N. J3; ‘ ' ‘11 u“ . “ “—-"\vz! A «‘ OVERDUE FINES: 25¢ per day per item RETUMING LXBRARY MATERIALS: PIace in book return to remove ‘charge from c1 rcuhtion records ELECTROCHEMICAL INVESTIGATION OF SOLVENT EFFECTS ON THE ELECTRODE KINETICS AND THERMODYNAMICS OF SOME TRANSITION-METAL REDOX COUPLES By Saeed Sahami A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 1981 ABSTRACT ELECTROCHEMICAL INVESTIGATION OF SOLVENT EFFECTS ON THE ELECTRODE KINETICS AND THERMODYNAMICS OF SOME TRANSITION-METAL REDOX COUPLES By Saeed Sahami Electrochemical methods were used in order to explore the influences of the solvent upon the electrode kinetics and thermodynamics of some transition-metal redox couples. For the following redox couples: (i) couples containing / aromatic ligands; Cr(bpy)§+/2+, Fe(bpy)§+/2+, Co(bpy)§+’2+ and Co(phen)§+/2+ (where bpy = 2,2'—bipyridine, phen = l,lO-phenanthroline), (ii) couples containing ammine and ethylenediamine ligands; Ru(NH3)g+/2+, Ru(NH3)5N082+/+, )§+/2+ )§+/2+ )3+/2+ Ru(en , Co(en and Co(sep (where en = ethylenediamine, sep = sepulchrate), and (iii) anionic redox couples such as Fe(EDTA)'/2- and Co(EDTA)'/2- Where EDTA = ethylenediaminetetraacetato), formal potential Ef were evaluated using cyclic voltammetry as a function of temperature in eight solvents (water, dimethylsulfoxide, N,N—dimethylformamide, N-methylformamide, formamide, Saeed Sahami propylene carbonate, acetonitrile, and nitromethane). The reaction entropies Asgc for each redox couple in each solvent were obtained from the temperature dependence of Bf using a nonisothermal cell arrangement. These measure- ments were done in order to understand the various struc- tural influences of the solvent upon the redox thermodyn- amics of such simple redox couples where the oxidized and the reduced forms have identical structures and the com- position of the coordination shell remains unchanged when the solvent is varied. These measurements coupled with extrathermodynamic methods such as the "ferrocene", and "tetraphenylarsonium-tetraphenylborate" assumptions, yield S-W estimates of the free energy MAG;C , entropy A(AS§C)S’W, s-w of transfer for the redox couple and enthalpy A(AH;C) of interest from water to other solvents. It has been found that the values of Asgc for all redox couples investigated here are substantially (up to MAO l mol‘l) larger in nonaqueous solvents compared cal. deg- with water. These entropic variations appear to corre- late well with the empirical "a" parameter as a measure of the degree of "internal order" of the solvent, but fail to correlate with the solvent "donor number". Small s-w for couples containing aro- negative values of A(AG;C) matic ligand were typically obtained as a result of partial compensation of the entropic terms by the corresponding enthalpic components. On the other hand, the large variations in free energy, and enthalpy of transfer for Saeed Sahami amine couples and anionic complexes correlate broadly with the "donor number" for the former system and with the "acceptor number" for the latter system. Normal pulse and d.c. polarography were employed to investigate the one—electron reduction kinetics of Co- + _ (en); , CoIII(NH3)5X and CrIII(NH3)5x (where x = F , N03, NCS_, N3, SOE', Cl—, Br- and NH3) in various solvents at mercury electrodes. Substantial variations in the experimental rate parameters were observed as the solvent was altered. The substantial decreases in corrected rate constants kcorr seen when substituting several nonaqueous solvents for water were traced to increases in the outer- shell component of the intrinsic free energy barrier (AGI)os‘ A roughly linear correlation between the observed solvent dependence of AG: for Co(en)?”2+ and the cor— responding values of asgc were found. This suggests that there is a significant contribution to (AG:)os from ex- tensive short-range reorientation of solvent molecules. In addition, it was found that the outer-sphere reaction mechanism provides the usual pathway for the reduction of these complexes at mercury/nonaqueous interfaces. ACKNOWLEDGMENTS I wish to express sincere thanks to Dr. Michael Weaver for his invaluable advice, guidance, encouragement, friend- ship, and enthusiasm during the course of this study. Thanks are given to Professor S. R. Crouch for his helpful suggestions as second reader. Financial support by Michigan State University, Depart- ment of Chemistry and the Office of Naval Research is grate- fully acknowledged. In addition, partial financial aids of the people of Iran, as administered by the Ministry of Science and Higher Education is acknowledged. I would like to thank my colleagues in the research group of Dr. Weaver for their friendship, and assistance during our association. I especially thank Dr. Ed Yee, Dr. Paul Tyma, Ken Guyer, Steve Barr and Ed Schindler. I wish to thank my parents and sisters for their under- standing and constant support. Finally, I would like to thank my wife, Jila, for her love, her patience and her encouragement. ii Chapter LIST OF LIST OF CHAPTER A. B. C. D. CHAPTER A. TABLE OF CONTENTS TABLES. FIGURES I — INTRODUCTION AND BACKGROUND Introduction. Mechanisms of Electron Transfer Redox Thermodynamics. Ionic and Reaction EntrOpies. II - EXPERIMENTAL Materials Reagents. 2. Solvents. 3. Transition Metal Complexes and Compounds Apparatus Electrochemical Techniques. 1. Sample Preparation and Reference Electrodes. Cyclic Voltammetry. Polarography. Preparative Electrolyses. U'IJ'IUON Potential of Zero Charge (PZC) Measurement iii Page vii xii (DO-EN 12 13 l3 13 1U l7 l8 l9 19 2O 2O Chapter CHAPTER CHAPTER A. B. III - SOLVENT TREATMENTS OF THERMODYNAMIC AND ELECTRODE KINETIC DATA FOR REDOX COUPLES. Solvent Dependence of Redox Thermodynamics. l. The Reaction Free Energy and Transfer Free Energy Concepts 2. Some Extra Thermodynamic Methods for Estimation of Transfer Free Energies. . . . . . . . a. The "Ferrocene Assumption". b. The "Zero Liquid Junction Potential Potential" Procedure. . . . . c. The "tetraphenylarsonium- tetraphenyl borate" (TATB) Assumption. . . . . . . . 3. Estimation of Transfer Free Energies for Redox Couples. A. Determination of Reaction EntrOpies for Redox Couples 5. Electrostatic Born Model For Calculating Transfer Free Energies and Reaction En- tropies of Redox Couples. Solvent Dependence of Redox Electrode Kinetics. . . . . . . . . . . . . . . 1. Evaluation of Activation Free Energies and Other Electrode Kinetic Parameters. . . . 2. Solvent Dependence of Intrinsic Barriers. . IV - SOLVENT PROPERTIES Classification. The Dipole Moments and Dielectric Constant. . . . . . . . The Donor- and Acceptor-Numbers iv Page 21 22 22 2A 2A 26 27 28 3O 35 37 37 141 AA “5 45 A7 Chapter F. Page Solvent "Internal Order", "a" Parameter . . . . . . . . . . . . . . . A9 Potential Range in Nonaqueous Solvents. . . . . . . . . . . . . . . . . . 50 Choice of Solvent . . . . . . . . . . . . . 50 CHAPTER V - SOLVENT EFFECTS UPON THE THERMO- DYNAMICS OF M(III)/(II) TRANSITION- METAL REDOX COUPLES . . . . . . . . . . 55 Introduction. . . . . . . . . . . . . . . . 56 Results . . . . . . . . . . . . . . . . . . 57 l. Ferricinium-Ferrocene Redox Couple. . . . . . . . . . . . . . . . . 57 2. Couples Containing Polypyridine Ligands . . . . . . . . . - . . . . . . 6A 3. Couples Containing Ammine and Ethylenediamine Ligands . . . . . . . . 75 A. Anionic Redox Couples . . . . . . . . . 8A Discussion. . . . . . . . . . . . . . . . . 88 l. Ferricinium-Ferrocene Couple. . . . . . 88 2. Polypyridine Redox Couples. . . . . . . 96 3. Ammine and Ethylenediamine Couples . . . . . . . . . . . . . . . . 113 A. Anionic Couples . . . . . . . . . . . . 129 CHAPTER VI - SOLVENT EFFECTS ON THE KINETICS OF UOWZD SIMPLE ELECTROCHEMICAL REACTIONS: COMPARISON OF THE BEHAVIOR OF Co(III)/(II) - TRISETHYLENEDIAMINE AND AMINE COUPLES WITH THE PREDICTIONS OF DIELECTRIC CONTINUUM THEORY . . . . 138 Introduction. . . . . . . . . . . . . . . . 139 Experimental. . . . . . . . . . . . . . . . 1A0 Results . . . . . . . . . . . . . . . . . . 1A1 Discussion. . . . . . . . . . . . . . . . . 1A7 Chapter CHAPTER VII — DETERMINATION OF REACTION D. CHAPTER A. B. LIST OF MECHANISMS FOR Co(III)- AND Cr(III)-AMINE COMPLEXES AT Hg/NONAQUEOUS INTERFACES. Introduction. Method for Distinction Between I.S. and 0.8. Mechanisms . . . . . Results 1. Co(III)-Amine Reactants 2. Cr(III)—Amine Reactants Discussion. VIII — CONCLUSIONS AND SUGGESTIONS FOR FURTHER WORK . Conclusions Suggestions for Further Work. REFERENCES. vi Page 166 167 168 169 169 176 176 185 186 191 19A Table LIST OF TABLES Voltage Range on Mercury and Platinum in Selected Solvents and Supporting Electrolytes Some Properties of Various Solvents Reaction Entropies for Ferricinium- Ferrocene Couple in Various Sol- vents . . . . As;C (ach - §Fc+) for the Ferricinium—Ferrocene Redox Couple in Various Solvents. Comparison with Predictions from Born Model Temperature Derivatives of Di- electric Constants for Various Solvents. Formal Potentials and Reaction Entropies for M(III)/(II) Poly- pyridine Redox Couples in Various Solvents. Free Energies, Enthalpies and Entropies of Transfer of vii Page 51 53 6O 63 65 68 Table Page M(III)/(II) Polypyridine Redox Couples from Water to Various Solvents. . . . . . . . . . . . . . . . . . 71 8 Formal Potentials and Reaction Entropies for M(III)/(II) Amine and Ethylenediamine Redox Couples in Various Solvents . . . . . . . . . . . . 77 9 Free Energies, Enthalpies, and Entropies of Transfer of M(III)/ (II) Amine and Ethylenediamine Redox Couples from Water to Various Solvents. . . . . . . . . . . . . . 81 10 Formal Potentials and Reaction Entropies for M(III)/(II) Amine and Ethylenediamine Redox Couples in Different Ionic Strength . . . . . . . . 85 11 Formal Potentials and Reaction Entropies for Fe(EDTA)-/2' and Co(EDTA)‘/2’ Redox Couples in Various Solvents. . . . . . . . . . . . . . 86 12 Free Energies, Enthalpies, and Entropies of Transfer of Fe(EDTA)-/2- and Co(EDTA)‘/2- Redox Couples from Water to Various Solvents . . . . . . . . . 89 ~viii Table 13 1A 15 16 17 Estimates of Transfer Free Energies for Ferricinium-ferrocene Redox Couple from Water to Various Other S‘W Obtained "'o _ ‘o Solvents A(GFc GFC+) Using Equation (5), Compared with Corresponding Transfer Entropies 5'“ for T=25°C. —o _"'o Ts-w for Co(en)3 Barrier A(AG Resulting from Substituting Various Nonaqueous Solvents for Water. Com- parison with Predicted Variations A(AG:):;¥C from Dielectric Continuum Theory. Calculated Values of the Outer- shell Intrinsic Barrier for Co(en)§+/2+ from Dielectric Continuum Theory. Experimental Rate Constants and Transfer Coefficients for Electro- reduction of Various Co(III)-amine Complexes at Hg/DMSO at 25°C. Experimental Rate Constants and Transfer Coefficients for Electro- reduction of Various Co(III)-amine Complexes at Hg/DMF at 25°C Experimental Rate Constants and Transfer Coefficients for Electro- reduction of Various Co(III)-Amine Complexes at Hg/Formamide at 25°C Experimental Rate Constants and Transfer Coefficients for Electro— reduction of Various Co(III)-amine Complexes at Hg/PC at 25°C. if n Page 153 156 171 172 173 175 Table 23 Page Experimental Rate Constants and Transfer Coefficients for Electro- reduction of Various Cr(III)-amine Complexes at Hg/DMSO, Hg/DMF and Hg/Formamide Interfaces at 25°C . . . . . . 177 xi Figure LIST OF FIGURES Page [Plots of A(AS;C)S-w for each polypyridine redox couple against the corresponding Born estimates 0 s-w A(ASrc) Born obtained from the O values of (ASrc Born from water and appropriate non— calculated aqueous solvent . . . . . . . . . . . . . . 100 Plots of A(ASI‘3,C)S-W for a given polypyridine redox couple against -a for each solvent . . . . . . . . . . . . 105 Plots of A(AS§’,C)S'W for each poly- pyridine redox couple against the "Donor Number" for the various non- aqueous solvents. . . . . . . . . . . . . . 107 Plots of A(AG;C)3’W and a(AH;C)S’W for Co(en)§+/2+ and Ru(NH3)g+/2+ against the "Donor Number" for each solvent. . . . . . . . . . . . . . . . 117 Plots of A(AS° )S‘W PC for a given amine redox couple against the corresponding Born estimates xii Figure 10 11 Page S-W Born obtained from the values 0 A(ASrc) of (AS; calculated for water c)Born and appropriate nonaqueous solvent. . . . . 121 Plots of A(AS]‘.2.C)S"W for each amine redox couple against the "Donor Number" for various nonaqueous solvents. . . . . . . . . . . . . . . . . . 12A Plots of A(AS;c)S-w for each amine redox couple against -a for the various solvents. . . . . . . . . . . . . . 127 Plots of A(AG;C)S‘W and A(AH;C)S-w for Fe(EDTA)'/2- against the "Ac- ceptor Number" for each solvent . . . . . . 132 Plots of Asgc for Fe(EDTA)-/2' against -a for the various solvents. . . . . . . . . . . . . . . . . . 137 Plots of the variation in the intrinsic free energy of activa- tion for Co(en)§+/2+ resulting from substituting various non- aqueous solvents for water, # s—w A(AG1) , against the correspond- ing reaction entropies Asgc . . . . . . . . 163 Comparison of the effect of specific iodide adsorption upon rate-potentials Figure 12 Page plots for the electroreduction of Co(NH3)5F2+ in mixed LiClOu + L1: supporting electrolytes in DMSO . . . . . . 180 Comparison of the effect of specific NCS' adsorption upon rate-potential plots for the electroreduction of Co(NH3)5NCS2+ in mixed LiClOu + NaNCS supporting electrolytes in DMSO. . . . . . . . . . . . 182 xiv CHAPTER I INTRODUCTION AND BACKGROUND A. INTRODUCTION Along with other types of solution reactions, most fundamental studies of the rates and mechanisms of elec- trode processes have been conducted in aqueous solution. There are several factors responsible for this situation, including the availability of numerous bulk and surface thermodynamic data for aqueous systems and the relative lack of such data in other solvents. However, there are a number of important limitations to the use of aqueous media for electrochemical reactions, both from theoretical and practical points of view. For example, the available range of electrode potentials in aqueous media is usually limited by cathodic hydrogen and anodic oxygen evolution. In addition many electrode reactions are complicated in water or do not even occur because of hydrolysis reac— tions. In contrast, the large potential range that is available at a number of electrodes in nonaqueous, particu- larly aprotic, solvents allows a wider variety of electrode processes to be examined than in water. These features also make aprotic and other nonaqueous solvents especially attractive for use in high-energy battery systems. Moreover, water is a decidedly atypical solvent from a physical point of view, so that large influences upon the thermodynamics and kinetics of electrode reactions could generally be expected when substituting nonaqueous solvents for water. Nevertheless, surprisingly little progress has been made in gaining a fundamental understanding of redox processes especially for inorganic complexes in solvents other than water, either in homogeneous solutions or at electrode sur- faces. The nature of the solvent is expected to have profound 'influences upon the kinetics of electron transfer re- actions. The observed effects arise from a variety of sources, such as changes in the relative stability of oxida- tion states caused by reactant-solvent bonding, electro- static interactions, shifts in complexation equilibria, alterations in reaction mechanism, etc. Indeed, the major difficulty in interpreting solvent effects on electrode kinetics, as well as on other types of chemical processes including homogeneous electron transfer, has been that a number of separate factors may be responsible for the observed changes in the kinetic parameters as the solvent composition is altered. The majority of studies of solvent substitution on the kinetics of electrochemical reactions have employed substitutionally labile cations. For these systems the observed effects can arise from changes in the composition of the coordination shell (inner-shell effect), as well as from reactant—solvent interactions (outer-shell contribution). Moreover, a number of the reactions studied up to now involve multi-electron and atom transfer [e;g., Cd2+ + 2e“ + Cd(Hg)] so that the charge and structure of the transition state is usually ill-defined (1-7). We have chosen to focus attention on transition- metal complexes because this class of reactant provides a large number of simple redox couples of related struc- ture. They often involve the transfer of a single Felectron for which both halves of the redox couple are stable in solution. Most importantly, the use of substi- tutionally inert octahedral complexes allows the solvent to be varied while keeping the composition of the reactant's coordination sphere constant. This approach therefore allows the "inner-shell" (coordination sphere) and "outer- shell" (longer-range solvation) effects to be investigated separately. B. MECHANISMS OF ELECTRON TRANSFER A unique feature of redox reactions compared with other chemical processes is that in many cases efficient electron transfer probably occurs without any significant specific interaction between the two reacting centers (8). Reactions proceeding via such pathways in which the primary coordination spheres of both reactants remain in- tact in the transition state have been termed "outer-sphere" (0.5.). However, when strong specific interactions occur between the reacting centers a more favorable pathway for electron transfer is usually expected to result. Not surprisingly, the rates of these "inner-sphere" (I.S.) reactions are sensitive not only to the structure of the reactants,but also to the nature and extent of their mutual interactions within the transition state. For redox reactions between metal ions, the I.S. and 0.8. reaction mechanisms usually correspond to cases where a 1i- gand coordinated to a reactant does, or does not penetrate the inner coordination Sphere of the other reactant during electron transfer. These basic notions and definitions, originally developed for homogeneous redox reactions (8), can be directly employed to the analogous heterogeneous (i;§., electrochemical) systems by noting that the elec- trode surface and the adjacent layer ("inner-layer") of the solvent molecules play the role of the co-reactant (9). It is obvious that 0.8: electron-transfer reactions are much easier to treat theoretically than I.S. pro- cesses since no chemical bonds are formed or broken in the former type (10). On the other hand, electrochemical I.S. reactions are of particular interest because they correspond to cases where the interactions between the reactant and electrode surface act to lower the activation energy for electron transfer. In order to select appropriate theoretical models and interpret electrochemical kinetic parameters, it is necessary to distinguish between outer-sphere and inner- sphere pathways. No direct method is available for the determination of electrode reaction mechanisms (except that chronocoulometry can be used for reactants having suf- ficiently stable adsorbed intermediates (11)). Recently, indirect methods for distinguishing between 0.8. and I.S. (anion-bridged) mechanisms have been developed for substi- tutionally inert cationic complexes (12). These tactics have successfully been used in aqueous solution for mechan- III and CPIII ism diagnosis of the reduction of Co com- plexes at mercury (9,13) and solid electrode surfaces (1A). These methods were employed in the present work for de- termination of electroreduction mechanisms of various COIII(NH3)5X and CrIII(NH3)5X complexes (where X = F', - 2- Cl', Br”, N3, NCS‘, N03, SO“ and NH3) at mercury/non- aqueous interfaces and are presented in Chapter VII. C. REDOX THERMODYNAMICS The thermodynamics of redox couples in different sol- vents can provide significant information about the in— fluences of the solvent structure upon the electrochemical reactivity. Thermodynamic parameters for redox couples in a given solvent are expected to be sensitive to the chemical nature of the coordinated ligands, the metal center and the charge on the reactant. Thermodynamic parameters can be obtained by measurements of the stan- dard or formal electrode potentials Ef for the redox couple of interest. This is due to the fact that in a given sol- vent, the difference between the partial molal free en- ergies of the reduced and oxidized halves of a redox couple ("reaction free energy") is related to the measured Ef by Equation (1). (aged - 63x) = 11ch z -nF Ef (1) In addition, the dependence of Ef upon temperature and the solvent composition can provide valuable information on the factors influencing ionic solvation, in particular the structural changes in the surrounding solvent that accom- pany electron transfer. In general, analyzing the free energies in terms of enthalpic and entropic components can provide more informa- tion than could be obtained from free energies alone. One effective method for evaluating such entropic and enthalpic data is through the employment of ionic entropies and par- ticularly reaction entropies (for redox couples) as is now discussed. D. IONIC AND REACTION ENTROPIES Partial molal entropies can provide useful information about the thermodynamic properties of a species in solu- tion. By definition (15) the partial molal entropy of the ith component of a system §i is the temperature de- pendence (under constant pressure and composition) of vi, the chemical potential of component i (-——) = 51 (2) Determination of partial molal entropies of single ions has been an important goal of thermodynamic studies in solu- tion. Strictly speaking, it is not possible to determine the ionic entropies of single ions, since only the partial molal entropy of an electrolyte (igeg, the sum of the ionic entropies for the cation and anion) is experimentally accessible (16). However, different methods are available for estimating single ion entropies. One may arbitrarily assign an entropy value to some ion and thus obtain a relative scale of single ion partial molal entropies. It is conventional for aqueous solution to use the scale based on the assumption that S§+(aq) = O (16). All other tech— niques involve some sort of extrathermodynamic assumption. Fortunately, most of these methods have yielded similar values of S§+(aQ) (17), which are not far from the con- 0 (16). An approximate value 1 ventional value of S;+(aq) cal deg- mol'l) was obtained of S§+(aq) = -5 e.u. (e.u. by each of these methods (17). Similar treatments have been employed for solvents other than water. The total entropies of solvated electro- lytes were divided into their ionic components by assign- ing a value for ionic entropy for the hydrogen ion (18). The division was made in such a manner that the ionic en- tropies for both cations and anions in a given solvent, when plotted vs. the ionic entropies of the corresponding ions in water fell on the same curve (17,19). It has been shown that the ionic entropies in any given solvent x, can be represented by Egon(X) z a + b Egon(H2O) (3) where a and b are empirical constants characteristic of solvent x and Sion(H20) is the absolute entropy of the corresponding ions in water (17,20). Although the ionic entropies of single ions can provide useful information on the interaction between an ion and the solvent molecules surrounding it, a variation of this concept is particularly appropriate when dealing with redox systems. One can consider Asgc (the so-called reaction entropy), as the difference between the ionic entropies of 10 the reduced and oxidized forms of the redox couple Sged- ng (= Asgc) (21,22). Under this definition A530 is the reaction entropy for one-half of.a complete electrochemical reaction. The values of ASEC in a given solvent are ex- pected to be sensitive to the relative extent of solvent polarization induced by the reduced vs. the oxidized forms of the redox couple. They are also of particular sig- nificance in redox kinetics because they provide a unique opportunity to monitor solvent structural changes in the vicinity of the solute as a result of adding an electron to convert the oxidized form into the corresponding re- duced species (22,23). . The utility of reaction entropies has been recognized recently by Weaver and coworkers (21). They have conducted a study of reaction entropies for a number of transition- metal redox couples containing aquo, simple monodentate and chelating ligands in aqueous media (21,2A). The values of Asgc for redox couples containing aquo and monodentate ligands were found to be affected by electrostatic factors and the hydrogen bonding between the solvent and bound ligands, but were relatively insensitive to the nature of the metal ion (21). However, the values of reaction en- tropies for couples containing chelating ligands were found to depend on the electronic structure of the oxidized and reduced metal cations as well as their charge and the nature of the coordinating ligands (21). In addition reaction 11 entropies for a series of copper(III/II)— and nickel (III/II)-peptide redox couples have also been determined in various media (25). Essentially no information is available on the solvent dependence of Asgc for any redox couple (especially octa- hedral transition-metal complexes with fixed coordination sphere) except for Fe(phen):3:+/2+ (phen = 1,10—phenanthroline) and its related derivatives in water and acetonitrile (26). Determination of reaction entropies for a given redox couple as a function of solvent should also help to under- stand the solvent structural factors influencing transfer free energies. Although appropriate redox couples are not abundant, it was found that a number of transition—metal redox couples such as Ru(III)/(II), Cr(III)/(II), Co(III)/ (II),:and Fe(III)/(II) containing ammonia, ethylenediamine and polypyridine ligands are suitable. These redox couples are substitutionally inert, sufficiently stable and electrochemically reversible or quasi-reversible. There- fore, their formal potentials and reaction entropies can be obtained using cyclic voltammetry. In Chapter V values of reaction entropy are presented for these redox couples measured in different solvents. CHAPTER II EXPERIMENTAL 12 A. MATERIALS 1. Reagents The reagents used in this work were analytical grade and used without further purification, except when other- wise noted. Anhydrous lithium perchlorate (from K & K or G. F. Smith), lithium bromide (Matheson Coleman and Bell) and lithium chloride (Fisher) were dried at ~180°C for sev- eral days. Lithium iodide (K & K) was dried over CaSOu at ambient temperature. Tetraethylammonium perchlorate (TEAP, Eastman) was recrystallized from water and dried in a vacuum oven at 80°C. KPF6 (P & B) was twice recrystallized from water and dried in a vacuum oven at 110°C for several days. Sodium thiocyanate (Matheson Coleman and Bell), nickelous nitrate (Fisher) and zinc perchlorate (G. F. Smith) were dried in a vacuum oven at 60°, A0° and 60°C, respectively. Mercury which had been triply distilled under vacuum was purchased from Bethlehem Apparatus Co. 2. Solvents Dimethylsulfoxide (DMSO), N,N—dimethylformamide (DMF), methanol (MeOH), acetonitrile (AN) and nitromethane (NM) all were Aldrich "Gold Label" grade. Formamide (F) was purchased from Eastman. Propylene carbonate (PC), 13 1A N—methylformamide (NMF), and hexamethylphosphoramide (HMPA) obtained from Aldrich. Propylene carbonate was further refluxed over calcium hydride (Fisher) under reduced pressure overnight, then fractionally distilled; only the middle 70% fraction was collected. Most of the solvents used were kept over freshly activated molecular sieves (Lind type 3A). The water content of most of these solvents was <0.05% as determined by an automatic Karl Fischer titrator. These solvents were kept in a dry box under nitrogen atmosphere. Water was purified by distillation from alkaline permanganate followed by "pyrodistillation", which consisted of cycling a mixture of steam and oxygen through a silica tube network held at 800°C for two days be- fore collecting the distillate. Water for synthesis and cleaning the glassware was purified by the use of a "Milli- Q" purification system (Millipore Corp.). 3. Transition Metal Complexes and Compounds Cr(bpy)3(C1Ou)3 complex (where bpy = 2,2'-bipyridine) was prepared by electrolyzing (25 ml) an aqueous solution containing 50 mM Cr3+ and 50 mM HClOu in 100 mM NaClOu over a stirred mercury pool held at -1100 mV li- a saturated calomel electrode (SCE), while continuously passing prepuri- fied argon to form Cr2+. This solution was then transferred using a gas-tight syringe to a deoxygenated suspension of (1.0 g) of 2,2'-bipyridine in (A5 m1) aqueous 10 mM HClOu. 15 The resulting black suspension of Cr(bpy)3(C10u)2 was bubbled with oxygen for one hour to yield a yellow precipitate of Cr(bpy)3(C10u)3 which was filtered, washed with ethanol and water, and dried in a vacuum desicator CT7). Co(bpy)3(C10u)3 was synthesized using the procedure of Burstall and Nyholm (28). CoC12-6H2o (2.A g) and 2,2v_ bipyridine (A.7 g) were heated with 501mlof water until com- plete solution had occurred. To this yellow solution 10 ml H202 and 10 ml HCl was added, and the mixture evaporated to a syrupy consistency. Then 50 ml of water was added, and the solution was treated with 10 m1 HClOu. The yellow precipitate was recrystallized from hot water and air-dried. The salt of NaIFeIII(EDTA)] (where EDTA = ethylenediamine— NNN'N'-tetraacetic acid) was prepared according to Reference (29) by treating freshly prepared Fe(OH)3 with a stoichiometric amounttdfthe disodium salt of EDTA. Heating at about 80-90°C with regular stirring produced a yellow solution. Slow evaporation of the resulting solution (vacuum aspirator) yielded yellow-brown crystals of NaEFeIII(EDTA)]~3H20 which is very soluble in water. The salt of NaECOIII(EDTA)J-uh2o was prepared according to the method of Dwyer et a1 (30). The compound Co(phen)3(C104)2 (where phen = 1,10- phenanthroline) was prepared by the method of Pfeiffer and Werdelmann (31). The salt of Fe(bpy)3(C10u)2 was obtained from G. F. Smith 16 and used without further purification. The Co(pby)§+ was prepared (in situ) by adding an excess of ligand to a solution of anhydrous C0012. Ferrocene (Fc) was purchased from Aldrich and used with- out further purification. Ferricinium picrate (Fc+) was prepared as described in Reference (32). The compound Ru(NH3)6(C10u)3 was prepared by dissolving the Ru(NH3)6'C13 (Matthey Bishop Inc.) in hot water; addi- tion of 1.0M solution of sodium perchlorate gave a white precipitate of perchlorate which was filtered, washed and dried. The salt of Ru(NH3)5NCS(010u)2 was synthesized according to References (22,33). Co(III)ammine complexes were prepared according to the following procedures. [Co(NH3)SCO3]N03-%H20 (3A) was used as the starting material for the preparation of Co(NH3)5F2+ (3A) and Co(NH3)SOSO3+ (35). The remaining cobalt-ammine complexes were synthesized by oxidation of CoC12: Co(NH3)g+ (35), Co(NH3)5NO§+ (37), Co(NH3)5Ncs2+ (38), Co(NH3)5N§+ (39), and Co(en)%+ (A0) (where en = ethylenediamine). These solid complexes were prepared as perchlorate salts. Synthesis of the Cr(III) ammine complexes followed standard published procedures. The double salt aquopenta- aminechromium(III)ammonium nitrate (Al) was used as the starting point for the preparation of Cr(NH3)SBr2+ (A1), 2+ 2+ 2+ Cr(NH3)5Cl (A1), Cr(NH3)5NO3 (A1), Cr(NH3)5F (A2). 17 2+ Cr(NH3)5NCS (A3), and Cr(NH3)5N2+ (AM). All solid com- 3 plexes were recrystallized from acidified water by pre- cipitation as the perchlorate or chloride salts. Samples Of Ru(en)3Br3 were kindly supplied by Dr. Gil- bert Brown of Brookhaven National Laboratory, and Co(sep)C13 (where sep=sepulchrate, see Reference (A5) for further de- tails) was kindly provided by Professor John Endicott of Wayne State University. B. APPARATUS Conventional two-compartment glass cells were employed for the electrochemical measurements. The working compart- ment which had a volume capacity of 10—15 ml was separated from the reference compartment by a frit of "very fine" or "ultrafine" grade manufactured by Corning, Inc. The average porosity of these frits was 1-3 um which prevented signifi- cant mixing of the two solutions on the time scale of 2-3 hrs required for most experiments. For most measurements, the working and reference compartments were filled with the same solution (except when otherwise noted) so that the solvent junction was formed between the aqueous reference electrode and the solvent of interest at the fiber tip separating the reference compartment and the reference electrode itself. The working compartment, the liquid junction formed in the frit, and part of the salt bridge between the working com- partment and the reference electrode were surrounded by a 18 common jacket through which water from a Braun Melsungen circulating thermostat could be circulated. The tempera- ture of the cell solution could be controlled within i0.05°C. C. ELECTROCHEMICAL TECHNIQUES 1. Sample Preparation and Reference Electrodes All non-aqueous solutions were prepared in a dry box under nitrogen atmosphere. These solutions were deoxygenated by bubbling with prepurified nitrogen or argon which had passed through a wash bottle containing concentrated H280” and finally through a bottle containing the non-aqueous sol- vent of interest for that experiment. For aqueous solu- tions, prepurified nitrogen or argon which had been passed through a V(II) solution was employed. Commercial saturated aqueous calomel reference electrodes (Sargent-Welch), either filled with saturated K01 (KSCE) or with saturated NaCl (NaSCE), were used for most thermodynamic measurements. In some cases a normal calomel reference electrode (NCE) filled with 1.0 normal aqueous KCl was used. For measure- ments in aqueous perchlorate media a NaSCE was employed instead of the KSCE because of the low solubility of KClOu which might precipitate in the liquid junction of the electrode and cause spurious potentials. A platinum wire placed in the working compartment served as the counter (auxiliary) electrode for most experiments. l9 2. Cyclic Voltammetry Cyclic voltammograms were obtained using a PAR 17AA polarographic analyzer (Princeton Applied Research Corp.) coupled with a Hewlett-Packard Model 70AAA X-Y recorder. Sweep rates in the 50-500 mV/sec range were used in this work. This arrangement allowed peak potentials.to be measured with a precision of il-2 mV. Several working electrodes were used in cyclic voltam- metric studies. For redox couples that exhibit formal po- tentials that are sufficiently negative to be examined at mercury electrodes, a commercial (Metrohm Model EAlO, Brink- mann Instruments) hanging mercury drop electrode (HMDE) was used. Platinum "flag" or glassy carbon electrodes were used for work at positive potentials (E > 0 mV vs. KSCE). The platinum "flag" electrode consisted of a 2 mm2 sheet of platinum spot—welded to a fine platinum wire. This electrode was pretreated by immersion in warm 1:1 HNO3 and activation by passage over a Bunsen burner flame. The use of a.Pt electrode in formamide and N—methylformamide solutions was not possible; instead,:a glassy carbon electrode was em- ;ioyed whenever necessary. 3. Polarography The same instruments that were used for cyclic voltam- metry were also employed to obtain dc, and normal pulse 2O polarograms. Sweep rates in the 1-5 mV/sec range were used. A dropping mercury electrode (DME) was used as the working electrode. Mercury flow rates of 1.5 mg/sec and column heights of 50 cm were used. The drop time could be mechanically controlled by means of a PAR 17A/70 drop timer to be 0.5, l or 2 sec. A. Preparative Electrolyses In preparing Cr2+ for the synthesis of Cr(bpy)3(C10u)3, constant potential electrolyses were performed with a PAR 173 potentiostat. A stirred mercury pool and a Pt gauze were used as working and counter electrodes respectively. The electrolyzed solution was bubbled with deoxygenated argon to prevent any reaction with atmospheric O2. 5. Potential of Zero Charge#(PZC) Measurement The PZC values for mercury in contact with various non-aqueous electrolytes were determined using a streaming mercury electrode and a digital voltmeter. Solutions were deoxygenated by bubbling with prepurified nitrogen prior to measurements. Then the potential differences be— tween a streaming mercury electrode and a SCE reference elec- trode were measured while changing the height of mercury reservoir. Beyond a certain height the potential became constant. This was taken as the potential of zero charge. CHAPTER III SOLVENT TREATMENTS OF THERMODYNAMIC AND ELECTRODE KINETIC DATA FOR REDOX COUPLES 21 A. SOLVENT DEPENDENCE OF REDOX THERMODYNAMICS l. The Reaction Free Energy and Transfer Free Energy Concepts In order to evaluate solvent effects upon thermodynamics of redox couples, it is useful to obtain estimates of the solvation energies and standard free energies of transfer. Consider the generalized electrochemical reaction pro- ceeding at a Galvani potential om: ox+e‘(¢m) 2 red (1) The free energies of the ground states I and II that are prior to, and following, electron transfer, can be ex- pressed as (A6,A7): GI = ng + “Z- - F(I’m (2) o =—0 GII cred (3) where 68x and aged are the partial molal free energies of the oxidized and reduced species, respectively, and no is e“ the chemical potential of the reacting electron. Since the overall free energy of reaction AG° (=G°[I - G?) for 22 23 Equation (1) Will by definition equal zero when ¢m = ¢$ (the standard Galvani metal-solution potential difference), then, —°=—° _—0= 0 F¢m cred ' cox AGrc (A) For convenience, we shall term (536d — 68x) the "reaction free energy" of the redox couple AGEC. The change in free energies of the ions forming the redox couple result- ing from changing from water (W) (as a reference solvent) -0 —O S‘W = O S‘W to a nonaqueous solvent (S),A(Gr - GOX) [ A(AGrc) 1, ed will therefore be related to the corresponding variation in s... ta. A(¢;) W. by S-W -FA<¢;)°'" = sS‘W + A(AG;C)F:-w (8) where A(E§C)s-w is the change in the formal potential for the redox couple of interest (versus those for the Fc+/Fc S-W c is the estimate of free energy couple), and A(AG;C)F of transfer for the Fc+/Fc itself obtained from Ag+ trans- fer data (A8) resulting from substituting another solvent for water (see notes to Table 7 for details). A. Determination of Reaction Entropies for Redox Couples Although the reaction entropy has been defined in Chapter I, it is useful to present this definition in the following form. One can consider the general re— action III ' n - + II t H M Lan + e (metal electrode) + M Lan (9) in which M is a metal which has trivalent and divalent oxidation states, L' and L" are neutral or anionic ligands and the number of L' and L" coordinated to M is given by 31 m and n, respectively. The reaction entropy ASEC of the MIIILfiLg/MIILfiLg redox couple following reaction (9) can be written as o --o - ..."' _ ASrc - Sred ' 86x I SII ' SIII (10) where €011 and S211 are the absolute ionic entropies of MIILfiLg (reduced) and MIIIL$L3 (oxidized), respectively. Since reaction (9) is only one-half of a complete electrochemical cell reaction, its equilibrium properties cannot be determined without resort to extrathermodynamic assumptions. However, there are a number of reliable methods for the quantitative estimation of individual ionic entropies, and especially Asgc. A sueful summary of these methods has been given by Criss and Salomon (17). For the present purposes, the most convenient method involves the use of nonisothermal electrochemical cells (6A,65). In this arrangement, the temperature of the working compart- ment (the half-cell containing the redox couple of interest) is varied while the temperature of the other half-cell consisting of some convenient reference electrode is held constant. In the present work values of asgc for each redox couple in various solvents were determined using either nonisothermal electrochemical cells "a" or "b" 32 n n a SCE(aq) | I0.1M LiC10u(solvent s) [0.1M LiClOu(s),MIII-MII IPt,Hg or Carbon A B C "b" SCE(aq)|0.lM TEAP(aq)| [0.1M TEAP(solvents)l0.lM TEAP(s),_ A B MIII-MIIIPt,Hg or Carbon C (where TEAP = tetraethylammonium perchlorate) In the above arrangements, the reference electrode (SCE) was held at room temperature and the temperature of the working compartment BC was varied over as wide a range as practicable (usually 30-60 deg. C); the thermal liquid junction (21) was formed within the region AB so that the unknown solvent liquid junction potential at A did not affect the temperature dependence of formal potential. The formal potential Ef across nonisothermal cells "a" and "b" was determined as a function of temperature. The temperature dependence of the formal potential measured here can be separated into three components (21) 33 f ttj tc f where ¢t2j is the Galvani potential difference across the thermal liquid junction within the region AB, ¢tc is the "thermocouple" potential difference between the hot and cold regions of the working electrode, and o? is the Galvani metal-solution potential difference at the working electrode. Since m Asgc = NET) (12) then if d¢tc/dT and d¢t£j/dT are known or can be estimated, Asgc can be obtained from measurements of dEf/dT. Follow- ing the arguments given or quoted in Reference (21) for aqueous media, it is very likely that the temperature derivative of the thermal junction potential is negligible in comparison With (dEf/dT). Since the thermocouple potential difference generated between the hot and cold regions of the mercury, platinum or carbon working elec- trode (or c0pper connecting leads) is also negligible (21), then to a very good approximation (dEf/dT) = (d¢?/dT) so that 3A dEf Asgc = F(-a-,f-) (13) It is seen in Tables 3, 6 and 10 (Chapter V) that the values of hsgc are essentially independent (within the experimental reproducibility of i1 e.u.) of the ionic strength u and composition of the supporting electrolyte in the thermal junction region for 0.025 S u s 0.02M. This supports the assumption used here for the determination of reaction entropy. The formal potential Ef which is required for determina- tion of Asgc was obtained from measurement of El/2’ the (polarographic) half-wave potential using cyclic voltam- metry. For a reversible cyclic voltammogram, E1/2 was obtained by bisecting the cathodic- and anodic-going peak potentials (66). There is a relation between Br and El/2 (67,68) as shown in Equation (1A) RT DII )1/2 E = E + - An ( (1A) 1/2 f nF DIII where DII and DIII are the diffusion coefficients of the reduced and oxidized species, respectively. It is obvious from Equation (1A) that the actual values of Ef will differ slightly from the experimental estimates due to the 35 inequality of the diffusion coefficients. However, the DII/DIII ratio is usually close to unity so that the E1/2 differs from Ef by only 2-3 mV. Therefore dE1/2/dT can be equated to dEf/dT and from that one can write dE _ 1/2 A8120 - F( dT ) (15) (where F = 23.06 cal mV"l mol“l) 5. Electrostatic Born Model for Calculating Transfer Free Energies and Reaction Entropies of Redox Couples There has been considerable effort to calculate the thermodynamics of transfer of single ions between various solvents. The simplest theoretical model is the Born di- electric continuum (69). This is an electrostatic model which treats the surrounding solvent as a structureless medium of uniform dielectric constant. It also assumes the ion to be a rigid sphere with crystallographic radius r. For the transfer of 1 mole of single ion from water to a given nonaqueous solvent, the Born free energy is given by (A8) 2 2 AG%(Born) = 5%E?- (A; - 3;) (16) € 8 S W 36 This equation can be written in the following form when we are dealing with a transfer of a redox couple from water (w) to a nonaqueous solvent (8) (70) 2 2 Z -W e N 1 1 ox red A(AG° )S = —§—(—- - ——)(——— - ) (17) re Born 8w as rOX rred where e is the electronic charge, N is Avogadro's Number, cw and as are the (static) dielectric constants in water and the nonaqueous solvent, ZOX and Zred are the charges on the oxidized and reduced species, and r and r are ox red the corresponding radii. The Born equation for estimation of reaction entrOpies of a given redox couple in any solvent is given by (70) ( §3¥(a,n€)(2§x zied) < 8) AS° ) = - .___ ___ _ ____ l rc Born a dinT rox rred where T is the absolute temperature, and the other terms have already been defined above. It is well known that the Born model yields estimates of solvation free energies and entropies for simple mono- atomic ions that are often in substantial disagreement with experiment, undoubtedly due in large part to the extensive short-range solvent order induced by such uncoordinated ions (70). This model might be expected to be more 37 applicable to the estimation of A(AG1°,C)S-w for the present work since we are dealing with complex ions with fixed coordination spheres which might act to prevent the ap- proach of solvent molecules to the metal center. B. SOLVENT DEPENDENCE OF REDOX ELECTRODE KINETICS 1. Evaluation of Activation Free Energies and Other Electrode Kinetic Parameters In order to evaluate the electrochemical kinetic data in different solvents, it is first necessary to consider the conventional formulations that attempt to describe the factors determining electrochemical reactivity. One such model which is especially applicable to outer-sphere path- ways is the "reactive-collision" model (71-73). For electro- chemical reactions this model can be expressed as 2 kob = K 2 exp(-AG /RT) (19) -l kob is the observed electrochemical rate constant (cm sec ), K is a transmission (electron tunneling) coefficient, Z is the electrochemical collision frequency and aGF is the free energy of activation. The free energy of 2 activation AG can be expressed as the sum of contributions arising from the individual events in the activation 38 process (73) AG5 = wp + (AG5) + (Ao’!)O (19a) is s In this equation Wp is the work (free energY) required to bring the reactant from the bulk solution to the reaction plane at the electrode (iii;’ to form the so-called pre- cursor state). (AG#)is is the "innerashell" reorganization energy which is the energy required to stretch or compress the metal-ligand bond distances and to change the ligand conformation. (aGI)O is the "outer-shell" term, the 3 energy required to rearrange and reorient solvent mole- cules surrounding the reactant. The inner-shell and outer-shell reorganizations must take place prior to electron transfer in order to attain the activated complex and facilitate the electron transfer process. The AG# in Equation (19a) can be rewritten as # = # AG Wp + AGcorr (20) where AG:O is the work (double-layer) corrected free rr energy of activation (i.e., the overall reorganization free energy). Using Aezorr’ Equation (19) can be expressed as k = K Z exp(-AG# /RT) (21) corr corr 39 where kcorr is the double-layer corrected rate constant in a given solvent. The corresponding relationship to Equation (5) for electrochemical kinetics can be derived by noting that the # _ # AGcorrEIGcorr - GE] can be separated into a potential- # G°) corr ' I _ n " I tial independent ( chemical ) part (Gcorr dependent ("electrical") part (G and a poten- (A6,A7). e ' GI)c The former component is related to the potential—dependent part of (GII - GE), F¢m (Equations (2) and (3)) by (A6, A7,7A) (0" - G° corr I (22) ) = a F¢ e COPP m Since in Equation (21) Z should be dependent only on the effective reactant mass (10a), it should be approxi- mately solvent independent. If K is also solvent independ- ent, the ratio of the double-layer corrected rate constant for a given reaction in water to that in another solvent ¢m at a fixed value of om, (kW/ks)corr’ will be related to the # )¢m corresponding free energies of activation (AGcorr w and (AG‘ )¢m b corr s y ¢m # ¢ ¢ - m _ # m RT £nu (9). The evaluation of the quantities a(AG;c)S"w [Equation (5)] and AS'" corr 0 [Equation (2A)] for a given electrode reaction is of fundamental interest since they provide a monitor of the purely chemical influences brought about by solvent substitution upon the thermodynamics and kinetics of electron transfer. Since neither absolute nor even relative values of ¢m in different solvents are strictly speaking thermodynamically accessible quantities, the evalua- tion of A(AG# )s-w corr c inevitably requires some sort of an extrathermodynamic procedure. As was discussed before, the TATB assumption seems to be a more reliable method than the other procedures. Therefore, the values of kcorr evaluated at a fixed electrode potential (versus the TATB scale) can be inserted into Equation (2A) to yield # s—w estimates of A 35), which are capable of dissolving multicharged cations and anions were 51 .opfiUOH ESHCOEEMHmusnlclmpumu H¢meo cameo .mom msoosvm .MN .muao> :H mom mamfipcmpOQ condomozn .mw mocmpohmm mo HI: canoe Eosm :oxmu muons .oumpoanopoo Edacoesmaznummpuop mm.au or 5.0 o.an co o.H m.en op m.H ca om.H- oe mm.o o.m- or m.o w: eoHooz mm.mu or 3.0- o.m- o» 3.0- w.mn cc o.o- w: oHame mm.au cc e.o H.m- oo o.H m.an oe e.H ca m.m- on mm.o o.m- op m.o m.mn op m.o m.mn oc o.o mm edema opaxomazm oGHEmELom oumconomo oafipuficouoo< opospooam oquOLpoon tahzuoEHQ lachoEHn ocoazoonm wcfixp03_ wcfiupoodsm n.mouzaopuomam wchLooosm one muco>aom pouooaom CH Escfiumam pcm assume: no omcmm owMuHo> m.a magma 52 used. Employment of these solvents not only minimizes the solution resistance (ohmic drOp), but also prevents the extent of ion association in the bulk solution. Table 2 summarizes solvents used in this work along with some of their physical and chemical prOperties. It is seen that the values of dielectric constant, donor number, acceptor number and solvent internal order "a" parameter vary over a wide range,which should allow the effects of such factors on both the electrode kinetics and thermodynamics to be explored systematically. 53 Soon HIHOE.Hmox CH LonESZ pocoa :cmEuso .Aamv mocmpomom .Ammv mucosomom Soon oznmo :0 pCoEoE mHOQHom o 0.0 0.:0 0H2 0.0e 00.H 00m coco: m m m Aaazzv ..... 0.0a 0.0m 0.00 03.: 0a A2 A movv ceasesonohocoeancosoxom 0.0 I m.0H 0.0m e.0e 00.m ommammov Aomzov ooaaooasneaccosao 0.0a- 0.0a 0.0m e.0m 00.m mflmmovzooz Amzov coasoEAooHacposaouz.z 0.: - a.mm m0a m0.m maomzooa Amaze ooaeeeaooaaecoz-z m.H I m.mm :ma m.moa m>.m mmzoom Amv oofiemspom 0.0a: m.a: 0H 0.0m K.H 00mmo Amoozv dosages: \wl m.m I m.wH H.mH 0.00 mm.: m mm w Aomv mumconpmo mcoazoosm 0000 :0 m.mHI m.ma H.2H 0.0m ::.m zommo AzH0m honoooo< psocom capuooamfim mmHodHQ .0 cache .mpco>aom msoapm> mo mofipsodopm mEom 5A Eopm :pooso Hmcsochz .Aomv mocmsomom uco>Hom wanHsomop HoE wop.Hmo CH pouoEmst =m= HmoHpHoEm HI HI p .Ava mocmpomom Boom ponssz gouaooo< ccmsuswo .oossaucoo .m oHooe CHAPTER V. SOLVENT EFFECTS UPON THE THERMODYNAMICS OF M(III)/(II) TRANSITION-METAL REDOX COUPLES 55 A. INTRODUCTION Variations in the solvent medium are expected to have large influences upon the thermodynamics of electron trans- fer reactions. Part of these effects can arise from changes in the composition of coordination shell of the reacting species as well as from reactant-solvent interactions ("in- ner shell" and "outer shell" effects, respectively). In order to distinguish between these two contributions, we have chosen to do a systematic study of solvent effects upon the thermodynamics of redox couples involving sub- stitutionally inert transition-metal ions. These redox couples in which the oxidized and reduced species are both stable in the solution phase have a general form of MIIILn/MIILn (where M = Ru, Co, Cr, Fe; L = amines, poly- pyridines, etc., and n = number of ligands) and involve incisingle electron transfer reactions. The general approach is to determine the formal po- tential Ef of each redox couple in a range of solvents having suitably different chemical and physical properties. In_addition, the temperature dependence of Ef is monitored in each solvent using a nonisothermal cell arrangement,. . giving values of reaction entropies As;C for each redox couple. These measurements coupled with extrathermodynamic 56 57 methods such as the "ferrocene", and "tetraphenylarsonium- tetraphenylborate" assumptions yield estimates of the free energy and enthalpy of transferring the redox couple from water to other solvents. B. RESULTS Four groups of M(III)/(II) transition-metal redox couples were studied; the ferricinium/ferrocene redox couple, cationic redox couples containing polypyridine ligands, cationic redox couples containing ammine and ethylenediamine ligands, and anionic redox couples containing ethylene- diaminetetraacetato ligands. Comparison between and within these groups will allow one to determine the effects of central metal ion, ligand, and charge upon the redox thermo- dynamic parameters as the solvent is varied. 1. Ferricinium—Ferrocene Redox Couple The ferricinium/ferrocene (Fe(C5H5)+/Fe(C5H5), redox couple was selected in order (1) to be used as an internal s-w £3 fer free energies of other redox couples, and8 oumHOHpoon uco>Hom MCHxsoz mwcmm m o .osoe H-woo H00 0 0 0L” Q om< .muco>Hom wsoHLm> CH oHosoo mcooopsmmIechHOHpsom Log mmHQOLucm COHpomom .m oHnt 61 000 00H0HH 20.0 00-0 0.0H 000 00H0H0 20.0 00-0 0.0H 0000 0000 2H.0 00-0 0H 000 0000 2H.0 00 00-0 0H 000 00H0HH 2H.0 00-0 0.0H H00 00H0H0 200.0 00-0 0H 000 00H0H0 2000.0 00Heeeao0H0000000 0H0 00Hoaa 20.0 00-00 0H 000 00H0H0 20.0 00 00-00 0.0H 00H0 0000 2H.0 00-0H 0.0H 000 00H0HH 2H.0 00-00 0H 000 00H0H0 2000.0 00on0Han0000000 00-0 0.HH 0000 0000 mH.0 00 00-0 0.HH 000 0000 2H.0 00-0 HH 000 00H0H0 2H.0 eHHAAHcooeo0 oWWLHQmHm -oo HIHoE >5 oumHogpomHm uco>Hom o cproz wwmwm Iwop H00. 002 0&00 .0essHeco0 .0 0H000 .0 0o 00_H000>Ho0000m0 2H.0__000000m0 2H.0_Heavmomaz "HHmo wch: AHomz 000003000 00H: ooHHHmv .m.o.m mzomzom 0:000> 000050 mHmHucmuomp .con000 zmmme u 0 0:0 emmH0= EchumHm u um mopopuomHm A0oumoHchv wcprozo .Auxmp 0000 .:.m NIH cquHs 00003000 ..:.o HIm.OH mo 00 pmumsHpmo COHmHomLQ HmquEHpqum .HHH pmudmno mo AmHv COHumsvm wch: 09 oocHELouoo "comm um mpcm>HOm oopmHH :H om\+om no adeppcm 00 COHpommmn .0000: mmHspmzuo mmchz Auxou 0000 :0: 08080000000 HHmo H080m£uochoc wchs 0000880 IuHo> OHHozo an oomm um oocHspoump ”momx muoosom .m> >8 8H Hmecmpoo H080om oHnHmpm>mmm ,o 0 00-00 0 0000 0000 2H.0 00mm 0 000 00H0Hq 2H.0 Hoceccoz 00 00-00 0H 0000 0000 2H.0 _ . sz0 0H pqu :OHUHH 2H.0 mcmcuoEOLUHz moonuoon 0o HIH08 >8 .oquOLpomHm uco>Hom wcproz owcmm 0 o .0800 HIme H00 0 m 00 n om< .0mscHeco0 .0 0H000 63 Table U. ASECK=§EC - §%c+) for the Ferricinium-Ferrocene Redox Couple in Various Solvents. Comparison with Predictions from Born Model. Asgca (Asgc Bornb Cal deg"l Cal deg-l Solvent mol"l mol-l Water -5 2.5 Formamide O 1.3 Methanol 3 6.“ N—Methylformamide H 2.0 Propylene Carbonate 11 2.6 Acetonitrile I 11.5 .9 Dimethylsulfoxide 12.5 3.3 Dimethylformamide 1“ 5.7 Nitromethane l“ 5.0 aReaction entropy of Fc+/Fc in listed solvent at 25°C; ob- tained from temperature dependence of Ef using nonisothermal cell arrangement "b" (see text). Experimental precision ca. :O.5-l e.u. bValue Of AS°C at 25°C predicted from the Born model; cal- culated from Equation (2) using dielectric constant data listed in Table 5. 6H (For definition of the terms used in Equation (1), see Equation (18) of Chapter III). According to the Born model, the reaction entropy for the Fc+/Fc couple is A330: -§%c+; therefore the simpler form of Equation (1) can be employed 2N dine l e " F 2eT(d2nT) (2) (AS;C)Born - ' in which r is the radius of the ferricinium cation, taken as 3.8 K (8H).. Values of dine/dlnT and literature sources for them are given in Table 5. 2. Couples Containing Polypyridine Ligands 3+/2+ 3 (where bpy = Formal potentials and reaction entropies for Fe(bpy) Cr(bpy)§+/2+,'Co(bpy)§+/2+, and Co(phen)§+/2+ 2,2'-bipyridine, and phen = l,lO-phenanthroline) were de- termined in various solvents. In addition, estimates of free energies of transfer A(aG;C)s-w, enthalpies of trans- fer A(AH;c)s-W, and entropies of transfer 13(AS‘EC’.C)S-W for the above redox couples when transferred from water to seven nonaqueous solvents were determined. These redox couples were selected for several reasons. The polypyri- dine ligands should provide an "insulating shield" around the central metal cation, and are not expected to interact strongly with the solvent so that the dielectric continuum treatments may provide a reasonable description of the 2 65 Table 5. Temperature Derivatives of Dielectric Constants for Various Solvents. S a _ 9&22 _ e2N (d2n€)b olvent e dfinT EET dlnT Water 78.5 1.360 9.65 Formamide 108.7 .98d 5'02 N—Methylformamide 182 2.5d 7.65 Propylene Carbonate 6u.9 1 14g 9.80 Acetonitrile 36.0 1.2f 18.56 Dimethylsulfoxide u6.7 1 our 12.h3 Dimethylformamide 36.7 1.113d 21.70 Methanol 32.6 1.143e 24.38 Nitromethane 36 1.23h 19.01 aDielectric constant at 25°C. bConstant term in Equations (1) and (2) for a given solvent calculated for T = 25°C. cReference 70. ds. J. Bass, w. I. Nathan, R. M. Meighan, R. H. Cole, J. Phys. Chem. 68, 509 (196M). eP. G. Sears, R. R. Holmes, L. R. Dawson, J. Electrochem. Soc. 102, 1&5 (1955). fG. J. Janz, R. P. T. Tomkins, "Nonaqueous Electrolyte Handbook", Vol. 1., Academic Press, N. Y., 1972. gR. Payne, I. E. Theodorou, J. Phys. Chem. 76, 2892 (1972). hc. P. Smyth, w. 5. Walls, J. Chem. Phys. 3, 557 (1935). 66 solute-solvent interactions. Indeed, these couples have been widely employed as inert outer-sphere reagents for homogeneous redox kinetics in aqueous media, and are an— ticipated to provide valuable model systems for investigat— ing outer-shell solvent effects upon electrochemical as well as homogeneous electron transfer rates. Some measurements of the solvent dependence of Ef for Fe(phen)§+/2+ and related couples (82) suggested that A(AG;C)SI-SZ may be quite small for such systems. It is therefore of interest to ascertain if such behavior, if confirmed for the other couples, is found for the structurally more sensitive en- tropic component A(AS§C)Sl-82, and also to test the ability of the conventional dielectric continuum treatments to pre- dict the magnitudes of these thermodynamic quantities. The comparison between Fe(bpy)§+/2+, Cr(bpy)§+/2+, and Co(bpy)?”2+ is of particular interest for exploring the influence of the electronic structure of the metal center upon the redox thermodynamics. Thus the iron and chrom— ium couples involve electron transfer into a t2g orbital (28), so that the charge should be extensively delocalized around the bipyridine rings via back bonding with the empty n-orbitals on the ligand (85). The cobalt couple involves 5 2 2s es tron will be localized at the metal center and the cobalt— 6 the transition t2g + t (28) so that the added elec- nitrogen bond distances will be substantially increased .in the lower oxidation state (85). Markedly larger values 67 of AS° have been seen in aqueous media for Co(bpy)%+/2+ re and Co(phen)§+/2+ (both 22 e.u. for ionic strength u = 0.05 M) (21) compared with those for the low spin couples + + e.u., respectively, for u = 0.05 - 0.1 fl (21,2h)); these , and Ru(bp3')§+/2+ (2, 3, and 1 effects have been attributed to differences in the extent of orientation of water molecules in the vicinity of the polypyridine rings (21,2h). It is therefore of interest to find out if such electronic structural effects upon asgc are obtained in other solvents. Table 6 summarizes the formal potentials Ef obtained for the polypyridine redox couples in each solvent at 25°C quoted relative to the corresponding values of Ef for fer- ricinium/ferrocene (Fc+/FC), [3;g;, Egc = Ef (redox couple) vs. s.c.e. — Ef(Fc+/Fc) vs s.c.e.], along with correspond-. ing reaction entropies Asgc. The formal potentials for each redox couple were obtained using either the oxidized or the reduced form of the reactant in the bulk solution as convenient, usually at a concentration of l mfl. Rever- sible or quasi-reversible behavior was normally obtained in that the cathodic-anodic peak separations were typically 60-80 mV. About 25 mfl of bipyridine or phenanthroline was added (as appropriate) in order to inhibit dissociation of the reduced complexes in solution. The absence of sig- nificant dissociation was confirmed from the equality of the anodic and cathodic peak currents and the lack of a 68 0802008 0;: 00.: 00 000- 0.0 000 00 00- 0.00 0.0 00003 $0 -9302 00.0 0 0 S 00- .0083 0.0.0 03 .00 0.0- 0.0.0 .000 0 0 0.0.0 0. 00830.00 000558 0.3 000 0.0 000 0 0 00 00.. 000000 200.0 080050 00.0 0 0 0 0 0.0.0 .007 000000 m00 H.o omv 0 000: 0 m 0 0 0.00 moan voaofiquH.o 00wxomasm 030050 0.00 0.00 00 000- m0 000 00 00- 0.0 2.. .0083 20.0 03.500 ao000¢ 000 00 000 3 00- .0083 .0400 0.0 000 00 000- 00 000 0.0 00- S 00.. 00003080 3008000 080Hzmo0m 0.0 50m OH 000: u m n.5m Ema: vm Nb: QOHOHAJSH.O 00080800m $000020 0.0 000 .2 000- .0 0 00 00- 00 00- 00003.?0 00002000 H .b bNH IV boon N mam. NN bml NN ma 1N303 a .O 000.03 :0om 00 0 00 0 00 0 00 0 00 0 A omHom + +N\+mAmmnv0o +N\+mA 0V m +m\+mA 0v 0 +m\+mfia0nmvoo .00:0>Hom 050000> 80 mmamsoo xo00m 0800H0hmmaom AHHV\AHHHV2.0om 00wmo008m 8oH0000m 080 0H00080pom H080om .o 0Hn0e 69 00 o om< 000 mm 00 0000000800000 000000000 A>8 om0vmm0000000m0m M000 000000-00000000V 000>000p 0000000>0000 hanwwms .00 00 0000000000000 000000000 0000000000 00 00000000000000000 .omm0 mo 00080000008 000000000 000>0000 000008800Ho> 00.00.0000.0 .00 0o .0 .00_0000>0000000000flwru0__000v000000 w0q0_ .0.0.0 00000000000 0000 000000 .0 00009 00 000000 000>000 0000 000 00SH0> 00000000 000 M 0.0 u 0 000000 000 00000 AAHV 0000000mv 000>000 0000 000 00008 000m 000 8000 0000000000 A01008 0.000 .00ov 0000800 +N\+mAmmnpznnom 0000000 0000000m0 .00000 000300000 00000: 00000000000 0800 00 00000880 momm .m> >8 000000000000 0000 00 000000 00000000ma80000000000 000 000000000 0080000 .01008 0:000 .000 000 00003 .A0000000 000 0x00 000v 0 00080m00000 0000 0080000000 I000 @000: 0m 00 0000000000 00000000800 8000 00000000 000>0om 000000 00 000000 00000 no 0000000 0000000mn .A0M00 000v 0000880000> 000000 M0000 00000000 .AAom\+0mvmm n A000000 00000V mm H ommv 00000000000 0800 00 000000 000000000\8=0 m n0000000m 000 m .0>.>8 00 000000 0080000 0000 00m 00 00>0m 000>000 00 000000 00000 000 000000009 0080000 .000000000 .0 0000B 7O dependence of Ef upon the added ligand concentration. The derived values of Ef were usually reproducible to within 1-2 mV. [As mentioned before (Equation (1“) of Chapter III) the actual values of Ef will generally differ slightly from the experimental estimates due to the inequality of the diffusion coefficients for the oxidized and reduced species. However, this difference is generally small (2-3 mV) and, most importantly, is similar for all the systems studied here so that it generally cancels when differences in Bf are considered, as in the present work.] For some systems, particularly with Co(bpy)§+/2+, larger peak separations (90-100 mV) were obtained, presumably resulting from slow electrode kinetics so that the derived values of Ef were known only approximately (:5-10 mV) under these circum- stances. Listed in Table 7 are estimates of the change in (Cged' 68x) for the polypyridine redox couples resulting from substituting the various nonaqueous solvents for water, A(AG;C)S-w, obtained from the corresponding values of (ABE-pf"W using Equation (3). o S-W = _ FC s-w o s—w A(AGrc) FMEf ) +.A(AGrc)Fc (3) (See Equation (8) of Chapter III for details.) Fc - )s w The apprOpriate values of A(Ef were obtained from the 71 :m a.a Am mw o: m.oa AW mus mm 5.0 AM mus memssmEOLan m.am m.HH Amnww om o.w Awnmw mofismspooasnpmefio Amumw ocfixooflsmflscpmefio Hm H.m Am mw Hm m.m Amnmw mm m.: Amumw mafippficoumoe :m o.w Amnmw mm m.w Amnmw mm m.m Amnmw oumconpmo mcoazdopm m.mH m.: Am mw ma H.: Amumw moHEprooasspmz-z . ii. a .3 o m a o m < o m a pcm>aom +mx+mAsanvoo +mx+mfisaavmm +m\+maagnvpo CH mmfiaopucm man A.HIHoE Hummo.amo HoE.HmoM CH mofidamcucm new mmfimmocm mmpmv .w magma ea mama EOLM Goudazoamo .mucm>aom msoapm> on pmumz Eomm mmadsoo xoomm mcfioaaza maom AHHV\AHHHVE mo memcmhe mo mofiooppcm cam .mmfiqamnucm .mmemem monk .5 magma 72 m4 93 ms dmu . oco oeop Am ouv nu pfiz o.m m.wm 0.5 Amnmw ooHEmELomahcpoEHQ m m m mm m a m.o mofixomazmamzposfio Am NV mom ON mom FoNl. . o L so be Am ov HH pH p a o.m Hm m.m HHHI mpmconpmo ocoazaopm Am ov o.m ma n.m HMO mofiEwELomHmcquIZ AH NV moan W OoN MoOl. Am.HV ooHEmapom has? 0 m . *0m\ om m + co Q o aimA : v o .umzcfipcoo .5 mfinme 73 .HIHOE.Hmox HH .mo canvas ou mumpzoom zanmnosg ohm omposo 3Im MA ooo pmoz .ooumsfiumm ma mofiEmELom IamzmeIz pom co>fiw mSHm> "Ammv monopommm Eonm :mxmu ocozumaonufic pom mm: oocmhmmom mo H>.ma magma :fi cofipwHHQEoo Eopm :mxmu muco>aom umos Lou mumo wo< .mcofiuoESmmm meaom mzoosvwco: op Loam; Eopm +w< mo wu< zwpocm mosh nonmcmpp mo mosam> unopwoom ca mocmhmmmfic Song cocamuno .oopmfia uco>aom msom3dmcoc ou mono: Eopm AHIHoE.HmoxV oaosoo osmooppoMIesacfiofippmm pom sommcmpu mo mwamco mosh wo mopMEHumm* .m mHQmE CH A20H0fiq fl H.o CHV uC®>HOm £06m how UmpmHH owmq mo mmzam> opmfipdopdam cmozpmn moosohmmmfio 80pm omQHMQQO .omumfia pcm>aom mzooscm Icoc on Loam: Eopm AHIHoE woo.Hmov 3Ionwmaom mzoosom Icon 0» Lopmz Eon“ AHIHoE.Hmo&v zlmfiommfiw wonwc pmzoa MACOHuQEmem mcoooppom mcfimz ..m.Hv o u 3wmaowcqv< pan» wcH Isommm >2 cocaouno mommnucoLMQ :H mozam> .Amv coauwzom wcfim: m magma :H co>Hw om\+om mbmpo> oaasoo xoomp comm pom 0mm mamfipcmuOQ HmEpom Bong vocfimuno .omumfia uco>aom msomsom Icon 0» poumz Eopm AHIHoE. Hmoxv 3ImA oocHom +m\+mficmvoo +m\+mAcmV2m +m\+mAmmzvzm .mucm>aom mzofium> ca mmaasootxooom mcHEmHo locoamcum ocm mcHE¢ AHHV\AHHHVZ pom mofiqomucm coapomom ocm.mamfiucmuom Hwenom .w canoe 78 mwza m m m m ocmnmeopsz mm: mm ome m w moHEmELomazcuoEHQ mm: mm map: a: NHHHI aeaxoeazmaanpmefio mam w w a a maeaeacoeaoa mmm :m anal w: mme opmconpmo ocmamooam 5mm . mm oon o: mmml ooHEmEpomamnumzlz me ma Hm:I :m Fowl mUHEmEcaom Ema ma moml ma new! hmumz 0mm nowm< womm nomm< momm pcm>aom em\+em +\+mm02mAmmzvsm +m\+mAaaavoo .emscapcoo .w wanes 79 .omeoHCoCmd ECHCoEEonCummCuop a H.o CH ooCHmpnoH .onOHq as mm :H emcHapnoa .mm mo pCoEoCCmmoE ooCCHooCQ CoH>mCoC OHCpoEEmpHo> oHmeme .mm no uCoEoCCmmoE ooosHomCQ zuHHHCSHomCHC .mm .0 .pm_ApCo>Homvonqu 2H.0—_Aomvonqu EH.o_ .o.o.m pCoEoowCCm HHoo mCHmDm .HIHoE Hlmoo .Hmo mam mpHCC mam mHCme CH oopmHHV mama pCmmeoo oHCpomHmHo opmHCQOCQQm on» UCm “Ammuv mdezoo mCHEw HHmEm on» Low opmHCQOCQQmV m m.m u C mCHomC wCHm: AAHV COHumsomv uCo>Hom Como Com HoooE CCom oCu anm coumHonmo COCpCo CoHuommmo I .ooCOC omHzmeuo mmoHCC oumHopuoon mEmm CH oomCoEEH .o.o.m mszo> .>E “:OHqu 2 H.o CH oHQCoo oCoooCCmMIECHCHOHCCmm Com HMHquCOQ HmEComo .HIHoE leoo .Hmo who muHC: mo UCm m quEmemem HHoo HCECmCuomHCOC mCHmC mm mo moCopCoqmo mCCumCmQEou Eomm omCHmuno qu>Hom oopmHH CH dezoo xoomp mo zqopqu CoHuowomn .Apxou oomv uppoEECpHo> OHHozo mCHm: omCprno .opmHoppooHo meow CH mHazoo oCoOOCCoM\ECH ICHoHCCom mzmpo> .>E CH opposo moouOC omHsmeuo mmmHCs oumHopuomHm wCHpCoaosm mo :OHOHA a H.o wCHm: .CECHoo umoH Com CH Cm>Hw pCm>Hom CH oHasoo xooop Com HmHuCoCOC HmEComm .oaachcoo .m mHnae 80 were required in order to prevent the dissociation of Co(en)§+ produced in the cathodic segment of the cyclic voltammogram,since equal cathodic and anodic peak currents were then obtained together with peak potential separa- tions that were typically in the range ca. 60-90 mVZ Meas- + urements of Ef values for Ru(NH3)g+/2+, Ru(en)§ /2+, Ru- (NH3)5NCSZ+/+, and Co(sep)3+/2+ in acetonitrile and nitro— methane were precluded by solubility restrictions; in addition, Ru(en)§+/2+ yielded irreproducible and ill- defined cyclic voltammograms in several solvents which restricted further the useful data that could be obtained for this couple. Estimates of the change in (aged — 58X) for amine redox couples resulting from substituting the various nonaqueous solvents for water, A(AG;C)S’W, were obtained from Equa- tion (3) and are listed in Table 9 . (These estimates are obtained using similar treatments employed for polypyridne M(III)/(II) couples.) The corresponding variations in Asgc for a given amine redox couple, A(AS§C)S'W, were obtained directly from the differences between the appropriate values of A8;c given in Table 8, and are also listed in Table 9 along with the corresponding enthalpies of transfer A(AH;c)S'w that were obtained from Equation (A). The valuesHom +m\+mgamvoe +m\+mgeavam +m\+mgmm2vam .AHIHoE HIwmo.Hmo CH moHQOCpCm mHIHoE.Hmox CH mmHQHmCqu oCm monCocm mopmv w oHnt CH mama Eopm ooumHsono .mpCm>Hom mCOHCm> 0» Logo; 80C“ mdesoo xoomm mCHEmHomCmHszm CCC mCHE< AHHV \AHHHVE ho ComemCB Co .on mmHQOCpCm UCm .Amv moHQHprCm .AHom * +\+mmozmflmmzvsm +m\+mfiddmvoo .oaachdoo .m mHame 83 .m mHnt CH ompmHH mpwv qumeoo oHCpoonHo oumHCQOCQQm on» ocm AmoHazoo mCHEm HHmEm oCu Com mpmHCQOCdamv m m.m u C msHomh wCHm: AAmV CoHumsomv pCo>Hom Como Com HoooE CCom on» song omumHsono AHIHoE.HmoxV mHasoo xoomC mo Commcmpp mo awCoCm ooCmm .w oHnoB CH uCo>Hom Como Cow oopmHH owm< Co mmsHm> mumHCoopdam Comzpmn mooCmCoMMHo Eogm ooCHmpoo .ooumHH qu>Hom msomzomCOC on Copmz Soap AHIHoE Hnmmo .Hmov 3ImfiommHom msoozom ICOC Op Cmumz EoCm AHIHoE.HMoxV 3IonmmHw zwmflowo Coon HACOHpQECmmm oCoOOCCmm mCHm: ..m.Hv o u swmfiomu .Amv CoHpmsom wCHm: m mHnt CH Co>Hw om\+om mCmCo> mHasoo xoomp Comm Com cum mHmHuCouOC HmECom Eopm ooCHmpno .oopmHH qu>Hom msoozom m ICOC on Loam: Eopm AHIHOE.HmoxV 3IonmoHom +N\+MAQmmVOO +N\+MAvaoo +N\+mfimmzvdm +N\+MAvadm +\+NmOZnAMmZV:m .gemsoeem oHsoH eqoaoeoHo sH monsoo xooom oCHawHooConnpm va oCHE< AHHV\AHHHVE.COM mmHmoepCm COHHowom CCo meHpCopom HoSHOC .OH opre .Auxmu oomv :m: pCmEowCCCCm HHmo wCHm: .Amomxv ooopuooHo ooCoCoCoC HoEono ooumpzumm MN >5 CH Coposv .HMHpCouoa HwEComC .zppossouHo> oHHomo wCHm: mozm Cqu ooCHopno .oquopuooHo oemm CH oHdsoo om\+ommmn>s CH ooposo moquomuooHo wCHuConsm mm :OHOHA SH.o wCHm: .uCo>Hom Co>Hw CH mHasoo xooog Com HmHuCoCOQ HCEComm 86 C C C p mwmI msz ooHEoEComHszoEHQ C C C a mom- emmu oonoCHsmHeseosHa H: mmmI ommI o o o oHHCpHCouoo< o o o o o o omeonCmo oConQoem C C C m wmon How: ooHsosCoCHHnoozuz C C C H onI mmmn ooHeosCom ma ooml mm m.» szl HmHI Hocmnumz m.e I NH I mHH m.mu ommu wmmHI cmm oomm< Comm Cum oowmq Comm Chm pCo>Hom Imquaeomvoo Imanaeomvom .muCo>Hom mCoHCm> CH moHasoo xooom Im\I A.m a COHusHom one Co mam m C .oom< UCo m Co CoHmeHECouoo ooosHooCQ CoH>mCon mHnHmCo>opCH zHHmuoBC op . omq oCm Cm Co muCoEmCCmmoE oocsHooCQ CoH>oCoC oHCpoEEmpHo> OHCCCCmo .owm4 CCm Cm Co mpCoEoCCmmoE ooUCHooCC muHHHCCHomCHo .HIHoE HIwoo .Hmo who muHC: .m HHoo HCECoCCOmHCOC wCHmC Cm Co ooCoo ICoQoo oCCmeoQEop Eoem ooCHmuCo pCo>Hom ooumHH CH oHQCOO xoomp Co onCpCm COHuomomo .ooscHosoo .HH oHoce 88 behavior with peak separations of 60 - 70 mV. Measure- ments of Ef for Fe(EDTA)'/2‘ in acetonitrile and propylene carbonate were precluded by solubility restrictions; in ad- tition, Co(EDTA)-/2- gave ill-defined and totally irrever- sible cyclic voltammograms in several solvents. Estimates of a(AG;C)S—w for CO(EDTA)-/2' and Fe(EDTA)-/2- were obtained from Equation (3) and are listed in Table 12. The corresponding variations in Asgc, A(As;C)S-w, along )S‘W with the enthalpies of transfer MAH;C for the two anionic redox couples are also listed in Table 12. C. DISCUSSION 1. Ferricinium-Ferrocene Couple The results presented in Table A for Fc+/Fc redox couple indicate that in contrast to the Born estimates (AS;C)BOPH, which are uniformly small and positive (1-6 e.u.), the experimental reaction entropies increase markedly from a small negative value in water (-5 e.u.) to sub- stantial positive values (ll-1h e.u.) in several dipolar aprotic solvents. These results clearly indicate that there are significant differences in the nature and extent of solvent polarization between ferricinium and ferrocene that are sensitive to the microscopic solvent structure. It was noted in Chapter IV, that the decreases in S: found for the transfer of a given cation from water to other solvents have been found by Criss and Salomon 89 CH Co>Hw oHasoo xoomp Como Com om Cm mHmeCouoa HoECOC EoCC ooCHouno .pCo>Hom msoosom ICOC ou Conn: EOCC AHIHoE.HmoxV zlonmo.mHv IHzCuoEHQ m.mH >.>H :H oonomHCm Hm.oHv IHmsooEHo m.wz 3.0m NH Aw.mHV oHHCuHCOCoo< m.w m.m 3.5 mCHEmECoC As.mv IHCsocEIZ m.: m.m o.: AH.mV oUHEmECom m.mm :.m N.H HH m m.H A>.mv Aw.mv HoCmCumz op on on on on on sumH omovo zImH omavo zumH ooovo zImH cmava snag cmavo :IaH ooava oso>Hom o n m o n m . o o Imanaeomv o ImquHom mCOHCm> op Coumz EoCC moHQCoo xooom Im\IAHom Como Com Co>Hm owm< Co moCHm> oumHCaoCddm Coozuon moocoCoCCHo Eopm ooCHmpno .CopmHH qu>Hom mCoozom ICOC op Loam: EOCC AHIHoE Iwoo .Hmov ZlmflommHom mzoozooCOC 0» Logo: EoCC AHIHoE.HmoxV 3Iwfiowx Coon HACOHCCECmmm oCoooCCoC wCHmC ..o.HV o u 3wonwc .Hmv CoHuosom wCHm: HH oHnt IdECmmm mBCB wCHms ..o.HV mI u 3wonwc oHCmB CH Co>Hw .ooscHosoo .mH oHooe 91 Q7 ,20) to be given by a characteristic "a" parameter for each solvent, where the value of "a" decreases as the internal order of the solvent decreases. As shown in Figure 2 (open symbols) it is seen that the experimental increases in (Sgc - §Fc+) in going from water to the other solvents do roughly parallel the corresponding "a" values in most solvents, as would be expected if.S§c+ varies with the solvent in a similar manner to S: for simple univalent cations, and if ch is not strongly dependent on the sol- vent. (Significant variations in SEC may occur, but will be of no consequence to the validity of the ferrocene assumption as long as they are accompanied by comparable variations in SFc+') It is interesting to note that the variations Of (SEC - §Fc+) for the most part do not cor- relate with the expected basicity of the solvent, as measured for example by "Donor Number" D.N. (81) (Figure 3 (open symbols)). A similar finding has been noted previously for monoatomic cations (20). The small negative value of (SEC — §§c+) in water has been noted previously (2“). This unexpected result has been ascribed to the delocalization of the reducing electron around the cyclopentadienyl rings leading to a net in- creased polarization of adjacent water molecules in the lower oxidation state (24). The enhancement of the water structure from the hydrophobic nature of the ferrocene molecule ("solvation of the second kind") (53,5fl) may also be a factor along with the involvement of quadrupole-dipole 92 interactions (5U). Such solvent polarization around the neutral ferrocene molecule may also occur in the other solvents, but is presumably outweighed by the greater tendency of the ferricinium cation to induce solvent ordering via ionjdipole interactions. In any case, the ferrocene assumption is clearly unsuited for estimating entropies of single ion transfer between different sol- vents, especially involving water or other hydrogen-bonded solvents. In view of the substantially larger observed variations in Asgc in changing from water to other solvents, A(AS§C)S-w, for the Fc+/Fc couple (Table u), compared with the corresponding dielectric-continuum predictions A(A8;c);;:n, it is of interest to compare these experimental results with the disparities noted previously between the values of transfer free energies for single ions AGE obtained using the ferrocene and alternative extrathermodynamic assumptions (98). As was mentioned in Chapter III, aside from the ferrocene procedure the most widely accepted approaches are: (l) the "tetraphenylarsonium-tetraphenylborate" (TATB") procedure; and (2) the "zero liquid junction po- tential" procedure (M8). Methods (1) and (2) have been shown to yield consistently similar values of AG? (usually within ca. 1 Kcal mole'l) between a wide range of solvents (A8,55). However, the values of AGE for ion transfer from water to other solvents, (AG3);;W, obtained using the 93 ferrocene procedure have been found to be consistently less positive than the corresponding values, (AGE)§‘W and (AG%)§-w, obtained using methods (1) and (2), respec- tively. Assuming for the moment that methods (1) and (2) S-W H " 0 yield the true transfer free energy (AGt)true’ the altera- tion in the free energy difference (3%0 — 5% ferrocene and ferricinium upon transfer from water to c+) between another solvent, A<5Fc - §§C+)S_w, can be obtained from Ms. - W = was?“ - wail-.11. TableZL3consists of estimates of A(U§C - 5%C+)s-w obtained using Equation (5) from values of A0; for Ag+ and Cu2+ tabulated in References U8 and 50, along with the corresponding values of TA(S%C - §%c+)s-w extracted from the data given in Table n. It is seen that the increasing S-W obtained for solvents of decreas- .. 0 __o values of Ao so Com monCoCo CoCmCmCu CoH wCHmC «Amy COHuosom Eopmo .m: ooCoCoCmm Co H>NH oHnt CH mums Eopm ompmHCOHmo +m< COC monCoCo CmCmaCu COH wCHm: .Amv COHpmsum Eopmn .oopmoHoCH conuoE on» wWWm: Hmv CoHumzom mAHv Cocuozu =C0deszmm< mznmm2 Co>Hw omosu Hmzoo ou noECmmm .om ooCoCoCom Co H> oHnoB EOCC +m EoCC CoumEHpmo mooumHH uCo>H0m on Loam: Eopm wCHowCo CH zImA+omU I o v CH COHpmHCm>o :.m m.5 o.m 0.: HoCmem: m.z m.m m.: H.m mHHCuHCOCoo< m.m H.: 5.m 5.m ooHEmECOCHACuoEHQ o.m m.m o.m o.m oonomHsmHzCuoEHQ 5.: . :.m m.m . m.H opwconpwo oCoH>Q0Cm m.H III o.m H.H mUHEmEhom HIHoE Hwox o.oAmv ooCuoz c.9Amv ooCuoz 0.9AHV oonpoz uCo>Hom o o o o CH+ mI I mmvae HIHos Hcog zImH+ m: I mmvaI m .oommne Com 3ImA+oml I ommve moHCOCpCm CoCmCmCB wCHoCoammCCoo Cqu ooCoQEoo .Amv COHumsom wCHm: ooCHmpoo 3ImH+omm I omwv< mpCo>Hom CoCuo mCoHCm> 0» nova: EOCC oHQCoo xooom oCoOOCCoCIECHCHoHLCom Com monCoCm comm CoCmCmCB Co momeHpmm deoHCmB 95 .S H.o u 1 CuwCoCum OHCoH Com : oHCmB CH Co>Hw moCHm> EoCC ooCprno mooumHH uCo>H0m on Loam: EOCC wCHowCo CH A+omm om omv CH CoHumHCm>C .muxou mom mAmv COCuozU :CoHudECmmm HmeCopoo COHpoCCw UHCUHH oCoN: hp Co>Hw omoCu Hosvo on ooECmmo ozhu zIm cho .oossHocoo .mH oHnoC. 96 by either method (1) and (2) are approximately correct, then from the data in Table 13 it follows that typically _ —O _ -0 A _O _ -0 . . —O _ _o A(GFc+ GFc+) m T (SFc ch+)’ 242—” that A(HFc HFc+ NC. This suggests that a primary reason for the probable ) break-down of the ferrocene assumption is simply the greater tendency of solvent dipoles to be polarized by the ferricin- ium cation compared with the ferrocene molecule, to an extent which is greater than predicted from the Born model and sensitive to the microscopic structure of the solvent. 2. Polypyridine Redox Couples The data presented in Tables 6 and 7 for polypyridine couples exhibit three interesting features. First, the values of asgc are markedly larger in nonaqueous solvents compared to water, especially in aprotic media where A(AS§c)s-w m 20-“0 e.u.. Second, there is consistently an approximate compensation between A(A8;C)S'W and l.\.(AH;c)S'W so that the values of A(AG§,’,C)S‘W are uniformly small and negative in the range 0 to -3 Kcal mol'l for all four poly- pyridine couples on the basis of the TATB assumption em- ployed here. Third, although the absolute values of As. than for Cr(bpy)§+/2+ and Fe(bpy)§+/2+ (Table 6), the values for the Co(III)/(II) couples are 15-20 e.u. larger Of A(AS;c)s-W in a given solvent are approximately the same for all four polypyridine couples (Table 7): The simplest theoretical treatment of such outer-shell 97 solvent effects is to utilize the Born dielectric continuum theory. This model might be expected to be more applicable to the estimation of A(AG;C)S"W for the present systems since the polypyridine ligands should act to shield some- what the solvent from the metal cation, and several com— plicating factors may cancel out in the measured difference of transfer free energies between the oxidized and reduced S-W forms. The Born estimates of A(AG;c) can be obtained from Equation (6) 2 Z A(AG;C)183;¥n = #(i - -1-)<—93‘- - £951) (6) Calculations using ZOX = 3, Z = 2, and radii appropriate red for the M(III)/(II) polypyridines (rOX = rred : 6.8 X (73)) o s-W yielded values of A(AGrc)Born for the various solvents here 1 that lie in the range -l.5 to l Kcal mol‘ Bearing in mind )s-w are probably that the experimental values of A(AG;C trustworthy only to within ca 1 Kcal mol"l due to the likely uncertainties in the TATB assumption (“8), the agreement can be considered to be reasonable. The comparison between the experimental and Born esti- mates of the reaction entropies is of greater interest since it enables the applicability of the Born model to be tested in a single solvent. Values of (AS° s-w PC Born = 6.8 A are given for each sol- calculated from Equation (1) for rox = rred vent in Table 6. The experimental values of asgc are seen to be typically in marked disagreement with corresponding 98 Born predictions (AS;C)Born‘ A milder test of the Born model isto compare the observed solvent dependence of asgc, A(AS;C)S'W, with the corresponding differences in o o 3"“ (Asrc)Born’ A (A3 (Table 6), indicating that the 0 re Born enhancement of solvent polarization ("ordering") in the tri- positive versus the dispositive oxidation states is in most cases greater than predicted from macroscopic dielectric considerations, probably as a result of dielectric satura- tion in the vicinity of the solute. The Born model also fails to account for the markedly larger values of Asgc seen for Co(bpy)?”2+ and Co(phen)§+/2+ compared with + + Cr(bpy)§ /2 and F'e(bpy)%+/2+ in each solvent. In recent years there have been a number of attempts Figure 1. 99 Plots of A(AS§’,C)S'W for each polypyridine redox couple against the corresponding Born estimates A(AS° )3"w obtained from the values of (As; rc Born c)Born calculated for water and the appropriate non- aqueous solvent using Equation (1) (see text). Key to this and Figures 2 and 3.‘ Redox couples: 0 Cr(bpy)§+/2+, I Fe(bpy)§+/2+, K. Co(bpy)§+/2+, ' Co(phen)§+/2+, O Ferricinium/ferrocene. Solvents: l, formamide; 2, N-methylformamide; 3, propylene carbonate; A, dimethylsulfoxide; 5, dimethylformamide; 6, acetonitrile; 7, nitro- methane. lOO 4o - ' ‘ so — - 'I' o E A 7 5 T. :7 . \« g 4 ‘ \ . 20 — ‘ _ ‘6 3 6 k) '3 O 00 3?: m 5‘ I0— 2 .. G O J l -5 o s w 5 - -l -l A(AS,%)Bom, col. deg mol Figure 1 IO 101 to provide more successful treatments of ion solvation, either by modifications to the Born model (93) or by the development of fundamentally new approaches (gua). How- ever, most effort has been devoted to the utilization of these treatments for the estimation of solvation free energies in aqueous solution, and little attention has been paid to the estimation of solvation entropies, par- ticularly in nonaqueous media (9Ub). It has been found .that reasonable agreement with experimental solvation entropies for monatomic cations in various aprotic solvents can be obtained using a modified Born model where the first solvation layer was assumed to be dielectrically saturated (9ub). Direct application of this approach to the present systems does indeed yield estimates of A830 that are larger than (AS° rc)Born?and in some cases closer to the experi- mental values. However, it is uncertain that the model is entirely appropriate to the present systems where the first solvation sphere is occupied by the coordinated ligands, and in any case it is unable to account for the observed variations of Asgc with the metal spin state or the small values of Asgc seen in hydrogen-bonded solvents. More sophisticated solvation treatments which take into account the molecular structure of the polar solvent (914a) should ultimately yield accurate descriptions of the experimental results. However, these models in their present form are not entirely applicable to the present systems since neither 102 chemical interactions between the complexes and their im- mediate environment nor dielectric saturation effects are fully taken into account (Qua). Such effects should pro- vide an important influence upon the redox thermodynamic parameters considered here since these quantities reflect the change in solvent polarization resulting from decreasing the solute charge from +3 to +2. The remaining discussion will therefore be concerned with the utilization of more "intuitive chemical" approaches for rationalizing the ex- perimental behavior. The uniformly positive values of A(AS§’,C)S'w indicate that the increase of the metal oxidation state from +2 to +3 yields a relatively greater enhancement in the extent of solvent polarization ("ordering") in the vicinity of the complex for nonaqueous solvents compared with the same process in water. Such differences can be simply explained by the unusually high degree of internal order exhibited by liquid water. Thus the additional cationic charge carried by the oxidized compared to the reduced form of the redox couple will generate a greater degree of solvent polarization in the vicinity of the solute in solvents having a smaller degree of internal order due to the relative ease by which solvent molecules can be disturbed from their bulk orienta- tion in response to the electric field. If the same factors that determine the ionic entropies of univalent ions §° also influence the values of Sax relative to Sged_ for the 103 M(III)/(II) polypyridine couples, it would be expected that A(As;C)S-w would be linearly related to -a. Such a plot is given in Figure 2. It is seen that there is indeed an approximate correlation between the values of A(AS§C)S'W for all four polypyridine couples (closed symbols) and -a. Thus relatively small values of A(ASl‘3,C)S"W ($15 e.u.) are observed in formamide and NMF that are expected to be polymerized to some extent via hydrogen bonding (l7). Larger values of a(As;C)S-w (20-“0 e.u.) are seen for the aprotic solvents PC, DMSO, DMF, and acetonitrile which are expected to have relatively small degrees of internal order. These solvents have sizable dipole moments which should encourage additional solvent ordering around M(III) compared to the corresponding M(II) polypyridine complexes via ion- dipole interactions. There is also the possibility that the observed solvent dependence of asgc may arise from variations in the ability of the solvents to engage in donor-acceptor interactions with the M(III) state to a greater extent than with M(II). If this factor does indeed provide a major contribution to isgc, then a correlation between MAS;c s-w and the donicity of the solvents would be expected. Although it is dif- ficult to formulate quantitative scales which reflect the electron donating abilities (or basicity) of solvents, one such measure which has proved useful is the so-called Donor Number (D.N.) (81). Figure 3 contains plots of Figure 2. 104 Plots of the variation in the reaction entropy a(As;c)S-W for a given polypyridine redox couple when changing from water to various nonaqueous solvents against -a, where "a" is a parameter related to the degree of "internal order" of each solvent (17,20). Values of A(AS§’,C)S-W taken from Table 7. The straight lines are drawn between adjacent points for a given redox couple in the various solvents. Key to redox couples and solvents as in notes to Figure l. 105 ‘1. 40% .2 Tomb _oo BImH 05 o mdvd _ m l5 -o, col deg"I mol" Figure 2 106 )S-W Figure 3. Plots of A(AS§C for each polypyridine redox couple against the "Donor Number" for the various nonaqueous solvents (81). Key to redox couples and solvents as in notes to Figure 1. 40 107 T. 30 r o E '3‘ ‘ T\' “o s \ 9‘ 20 v $ . a)" . OE . o 5 4 U) <1 6 <1 3 l0 0 J l l 0 IO 20 30 Donor Number Figure 3 108 A(A8;C)S-w against the values of D.N. quoted in Reference 81. In contrast to Figures 1 and 2, it is seen that there is no correlation between the values of D.N. for the various solvents and A(AS§C)S‘W. On the basis of Figures 1—3, it therefore appears that the large changes in Asgc observed when the solvent is varied are primarily determined by the relative ability of the tripositive M(III) polypyridine complex compared to the corresponding M(II) species to disturb the bulk solvent structure and reorientsolvent molecules within its vicinity. The use of the macroscopic dielectric constant in the Born model presumes that such solvent polarization is minor. Nevertheless, it is interesting to note that at least qualitatively similar variations in Asgc with the nature of the solvent are predicted by the "a" parameter, and the simple Born treatment, inasmuch as the correspond- ing plots in Figures 2 and l have similar shapes. This similarity reflects the interrelationship between the internal order of solvents and their macroscopic dielectric properties, and suggests that both these factors play a major role in determining the alterations in the degree of solvent order- ing induced by M(III) vs. M(II) polypyridines as the solvent is varied. In contrast, the almost complete lackImfcor- relation between 13(11381‘i,’,c)s"W and the solvent Donor Number suggests that the changes in relative solvent polarization on the nature of solvent only depend to a minor extent, if 109 at all, on the ability of the solvent to coordinate to the cationic solute. Although there may well be substantial variations in solvent polarization in the vicinity of the M(III) polypyridine complexes as the solvent is altered arising from variations in the solvent coordinative abili- ties, if present they appear to be largely compensated by similar changes for the corresponding M(II) complexes. Nevertheless, the apparent sensitivity of AS° rc to the sym- metry of the orbital occupied by the reducing electron sug- gests that the extent of solvent polarization in the oxi- dized state relative to the corresponding reduced form in a given solvent is indeed sensitive to local, and presumably short-range, solvation factors. The strikingly smaller values of Asgc (l-H e.u.) seen in aqueous solution for Cr(bpy)§+/2+, Fe(bpy)§+/2+ (Table 6), FeIphen)§+/2+, and Ru(bpy)§+/2+ (21,2A) compared with the values for Co- (bpy)%+/2+ and Co(phen)?”2+ (22 e.u.) probably arise from the delocalization of the reducing t electron around the 28 aromatic rings for the Fe(III)/(II), Ru(III)/(II), and Cr(III)/(II) couples; this delocalization will be largely absent for the Co(III)/(II) couples which involve the 6 5 2 2s 7 t2398' (21,2U), this electron delocalization may influence Asgc electronic transition t As noted previously by inducing an increase in solvent polarization in the vicinity of the aromatic rings in the reduced state com- pared with the oxidized form which will counteract the 110 normal entropy increase resulting from the decrease in solvent polarization close to the metal redox center. Evidence supporting this contention includes the negative value of Asgc (-5 e.u.) found for Fc+/Fc in aqueous solu- tion (2“). The structure of Fc+/Fc differs from the poly- pyridine couples in that the compact "sandwich" structure of the former couple should prevent the close approach of solvent molecules to the metal redox center that can occur along the channels formed by the more open polypyridine rings. Therefore the only major factor contributing to isgc for the Fc+/Fc couple is presumed to be the additional solvent polarization in the reduced state arising from the delocalization of the added ligand around the cyclopenta- dienyl rings, yielding a negative value of asgc (2A). As noted above, the values of Asgc for Co(bpy)§+/2+ and Co(phen)?”2+ compared with those for Cr(bpy)§+/2+ and Fe(bpy)§+/2+ are also consistently 15-20 e.u. larger, not only in water, but also in all seven nonaqueous sol- vents (Table 6). This simple result is surprising; the tendency of the various solvents to be oriented by the delocalized electron might be expected to be dependent to some extent upon solvent properties such as the extent of internal order or the amlity to act as an electron acceptor. However, the behavioral simplicity may be misleading in that it could arise from a fortuitous cancellation between several effects. Thus the degree of internal order of several of 111 the solvents used here vary roughly with their expected tendency to act as electron acceptors as measured by the sso-called "acceptor number" (81). The extent of solvent c)rientation induced near the aromatic ligands could remain gaiJUlar when changing, for example, from water to DMF since tacoth the degree of internal order and electron accepting eafbility of the solvent are thereby diminished. The approximate compensation between corresponding \railues of TA(ASl"-3,C)s"W and A(AH§’,C)S""W for polypyridine couples srixelding markedly smaller values of A(AG;C)S’W (Table 7) huats often been observed for entropic and enthalpic quanti- tziees in electrolyte solutions (95). , Such a compensation is Iezcgoected since the (entropically unfavorable) orientation of scaZLvent molecules as a result of ion-dipole interactions, :fcazr example, would necessarily yield favorable enthalpic Glazinges. Although A(AG;C)S’W is frequently close to zero, ‘tluea values are typically negative (at least on the TATB S<3£ile) so that the entropic factors appear to provide the predominant influence upon the free energies of transfer. Measurements of reaction entropies for the Fe(phen)§+/2+ aluCi related redox couples having methyl groups substituted al?<:und the phenanthroline ring have been previously com- Euilaed in acetonitrile and water (26). The value of Asgc gisven for Fe(phen)?”2+ in acetonitrile (25 e.u., u = 0.1 (253)) is close to our value for Fe(bpy)§+/2+ in this solvent (23 e.u., Table 6). However, the value of isgc reported in 112 Reference (26) for Fe(phen)%+/2+ in water (-20.5 e.u.) is markedly different than the previous determinations for Fe(phen)?”2+ and Fe(bpy)§+/2+ (3 and 2 e.u., respectively, p = 0.05 (21)). Since values of A550 close to zero have galso been given earlier for these and other low-spin M(III)/- (II) polypyridine couples in aqueous solution (96), the ciisparate value for Fe(phengw2+ quoted in Reference 26 is presumably in error. One possible source of this dis- crepancy is the confusion that can be caused by the in- discriminate use of alternative entropy scales without clearly identifying which scales are being employed. As pointed out in Reference (21), the values of asgc obtained from a nonisothermal cell arrangement as employed here differ markedly from the frequently quoted "reaction en- tropies" ASE that actually refer to the overall entropy Change for an electrochemical cell containing a hydrogen reference electrode; it can be shown that (211) A330 AS° + 20.5 e.u. Some, but not all, of the "reaction H entropies" quoted in Reference 26 are actually values of AS° rather than A830. H In the next section values of Asgc and A(AG;C)S'W ob tained for amine and ethylenediamine redox couples will be discussed and compared with those for polypyridine Couples . 113 :3. Ammine and Ethylenediamine Couples Inspection of the data presented in Tables 8 and 9 Ireveals that substantial changes in the redox thermody- 1ruamics of ammine and ethylenediamine redox couples occur ‘vvhen the solvent is varied. Two main features are appar- esent. Firstly, the values of A(AG;c)S'w vary over a wide :rrange, from ca. -u Kcal mol"1 in nitromethane to around 8 IK:cal mol—1 in DMSO, the values being usually within ca. 1:).5 - l Kcal mol"l for all four amine couples in a given Solvent. Even larger variations in 13(AHé’,c)S"w are seen C ca. -l.5 to 15 Kcal mol-l). The solvent sensitivity of .£3(AG;C)S"W contrasts with the behavior of the M(III)/- C II) polypyridine couples, where the values of A(AG;C)S‘W ‘vwere typically small and negative (Table 7). Secondly, ‘tzhe values of asgc are uniformly and markedly larger in rlonaqueous media compared with water, especially in aprotic ssolvents where A(AS§’,C)S'w approaches 30 e.u. Broadly ssimilar values of A(AS;C)S-w have also been observed for the Ibolypyridine couples, so that the differences in A(AG;C)S‘W t>etween the saturated amine and polypyridine couples are czhiefly due to the enthalpic component A(5H;C)S'w. How- eaver, the values of Asgc in a given solvent are, as before, ssensitive to the nature of both the metal and the co— <3rdinated ligands. As for polypyridine couples, it is instructive to compare the experimental values of A(AG;C)S-W, A330, and 114 23(A8;C)S-w for amine and ethylenediamine couples with the czorresponding predicted values from the Born model 23(AG° c)Born’ (Asoc)Born’ and A(ASrc gogn' These latter cauantities were obtained from Equations (1) and (6). s- w ‘Ufialues 0f (AS;C(Born and A(AG° rc Born calculated from Equa- ‘t;ions (1) and (6) for Zox'= 3, Zred = 2, and Pox = rred = ;E;.5 A (appropriate for the small amine couples (73))are gg;iven in Tables 8 and 9, respectively. Comparison of A(AG° c)Born with the corresponding ex- 1;>erimenta1 values A(Ach)S W (Table 9) reveals, not un- eaexpectedly, that the Born predictions are frequently in 21.arge and even qualitative disagreement with experiment. IIIn particular, large positive values of a(AG;C)S’W (ca. ES-8.5 Kcal mol-l) are observed for all five amine couples :fi.n the strongly basic solvents DMSO and DMF (D.N. = 29.8 {Elnd 26.6, respectively (81)) in contrast to the negative ‘Kralues Of A(AG° c)Born predicted for these solvents (Table 59). Nevertheless for the other five, less basic, non- Elqueous solvents the values of 13(AG;’.C)S-w and A(AGrc Eggn Iatgree at least qualitatively and are indeed in close agree- Iilent for the weakly basic solvents propylene carbonate, Etcetonitrile, and nitromethane (D.N. = 15.1, lh.l and 2.7, IPespectively (81)) for which negative values of A(Ach)s-w Eire observed (Table 9). [Although these transfer free Genergies naturally rely upon the choice of water as the 'reference solvent, water also appears to be a relatively 115 tweak electron donor (D.N. : 18 (81)).] These considera- tzions therefore suggest that long-range solvation influences rnay provide an important part of the additional solvation eanergy for the oxidized versus the reduced forms of these .I?edOX couples, at least in solvents of low basicity where sshort range solvent-solute interactions of the donor- .Eicceptor type should be relatively weak. However, if donor-acceptor interactions are instead jg>roviding the predominant contribution to the solvent— y Mayer et a1. (97), as well as for the other amine couples <::onsidered here, a linear correlation between the experi- Iriental values Of A(AGiicfi"W or A(AH;C)S'W and the solvent ZEDonor Number (or a related measure of the solvent basicity) ‘vwould be expected. Figure A consists of such plots for C30(en)§+/2+ and Ru(NH3)g+/2+. [Similar plots were obtained ifor Ru(en)%+/2+, Ru(NH3)5NCS2+/+, and Co(sep)3+/2+ but Eire omitted for clarity.) It is seen that there is indeed £1 reasonably linear correlation for both A(AG;C 5’" and A (angcfi‘w with the solvent D.N. for both couples in the ssix nonaqueous solvents for which Donor Numbers are avail- Eible, although the values of A(aG;C)S'w and A(AH;C)S’W ign nitromethane are decidedly less negative than expected. IX related plot of Ef for Co(en)§+/2+ [meaSured versus the "reference solute" couple bisbiphenylchromium (I/0)] against D.N. for a number of nonaqueous solvents has previously Figure A. 116 Plots of the variation in the free energy of reaction, a(AG;C)S‘W, and the enthalpy of re- action, A(AH;C)S‘W, for Co(en):33+/2+ and Ru(NH3)g+/2+ when changing from water to various nonaqueous solvents against the "Donor Number" for each solvent (81): Closed symbols: a(AG;C)S-w. Open symbols: A(AH;C)S‘W. Redox couples: a, o, Co(en)§+/2+;I, 0, Ru(NH3)g+/2+. Sol- vents in this and Figures 5, 6 and 7: l, formamide; 2, N—methylformamide; 3, propylene carbonate; u, dimethylsulfoxide; 5, dimethylformamide; 6, acetonitrile; 7, nitromethane. The straight lines are drawn between adjacent points for a given redox couple in the various solvents. 117 _ _ _ 0 l5“- .-e e 5,..llsflea IO . Donor Number Figure A 118 t>een shown by Mayer et al. to be approximately linear (97). 'JThis result provided the chief basis for their assertion tzhat donor-acceptor interactions between the solvent and ‘t;he acidic amine hydrogens on Co(en)§+ provided the pre- avrailing contribution to the solvent influence upon the Jr'edox thermodynamics of Co(en)§+/2+. Although the present ciuata do not entirely contradict this conclusion, they sug- ggpest instead that such short-range interactions may be of ';>:redominant importance only with the more highly basic ssr Ru(NH3)g+/2+, Ru(en)%+/2+ and Co(en)§+/2+, and C3<>(sep)3+/2+ couples that contain eighteen, twelve, and ESILx amine hydrogens, respectively, is somewhat surprising C311 this basis. One plausible explanation is that there 5.55 only one solvent molecule strongly coordinated to each Einnine center anyway as a consequence of electrostatic and fistseric limitations. Another surprising result is the EIpparent insensitivity of A(AGE’,C)S-w to the electronic EStructure of the metal center in the reduced state. For 119 3+/2+ (example, Ru(en)3 and Co(en yield comparable values )3+/2+ 3 (of A(AGI°,,C)S-w in both DMSO and DMF (Table 9). This be- ldavioral simplicity may well have some utility in that slalues of AEgc could presumably be predicted with some (zonfidence for redox couples for which measurements of Ef Ieare impractical [e.g., Co(NH3)g+/2+]. One inevitable difficulty in interpreting such experi- S-W Iriental estimates of a(AG;C) lies in the uncertainties :i.nherent in the extrathermodynamic assumption required :ffor their evaluation. Thus the values of A(AG;C)S'W based <:>n.the ferrocene scale (given in parentheses in Table 9) ga;re up to 3,5 Kcal moi-l larger than those based on the CEEATB scale; the former values are uniformly positive except :i.n.nitromethane (Table 9) so that it would be concluded ‘tzhat the Born model is noticeably less successful for pre- 3gvents of relatively low basicity such as propylene car- tflbrlate and nitromethane give rise to values of a(A8;C)S-w tllat are comparable to, or even larger than, those ob- tziined in the strongly donating solvents DMSO and DMF. leso, if such donor-acceptor interactions were important it would be expected that the values of A(AS;C)S-w in a given solvent would be greater for couples containing likely electron acceptor sites compared to couples of similar size and charge type not containing such ligand sites. In fact the opposite appears to be the case. For example, the values of A(AS?C 5“" in each nonaqueous solvent listed in Tables 7 and 9 increase in the sequence Co(en)§+/2+ < Co(sep)3+/2+ < Co(bpy)?”2+ ” Co(phen)?”2+ even though )§+/2+ 3+/2+ contain a total of twelve and Co(en and Co(sep) six amine hydrogens, respectively, and the last two couples contain no amine hydrogens or other clearly identifiable acceptor sites. A more successful correlation than Figure 6 is ob- tained by plotting the experimental values of A(AS;C)S-W Figure 6. 123 Plots of A(A8;’_c)5-W for each amine redox couple against the "Donor Number" for the various non— aqueous solvents. Redox couples: 0 , Co(en)§+/2+- I , Ru(NH3)g+/2+; O , Ru(en)§+/2+; A , Co(sep)3+/2+. 124 30r- 20 Donor Number IO Figure 6 125 for each couple against -a for each nonaqueous solvent (Figure 7), where "a" is an empirical parameter (17,20) that provides a measure of the degree of "internal order" (the extent of association between solvent molecules in the bulk liquid (17)). It is seen that A(AS‘I’,C)S"'w increases almost uniformly with decreasing solvent internal order. These plots have similar shapes to those for the poly- pyridine redox couples (Figure 2), although the present plots are significantly less linear and have smaller lepes. ‘The success of this correlation suggests that the values of AS° are at least partly determined by the ease by re tNhich surrounding solvent molecules are able to reorientate aiway from their bulk structure in response to the enhanced tailectric field around the oxidized versus the reduced forms CDIT the redox couple. These results therefore argue against the predominant j1rr1portance of solvent-solute donor-acceptor interactions in Cieaetermining the degree of this additional solvent polariza- t::1.cnn Although at first sight surprising, this conclusion :iuss quite compatible with the apparent sensitivity of the f‘n:~Iee energy term A(Ach)S"W to solvent basicity since the e177171301310 terms Asrc and hence A(ASl‘ZC)S"W should respond 13C) the extent of solvent ordering induced, rather than the =3't32rength of the donor-acceptor interactions themselves. Pr‘ ovided that such enthalpic-based interactions are suf- f:‘LQiently strong to ensure that the solvent molecules in Figure 7. 126 Plots of A(AS§C)S-w for each amine redox couple against -a, where "a" is a parameter related to the degree of "internal order" of each sol- vent. Redox couples: . , Co(en)§+/2+; . , Ru(NH3)g+/2+S . ’ Rummy/2+; . , Co(sep)3+/2+. Key to solvents as in notes to Figure 4. 30 127 col. deg?" mol" 7 4 .3 .. a)“ Q 3 (013' I0— q 2 <1 0 l . I I O 5 IO l5 -o , col. degT' mol" Figure 7 20 128 contact with the amine ligands are strongly oriented, variations in the strength of the donor-acceptor inter- actions may have only a relatively minor influence upon the extent of this orientation. Indeed, the markedly larger experimental values of Asgc in a given solvent com- pared to the Born predictions (Table 8) suggest that there commonly is extensive additional short-range solvent polarization induced by the oxidized form of the redox couple, most likely involving oriented solvent molecules in the first solvation sphere. Nevertheless, some influence of solvent donicity upon .Asgc for couples containing electron acceptor sites rnight be expected. Indeed, a comparison of the plots of 23(Asgc)s’w versus D.N. for the saturated amine couples (leigure 6) with the corresponding plots for the polypyri- Cizine couples (Figure 3) reveals that the values of £3 (:Asgc)s'w for the former systems tend to increase more C <::r decrease less) with increasing D.N. in comparison with 'tzlrnose for the latter systems. Further, a number of aquo :r=lution (21). These differences are most likely due, at jlosseast in part (23), to the greater extent of hydrogen 1=>~::>nding between the more acidic hydrogens on the aquo 3~21.gands with surrounding oriented water molecules (21). 129 In view of the foregoing discussion it is interesting to examine the effects of donor-acceptor interactions between anionic redox couples and solvent molecules upon the redox thermodynamics. These effects are now discussed in the following section. 4. Anionic Couples Inspection of the data presented in Tables 11 and 12 indicates that the redox thermodynamics of Fe(EDTA)'/2' and Co(EDTA)'/2‘ vary considerably with the nature of the solvent. Similar to the cationic redox couples, the values of Asgc are larger in nonaqueous media than in water, which resultsixluniformly positive values of a(A8;C)S'w. The formal potentials for the two anionic redox couples (quoted versus Fc+/Fc) become more negative (i;e;, the values of A(aG;C)S'W become more positive) when water is replaced by other protic and subsequently aprotic solvents. These data indicate that the predominant contribution to A(AG;C 8'" arises from the enthalpic component A(AH;C)S‘W. As expected the simple dielectric continuum Born model is unable to predict the observed variations in A(AG;C s-w .for the anionic redox couples. Similar to the cationic I°edox couples the interactions of Fe(EDTA)'/2- and Co— (IZDTA)—/2' with the solvent molecules can be discussed in t:errms of donor—acceptor interactions. It has been sug- gested by Gutmann and coworkers (89-91) that the solvent 130 generally can be regarded as an electron acceptor when interacting with anions. Figure 8 consists of plots of values of A(Ach)s-w and A(AI—Iéicfi"W against the solvent acceptor number (73) for Fe(EDTA)'/2’ couple. It is seen that there is a reasonably good correlation between S-W S-W A(Ach) or A(Ach) and the acceptor number. In order to explain these observations, one should consider the interaction of solvent molecules with both the oxi- dized and the reduced forms of the redox couple. In the two anionic complexes considered here a charge decrease in the central metal ion upon reduction will lead to a more net negative charge on the reduced species which in turn en- hances its donor property and stabilization compared to the oxidized form. Such a difference in stabilization of the reduced and oxidized forms of the redox couple shifts the formal potential to a positive direction (Elia: A(Ach)S-w shifts toward smaller value) as the acceptor number of the solvent increases. Similar to the cationic complexes containing poly- pyridine and amine ligands, it is interesting to note that the values of A(AG;C)S'W for Co(EDTA)'/2' and Fe(EDTA)'/2- .are also insensitive to the electronic structure of the nietal center. Table 12 reveals that there is an excellent .aégreement between values of A(AG;C)S'W for the two (EDTA) <3 formamide > N-methylformamide 135 (Table 11). Plots of Asgc versus donor number or acceptor number for the two (EDTA)-complexes exhibit little correlation. On the other hand, similar to the cationic redox couples containing polypyridine and amine ligands a more success- ful correlation is obtained by plotting the experimental values of A830 versus "a" (Figure 9). Figure 9 shows that As;C increases almost uniformly as the extent of association between solvent molecules decreases. These results further indicate that the values of Asgc when the solvent is varied are mainly determined by the ease by which surrounding sol- vent can be disturbed from their bulk structure in response to the electric field. It is apparent from the above considerations that a number of molecular factors can contribute towards the thermodynamics of outer-shell solvation even for the archetypically simple one-electron redox couples considered here. Nevertheless, an encouraging overall feature of these results is that the dependence of the redox thermo- dynamic parameters upon the nature of the central metal, the coordinated ligands, and the surrounding solvents fall into clear patterns which should allow predictions of the solvent—dependent behavior of structurally related redox couples to be made with some confidence. 136 Figure 9. Plots of A8?0 for Fe(EDTA)_/2- against -a for the various solvents. 137 .-_oE ._-oop so am 4 H _ _ 0 “:20 r .5 0 100.2 I o 820 I nlu I o “.22 n 5 o .1 b p _ DON-IL O D 5 . O 5 -0, Col. deg". mol" Figure 9 CHAPTER VI SOLVENT EFFECTS ON THE KINETICS OF SIMPLE ELECTROCHEMICAL REACTIONS: COMPARISON OF THE BEHAVIOR OF Co(III)/(II)- TRISETHYLENEDIAMINE AND AMINE COUPLES WITH THE PREDICTIONS OF DIELECTRIC CONTINUUM THEORY 138 A. INTRODUCTION As noted in Chapter I, the majority of studies of solvent substitution on the kinetics of electrode reactions have employed substitutionally labile cations where the observed effects can arise from changes in the composition of the coordination shell (inner-shell effect), as well as variations in the energy required to reorganize solvent molecules beyond the primary coordination shell (outer- shell contribution). In this chapter electrode kinetics of substitutionally inert reactants are presented. Electrode kinetic parameters for Co(en)§+/2+ couple evaluated at mercury electrodes in Iwater and six nonaqueous solvents are discussed. In addi- ‘tion, the solvent dependencies of the rate parameters are czcmmmred with the predictions of the dielectric continuum Ijnrodel formulated by Marcus (10a). Rate-potential data are EELleo given for the reduction of the structurally similar + in these solvents. <2: complexes Co(NH3)g+ and Co(NH3)5F2 Each of the three reactants studied here are expected to 17" educe via outer-sphere mechanisms on the basis of their 7t2> eahavior at the mercury-aqueous (13,75) and mercury-non- EEi.<:_;ueous interfaces (see Chapter VII). 139 140 B. EXPERIMENTAL Heterogeneous rate constants kapp as a function of electrode potential (13) were obtained for the reduction + of Co(en)§+, Co(NH3)g+, and Co(NH3)5F2 at a dropping mercury electrode (d.m.e.) by means of d.c. and normal pulse polarography. The d.m.e. had a mechanically controlled drop time of 2 sec. Reactant concentrations between 0.5 and l mM_were usually employed. The analyses of polarographic waves utilized the methods due to Koutecky (98), and Oldham and Parry (99). These methods are very suitable for ir- reversible polarograms, and allow rate constants in the range of 10"Ll to 4 x 10"2 cm/sec to be evaluated reliably. 'The reductions of Co(NH3)2+ and Co(NH3)5F2+ are totally :irreversible (i.e., no significant back reaction) since the Ioroducts rapidly yield solvated Co(II) which cannot be :reeoxidized to Co(III) except at markedly more positive po- ‘tzwentials (13). The greater stability of Co(en):+ can result :i.11 significant anodic back reaction contributions to the I;><:>1arographic reduction of Co(en);+ in several solvents as '€E>‘Vridenced by the presence of significant anodic current on '12: ltle return scan of cathodic-anodic cyclic voltammograms. 355E1:>wever, this unwanted complication was eliminated where :zf3L:1:* Zn2+. These cations preferentially complex the ethylene- <:3L-:1.amine released upon formation of Co(II) which acts to en- <:: <:>urage dissociation of the remaining Co(en)§+ and therefore 141 eliminate the anodic back reaction. Values of kapp for Co(en);+ could therefore be determined at significant cathodic under-potentials as well as over-potentials which assisted the evaluation of rate parameters in media where the measured formal (143;, "standard") rate constants kgpp were fairly large (>10'2 cm/sec). The measured rate constants were generally reproducible to within ca. 10—20%. Formal potentials for the Co(en)§+/2+ couple were obtained in the same electrolytes using cathodic-anodic cyclic voltammetry as was described in Chapter V. An aqueous saturated calomel electrode (s.c.e.) was used as the reference electrode, although for convenience elec- trode potentials were quoted here versus the formal poten- tzial for the ferricinium/ferrocene redox couple (Fc+/Fc) cietermined in the same solvent and supporting electrolyte. ;E7urther experimental details are given in Chapter II. C. RESULTS Table 14 summarizes rate—potential data for the one- €52 :1.ectron reduction of Co(en);+ in each solvent expressed eaL_=s; an apparent (experimental) cathodic rate constant kgggo erleasured at -800 mV versus the ferricinium-ferrocene (Fc+/Fc) (:3 <:>Wuple in the same electrolyte. Also listed are the apparent <:='=52.thodic transfer coefficients aapp obtained from the GE>1=>-::jperimental Tafel plots using dapp = -f-l(8£n kapp/SE)u Where f = F/RT, and u denotes a given electrolyte composition + <:: 539 ). (The choice of -800 mV vs Fc /Fc minimized the extent 142 mIonm mIOHxs.H mHOH CIOHH: m.o oIOon.H ssoHoHH am.o 5IOme w.o oIonm caeme 2H.0 oIOme mIOme.w oeoH CIOme.m mw.o oIOme zeoHoHH 2H.o omen 5.o Hmm.o Haame 2H.0 mIOme.H mIQonH cam mIons 5.o mm.o HsoHoHH EH.o za mIonm.s mmo o.o mIonm naeme 2H.o HIOme mIonm.s mmo mIOHxHH 5.o NIons ssoHoHH mH.o oi mIOHx: mam mm.o mIonm.m caeme 2H.o :IOme.o mIOer mam mIOme.H mm.o mIOme.m nsoHoHH mH.o azz mIonoH mIonm.m com mIOHsm.H ma.o mIonm.m eaoHoHH.mm.o mIOme.m mom o.H mIOme haame 2H.o IOme.H IOme.s me IOHxH o.H IQme HoHoHH 2H.0 ooHEcsCoa m m m m C mIeme.m mIeme ewe eme me.e Home moans as.e mIonm mIonm mom ome mm.o HoOHe womag.mH.o Cops: HIm.Eo Hum.Eo om\+om HIm.Eo HIm.Eo opmHopuoon uCo>Hom m> >8 CCOo dam m I Choc Cam and C C: o Ca o m ooome o o coome comm pm mooonoon zgzogoz um oHasoo +m\+mACovoo one CoC nCouoeoCoa oHpoCHx HmoHEoLoosfiedfim Lo m92¢bcmqm 2m; Q . m m me ooCHopCoo CoHusHom and C .H mCHm: mHooE Cowman CH ooCHECopoo .om\+om meHowm oHQCOo +WACovoo Com HmeCouoa HCECOC .Hexoo ocnv 5.OIo.o a x no oCHm> mCHCCOQmoCCoo EOCC ooCHouCo .qumeoo mung HCECoC Couooppoo CozmHIoHCCoQ .mHooE ooumum CH Hum um ooCCmmoE . H . Hz 88 me ooCHmpCoo CoHpsHom . +m .HcHO O .osHae ocooHoaoCome .+ch as S +m SE N8 UOCHQvCOO COHUSHOWW O 5 CCC m n LN mep wCHECmmm HHV COHumsom wCHm: m .o.Hv pCmumCoo mung =Hm8goms pCoCmaCCpo88muHo> OHHozo o .wooH ooCoCoCom .ocsca .m .828 .omzo .oa ”HeomvaemH .HM ..Ecso .nsea .e .oesaa .m .z< HQOOH oosoCoCom .822 ”on ooCoCoCom .oUHECECom MHOH ooCoCoCom .Copm3 "AHV COHpmzvm CH om>OHQ8o Ce Co moCHw> ooCoC CCm mo>CCo m I 8U opm8Hpmo on own: memo moCmuHoono oconuooHo Co woogsom ado .Apxou oomv 5.0Im.o 8 Ho oCm m u LN poCu wCHECmmm AHV CoHmeqm wCHm: oomnx Co mCHm> wCHoConoCHoo EOCC ooCkuno .om\+om m> >8 oowI pm uCCumCoo camp Couooppoo CozmHIoHCCoQo ooCHmpno .ooumoHpCH oszosuooHo CCC uCo>Hom CH pCoHonCooo CoCmCmCu oHUOCpmo uCoCqu< 143 \+95 oHazoo oCooogpoCIECHCHoHCCoC COC How mquOCpooHo oCm pCo>Hom CH COHpoCUoC +m Com .agme\aacs cemvga\eva I a soCC C .CHCQE 08mm CH Aom uCopoq HmECoC .m> >8 cowl pm oopzmon .oopmoHCCH ACoVoo Com pCmmeoo dump AHouCo8HCodxov pCoCmQC\+>o% Hlm .EO Him .53 QDCAHOPUOGHM UC®>HOW CCoo and C CCoo dam .Qam mI x o .13; . Z 144 of data extrapolation that was required, and provided a convenient basis for the kinetic analysis described be- low.) Since the Tafel plots were essentially linear over the ca. 200 mV overpotential range that was typically accessible, a single value of ka and a suffice to DD app describe the rate parameters in a given electrolyte. Values of the apparent formal rate constants kipp for Co(en)?”2+ were determined by interpolation or extrapola- tion to the appropriate formal potential Ef in each electrolyte. In most cases the electrolyte composition was chosen to be 0.1 M lithium perchlorate or 0.1 M tetra- ethylammonium perchlorate (TEAP). These electrolytes probably exhibit negligible specific adsorption at the small to moderate negative electrode charge densities qm chere the kinetics were monitored in nonaqueous media (100), and perchlorate anions have only a small tendency tso form ion pairs with the cationic reactant. In aqueous media 0.1 M and 0.4 M potassium hexafluorophosphate were IJIESGd as supporting electrolytes since the kinetics were Iflfileeasured at small positive values of qm where perchlorate EES'IDecific adsorption is quite noticeable. Hexafluorophos- iI:>fikuate adsorption is sufficiently weak so that small posi- ‘123 :Lve values of the potential across the diffuse layer ¢d 'EEi—Jtae obtained under these conditions (75, 101, 102). The choice of these electrolytes therefore enabled the DEF‘IEEquired diffuse-layer corrections to the cathodic rate j5:3’<‘~Ei.rameters to be made with some confidence using the 145 relation (e.g., Reference 75) E _ E In kcorr - 2n kapp + f(zr - a (l) corr)¢d where kEorr is the "double—layer corrected" rate constant corresponding to the measured value kgpp trode potential E, Zr is the charge on the reactant, and at a given elec- acorr is the transfer coefficient after correction for double-layer effects. This last quantity can be obtained from a usin app g aapp I zr<3¢d/BE)n L 1 - (Bod/8E)u aCOI‘I' = (2) Equations (1) and (2) involve the assumptions that the :r’eaction site lies at the outer Helmholtz plane (o.H.p.) éaerd that discreteness-of-charge effects are negligible (f 7'5). However, they have been shown (13,75) to be ap- I:>:r~oximately consistent with experimental kinetic data for (:3 (>(III) amine reductionsix1a wide range of aqueous sup- iEZ>Ic3rting electrolytes when "d is calculated from double- :]—-EELyer compositional data using the Gouy-Chapman—Stern (008) ‘13: Irzeory (103). The required values of ¢d in aqueous media q‘“"> a corr' —800 f The resulting values of kcorr and kcorr are also listed in Table 14. In a given solvent, it was found that the corresponding values of k determined in the various corr electrolytes, including 0.5 M LiClOu as well as 0.1 M LiClOu are typically in reasonable agreement (Table 14), which supports the approximate validity of the double-layer corrections. 147 -800 f It is seen that the values of k r as well as kcorr cor vary markedly with the nature of the solvent, being sub- stantially smaller in nonaqueous media, particularly DMSO and DMF, compared with the corresponding rate constants in water. In view of these marked solvent influences upon + 2+ the electrode kinetics of Co(en); / , it is Of interest to ascertain if the structurally simpler Co(NH3)g+/2+ couple exhibits similar behavior. The kinetic parameters for Co(NH3)g+ reduction are summarized in Table 15, along with those for Co(NH3)5F2+ reduction. The latter exhibits similar rate parameters bathe Co(NH3)g+ reduction in aqueous media (13) yet carries a smaller net charge so that the possible influence of varying Zr upon the solvent effects can be assessed. Inspection of Table 15 reveals that the corresponding values of k-800 2 corr for Co(NH3)g+ and Co(NH3)5F + reduction in most solvents are within a factor of three or so of each other, whereas those for Co(en);+ reduction tend to be between five and tenfold smaller. D. DISCUSSION Following the treatment given in Chapter III for evalua- tion of electrode kinetic parameters in different solvents Equation (3) (Equation (24) of Chapter III) was used to ob- )5 )S-W tain estimates of A(AGcorr c , the change in the chemical part of the activation free energy for a given reaction when a nonaqueous solvent was substituted for water. 148 .uCo>Hom mHCp CH mpHHHCCHOm pCopomoC pCoHoHCCCmCH 0p 63o mHHCuHCOHoom CH ooCHouCo poC mews memo oHuoCon H.2H H Iosoop +mmmAm we on on oCOCpoom oCo p on mom .mHHopmo HonCCC Comv mzvoo CoC m I CN och +mH mzvoo CoC m .zHo>HuoonoC .CoHp LN Hosp wCHECmmm AHV CoHpmsom mCHm: ooCHmpno mommmx Co oCHo> oouozo o» wCHoCOQmoCCOo pComeoo dump Couoopnoo CoonIoHnsomo Can one .aHmm\ a semVHa\emIv I o 8oCC ooCHouCo .oopooHoCH opmHoguooHo oCo pCo>Hom CH uCoHOHCCooo CoCmCoHp uCoCodd< .oHooE o8mm CH oHCCOo oCooOCCoCIECHCHoHCCoC Com HoHuCoHOQ HCEHOC um ooszoo8 anoumoHoCH oquoppooHo oCm pCo>Hom CH pCmumCOo mama AHmpCoEHConoV uCoCoad >8 Cowl mIonoH e.o mIOme.m mIOme.H m.o aIOHxHH eoHOHH 2H.o ago oIOHx5.H mo.o oIOHx5 oIonm.H o.H mIOmeH :oHoHH 2H.o omzo mIOme.m oo.o mIonm mIOme mo.o m.o aoHoHH 2H.o om mIOer oo.o sIonm.H mIOme om.o sIonm aoHoHH 2H.o 8:2 mIonm o5.o MIOme.m mIonm.H mm.o mIOme eoHOHH 2H.0 ooHeoECom ma mm.o m me mo.o m meme 2H.o Coos; Him.EO HIW.EO Hlm.Eo Hlm.EO ®D%HOLPO®HM UQC®>HOW Cnoo ago and CHoo Coo ago a a x a o Ix ooomI o ooomI ooomI aoom m m o m :oHeosoom +ma H mzvoo soHuosoom +mH mzvoo .ocmm Um mm©0gpomflm hLSOLOE um +NmmAmm2vOO UCQ +WAMIZvOO MO COHQOSUOK COLDOQHQ IOCO 030 LCM mthQEMPGW Ofipmgfix HGOHEOSOOLDUQHM MO OOCQUCOQOQ HCQ>HOW .mH OHDQE 149 o ) m _ # s—w s corr " A(AG ) (3) RT fin (kW/k 00?? C In this equation kW and kS are the double layer corrected rate constants measured at a constant Galvani potential in water and nonaqueous solvents, respectively. # )s-w As mentioned in Chapter III evaluation of A(AG corr c like A(AG;3,C)S'w requires an extrathermodynamic assumption. If the ferrocene assumption ii; correct, then the values of kcorr evaluated at a fixed electrode potential (-800 mV) versus Fc+/Fc given in Tables 14 and 15 can be inserted directly into Equation (3) to yield estimates of a(AG:0rr):-w Since, the "tetraphenylarsonium-tetraphenylborate" (TATB) assumption is a more reliable procedure than the ferro- cene assumption (see Chapters III and V), it is prefer- able to apply a correction to the electrode potentials employed in each of the various nonaqueous solvents in order to take into account the likely deficiencies of the Fc+/Fc and convert the free energies to the TATB scale. Therefore the value of kcorr in each nonaqueous solvent that was inserted into Equation (3) was obtained at an electrode potential differing from —800 mV vs. Fc+/Fc by an amount AE found from -FAE = A(Aegc);;w (u) o S-W o s-w + where A(AGrc)Fc is the value of A(AGrc) for the Fc /Fc 150 couple in a given nonaqueous solvent on the TATB scale. [Literature estimates of A(Ach);;w are given in Table 7.] ' # s-w 3+ The resulting values of A(AGcorr)o for Co(en)3 and Co(NH3)g+ reduction on the TATB scale are listed in Table 16, along with the corresponding estimates of A(AG;C)S’W for the Co(en)§+/2+ couple which are taken from Table 9. (Although there are inevitable uncertainties in the use of such extrathermodynamic procedures, the values of e s—w -0 s-w rc)c similar to the values of A(Acrc) are prob- A(AG ably accurate to about :1 Kcal mol-l.) It is seen that the values of A(AG:C):-w for Co(en)§+ reduction are uniformly positive and larger than the cor- responding values of A(AG;C)S-w; iLQL, the destabilization of the transition state for Co(en);+ reduction relative to the bulk reactant when substituting nonaqueous for aqueous media is uniformly greater than that for the bulk product. Although values of a(AG;c)S'W for Co(NH3)2+/2+ are unob— tainable, they are likely to be closely similar to those for Co(en)§+/2+ (Chapter V) so a similar result probably also applies to the amine couple. It was shown in Chapter V that the values of A(AGI‘B,C)S-W for M(III)/(II) amine and ethylenediamine couples are much larger than the dielectric continuum (Born) predictions; they were interpreted in terms of donor-acceptor inter- actions between the amine hydrogens and the solvent mole- S-W cules. Thus A(AG;C has been shown to increase 151 Table 16. Estimates of the Variations in the Potential— independent Free Energy of Activation A A(AGrc) (Table 16) it is seen that the values of A(AG’IF"W are 1 uniformly positive; they approach 5 Kcal mol- for DMSO 153 Table 17. Experimental Estimates of the Variations in the Intrinsic Barrier A(AG;:)S"w for Co(en)§+/2+ Resulting from Substituting Various Nonaqueous Solvents for Water. Comparison with Predicted Variations A(AG:)S;YC from Dielectric Continuum Theory. b # s-w # S-w A(AGi)calc A(AGi) l Kcal.mol." ~13 c d Solvent Kcal.mol Re = m Re = 2(a+L) Formamide 1.8 -0.9 —O 3 NMF 2.3 -0.8 -0 2 PC 2.7 -0.8 -0 2 AN 1.8 -0 0 3 DMSO 4.9 -l.3 -0.6 DMF 4.7 —l.0 -0.3 aObtained from values of k5 listed in Table 14 using Equation (6). COI’I‘ bDifference between dielectric continuum estimate of the outer-shell intrinsic barrier (AGi a )OS in given nonaqueous solvent and that for water obtained from Table 18 using Equation (7). cSee footnote c of Table 18. dSee footnote d of Table 18. 154 and DMF. As noted above, it is likely that the mainten- ance of a constant ligand compoisition around the reactant will keep the inner-shell contribution to the reorganiza— tion energy, and hence to AGf, approximately constant as the surrounding solvent is varied. It is therefore probable that any variations in A0: resulting from altering the solvent are due to variations in the outer-shell contribu- "> i 08' As mentioned in Chapter III the usual theoretical model tion (AG for outer-shell reorganization treats the surrounding solvent as a uniform dielectric continuum, which accord- ing to Marcus (10a,78,104) yields the following expres- sion for the intrinsic barrier: 2 e 1 1 l l 8 a Re eop as where e is the electronic charge, Eop and as and static solvent dielectric constants, a is the radius are the optical of the (spherical) reactant, and Re is twice the distance from the reacting species in the transition state to the electrode surface; i;g;, the distance from the ion to its "image" in the metal. The (l/Re) term in Equation (7)‘ therefore describes the stabilization of the transition state relative to the reactant ground state afforded by the presence of imaging interactions with the metal 155 electrode (10a,104). However, it has been pointed out that this term could overestimate the importance of image forces since Equation (7) ignores the screening effect of the surrounding ions (105). It appears to be likely that the reaction sites for Co(III) amine reduction lie outside the primary inner layer of solvent molecules, and close to the outer Helmholtz plane (13) (o.H.p.) where some dif- fuse-layer screening of the image interactions can be expected. Consequently, values of (AGI)os were calculated from Equation (7) for the various solvents in two ways (Table 18). Either Re was set equal to infinity (igegg imaging was neglected) or taken as 2(a + L), where a is the reactant radius and L is the length of the solvent molecule L, since there is evidence that the thickness of the inner layer in some nonaqueous solvents roughly cor- responds to L (106). The value of L was taken as 3 A for water (107), and 6 A for the nonaqueous solvents (106); a was taken to be 3.5 A (appropriate for Co(en)§+/2+ and cOINH3)§*/2* (73)). #)s-w Values of A(AG1 calc obtained from the difference g i)os in each nonaqueous solvent with that in water given in between the corresponding calculated values of (AG Table 18 and are also listed in Table 17, both for R = m and Re = 2(a + L). It is seen that in both cases e small negative values of A(AG’1£)S"w are typically obtained, in contrast to the larger and positive experimental values 156 Table 18. Calculated Values of the Outer-shell Intrinsic Barrier for Co(en)?“2+ from Dielectric Con- tinuum Theory. wag: Solvent op = Kcal.mol-l Kcal.mol-l Water 1.775 6.3 4.7 Formamide 2.090 5.4 4. NMF 2.050 5.5 4.5 PC 2.013 5.5 4.5 AN 1.800 6.0 5.0 DMSO 2.178 5.0 4.1 DMF 2.036 5.3 4.4 aValues of cop for each solvent obtained from refractive indices n listed in "Handbook of Chemistry and Physics", Cleveland, Ohio. CRC Press, bEstimate of the outer-shell intrinsic culated from Equation (7), (e2/8 = 40 solvents. CCalculated from Equation (7) assuming that a and Re = dCalculated from Equation (7) assuming e aqueous solvents (see text). barrier (AG7) cal- 1 cs .29), for listed Values of as are listed in Table 2. that a 3.5 A, 3.5 A, R = 2 (a + L), where L = 3 A in water and 6 A in non- 157 obtained for Co(en)§+/2+. (Similar results were also ob- tained using other plausible values of a and Re). It is therefore concluded that the solvent dielectric con- tinuum model is unable to account for the observed sol- vent dependence of the electrochemical kinetics of Co(en)§+/2+. Values of A(AG’-:.:)S-W cannot be obtained for Co(NH3)g+/2+ since the formal potentials for this couple are unknown. # s-w corr)o for Co(NH3)g+ re- However, the values of A(AG duction are only marginally smaller than those for Co(en)§+ reduction (Table 16), and consistently larger than the values of A(AG§C)S_W for Co(en)§+/2+ and other + + amine redox couples (including Ru(NH3)g /2 ) (Table 9). is 0.5 - 0.7 (13), it follows +/2+ 3+/2+ 3 would likely yield values of A(AG:)S'w which are in quali- Therefore given that acorr from Equation (5) that Co(NH3)g as well as Co(en) tative disagreement with the dielectric continuum pre- dictions. Two factors appear most likely to be responsible for these apparent discrepancies between theory and experi- ment. First, it seems feasible that the electron tunnel- ing probability within the transition state (E;E;) the transmission coefficient K in Equations (21) and (27) of Chapter III) could be substantially smaller in some non- aqueous solvents than in water as a result of the probable differences in inner—layer thickness that were noted above. 158 Such a situation would render Equation (6) invalid and S-W yield values of A(AGi) that are falsely large. If the distance D between the reaction plane and the elec- trode surface (= 0.5 Re) is given roughly by D = (a + L), D may well increase from 6.5 A in water to around 8-9 A in nonaqueous solvents of intermediate molecular weight such as those considered here. Although the question of whether outer-sphere electron transfer is commonly non- adiabatic (K << 1) or adiabatic (K m 1) has been the sub- ject of extensive debate (108), the likely dependencies of K upon the distance between and the nature of the redox centers are largely unsettled. However, recent electron tunneling calculations (109) for Fe(OH2)g+/2+ self- exchange in homogeneous solution indicate that K falls rapidly as the internuclear distance increases above about 6 A (ELgL, K m 10-3 at 6.9 A (109)). Comparable results have been obtained with tunneling calculations performed for heterogeneous Fe(OH2)g+/2+ exchange (110). If the reactant indeed does not penetrate the inner layer of solvent molecules in the transition state for electron transfer (igeg, outer-sphere electrode reaction pathways are followed (9,111),then the resulting increases in D when substituting nonaqueous solvents for water could be responsible for the smaller values of kgorr in the former media via smaller values of K rather than larger values of AG: (Equation (27) of Chapter III). 159 Nevertheless, it seems likely that the observed be- havior is at least partly due to variations in (AGI)os arising from the more extensive changes in short-range solvent structure that may be necessary in order to sur- mount the Franck—Condon barrier in nonaqueous media. Al- though the likely contribution of such short-range reactant- solvent interactions has been widely recognized (71), it is difficult to provide theoretical estimates of their con- tribution to (AG7) i monitor of the extent of solvent structural changes ac- os‘ However, a valuable experimental companying electron transfer can be obtained from measure- ments of reaction entropy Asgc of individual redox couples (21). As mentioned in Chapter V, experimental values of reaction entropy have been found to be sensitive both to the nature of the coordinated ligands and the surrounding solvent to a much greater extent than predicted by the dielectric continuum (Born) model. This illustrates the importance of short-range ligand-solvent interactions to the changes in solvent polarization ("ordering") brought about by electron-transfer. It was shown in Chapter V that the values of As;C for Co(en)%+/2+ (and also Ru(NH3)g+/2+ and Ru(en)§+/2+) are substantially (up to 30 e.u.) larger in nonaqueous media, particularly DMSO and DMF, compared to the cor- responding quantity in water. These variations in isgc, A(AsgC S'", were found to increase as the extent of 160 "internal order" (17) of the bulk solvent decreases; 142;, when going from highly structured solvents, especially water, to polar yet more weakly associated liquids, especially PC, DMF, and DMSO. Such sensitivities of A819,c to the solvent medium might be expected to be reflected also in variations in the outer-shell part of the intrinsic barrier (74). Thus the formation of the transition state for Co(en)§+ reduc- tion in DMSO, for example, is expected to involve a much greater decrease in solvent polarization than the cor- responding process in water in view of the large positive value of A(Asgc 3'" for DMSO (15 e.u. (Table 9)). This difference will not affect the intrinsic barrier if # s-w _ o s-w , A(AGcorr) - acorr (AGrc) (Equation (5)), i.e., when the solvent effect upon the transition-state stability is that expected for a (hypothetical) stable cation with a structure identical to that of the transition state but having the charge (Zr - acorr)‘ However, in actuality the transition state is reached via the reorganization of nuclear coordinates while the reactant charge remains 16 fixed, electron transfer occurring rapidly (mlO- sec) once the transition state is formed (112). The required solvent reorientation will therefore be unaided by a con- comitant variation in the reactant charge so that these solvent structural changes should involve an additional component of the activation energy which will contribute 161 to the intrinsic barrier. Generally, therefore, the presence of greater differences in the extent of solvent polarization between the oxidized and reduced halves of the redox couple would be expected to yield larger values of (AGI)os' However, the likely magnitude of the effect is difficult to assess. 3+/2+ 3 couple (Table 17) against the corresponding values of Figure 10 is a plot of A(AG:)S—w for the Co(en) AS;c in each solvent, taken from Table 8. It is seen that there is a roughly linear correlation between A(AG:)s-w and AS° suggesting that there is indeed a I'C’ contribution to AG: arising from specific short—range sol- vent polarization not considered in the dielectric con- tinuum treatment. Thus AG: as well as AS;C increases as the extent of association between bulk solvent molecules decreases, such as the extent of hydrogen bonding in the sequence water, formamide, NMF, and DMF. The progressively greater decreases in the extent of solvent polarization that attend the formation of Co(en);+ from Co(en);+ in this sequence also appear to require that additional energy be expended to reach the required degree of nonequilibrium solvent polarization in the transition state. A similar correlation between Asgc and AG: has been demonstrated for a series of outer-sphere electron transfer processes in homogeneous aqueous media, including reactions where the reorganization of outer-shell solvent provides the Figure 10. 162 The variation in the intrinsic free energy of activation for Co(en)§+/2+ resulting from substituting various nonaqueous solvents for water, A(AG:)S-w, plotted against the corres- ponding reaction entropies isgc. Values of A(AGi)S'W obtained from formal rate constants kgorr given in Table 14 using Equation (6). Values of As;C (determined at u = 0.1) taken from Table 8. A(AGi’Ww kcal. mol." 163 ask. col. deg." mol."| Figure 10 I I 5 " o . omso DMF 4 _ .. 3 _ _- O PC NMF O 2 _ ._ O I? III I _ - 0+H20 ' ' 45 50 164 dominant contribution to AG: (23). Other kinetic data for simple outer-sphere redox pro- cesses involving substitutionally inert reactants in non- aqueous solvents are sparse, both at electrodes and in homogeneous solution. However, the values of kex the rate constant for the homogeneous self-exchange of Fe(phen)§+/2+ and related couples are 1-2 orders of magni- tude smaller in acetonitrile than in water (113,114). These reactivity differences are not predicted by the con- ventional dielectric continuum model of electron transfer. Thus inserting the relevant dielectric constants into the usual expression for the outer-shell barrier to homogeneous self—exchange (115) (assuming that the distance between the reacting centers in the transition state is twice the reactant radius of 6.8 A (73), yields the prediction that kex should be very similar in water and acetonitrile (about 20% larger in the latter solvent). Interestingly, this decrease in kex is again accompanied by a substantial in- crease in AS;c (Table 6). This behavior indicates that the observed decreases in ke arise from the greater changes x in short—range solvent polarization around the polypyridine complexes that are apparently required in order to induce electron transfer in acetonitrile. The variations of kex for the ferricinium/ferrocene couple between different non- aqueous solvents have also been reported to differ from the dielectric continuum predictions (116). 165 It should be noted that the likely limitations of the conventional dielectric continuum model in describing both the thermodynamics of outer-shell solvation and the outer-shell contribution to the reorganization energy for electron transfer has frequently been noted (71,117,118). Indeed, theoretical models of solvation have recently been developed which take into account the spatial dispersion of the surrounding solvent structure (71,117,118). In principle, these models allow the various short-range vibrational and reorientational motions of the solvent to be treated, although they still do not consider the exist- ence of specific interactions between the coordinated ligands and the nearest—neighbor solvent molecules. Such interactions are indicated from the redox thermodynamic measurements to be important for the present reactants (Chapter V). CHAPTER VII DETERMINATION OF REACTION MECHANISMS FOR Co(III)- and Cr(III)- AMINE COMPLEXES AT THE Hg/NONAQUEOUS INTERFACES 166 A. INTRODUCTION It was noted in Chapter I that variations in the solvent medium can influence the rates of electron-transfer pro— cesses by changing the reaction mechanism. In order to interpret electrochemical kinetic parameters and to treat them theoretically, it is necessary to identify the reac- tion mechanisms. As noted in Chapter I two different path- ways for the electron-transfer can be considered. (i) "outer-sphere" (0.8.) and (ii) "inner-sphere" (I.S.). Electron transfer during O.S. reactions takes place with the reactant center located at the so-called "outer Helm- holtz plane" (o.H.p.) which is the planecfi‘closest approach for reactants whose coordination spheres do not penetrate the layer of solvent molecules that are specifically ad- sorbed on the electrode surface. In this case only weak, nonbonding interactions occur between the reactant and the electrode in the transition state (12). During electrode reactions that proceed by I.S. pathways, one (or more) of the ligands in the reactant's primary coordination sphere penetrates the OHp and is attached to the electrode surface in the transition state (12). In this chapter electroreduction kinetics of various coIII(NH3)5X and CrIII(NH3)5X (where x = NH3, F“, 01‘, 167 168 _ 2- - _ Br , SOLl , N03, N3 Hg/DMF, Hg/Formamide and Hg/PC interfaces are reported. and Ncs‘) complexes studied at Hg/DMSO, B. METHOD FOR DISTINCTION BETWEEN I.S. AND O.S. MECHANISMS The primary method develOped for distinguishing between I.S. and 0.8. electrode reactions for cationic reactants is based on the response of the reaction rate to changes in specific ionic adsorption of the supporting electrolyte (12). This method has successfully been used in aqueous media formechanism diagnosis of the reduction of COIII III and Cr complexes at mercury (9,13) and solid electrode surfaces (14). The method consists of measuring the reaction rate of a complex at a given electrode po- tential, first in the absence and then in the presence of an anion which is known to be specifically adsorbed on the electrode surface and which cannot act as a bridging ligand between the reactant and electrode surface (12). If the complex of interest reacts by an I.S. pathway, the transi- tion state will be formed at the "inner Helmholtz plane (in) and the presence of an anion which is strongly ad- sorbed on the electrode will lead to a competition for adsorption sites which should raise the energy of the transition state and produce lower reaction rate (12). By contrast, if an 0.8. reaction pathway is involved, 169 the addition of a strongly adsorbing species should pro- duce negative changes in the average potential at the oHp. This will lead to large rate enhancements as a consequence of more favorable electrostatic interactions for cationic reactants (12). C. RESULTS The electroreduction kinetics of various COIII(NH3)5X and CrIII(NH3)5X complexes were studied as a function of electrode potential in four different nonaqueous media. These substitutionally inert complexes were selected be- cause they can be reduced via relatively slow one-electron reactions, allowing their rates to be measured quantita- tively. Moreover, these systems are reduced irreversibly at the dropping mercury electrode (d.m.e.); the back oxida- tion rates are negligible, which allows d.c. and normal pulse polarography to be used to monitor the electrode kinetics. (The absence of anodic back-reactions for these reactants were confirmed by cyclic voltammograms obtained at a hanging mercury drop electrode.) 1. Co(III)-amine Reactants In order to identify the reduction mechanism as either inner- or outer-sphere, the reduction rates of each Co(III)- amine complexes were examined both in the absence and in 170 the presence of anionic specific adsorption of the support- ing electrolyte. Since anion specific adsorption seems to be negligible for LiClOu under the experimental conditions employed for the nonaqueous solvents used here (100,106, 119), it was used as the main component of the supporting electrolyte. For mechanism diagnosis, a mixed support- ing electrolyte with the general form of (0.1-a) M LiClOu + aM M with a = 0.01, 0.02, 0.03 M and x 01’, Br‘, I' and SCN' was used. Electrocapillary and differen- tial capacity measurements have shown that these anions are specifically adsorbed at the Hg/formamide (120), Hg/ DMSO (100a), Hg/DMF (119b, 121) and Hg/PC (122) interfaces. Tables 19 and 20 summarize the apparent(experi- mental) rate constants kapp for the reduction of co- balt complexes measured at (or extrapolated to) -350 mV vs. normal calomel reference electrode (NCE) both in the presence and absence Of added SCN’ at a constant total ionic strength in DMSO and DMF. Also listed in Tables 19 and 20 are the apparent cathodic transfer coefficients aapp obtained from the experimental Tafel plots for re- duction of each complex in 0.1 M LiClOu. Table 21 summarizes ka for the reduction of cobalt pp complexes measured at (or extrapolated to) -350 mV vs. NCE in 0.1 M LiClOu and 0.08 M LiClOu + 0.02 M LiCl as supporting electrolyte in formamide. In addition values of aapp measured in 0.1 M LiClOu for each reactant are 171 Table 19. Experimental Rate Constants and Transfer CO- efficients for Electroreduction of Various Co(III)-amine Complexes at Hg/DMSO at 25°C. Complex OLappa #5886) kaggoc k-BSOd Co(NH3)g+ 1.0 2.4 x 10"6 ---------- 9.1 x 10'6 Co(NH3)5F2+ 0.65 1.9 10‘6 ---------- 5.0 10'6 Co(NH3)5NO§+ 0.74 .9 10'“ 1 6 x 10‘3 2.2 10‘3 Co(NH3)5NCS2+ 0.76 .0 10‘“ 3 9 x 10‘“ 4.9 IO'Ll Co(NH3)5N§+ 0.66 5.9 10‘5 1 4 x 10'” 1.8 10‘” Co(NH3)5C12+ 0.78 2.8 1.3 ---------- Co(NH3)530Z 0.40 1.1 10‘5 ---------- 2.7 10"5 obtained from 0.1 M LiClOu. aApparent cathodic transfer coefficient in 0.1 M LiClOu a app bApparent rate constant evaluated at -350 mV vs. -( 2.3 RT F )( 310g k app) aE u NCE in cApparent rate constant evaluated at -350 mV vs. NCE in 0.02 M NaSCN + 0.08 M LiClOu electrolyte. dApparent rate constant evaluated at -350 mV vs NCE in 0.03 M NaSCN + 0.7 M LiClOu electrolyte. 172 Table 20. Experimental Rate Constants and Transfer 00- efficients for Electroreduction of Various Co(III)-amine Complexes at Hg/DMF at 25°C. tar" as“ Co(NH3)63+ 0.9 1.5 x 10'“ 5.0 x 10‘” Co(NH3)5F2+ 0.7 4 0 x 10‘5 7.9 x 10‘5 Co(NH3)5NO§+ 0.66 5 2 x 10‘3 .......... Co(NH3)5Ncs2+ 0.57 3 8 x 10‘3 7 2 x 10'3 Co(NH3)5N§+ 0.52 1.2 x 10"3 2.6 x 10‘3 Co(NH3)SCl2+ ‘ m1.6 x 10"1 aApparent cathodic transfer coefficient in 0.1 M LiClOu. bApparent rate constant evaluated at -350 mV vs NCE in 0.1 M LiClOu. cApparent rate constant evaluated at -350 mV vs NCE in 0.02 M NaSCN + 0.08 M LiClOu electrolyte. 173 Table 21. Experimental Rate Constants and Transfer Co- efficients for Electroreduction of Various Co(III)- amine Complexes at Hg/Formamide at 25°C. 4.133" 533““ Co(NH3)2+ A 0.95 4 0 x loé6 .5 x 10"5 Co(NH3)5F2+ 0.76 8.9 x 10'6 2.8 x 10"5 Co(NH3ISN0§+ 0.63 3.6 x 10‘3 5.7 x 10‘3 Co(NH3)5NCS2+ 0.62 1.0 x 10"2 1.7 x 10"2 Co(NH3)5N§+ 0.47 9 1 x 10’” 1.5 x 10"3 aApparent cathodic transfer coefficient in 0.1 M LiClOu. bApparent rate constant evaluated at -350 mV vs NCE in 0.1 M LiClOu. cApparent rate constant evaluated at —350 mV vs NCE in 0.02 M LiCl + 0.08 M LiClOu electrolyte. 174 also listed in Table 21. Experimental rate constants kapp for the reduction of cobalt complexes in 0.1 M LiClOu in propylene carbonate are given in Table 22 along with their transfer coefficients dapp. No accurate measurements could be done in propylene carbonate using mixed electrolyte. This was due to in- solubility of the cobalt complexes in the presence of small amounts of halide ions. The reduction of most cobalt-amine complexes in 0.1 M LiClOu in four nonaqueous solvents employed here were found to yield normal polarographic waves. Polarographic waves for Co(NH3)5012+ reduction exhibited small anodic currents just prior to the cathodic waves both in DMSO and PC. In propylene carbonate and formamide small anodic currents 2+ at the were observed for the reduction of Co(NH3)5NCS bottom of the polarographic waves. Electroreduction meas- urements of Co(NH3)SSOZ were precluded in DMF and PC due to its low solubility. In DMF rate constants for cobalt-amine complexes were not possible to measure in the presence of halide anions. This was mainly because of anion-induced mercury dissolu- tion and the appearance of maxima in the presence of Br‘ and I' and also insolubility of complexes in the presence of C1“ anions. In DMSO the reduction of most Co(III) complexes in the presence of Cl’, Br“, and I- could only be monitored by the use of shorter drop times, (0.5 sec) and analyzing the tOp middle portion of the polarograms. 175 Table 22. Experimental Rate ConstantsenuiTransfer Coef- ficients for Electroreduction of Various Co(III)-amine Complexes at Hg/PC at 25°C. Complex “appa k;;:5b Co(NH3)g+ 0.65 1.4 x 10‘5 Co(NH3)5F2+ 0.67 m7.9 x 10‘7 Co(NH3)5NO§+ m0.38 .2 x 10'3 Co(NH3)5NCSZ+ 0.59 4.5 x 10'3 Co(NH3)5N§+ 0.38 1.7 x 10‘3 Co(NH3)5C12+ 0.54 2.5 x 10‘2 aApparent cathodic transfer coefficient in 0.1 M LiClOu, bApparent rate constant evaluated at -125 mV vs NCE in 0.1 M LiClOu. 176 2. Cr(III)-amine Reactants Table 23 summarizes the apparent rate constants along with the values of aapp for reduction of each Cr(III) complex measured at a convenient potential vs. NCE in 0.1 M LiClOu in three solvents, DMSO, DMF and formamide. Electro- reduction kinetic measurements for the chromium complexes in PC were precluded. This was because of the lack of reproducible polarograms and undefined limiting currents. Since the Cr(III)-amine complexes are reduced at very negative potentials at which even iodide (which is one of the strongest adsorbing anions) does not seem to be es- pecially adsorbed, no mechanism diagnosis could be obtained when rate constants in pure and in mixed supporting elec- trolytes were compared. Indeed, significant rate enhance- ments due to addition of I- could only be observed for complexes which exhibited more positive reduction poten— tials like Cr(NH3)SBr2+. For other Cr(III)-amine com— plexes almost no variation in rate constants were observed in the presence and in the absence of added iodide. D. DISCUSSION Inspection of the data presented in Tables 19—21 in— dicates that except for Co(NH3)5012+ reduction (Table 19), reaction rates of all other Co(III)amine reactants that were examined here are markedly accelerated at a given 177 .HCO>Hom Como CH :oHoHH s H. o CH moz .m> >8 CH HoHpCouoa Umposo um oouosHo>o pCoumCoo bump HCOCmqo< Q .uCo>Hom Como CH :OHUHH a H.o CH CCOHOHCCOOO CommCmnp OHCOCuoo uCosmoQCC NIOH x m.m sm.O mIOH x .: Om.O m..OH x 5.m OH.O +mCmmHmszCO mIOH x 5.m m5.O HIOH x .m OO.O sIOH x 5.m Om.O +mHOmHmszCO OH x m.m Om.O OH x :.H sm.O OH x O.m Hm.O mzmHmszCO OI OI mI +m :IOH x H.m mO.O :IOH x H.H HO.O sIOH s H.H OO.O +mmOZmHmszCO OIOH x O.m CO.O OIOH x m.5 HO.O OIOH x 5.O mO.O +mamHmmvaO mIOH x O.m NO.O mIOH x m.m m5.O mIOH x O.H Os.O +mHmszCO Coax Como oomx Como Coax ammo OOOOHI oOOHHI oOOmHI onQEoO ooHeoesoE EEO Omzo comm um moomppouCH ooH8m8Com\wm CCo aza\wm omzm\wm um moxOHQEOQ OCHECI .wHHHVCo mCoHCo> Co COHCOCUOCOCHOOHM pom mpCOHOHmCooo ComemCE UCm muComeoo mpom HmuC08HCogxm .mm OHCCB 178 electrode potential by the addition of adsorbed non-reacting anions. Figure 11 shows rate-potential data for the reduction of Co(NH3)5F2+ in the presence and absence of added iodide in DMSO. It is seen that the addition of iodide results in a significant rate enhancement which becomes gradually less pronounced at more negative potentials as adsorption of iodide diminishes. In Figure 12 rate-potential data for the reduction 2+ 3 in DMSO are shown. Essentially similar responses to NCS‘ of Co(NH3)5No in the presence and absence of added NCS‘ adsorption are also exhibited by all Co(III)-amine com- plexes (except for Co(NH3)5Cl2+) in DMSO and DMF. The only difference being that quantitatively larger enhance- ments result with tripositive Co(NH3)g+ while smaller rate enhancements are obtained with the less highly charged Co(NH3)5sofi. This behavior is in qualitative agreement with that expected for an outer-sphere electrode reaction mechanism with a cationic complex whose concentration at the elec- trode surface is increased by the greater electrostatic attraction it experiences when anions are adsorbed on the electrode surface. These observations therefore indicate that all the cobalt complexes studied here (except Co(NH3)SCl2+)are ap- parently reduced via outer-sphere pathways. In the case of Co(NH3)5012+ addition of NCS‘ in DMSO results in a Figure 11. 179 Comparison of the effect of specific iodide adsorption upon rate-potential plots for the electroreduction of Co(NH3)5F2+ in mixed LiClOu + LiI supporting electrolytes in DMSO. Symbols are experimental points in (0.1-X) M LiClOu + xM LiI with x = 0 (I), 0.01 (o), 0.03 (A). 180 A -20_ A 2_ A o A I8 _25- A A O .. U) I . A o E A ° a. O . e -30- ° - x O 9 " o .9 -3.5— ' - I .40 1 1 1 l 450 500 550 600 650 "E, mV vs NCE Figure 11 Figure 12. 181 Comparison of the effect of specific NCS- adsorption upon rate-potential plots for the electroreduction of Co(NH3)5NO§+ in mixed LiClOu + NaNCS supporting electrolytes in DMSO. Symbols are experimental points in (0.1-X) M LiClOLl + XM NaNCS with X = 0 (I), 0.01 (O), 0.03 (A ). log kapp, cm. sec". .01 U1 . 8 4.5 5.0 182 A (3 A [5 (3 I. is (3 £> (3 O - <3 -. II I. l! 1 I 1 200 250 300 350 “E, mV vs. NCE Figure 12 183 slight decrease in reaction rate (Table 19) instead of the marked increase observed with the other cobalt complexes. The most probable explanation for this behavior is that an inner-sphere pathway is followed by this complex with the coordinated chloride anion attached to the electrode sur- face in the transition state. Measurements at the Hs/Hzo interface (13) have shown that Co(NH3)g+, Co(NH3)5F2+ and Co(NH3)SSOZ are almost certainly reduced via O.S. pathways since they lack co- ordinated ligands that significantly specifically adsorbed in the potential region where the kinetics were monitored. Of the various pentaammine cobalt complexes studied in Reference 13 at the Hg/H2O interface only Co(NH3)5NCS2+ was found to reduce via a pure inner-sphere mechanism. 2+ (Although reduction of Co(NH3)501 at the Hg/H2o was too fast to be measured accurately (13), it is very possible that this reactant is also reduced via I.S. mechanism due to strong adsorption of Cl" at the mercury surface.) 2+ 3 reduce via mixed 0.8. and I.S. mechanisms (13). Complexes of Co(NH3)5N0 and Co(NH3)5N§+ were found to Although no mechanism diagnosis could be obtained for reduction of Cr(III)-ammine complexes at the Hg/non- + aqueous interfaces studied here (except for Cr(NH3)SBr2 which was found to reduce via O.S. mechanism), it is very probable that all of these Cr(III) complexes are reduced via O.S. pathways. The reasons for the last 18A statement are: (i) these Cr(III) complexes are reduced at very negative potentials at which the anion specific adsorption are very weak. (ii) In addition, among Cr(III)- amine complexes studied in aqueous media (9) at the mercury electrode, only Cr(NH3)5NCS2+ and Cr(NH3)SBr2+ were found to reduce with dominating anion-bridged (I.S.) pathways. Since in the present work it was found that even Cr(NH3)5Br2+ with a traditionally good heterogeneous bridging ligand, Br', is not reducing via I.S. mechanism, therefore one can conclude that all CrIII(NH3)5X complexes studied here are reduced via outer-sphere mechanisms. The inability of mercury/nonaqueous interfaces to induce I.S. mechanisms is understandable since anion adsorption is known to be somewhat weaker in most non- aqueous media, compared to aqueous media (123). Apparently this is due to the fact that nonaqueous solvents compared to water are more strongly adsorbed on the mercury elec— trodes (119b). Therefore, there is a competition between anions and solvent molecules to adsorb on the electrode surface. This effect is probably more pronounced when the anion in the coordination sphere of the reactant which has less freedom wants to act as a bridging ligand between the electrode and the metal ion center. CHAPTER VIII CONCLUSIONS AND SUGGESTIONS FOR FURTHER WORK 185 A. CONCLUSIONS The results obtained in the present work demonstrate that the chemical nature of the solvent can play an im- portant role both in the thermodynamics and kinetics of electron transfer, even when the solvent is excluded from the reactant's coordination sphere. The large values of reaction entropy Asgc for all M(III)/(II) redox couples in the nonaqueous solvents com- pared to the corresponding values in aqueous media, are due to the greater enhancement of solvent polarization in the vicinity of the complex for nonaqueous solvents. These observations can be explained by the unusually high degree of internal order exhibited by liquid water. The large changes in Asrc when the solvent is varied are primarily determined by the relative ability of the tripositive M(III) complex compared to the corresponding M(II) species to disturb the bulk solvent structure and reorientate solvent molecules within its vicinity. The values of Asgc for each redox couple were found to increase as the extent of internal order of the bulk solvent decreased (Figures 2, 7 and 9). Large differences in AS; in a given solvent 0 were observed for couples having different coordinated ligands. Thus M(III)/(II) amine and ethylenediamine couples 186 187 gave values of asgc that were ~15 e.u. larger in a given solvent than for the corresponding polypyridine couples (see Tables 6 and 8). The different Asgc values for analogous Co and Cr, Fe, and Ru couples in a given solvent indicate that the electronic structures of the metal redox center can also have a significant effect on the reaction en- tropy. The high-spin Co(III)/(II) couples exhibited values of Asgc that were ~20 e.u. larger than for the low—spin Ru(III)/(II), Fe(III)/(II), and Cr(III)/(II) couples con- taining the same ligands (Tables 6 and 8). It would appear from these results that in a given solvent two redox couples will have comparable reaction entropies when they have the same coordination sphere and when the electronic struc- tures of the two central metal ions are similar. For example, similar values of As; for Cr(bpy)§’+/2+ and ' c Fe(bpy)§+/2+ couples in water, prOpylene carbonate and acetonitrile can be mentioned (see Table 6). The variations in A330 for the ferricinium/ferrocene re- dox couple between water andzanumber of nonaqueous solvents provide a major contribution to the apparent breakdown of the ferrocene assumption for estimating free energies of single ion transfer. This is simply because of the greater tendency of solvent dipoles to be polarized by the ferri- cinium cation compared with the ferrocene molecule. W Small negative values of A(AG;C)S- , [free energy of transfer for a redox couple from water to a given nonaqueous 188 solvent], for couples containing aromatic ligands were typically obtained. These are due to partial compensation of the entropic terms by the corresponding enthalpic com- S-w for cationic ponents. The resulting values of A(Ach) complexes containing ammine and ethylenediamine and anionic redox couples were found to vary considerably (ca. -A to 1A Kcal mol'l) with the nature of the nonaqueous solvent. These behavioral differences (between polypyridine and ammine couples) are due to the strong donor-acceptor inter- actions between the nearest-neighbor solvent molecules (as donors) and the acidic amine hydrogens (as acceptors). The correlation obtained between the values of a(AG;C)S-w for the ammine couples and the basicity of the solvent as determined by the Donor Number are shown in Figure A. For anionic redox couples,such as Fe(EDTA)'/2‘, the solvent molecules are acting as an acceptor toward the molecule of EDTA; therefore the values of (”Gags-W decrease with an in- creasing solvent Acceptor Number (see Figure 8). A useful generalization that :might be made from the results in this work is the apparent insensitivity of a(AG;C)S'W to the electronic structure of the central metal ion. For ex- _ample, Ru(en)§+/2+ and Co(en)%+/2+ in both DMSO and DMF (Table 9), and Fe(EDTA)-/2- and Co(EDTA)-/2' in methanol There- (Table 12) gave comparable values of A(AG;C)S’W fore, for redox couples for which measurements of Ef are- impractical [e.g., Co(NH3)g+/2+], the values of AEf 189 between pair of solvents could be predicted with some con- fidence using A(Ach)S‘w values of analog Ru(III)/(II) couple. Studiescxfreaction mechanisms at the mercury/nonaqueous interfaces for reduction of various Co(III)- and Cr(III)- amine complexes indicate that the outer-sphere mechanism is the usual pathway for electron transfer. This is due to the fact that specifically adsorbed anions are not strongly adsorbed at the mercury/nonaqueous interfaces. The lack of adsorption at the mercury electrode prevents formation of anion bridge (between the electrode and metal ion) during the transition state which is necessary for inner- sphere pathways. The double-layer corrected rate constants obtained for the reduction of Co(III)-amine and Co(III)—ethylenediamine complexes were found to be smaller in all nonaqueous sol- vents compared with water. These rate changes indicate that there are large increases in the outer—shell component of the intrinsic free energy barrier to electron transfer (AG:)os when water is replaced by nonaqueous, particularly aprotic, solvents. Such solvent dependencies of (AG:)os are much larger, and in even qualitative disagreement with the predictions of conventional dielectric continuum model (Table 17). These discrepancies between theory and experi- ment are probably due to the fact that this model does not consider any specific short-range interactions. Indeed, 190 a roughly linear correlation that was observed between the # )3+/2+ 3 experimental solvent dependence of AG1 for Co(en and the corresponding values of Asgc (Figure 10) suggests that there is a contribution to AG: arising from the short- range reorganization of solvent molecules. Another factor that might be responsible for the observed differences between theory and experiment is the electron tunneling probability within the transition state. This could be significantly smaller in some nonaqueous solvents as a result of the probable increase in the distance between the reacting molecules and the electrode surface. There— for, this could be responsible for the smaller rate con- stants observed in nonaqueous media. The results obtained in the present work are important because they provide the first clear-cut demonstration that the dielectric continuum model can provide a seriously in- adequate account of the influence of the outer-shell solvent upon the electrochemical kinetics as well as the thermo- dynamics of simple inorganic redox reactions. In addition, they illustrate the important influence of short-range solvent-solute interactions upon the redox thermodynamics and electrode kinetics of these redox couples. 191 B. SUGGESTIONS FOR FURTHER WORK The conclusions reached in the previous section regard- ing the factors responsible for the discrepancies observed between the dielectric continuum theory and experimental values are somewhat clouded by the uncertainty to what extent these reactivity differences between the various solvents are due to variations in the efficiency of elec- tron tunneling rather than in the free energy of activa- tion for electron transfer. Further studies with suitable systems are required to distinguish between these two factors. In principle, such distinction could be made by careful studies of the temperature dependence of the electro- chemical rate constants. One possible experiment which seems to be useful involves the employment of a binary mixed solvent in which a strongly adsorbing nonaqueous solvent with small solvation ability (of the bulk reactant) is added to water. Employment of such a system should allow one to separate the contributions to the measured solvent effects upon electrochemical kinetics from solvation of the bulk reactant and the transition state which is formed in the interfacial region. Thermodynamic measurements (i;g;, Asgc and Bf) can assist us in finding that whether there is any change in the bulk solvation of the redox couple in mixed solvent and pure aqueous media. The corresponding changes in the interfacial solvent environment can be 192 obtained by double-layer capacitance measurements. Find- ing the suitable binary mixed solvent (i.e., with a non- aqueous solvent that is strongly adsorbed to the electrode but does not change the bulk structure), electrode kinetics of various reactants such as Co(en)_.33+/2+ can be measured. If the rate constants in this mixed solvent are substantially smaller than that in pure water, then it is very possible that the rate decreases observed in pure nonaqueous sol- vents for Co(III)—amine and ethylenediamine complexes (Chapter VI) are also, mainly due to decreases in the elec- tron tunneling probability through the thicker nonaqueous solvent layer compared to water. These and similar studies would be worthy of examination in order to find out to what extent the intrinsic barrier AG: is sensitive to the nature of the solvent and how the reactant-solvent inter- actions may influence AGi. 0f the redox couples studied in Chapter V, some were found to be unsuitable for kinetic measurements at mercury electrodes. This is due to the fact that their formal potentials are more positive than the anodic limit of mercury. It is possible to investigate the electrode reduction kinetics of these couples [Co(bpy)§+/2+, )§+/2+, and Co(phen)§+/2+ Fe(bpy ] at solid metal electrodes such as Pt, Au and Ag on account of the wide potential ranges available on these metals in contact with nonaqueous media. In addition, it would be interesting to examine the 193 effects of varying the nature of the electrode metal upon the electrode kinetics of various Co(III)—amine, Co(en)?”2+ and Co(EDTA)-/2- complexes in different nonaqueous sol- vents. 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