertainties in the work term correct ions206 are absent for intramolecular reactions. The treatment of electron transfer between an attached reactant and an electrode surface contains closely analogous advantages and can usefully be perceived as a heterogeneous "intramolecular" reaction.199’200 Studies of electron-transfer kinetics between surface-bound molecules and electrodes as a function of temperature are as yet uncommon.l%’197’198’204’2n Brown and Anson have determined that A8 I 106 s."1 for the reduction of 9,10-phenanthrenequinone at graphite.196 However, this reaction involves a proton-transfer step preceding electron transfer which precludes extraction of the true frequency factor As in the absence of thermodynamic data for the former equi- librium. Sharp and coworkers have obtained some interesting results for the ferrocene/ferricinium couple bound to a platinum elec- 197 , 198 trode values of k: for this couple were reported as a function of temperature in acetonitrile and sulpholane. The frequency factor Aa was reported to be 3x108 s"1 in acetonitrile197 and 2x108 s“1 in 198 v: sulpholane. Assuming that the inner-shell reorganization AGi comprises about 52 of the total reorganization energy,197 and vin and Vout are"’1013 s-1 and ”2xlOn s-l, respectively, vn is estimated to be -1 about 2xlOlz s . From the usual dielectric continuum expression neglecting the influence of the reactant-electrode image interactions54 and using literature values of the optical and static dielectric .. v: constants and their temperature derivatives207 209 Asin is calculated 1'. 211 1 -1 to be -12 J deg- mol"1 in acetonitrile and -7 J deg"1 mol in sulpholane. From these values of A8 and Vn using Equations 4.34 and 4.37, estimates of Kel of about 6x10-4 in acetonitrile and 2xlO-4 in sulpholane are obtained, indicating that the electronItransfer reaction is moderately nonadiabatic under these conditions. C. _A_p_ Experimental Estimate 9; the Electron-Tunnelipg Distance for Some Outer-Sphere Electrochemical Reactions (Accepted for publication in J . Phys. Chem.) 1. Introduction An important question in the treatment of electron-transfer reactions concerns the magnitude of the frequency factor, A, in the expression kob - A exp(-Wp/RT) exp(-AG:t/RT) (4.38) where kob is the observed rate constant, WP is the work required to bring the reactants together (or the reactant to the electrode surface), and AG; is the free-energy barrier for the elementary electron-transfer step. Although sophisticated theoretical methods have been developed for evaluating A92: from structural and thermo- dynamic information, there remains considerable uncertainty as to the numerical values of the frequency factor for outer-sphere pathways.9’10914:15:17.23,28,213 212 In the recent literature it has been emphasized that outer- as well as inner-sphere redox reactions in homogeneous solution and at electrode surfaces can usually be viewed as involving formation of a reactive precursor complex from initially separated reactants followed by the rate-determining transfer 9.10.14.15.17,1s,23,2s,3o,31,213,214 step. Thus the observed rate constant can be formulated as k - K k (4.5) ob p et where KP is the equilibrium constant for forming the precursor state and ket is the rate constant describing the elementary electron- transfer step. When applied to outer-sphere pathways, this approach can be termed an "encounter preequilibrium" treatment. It views the reaction as taking place via the unimolecular activation of a weakly interacting reactant pair having a suitably close proximity and geo- metrical configuration to enable electron transfer to occur once the apprOpriate nonequilibrium nuclear configuration has been schieved.17’23’211‘213 According to the encounter-preequilibrium treatment, the frequency factor can be expressed 8823,211,213 A - VnPnKelxo (4.39) where Vn is the nuclear tunneling factor, In is the effective frequency for activating nuclear reorganization modes,I<::1 is the electronic 213 transmission coefficient at the distance of closest approach of the reactants and K0 is the statistical part of the precursor stability constant KP where KP I Koexp(-Wp/RT) (4.40) For electrochemical reactions the statistical factor K: can be . 211' expressed simply as I ére (4.41) where ore is the thickness of a "reaction zone" beyond the plane of closest approach within which the reactant must reside in order to contribute significantly to the overall reaction rate. The value of are is determined by the need for the reactant and surface to be in sufficiently close proximity to achieve significant overlap of donor and acceptor orbitals, and hence nonzero values of the transmission coefficient Ke1 for a given reactant orientation (vide infra). The composite term KZIX: (tczldre) appearing in Equation 4.39 for electro- chemical reactions can therefore be considered to be an "effective 0 reaction zone thickness". If Ke1<1, the reaction is termed "nonadiabatic", whereas "adiabatic" processes are those for which K21 ~l. Since the magnitude of Gre is determined by the dependence of Kel upon the donor-acceptor separation distance, markedly smaller values of K21 Are are anticipated for the former compared to the latter 0 processes as a result of smaller values of Gre as well as Kel. 214 The statistical factor for homogeneous reactions, K2, is more complex than 1: yet entirely analogous, corresponding to the pro- bability of finding one reactant within a reaction zone of thickness 6rh beyond the bimolecular contact distance. This term can be estimated approximately from9,15,17,213 2 h _ 3 K0 41:11:11 Grh/lO (4.42) where N is the Avogadro number, and rh is the distance between the reacting centers when in contact. Recent 5p initio calculations for some homogeneous outer-sphere 14,15,17,215 reactions indicate that Ke1 can be substantially below unity even at a relatively small internuclear separation rh, decreasing sharply with increasing r. This corresponds to relatively small values 9,213 of K21 6th (<18, vide infra). It would be extremely desirable to obtain an experimental measure of such quantities. In the approach decribed here, estimates of K‘e’ldre for several outer-sphere electro- chemical processes are obtained by a relatively direct method involving the comparison of rate constants for these pathways with those for structurally related electrochemical reactions occuring via geometri- cally well-defined ligand-bridged transition states. The results provide evidence that heterogeneous, as well as homogeneous, electron- transfer processes can be significantly nonadiabatic. 215 2- 9221M The virtue of comparing rate parameters for corresponding electrochemical reactions occuring via outer- and inner-sphere (ligand- bridged) pathways can be seen by noting that in contrast to the former, unimolecular rate constants for the electron-transfer step involving a ligand-bridged precursor state, kiss-'1), can often be determined directly from the overall rate constant, k::, using Equation 4.5 since where Pp is the precursor state concentration (mole cmfz) corresponding to a given bulk reactant concentration Cb. The values of k:: can be expressed as kis - I‘ is _ * et nvurel exp( AGet/RT) (4.44) where K:: is the electronic transmission coefficient for the ligand- bridged reaction pathway. In view of Equations 4.38-4.41 the work- corrected rate constant for the corresponding outer-sphere electro- chemical pathway, k08 corr’ can be expressed as * corr n a el re exp('AGet/RT) (4.45) * Provided that AGét, Tu, and Vn are unaffected by surface attachment at a given electrode potential (vide infra), evaluation of the rate 216 . as is . o . 6 ratios kcorr/ket enable estimates ofI .maaaou unoomhom a“ ooumaa .m .Howucouom ooouuooao um ooumoaona hasnuoe no no we mmwsoaaom moauomon ooouuooao HHouo>o now unnumnoo moon oo>uomoo a monsoon omoznmlnouno a mo “monsoon Aoowowuolomowwav muonemlnomcw n mH 6 fi x x x . 1 m m m N u mOH N NuOH N- euoH N H oNN H +Nz A see u m N N um um m H moH H euoH q- muoH e oNN H +Nmoz A ace 0 n N . l . um um m0 .H m o H o- ouoH N ouoH 0 com +Na H see u ouoH x n.m euoH x 0.4 moN mo NemmHNzovcu o N an . an . .H . oIOH n N ouoH m N nae mo +mH moo u oH- oH x H- oH x H ooo mH n- e- n- m m um um m0 .H NuoH o ouoH m com +NHo H mzv o 1 H- OH x m oH z m- coo mH N. N. m m m I ma an m0 H oH m NIOH H NuoH e coo +Nz H zzv o . m.o m.oH x N mICH x H coo mH +NmozmHmmzvhu Him So In 30 In 50 wow m> .>:— as «when am a wuoo Hno mu moanumm unouooom «HaH mos me e was a o e o a o .uonu um ooomuouna mooono oeueHH Boom oenHeuoo .euefioeauouna oomofinnlonewwa wnH>Ho>nH noun nomenenunnouuoeae How uneuenoo eueu ueanooaofianae .cm eonenoweu Scum nexeu mmq.¢ nOfiuenom Scum oonwaueuoo .eueue noennoenn euonneluennw one you uneuenou mafiafioeum o .Aeaaeueo How cam one mm eeev onean nowuueen one umnmewuneuon ewene>e one me one one .uonnnn owneso uneuoeou one ea N opens .Hnueam.oINanne man a ewe wnHen pox mo enHe> wnHononmeuuoo Scum oenfianouon .mesnuen onennmlueuno now oneuenoo eueu oeuoounoouxnoso 219 this supports the validity of the former estimate in view of the closely similar coordination properties of -N; and -ncs‘.3° Each of the five Cr(III) aquo reactants in Table 4.1 undergoes electro-reduction via sufficiently rate-dominating outer- or inner- sphere pathways so that only kg; or k:: can be evaluated for each reac- tant. Nevertheless, an approximate estimate of kzgrr/kiz for these structurally related rections can still be obtained as follows. As noted previously by Weaver.73 the values of kg“ for Cr(0H2)3+, Cr(OHz)SSOz, and Cr(OHz)5F2+ reduction are closely similar when eval- uated at their respective formal potentials. This indicates that the intrinsic electronrtransfer barrier is approximately independent of the nature of the sixth ligand, even though the coordinating pro- perties of 0B2, 80:. and F- differ widely. These values of kgzrr’ listed in Table 4.1, are therefore also likely to be close to those for Cr(0H2)5NCSZ+/+ and Cr(OH2)5N§+/+ which cannot be measured but for which the corresponding values of k:: are known, enabling the desired estimate of k08 lk18 to be obtained (Table 4.1). corr et 3. Discussion Inspection of Table 4.1 shows that the resulting values of k08 lkls for Cr(III) aquo reduction, ca. 0.2 g, are ca. 10-30 fold corr et smaller than those for the Cr(III) ammine reductions, ca. 5 X. Quan- titative interpretation of these results can be made by referring to Equations 4.44 and 4.45. Of the various terms,1‘n andvn will almost certainly have the same values for the corresponding inner- and outer- sphere pathways. Thus \51 is determined chiefly by the metal-ligand 220 stretching frequencies211 and Fu is usually close to unity, being dependent upon the magnitude of AG:t rather than the transition-state geometry. The reorganization energy AG:t may differ significantly for corresponding inner- and outer-sphere pathways, arising both from differnces in the inner-shell (metal-ligand) and outer-shell (solvent) reorganization terms. Ligand bridging may yield some decreases in the inner-shell component of AG:t arising from the influence of surface attachment on the Cr(III)-ligand bonding. However. there is scant evi- dence for such catalyses with Cr(III)/(II) and Co(III)/(II) electrode rections, even at surfaces such as platinum and gold that bind inor- ganic ligand bridges much more strongly than does mercury.218 Surface attachment may yield an alteration in the outer-shell component of AG:t since this is predicted to diminish as the distance between the redox center and the surface decreases, as a result of greater image stabilization of the transition state.13 With the azide and isothiocyanato bridges, the redox center is estimated to lie about 5-6 3 from the surfce.219 Provided that the outer-sphere transition state is formed with the reactant in contact with a monolayer of inner- 1ayer water molecules (pige_;p§pe), the redox center will be about 6.5 8 from the surface, based on a reactant crystallographic radius of 3.5 X and a water molecule diameter of 3 3.216 0n the basis of the well- * known relation for the outer-shell component of AGet due to 13,220 kos Marcus, corr is predicted to increase by only ca. 50: upon decreasing the reactant-electrode separation from 7 to 6 8, and by only ca 3-fold from 7 to 5 X. It therefore appears likely that AG:t only differs to a small extent between corresponding outer- and inner-sphere 221 pathways involving thiocyanate or azide bridges. The similar values of as is 2+ 2+ . corr/ket seen for Cr(NH3)SCl and Cr(NH3)5N3 reduction (Table 4.1), even though the Cr(III) - surface distance is expected to be ca. 2 X smaller for the former reaction, lends support to this assertion. To a first approximation, then, from Equations 4.44 and 4.45 the s lkis rate ratios ko corr et for the present system can be related to the effective reaction zone thickness for the outer-sphere pathways, 0 . Ke16re, simply by kos mistK o is corr et el S‘s/“.1 (4°46) Since the ligand bridge should facilitate overlap between the surface donor and Cr(III) acceptor orbitals it is anticipated that the inner- sphere pathways are adiabatic, i.e. K18*1, If indeed K19 ~ e1 e1 1, then the values of kzzrr/kéz, ca 5 X and 0.2 X, can be identified directly with the effective reaction zone thickness K215re for the ammine and aquo ::0 12K: - 1. o Ke1 1 Figure 4.2 is a schematic representation of the dependence oftcel upon r. The magnitude of K215te will equal the area under the curve bounded by the distance of closest approach, for example the shaded area ATA"C. Taking <1=la6 2&1. it follows that K: ore (0.5 8 if K: 1 1 <1. whereas Ko 6r > 0.5 X if K0 =1. The above estimate of K0 5r for e1 e e1 e1 e the Cr(III) aquo reactions, ca 0.1 - 0.3 8. therefore suggests that K21 < l at the plane of closest approach for the aquo cations, so that x=0. However, this estimate of Kzldre may be ca 1.5 to 2-fold too small as a result of the likely differences in Aczt between the inner- and outer- sphere pathways noted above, although it may be too large if Ki: Sr is the e < 1. Another factor which would decrease the apparent value of K21 224 e do .muneuueon sense now be On :mmononzu econ noHoueou o>Huoouue: may no eon~e> unHononeoquu can oceeonneu meeue oo:uuesnee0nu one oeoese e;h .aHo>Huuonmon .euceuoeou .osoe one on—ee Auuuvuu new announce amino—u mo menene ocuenHuHune anemonnen ..n.n one ..<.< .u ooceuoHo :oHuenenom soomuueuonuneuoeon een awe—ewe noHuueon Heuuaonu Ho neuuueHe omoxemlnouno an new a uneququuoou nadmmqlenemu ounOuuUOHo we moan uHueEogum .~.c omnmum b 119.?! I .. 3.23.2: I I 225 possibility that a specific reactant orientation is required either to enable the reactant to approach the electrode more closely or to pro vide more effective coupling of the surface donor and Cr(III) acceptor orbitals. Such factors have recently been considered in detail for 14.15.17.215 In any case, we conclude that Fe(OH2)2+/2+ self exchange. outer-sphere electron transfer involving the Cr(III) aquo reactants only approaches adiabaticity for electron-tunneling distances very close to the plane of closest approach of these cations (represented by 853" in Figure 4.2), around 6-7 X from the electrode surface. On the other hand, the estimate of K215 re for the Cr(III) ammines, ca 5 2, suggests that electron transfer to these reactants remains adiabatic even for reaction sites several Angstroms from the plane of closest approach (represented by AIA" in Figure 4.2). The exact value of Keglfire for the amine reactants is in one respect subject to greater uncertainty than for the aquo reactants in that the magnitude of the work-team ("double-layer”) correction upon k.ob is somewhat greater for the former.216 Moreover, the work-term correction employed assumes that the reaction occurs only at the outer Helmholtz plane (oHp), whereas the large value of Kzlére suggests that the effec- tive reaction zone is relatively thick. Given that the ammine reac- tants can probably penetrate inside the oHp, this work-term correction may well be an underestimate, so that kgzrr and hence K21 are actually smaller than the present values. Given that the aquo reactants are marginally adiabatic at their plane of closest approach, from the reaction site differences noted above it would be expected that ~2 X for the ammines, yielding K215re ~2-3 3. One factor which may enhance 226 Kzldre for the ammine versus the aquo complexes is the likely greater ligand character of the acceptor orbital on the former reactants,15’215 leading to greater electrode-reactant orbital overlap at a given electrode-reactant separation distance. The difference in the effec- tive reaction zone thickness between the aquo and ammine reactants is therefore roughly compatible with the likely differences in the reac- tion sites if the dependence of Ke1 upon the surface-reactant separa- tion is similar for these reactants, with Ke1 decreasing below unity for surface-reactant separations greater than ca. 6 3. Taking I‘n I 2.5 and “n I 1.2 x 1013 s"1 for the present reactions223 it is deduced from Equations 4.39 and 4.41 that the 4 1 overall frequency factor A is ca. 6 x 10 and 1.5 x 106 cm.s- for the aquo and amine reactants, respectively. Both these values are 3 -l somewhat larger than the frequency factor, ca. 5 x 10 cm s , derived from the conventional collisional model assuming adiabatic 54’211 It should be noted that the encounter preequilibrium behavior. treatment employed here represents a departure from the collisional model since the latter views the reaction as being consumated only by collisions between the reactant and the electrode surface (or a coreactant).211 It is of interest to compare the above estimate of A for the Cr(III) aquo reactants with that obtained for Cr(OHz):+ reduction under the same conditions from the temperature dependence of k2: . We can rr write54 08 - * * kcorr A exp(ASi/R) exp(-AHi/RT) (4.48) 227 * a . . where ASi and AHi are the work-corrected "ideal" entropies and * enthalpies of activation which form the components of Acet at the particular electrode potential at which kon is obtained.54’228 corr The * activation enthalpy AHi can be obtained directly from the Arrhenius slope of In “23:: versus (l/T), being measured at a constant electode potential using a nonisothermal cell arrangement.54 53.54 The value of As: can be obtained from + AS. (1.19) where<1corr is the work-corrected transfer coefficient,As:c is the so- 55 * called reaction entropy of the redox couple concerned, and ASin is I: the intrinsic activation entropy.225 From the data given in reference 54. at -800 mV vs. sce, k°a I 5.5 x 10"5 cm s.1 (25°C), AH: I 17.5 corr -l 226 . o . -l -l kcal. mol , corr 0.50. ASrc 49 cal. deg mol 3.5 cal. deg.1 mol-1.225 d 13* ’ an int Inserting these data into Equations 4.49 and 1.19 yields A I 9 x 103 cm.s-l. (This calculation cannot be performed for Cr(III) ammine reductions since the As:c values are not known with sufficient accuracy.) The ca 7-fold discrepancy between this and the above estimate of A probably arises in part from the very approximate nature of Equation 1.19. This relation presumes that the transition-state entropy is unaffected by the proximity of the reacting ions to the electrode surface, whereas it is likely that as: and AH: are much more sensitive . . * . . than is the overall barrierAGe to the solvating environment at the 1: interface and in the bulk solution. Indeed, it is found that the acti- 228 vation parameters for these and other reactions are rather more sensi- k0 I corr tive than is to the nature of the electrode material, surpris- ingly small frequency factors being typically obtained at solid metal 136,187 surfaces (see section IV.D). (“9.0mm The foregoing treatment provides a relatively direct, albeit very approximate, experimental method for evaluating the effective electron? tunneling distances for outer-sphere electrochemical reactions. It exploits both the close relationship between the energetics of corres- ponding inner- and other-sphere electrode reactions and the information that can be derivedzm’221 on the reactant-electrode separation dis- tance from the magnitude of the double-layer effects in electrochemical kinetics. A strictly analogous approach cannot be employed for homo- geneous processes due to the inevitable changes in reactant coordina- tion between otherwise related inner- and other-sphere pathways and the lack of a means for subtly altering the electrostatic interactions between ionic reactants in solution. Although it would not be surprising if similar differences in the internuclear distances and hence K: 6; also arise between aquo and l ammine complexes in homogeneous electron-transfer reactions, the sol- vating environments may be sufficiently different to that pertaining to 227 the present electrochemical reactions to bring other factors to the fore. Indeed, the larger rate ratios for Co(III) ammine versus aquo reactants observed at mercury electrodes relative to that obtained with 220 a given reductant in homogeneous solution suggest that these differ- 229 ences in K215r may well be smaller in the latter environment. Never- theless, the present finding that outer-sphere electrochemical reac- tions can be at least marginally non-adiabatic bears a close resem- blance to the interpretation of some anion catalytic effects upon homogeneous outer-sphere reactions between cationic complexes225 as well as to the results of the recent pp M calculations noted above. 14, 15.17 ,215 Similar calculations have yet to be performed for electron-transfer processes at metal surfaces. They would provide an invaluable guide to the further interpretation of the experimental data. The present results therefore are at variance with a previous suggestion that the effective electronetunneling probabilities should be much larger at metal surfaces due to the multitude of electronic energy states in the vicinity of the Fermi level that are available for coupling with the reactant orbitals.231’232 Further support to the present findings is given by the observations of Weaver and Li that both the unimolecular rate constants and frequency factors for the electro-reduction of pentaamminecobalt(III) bound to a mercury surface via organic bridges are decreased markedly upon interruption of bond 200 '2 18 ,233 These observations conjugation in the bridging ligand. serve to highlight the previously neglected role of nonadiabatic electron tunneling in influencing electron-transfer reactivity at electrode surfaces as well as in homogeneous solution. 230 D. The Influence of the Electrode Surface Copppsition pp Redox Reactien Pathways and Electrochemical Kinetics 1. Introduction .A key question in the study of electronrtransfer reactions at electrodes concerns the role of the metal surface composition in deter- mining the kinetics of such processes. A useful method of varying the surface composition in order to address this question is to utilize the underpotential deposition phenomenon. Thus, redox reaction kinetics at UPD lead/silver and UPD thallium/silver electrode surfaces are examined here and are compared with the kinetics of corresponding reactions at silver and mercury surfaces. The purposes of this study are first to establish the reaction pathways, either inner- or outer-sphere, for the reduction of several metal complexes at different surfaces, and second, to uncover any "electrode-specific" factors controlling electron- transfer reactivity. A number of previous studies have examined the influences of the electrode material on the kinetics of outer-sphere redox reac- 109,111 tions. For the most part, reactivity differences have been traced to differences in electrostatic double-layer effectsl’s'm’239 (i.e. "¢2 effects") at various electrodes. Nevertheless, in several cases more complicated behavior has been uncovered.uo’136 This study is somewhat more general in that the reductions of a number of metal complexes potentially capable of following inner-sphere (ligand- bridged) pathways are also scrutinized. In order to compare the energetics of inner- and outer-sphere reactions on a common basis 231 considerable use is made of the encounter pre-equilibrium model proposed in Section IV. A. This model provides a means of separating enviromental factors, defined here as any factors affecting the relative interfacial concentration of the reactant, from additional elements contributing to reactivity. For a number of reasons one-electron reductions of chromium(III) amine and aquo complexes were selected for study. First, these reactions occur over a suitably negative potential range. (The UPD Tl/Ag surface is unstable at potentials positive of circa. -950 mV versus a.c.e.). Secondly, such complexes are substitutionally inert in the oxidized state. Therefore the ligand composition of each reactant in the transition state is known with certainty. Finally. such reactions have already been investigated extensively at. ailver85.130.199,204 30,54,216,240 and mercury electrodes. 2. Results and Discussipn 8- MW It is desired to separate environmental factors from other fac- tors influencing reactivity. 'Hhis is conveniently accomplished (in principle) by separating the observed electron-transfer rate constant k into a precursor formation constant KP containing the terms relating to the relative interfacial concentration of the reactant, and a first- order rate constant ket for the elementary step. For inner-sphere reactions KP can be expressed as a formal equilibrimm constant for reactant adsorption, such that: 232 KP I I‘ICb (4.43 ) where rand Cb are the surface and bulk concentrations of the reactant, respectively. For outer-sphere reactions we have written (cf. Equation 4.40): KP - 5r exp (-wp/sr) (4.50) where Sr is the reaction zone thickness and the work term Wp equals, in the simplest case, “2. The magnitude of 5r is determined by electron-tunneling considerations. We have been able to deduce from experimental data that the values of 5r at the mercury-aqueous interface are approximately 2 x 10.9 cm for chromium aquo couples and 5 x 10-8 cm for chromium ammine couples (Section IV. C). In lieu of additional infomtion, these values will be employed for other electrode-solution interfaces as well. It will be expedient in the discussion to follow, to consider outer-sphere reactions and inner- sphere (or potentially inner-sphere) reactions separately. b. ,Beduction Kinetics p£_Cogplexes Containipg Potential Bridggpg Ligands In order to minimize electrostatic work terms the apparent rate constants reported in this section and the next were obtained in weakly adsorbing electrolyte solutions of high ionic strength [either 0.5 M NaClO4 or 0.04 M La(0104)3]. Reactant concentrations typically were 1 m!. In order to avoid decomposition of the aquo complexes and precip- 233 itation of Cr(II), the electrolyte solutions were made moderately acidic (pH 2 2.5). At the UPD metal surfaces, rate constants were measured by using pulsed rotating disk voltammetry as outlined in Chapter II. uncertainties in the rate constants amount to a factor of 2 to 3, which is typical of what can be achieved at solid metal elec- 85.92.109.136 trodes. (The reproducibility is considerably greater for consecutive rate measurements within a given experiment). Apparent rate constants for reactions at silver and mercury surfaces were extracted from previous reports from this laboratory. For a number of reactions at these two surfaces, Guyer and Weaver199 have also reported directly measured values (fast cyclic voltammetry method) of ket’ For several reactions at silver. mercury, UPD lead/silver and UPD thallium/silver. apparent rate constants at I700 mV versus a.c.e. are assembled in Table 4.2. This potential was selected in order to mini- mize the extrapolations which are necessary in order to compare rate data obtained at different surfaces. Rate constants for Cr(NH3)SCl2+ reduction at silver85 and at UPD lead/silver are plotted against elec- trode potential in Figure 4.3. Relative reactivities are compared for reactions at silver85 versus the UPD metal surfaces (Figure 4.4) by plotting log k values (at -700 mV) at one surface against those ob- tained at another. The results given in Table 4.2 as well as Figures 4.3 and 4.4 indicate that underpotential deposition of either thallium or lead causes a remarkable decrease in electron-transfer reactivity at the silver-aqueous interface. Rates at UPD Pb/Ag and UPD Tl/Ag are also lower than those found at mercury. All seven reactions are known to 234 .mm eoneueweu Boom nexeu eueoe smnHmmzvno X . um . 1 m oH e H NuoH m e N +N OHxN one.o N- HomHOvano a- m- . +N . onm ona OHxN.m OHxN.N HumHmmzvho n- e- m. H- +N m m N on N . K H m.oH N e-oH o H NuoH m +Nz.Ho we 0 onm onm onm.e onN- mzmHmmzvuo N- on on m: +N m N on . an . N H euoH m N m.eH m m naeH N +Nmoz Ho me o m m e no x Ba x m Ba x m Bo x u H- euoH e e-OH m H- mL: 0 H- maoH N +Nmoz A mzv o aaHHHaeu an: emoH an: «museum: asu>HHm uamuummm .>a 8N- a m .2533 253:5 Hefiuneuom wnfinfieunoo mexeanaoo mo nowuunoem ecu mom maneumnou euem unopenn< .N.q eHoeH 235 l l I 1' l / -1 ._ / q / / ’2 "' UPD lead “ v‘hfl MI 8"”! .8 3 -3 I. d ./ / / _‘ 1 l I l l -600 -800 INIX) Figure 4.3. Log of apparent rate constant for Cr(NH3)SCl2+ versus electrode potential at UPD lead/silver and at silver. 236 i *T Tv T I ] E .2 7.? -o — n '5 0 CL :1 r _ h. (D '3 2 -2 II- — E 3 7. 3 - .- . x 2 s g C - ”4 _ .- 4 C - 5 ._ I O - 3 e , ‘0 I 5 _6 l l l l L l -s -4 -2 0 log k at silver Figure 4.4 Log of apparent rate constant at UPD lead/silver or UPD thallium/silver versus log of apparent rate constant at silver. Key 2+ 2+ 2+ . ; (2) Cr(H20)5NCS ; (3) Cr(NH3)SN3 , 2+ 2+ to reactants: (1) Cr(NH3)5NCS 2+ 2+ (4) Cr(H20)5N3 ; (5) Cr(NHa)SC1 ; (6) Cr(H20)SC1 ; (7) Cr(NH3)SBr 237 follow inner-sphere reduction pathways at mercury and silver. Gener- ally inner-sphere pathways yield larger rate constants than the corresponding outer-sphere routes since KP values for the former are larger. It is reasonable to suppose that the relatively slow rates at the UPD metal surfaces might be due to a change of mechanism from inner- to outer-sphere or due to decreases in Kp values for inner- sphere routes in comparison to those at mercury and silver. A number of tactics were used in attempting to establish whether and to what extent adsorbed precursor complexes are involved in reac- tions at underpotentially deposited lead and thallium. The problem is made difficult because precursor adsorption, if it occurs at all, should be fairly weak at the UPD metal surfaces and therefore difficult to detect. A fairly indirect approach for detecting adsorbed reactants involves monitoring rate responses to systematic alterations in double- layer structure caused by the adsorption of iodide anions.73‘216’241'242 Rates of outer-sphere reactions involving cations are expected to be accelerated following the addition of iodide since the total charge at the electrode surface will be made more negative and work terms will become more favorable. 0n the other hand, inner-sphere reactions involving anionic bridging ligands are decelerated, at least at mercury and silver, evidently because of unfavorable Coulombic interactions between the incoming ligand and adsorbed anions.73 Table 4.3 summarizes the rate responses at I800 mV for several reactions at UPD Pb/Ag following the addition of 30 m! I-. Also included are semi-quantitative estimates of the rate increases expected for bona fide outer-sphere reactions. These estimates were 238 Table 4.3. Effects of Iodide Addition on Rate Constants at UPD Lead/Silver Alog k-BOO (calculated -800 assuming Alog k (observed outer-sphere Reactant after adding iodide) reactivity) 2+a C’(32°)5C1 0.69 0.31 Cr(NH3)5c12+a 0.42 0.28 Cr(NH ) Br2+a 0.4 0.29 3 5 2+b Cr(H20)5N3 0.43 0.24 Cr(H20)5NCSZ+a 0.32 0.30 Cr(NH ) NCSZ+C 0.50 ---- 3 5 3+3 Cr(NH3)5H20 0.47 0.45 Cr(H20)2+a 0.64 0.47 a. Initial electrolyte: 0.5M NaClOA; final electrolyte: 0.47M NaClO4 + 0.035 NaI. b. Initial electrolyte: 0.5M NaClO 0.49M NaClO4 + 0.01 M NaI. c. Initial electrolyte: 0.2M NaClO 0.17M NaClO4 + 0.03 e NaI. 4; final electrolyte: 4;fina1 electrolyte: 239 obtained by estimating the surface concentrations of specifically adsorbed iodide and perchlorate ions as well as the electrode charge from capacitance measurements, combining these to calculate the difference in 02 values (Equation 1.11) between perchlorate plus iodide and pure perchlorate electrolytes, and then inserting this difference into the Frumkin equation (1.16) together with the appropriate values of o and z. (Estimated values of 02 in various electrolytes are plotted against electrode potential in Figure 4.5). Table 4.3 indicates that the addition of iodide causes an increase in reduction rate for potentially inner-sphere reactants as well as for reactants 4. such as Cr(NH3)5H203 which lack obvious bridging ligands. At UPD thallium/silver. rate constants for Cr(NH3)5NCSZ+ and Cr(NH3)SCl2+ reduction are also increased by iodide. Such results suggest that each reaction listed in Table 4.3 follows an outer-sphere mechanism. Nevertheless, a certain ambiguity remains concerning this mechanism diagnosis since the overall rates of weakly inner-sphere reactions may still be accelerated by adsorbed anions if the competing outer-sphere route is sufficiently influenced by alterations to the double layer structure to become the predominant reaction pathway.216 A safe conclusion would be that these reactions are at least not strongly inner-sphere processes. A second approach, used previously for reactions at mercury.30 employs free anions as models for ligand-induced complex ion adsorp- tion. Values of Kp for five anions at silver. UPD thallium/silver and UPD lead/silver are listed in Table 4.4. These were calculated from adsorption data given in Chapter III. 0n the basis of these results, 240 E. mV vs. see Figure 4.5. Diffuse layer potential at UPD lead/silver. Electrolytes: (c) 0.4711'tla0104 + 0.03fllNaI. 62 versus electrode potential (a) 0.5§_NaF; (b) 0.5!.NaC106; I l l I I o - a .. / _20 _. 4 -40 y— -‘ '60 l 1 l l -800 -1200 4600 241 .mz .Ho .Imuz .IH .Inm .IHU u x .xez mHood + nez magic on" meuhHouuoeHe mo nOHuHmonaou .o I s I .Imz no Imoz .IH .Ium .IHo I x .xez zHoo.o + OHoez zmmo.o eH eeuHHouuooHe mo nOHuHeonaoo .eequenuo oeuon emoHn: .e . m N . um . N . N . mIoH N N oIOH e H eIoH e H noIOH m N I z an an N . I an . mIoH HA oIoH o mIoH m H nIOH N H Imoz x .l x O x )- x o H mIOH H mIOH o N mIOH H mIoH m H I x n n . x . Hm mIOH N oIOH N 1HIOH m m oIoH N H I an x . Ba x Eu x . Eu x I Ho nIoH m H NIoH n «IoH m H NIoH H I n n n n mHNo>HHmV e anaHHHmeu ciao e «Huo>HHmv e «HemmH case M aoHa< >8 onml >a ooml neuemueunH enoeno< \eoonuoeHm oHHom ue nOHunnomo< nown< now euneuenoo anHHoHHHnom Heauom .q.e eHoeH 242 differences of circa. 102 would be expected between apparent rate constants at silver compared to UPD metal electrodes. Values of ket were calculated for reactions at the latter surfaces by assuming that Kp (complex) equals Kp (anion). These ket values are listed in Table 4.5 together with values for reactions at mercury and silver. (Values of ket at I700 mV at UPD thallium/silver were estimated by estimating Kp (anion) and ket at several potentials negative of I950 mV and extrapolating to I700 mV). It is clear that Kp values estimated in this manner can account partially for the disparities in apparent rate constants between various electrodes. Nevertheless, some differences remain. Evidently, there are additional factors beyond environmental effects or else the magnitudes of the Kp (complex) values have been systematically overestimated. The latter explanation is a distinct possibility, especially for the ammine complexes, in view of Weaver’s 30 findings at mercury. Particularly at potentials as far negative as -700 mV values 0f KP (anion) probably represent, at best, only upper limits for Kp (complex) .30 An alternative assumption is that each complex reacts via an outer-sphere route at the UPD metal electrodes. Values of ket estimated according to this assumption are also listed in Table 4.5. For reactions at UPD lead/silver the estimated ket values agree quite closely (within a factor of five or less) with those found at mercury. The single exception is the reduction of Cr(H20)5NCS2+ for which the estimated ket value at UPD Pb/Ag exceeds that at mercury by a factor of twenty. In view of the close agreement for the others, this represents reasonable evidence for the existence of a ndldly catalytic inner- 243 u n e HAHm\ 3Ivnxe Hoa\x u x oeSnmm< o AnOHnevnx\x u Hex oeanem< 9 .mm eoneueweu Bonn euen e OHxn OHxN.H OHxN OHxH NOmHmszsO N O O s +N III III , n N x um um o X .I H eOH O mOH N «OH O H «OH m +NHO HO mv O m N x . an . H mOH O N Om Oe ON ON NOH m m +NHO H OzO O III III. N n N um um .H mOH N m NOH O ON +Nz HO OO O Om H.O NH N.O O N.O +m2mHmOzOuO OHxN NN Ome.H mN mOzmHOvaNO s m +N m m m Mn m o O m o m m H- NOH s H- N O H- OH H- s O H- s H- Om +NOOz H OzOhO oanHHHenu oEnHHHenu ooeeHam: ooeeHnm: ehunouez ene>HHm ONO ONO .>a ooNI u m .enOHuoeom Hene>om mo meow nemenenHInouuoeHm mneuneaeHm emu How euneuenou euem mo eonHe> oeuenHumm .m.q eHoee 244 estimated log k,, at UPD lead 1 l l l l ' o 2 4 log ke, at silver Figure 4.6. Estimated value (outer-sphere assumption) for log ket at UPD lead/silver versus log ket at silver. Reactants as in Figure 4.4. 245 sphere pathway for Cr(H20)5NCS2+ reduction at UPD lead/silver. 0f the seven complexes, Cr(H20)5NCS2+ would be the most likely to react via an adsorbed precursor state since aquo chromium complexes are more strongly adsorbed than the corresponding ammine complexes at other surfacesiio’85 and since free thiocyanate adsorbs more extensively than either chloride or bromide (cf. Section III. D). Estimates of log ket at UPD lead/silver are compared with values log ket at silver in Figure 4.6. In contrast to the findings with apparent k values (Figure 4.4), the rate constants for the elementary step correlate fairly well, although there is a fair amount of scatter. Rate constants gathered at UPD thallium/silver are difficult to compare quantitatively with those gathered at mercury since the re- quired extrapolations for either data set are uncertain. In view of these difficulties the ket values which are estimated for reactions at UPD thallium/silver based on outer-sphere reactivity are compared in the form of rate ratios with those at mercury at both I700 and I1000 mV (Table 4.6). At I1000 mV the work corrections for rates at UPD Tl/Ag can be made with certainty and turn out to be small since ¢2 20. The ket estimate for Cr(NH3)5NCS2+ reduction at mercury is probably also trustworthy.3o However the azido- and chlorOI complexes are suffi- ciently weakly bound at mercury that the potential dependence of RP cannot be assessed.30 Nevertheless for the thiocyanato complex the value of log KP evidently diminishes by 0.6 in changing the potential from I700 mV to I1000 mV.3o In order to estimate ket at I1000 mV for the azido and chloro complexes similar decreases of K1) between I700 and I1000 mV were assumed to occur. The ket values estimated in this 246 manner were used to calculate the rate ratios at -1000 mV that are listed in Table 4.6. The rate ratios at I700 mV also are uncertain because of difficulties in establishing accurately the degree of perchlorate adsorption at UPD Tl/Ag and therefore the value of dia/dE which is required in order to extrapolate the work corrections. Nevertheless, the ratios at either potential suggest that Cr(NH3)5NCS2+ may well be adsorbed at UPD thallium/silver while the other complexes probably are not. In particular the ratios of 0.3 for the azido and chloro complex reductions are consistent with those found for bona fide outer-sphere reactions (cf. following subsection). Taken ip toto, the various analyses and observations suggest that the best interpretation of the rate data is that reactions which ordin- arily follow inner-sphere reduction pathways instead follow outer- sphere routes at the UPD metal surfaces. The exceptions are the reduc- 2+ 2+ tions of Cr(H20)5NCS at UPD lead/silver and Cr(NH NCS at UPD 3)5 thallium/silver. Apparently both proceed via weakly adsorbed precursor complexes. Given these interpretations it appears that differences in electron-transfer reactivity for inner-sphere (or potentially inner- sphere) reactions between different electrodes can be accounted for completely by considering the likely differences in precursor stabili- ties. This behavior is markedly different to that observed for the corresponding homogeneous inner-sphere reactions. Thus the chloro- bridged exchange reaction between Cr(II) and Cr(III) aquo complexes is perhaps 108 faster than the corresponding outer-sphere exchange.243 En- hanced precursor stability for the inner-sphere mechanism can account 30 for only about a factor of 103 at most. The remaining five orders of Table 4.6. Ratios 247 of Estimated ket Values for Reactions at UPD Thallium/Silver and Mercury. (le/k Hg)-7OO (le/k Hg)-1000 Reactant et et et at Cr(NH3)5NCSZ+ 1 x 102 10 2+ Cr(NH3)5N3 2 5 0.3 2+ Cr(NH3)5Cl 30 0.3 248 magnitude must be attributed to a lowering of the Franck-Condon barrier and improved electronic coupling for the elementary step. Evidently when two metal centers are simultaneously activated as in homogeneous reactions, there exist opportunities for synergistic and cooperative behavior which are unavailable in unimolecular electrochemical reactions. c. Beduction Kinetics ipi_Copplexes iecking Bridging Ligands The second group of reactants for which electron-transfer reduction kinetics were scrutinized consists of complexes lacking obvious bridging ligands. These reactants or their cobalt analogs appear to be reduced via outer-sphere mechanisms at gold, platinum. silver and mercury surfaces.85’92‘109'110’241’242 Thus, it is rea- sonable to suppose that such reactants follow outer-sphere reaction pathways at underpotentially deposited lead and thallium surfaces as well. Indeed, for most of the complexes it would be difficult to envisage transition-state geometries corresponding to alternative inner-sphere routes. Apparent rate constants and transfer coefficients at I1000 mV for the reduction of outer-sphere reactants at mercury and the two UPD metal surfaces are listed in Table 4.7. Unfortunately the reactions are too slow to be monitored at silver. Also listed in Table 4.7 are work-corrected rate constants k r’ which were calculated from the cor Frumkin equation:45’47 ’239 lnkcorr I lnk + (IIRT)[(z-n°‘corr)F¢r] (1.16) 249 NonH oonoueuou .qm ouneneueu u o "NHOOHOOOH mOO.O O NOOHOOO mN.O o “ONH NOOONONON O NOOHOOz mH O x x . w N-OH O N-OH N HO O O «HON ONO : N-OH a N.N H.N ON.O N.ONNOONoa +NHON=OOO OH x H OH x H H0.0 O