11028
J. Phys. Chem. B 1999, 103, 11028-11035
Effect of Position of Polyether Attachment on the Electron Self-Exchange Activation Barrier Energies of Redox Polyether Hybrid Molten Salts Enders Dickinson, V, Hitoshi Masui,† Mary Elizabeth Williams, and Royce W. Murray* Kenan Laboratories of Chemistry, UniVersity of North Carolina, Chapel Hill, North Carolina 27599-3290 ReceiVed: July 22, 1999; In Final Form: October 12, 1999
We have synthesized highly viscous, room temperature molten salts by associating [M(bpy)3]2+ cations (M ) Ru or Co, bpy ) 4,4′-bipyridine) with polyether-tailed 2-sulfobenzoate anions. Microelectrode voltammetry in the undiluted melts yields, on the basis of the coupling of electron hopping with physical diffusion, electron self exchange rate constants for the CoII/I and RuIII/II couples. Activation studies show that homogeneous electron transfers in the melts have large activation barriers (34-39 kJ/mol) that are similar to those of melts in which the polyether chains are covalently attached to the [M(bpy)3]2+ cations via 4,4′-bipyridine ester linkages (26-29 kJ/mol) and the counterion is perchlorate. The similarity of the activation barriers indicates that the large activation barriers do not result from a peculiar inner-sphere reorganizational barrier term caused by covalent linkage of the “solvent” (the polyether chains) to the bipyridine ligands. Also reported are physical diffusion constants, ionic conductivities, and viscosities. The number of ethylene oxide segments in the polyether tails seems to be an important determinant of physical diffusion rates and viscosity.
Introduction Our laboratory has a long-standing interest1 in electrochemical measurements in rigid and semisolid media (redox polymers, viscous ionic liquids, glasses, etc.), with the objective of understanding the microscopic effects of rigid environments on physical mass transport rates and electron transfer dynamics of electroactive entities. Measurements of the rates of homogeneous electron transfers have exploited the sensitivity of rates of charge diffusion to coupling between electron self exchange and physical diffusion in mixed valent, electrogenerated diffusion layers formed around working electrodes. When the electron self exchange (or “hopping”) transport rate (DE) is comparable to, or faster than, that of physical diffusion (DPHYS), the measured or apparent diffusion coefficient (DAPP) becomes enhanced by the former and yields values of the electron-transfer rate constant, kEX. Seeking semisolid, amorphous materials with structures readily manipulable to assess relations between kEX and structure, we developed2,3 a class of compoundssredox polyether hybridssby synthetically combining short polyether chains with redox active molecules (or ions), resulting in amorphous, highly viscous, and ionically conductive electroactive melts. In the first generation of redox polyether hybrids,2 polyether oligomers were directly, covalently attached to redox active moieties such as ferrocene, metal bipyridine complexes, perylene, and metalloporphyrins. Homogeneous electron transfer rate constants were measured for a variety of these molten semisolids. The room temperature melt rate constants (kEX) are uniformly smaller than, and the thermal activation barrier energies for kEX larger than, those of the analogous nonhybridized redox moieties in dilute fluid solutions. The thermal energy barriers in the redox polyether hybrid melts are larger than outersphere reorganization energy barriers predicted for the various redox moieties using classical Marcus theory,4 assuming an ether-like solvent environment.2a † Present address: Department of Chemistry, Kent State University, Kent, Ohio, 44242-0001.
The reason(s) for the large electron transfer activation barrier energies of redox reactions in semisolid environments has not been established. We have speculated2a that the enlarged barriers for metal bipyridine (bpy) redox polyether hybrids might reflect (i) a peculiar “inner-sphere-like” barrier term associated with the linkage between the bpy ligand and its “ether solvent shell” and/or (ii) thermal activation of reorientation dynamics of the ether dipoles in the “solvent shell” (i.e., solvent dynamics). The first of these ideas can in principle be tested by attaching the polyether oligomer to the counterion of an ionic redox moiety instead of to the moiety itself. The way was opened to such a test, which is reported here, by developing a straightforward synthetic route to a second generation of redox polyether hybrids, which we term “counterion-tailed” (abbreviated CItailed) melts.3 This paper presents results for DPHYS and kEX in semisolid (undiluted) melts composed of [M(bpy)3]2+ cations (M ) Co, Ru) with polyether-tailed 2-sulfobenzoate counter-anions. In the previous paper,3 these complexes were abbreviated as [Co(bpy)32+](MePEG-BzSO3-)2 and [Ru(bpy)32+](MePEG-BzSO3-)2; here, we will use the notation CoII-CI-tailed and RuII-CI-tailed (see Chart 1). The results for the two counterion-tailed melts will be compared to the analogous ligand-tailed melts in which the polyether chains are attached directly to the ligands of the metal bipyridine complexes and the counterions are perchlorate ions. These latter melts will be abbreviated as “ligand-tailed” melts, CoII-Lig-tailed and RuII-Lig-tailed (see Chart 2). Ionic conductivities and viscosities will also be compared in the two sets of melts. Experimental Section Syntheses of the counterion-tailed and ligand-tailed metal complexes have been described in previous publications.2a,b,3 The counterion-tailed melts are similar in color to solutions of their crystalline perchlorate counterparts. Measurements of glass transition temperatures by differential scanning calorimetry, of viscosity by rotating cone viscometry, of ionic conductivity by
10.1021/jp9925233 CCC: $18.00 © 1999 American Chemical Society Published on Web 11/23/1999
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J. Phys. Chem. B, Vol. 103, No. 50, 1999 11029
CHART 1
CHART 2
ac impedance of melt films on interdigitated array electrodes, and of charge transport diffusion coefficients DAPP by microelectrode voltammetry were carried out as described before.2a,b,3 Data presented here are (mostly) averages of multiple determinations, and conclusions drawn from them have been inspected for statistical validity.5 Calculations and activation plot analyses include propagation of errors from experimental values. Results and Discussion Charge Transport Measurements. We choose, for the comparisons in this paper, combinations of electroactive metal complex and polyether chains with similar physical dynamics properties, with the aim of minimizing any effects of those properties on the electron self-exchange dynamics kEX of the metal complexes. The central criterion for selecting the struc-
tures shown above was similar numbers of ethylene oxide (EO) units per metal complex unit; the CoII-CI-tailed and RuII-CItailed complexes each contain 14 EO units/metal, and the CoIILig-tailed and RuII-Lig-tailed complexes contain, respectively, 18 and 14 EO units/metal. This “equal-tail content” strategy is rooted in previous observations2a that physical diffusion rates, ionic conductivity, and viscosities of ligand-tailed metal complexes (such as the above CoII-Lig-tailed and RuII-Lig-tailed complexes) seem to be quite sensitive to the chainlengths of the polyether oligomers attached to the ligands. The strategy is shown here to have a rational basis in terms of “free volume” content. Microelectrode cyclic voltammetry of the (undiluted) CoIICI-tailed melt (Figure 1, right side) displays well-defined CoIII/II oxidation and CoII/I reduction waves; the well-defined RuIII/II
11030 J. Phys. Chem. B, Vol. 103, No. 50, 1999
Dickinson et al.
Figure 1. Cyclic voltammograms (2 mV/s) of undiluted counterion-tailed melts at a ∼11 µm diameter Pt microdisk electrode at indicated temperatures.
oxidation wave observed in the RuII-CI-tailed melts is shown in Figure 1, left side. It is notable that the currents for CoII/I reduction are much larger than are those for CoIII/II oxidation, although the [Co(bpy)3]2+ complex is the reactant that diffuses to the electrode to accomplish both reactions. This actually wellknown6 effect for the Co complex reaction is caused by a large difference2d between the electron self exchange rate constants of the [Co(bpy)3]2+/1+ and [Co(bpy)3]2+/3+ couples. The kEX of the CoIII/II couple is so slow that it does not contribute to the charge diffusion rate; i.e., currents for the CoIII/II oxidation thus measure physical diffusion of the CoII complexes. The kEX for the CoII/I wave is much larger and thus enhances DAPP; the model for the connection of kEX to DAPP is based on a cubic-lattice electron hopping approximation known as the Dahms-Ruff equation:7
DAPP ) DPHYS + DE ) DPHYS +
kEXδ2 C 6
(1)
where DE is the so-called electron diffusion coefficient and measures the electron self-exchange dynamics, δ (cm) is the average center-to-center distance of charge displacement in the melt accomplished by the electron transfer, and C (M) is the total concentration of metal complex sites.8 Since DAPP of the CoIII/II wave is not significantly enhanced by electron selfexchange (small CoIII/II kEX6), its DAPP serves conveniently to measure DPHYS of the [Co(bpy)3]2+ complex in the CoII-CItailed melt. Since the counterion-tailed [Co(bpy)3]2+ and [Ru(bpy)3]2+ melts are isostructural, we assume that DPHYS derived from the CoIII/II wave of the CoII-CI-tailed melt also applies to the RuII-CI-tailed melt, allowing calculation of kEX for the RuIII/II reaction from its DAPP. This assumption had been previously applied to the ligand-tailed melts.2b DPHYS in the Co complex melts was measured using potential step chronoamperometry, stepping to the diffusion-controlled
Figure 2. Activation plots of DPHYS (lower plot, 9) and DE (upper plots) for undiluted CoII-CI-tailed melt (2) and RuII-CI-tailed melt (b).
plateau of the CoIII/II wave, and analyzing the ensuing currenttime transients with the (linear diffusion) Cottrell equation9 as I vs t-1/2 plots, as shown in Supporting Information (Figure S1). These experiments were done at varied temperatures; the temperature dependency of DPHYS in the CoII-CI-tailed melt is shown in Figure 2 (9), and the thermal activation barrier EA,PHYS derived from the slope is given in Table 1. The results are also given there, from a previous report,2a for DPHYS and EA,PHYS of the CoII-Lig-tailed complex melt and those correspondingly for the RuII-CI-tailed and RuII-Lig-tailed complex melts.2b Comparison of the DPHYS and EA,PHYS results for the CoII-CItailed and CoII-Lig-tailed complexes shows that the physical
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J. Phys. Chem. B, Vol. 103, No. 50, 1999 11031
TABLE 1: Electron Transfer and Physical Dynamics Results for Undiluted Co and Ru Melts [M(bpy)3] complexa
Co-CI-tailedb
DPHYS c (25 °C) (cm2/s) EA,PHYS d (kJ/mol)
(8.0 ( 0.2) × 10-13 79 ( 1
DAPP (25 °C) (cm2/s) DE (25 °C) (cm2/s) EA,ET (kJ/mol) kEX g (25°C) (M-1 s-1) kEX0 h (M-1 s-1) TG (°C) η i (25 °C) (cP) σION (25 °C) (Ω-1 s-1) EA,ION j (kJ/mol) DCION (25 °C) (cm2/s) tM k (25 °C) DCION/DE
(5.9 ( 0.3) × 10-10 e (5.9 ( 0.4) × 10-10 39 ( 2 (2.6 ( 0.2) × 105 (1 ( 1) × 1012 -10 4.0 × 106 (1.5( 0.01) × 10-8 123 ( 2 (3.9 ( 0.4) × 10-12 0.17 0.0066
Co-Lig-taileda,b Co
Ru-CI-tailedb
III/II
CoII/I
(2.5 ( 0.5) × 10-13 79 ( 1
(2-8) × 10-13 d ∼79d
(3.0 ( 0.5) × 10-9 (1.1 ( 0.2) × 10-9 f 29 ( 4 g (5.2 ( 0.9) × 105 f (2 ( 2) × 1011 -24 1.8 × 106 (1.4 ( 0.01) × 10-7 66 ( 2 (2.5 ( 0.4) × 10-11 0.02 0.0083
(4.2 ( 0.2) × 10-10 e (4.2 ( 0.3) × 10-10 34 ( 3 (1.8 ( 0.2) × 105 (1 ( 1) × 1011 -13 na (1.1 ( 0.01) × 10-8 126 ( 2 (2.6 ( 0.4) × 10-12 0.24 0.0063
Ru-Lig-taileda,b Ru
III/II
(2-8) × 10-13 d ∼79d 1.1 × 10-9 d 1.1 × 10-9 26 ( 2 5.0 × 105 (2 ( 10) × 1010 -2 8.7 × 106 (1.1 ( 0.01) × 10-8 124 ( 2
a M-Lig-tailed (M ) Co, Ru) data from ref 2a,b. b See ref 8. c From Cottrell slope (ref 9) chronoamperometry. d Physical diffusion rate and activation as measured in isostructural Co melt. Indicated average slope of DPHYS activation plots in Figure 2 and ref 2a. e Measured from steadystate currents and eq 3. f From ref 2a, corrected for electronic migration, which lowers the result by about 3-fold. g Calculated via eq 2. h Intercepts of activation plots of DE (Figure 2), converted to rate constants using eq 2. i Average viscosity from a minimum of three rotation rates. j Average slope of ionic conductivity activation plots (Figure 4) around 298 K. k tM ) transference number of the metal complex.
constants, energy barriers EA,ET (Figure 2, 2 and b, respectively) and thermal activation prefactors (kEX0) as given in the table. Previous results2a,b for these parameters in the Co-Lig-tailed and Ru-Lig-tailed melts are also found in Table 1. Comparison between the counterion and ligand-tailed melts shows that the electron-transfer dynamics are generally similar but slightly slower in the counterion-tailed melts. As discussed before,2a the enthalpic activation barrier energies for the electron self-exchange reactions in the four melts can be equated with their activation free energies assuming that the reactions are symmetrical (isotopic) self-exchanges11 (reaction entropies and entropies of activation are zero). Thus, EA,ET is the same as ∆G* in the classical Marcus relation:4
[
kEX ) KAκν exp -
Figure 3. Current decays for chronoamperometric potential steps (500 mV, across the CoII/I wave) in undiluted CoII-CI-tailed melt at indicated temperatures.
diffusion dynamics of counterion and ligand-tailed melts (with “equal-tail content”) are similar. The DAPP for the CoII/I couple was obtained (Table 1) using potential steps to the wave’s plateau; the faster, electronhopping-enhanced charge diffusion now produces (Figure 3) radial diffusion conditions (steady-state currents ISS) after awhile. (The Figure 3 currents greatly exceed those in Figure S1, with a consequently larger iRUNC effect and a slowed cell time constant, as seen by the “roll-over” current hump in Figure 3. At higher temperatures, increases in melt ionic conductivity shorten the cell time constant so that steady currents are attained more quickly.) The radial diffusion currents in Figure 3 are analyzed with the relation10
ISS ) 4nFrDAPPC
(2)
Table 1 shows that DPHYS is negligible in relation to the obtained DAPP values for the CoII-CI-tailed and RuII-CI-tailed complex melts, leading by eq 1 to electron self-exchange rate
]
∆G* kBT
(3)
where kEX0 ) KAκν, KA is the precursor formation constant, ν and κ are the frequency and electronic factors, respectively, and kB is the Boltzman constant. In the classical theory, ∆G* is composed of contributions from inner- (λIS) and outer- (λOS) sphere reorganizational energy barriers (∆G* ) λ/4, where λ ) λIS + λOS).4 The inner-sphere barrier energy is associated with changes in nuclear configurations in the reactants as they become activated, and the outer-sphere barrier energy is associated with that of solvent dipole reorganization. Considering that the Co and Ru complexes in their melts reside in an ether-like “solvent”,12 one can calculate that λOS/4 ()∆G*OS) for the CoII/I and RuIII/II self-exchange reactions is about 9 kJ/mol.2a This free energy of activation is smaller, by substantial factors of 3-4, than the experimental electrontransfer barriers (EA,ET, Table 1) meaning (as seen before2a) that some other factor(s) contributes substantial barrier energy requirements to the electron self-exchanges. Hypothesizing on the nature of such factor(s) in previous publications,2 we noted that the activation barrier energies (in Co-Lig-tailed and Ru-Lig-tailed melts) might be (a) a peculiar “inner-sphere-like” barrier term occasioned by the linkage between the bpy ligand and its polyether “solvent” and/or (b) a thermal barrier associated with reorientational dynamics of the ether dipoles in the “solvent shell” (e.g., solvent dynamics13). The results for the counterion-tailed Co-CI-tailed and RuCI-tailed melts provide a test of the first of these possibilities,
11032 J. Phys. Chem. B, Vol. 103, No. 50, 1999 according to which their EA,ET values should be smaller than those of the ligand-tailed melts Co-Lig-tailed and Ru-Ligtailed. The experimental results (Table 1) show that the reverse is actually the case so that the interesting possibility of (a) can be discounted as a governing factor. The source of the large barrier energies to electron transfers in these melts thus remains a significant puzzle. The prime suspects are solvent dynamics effects on the CoIII/II and RuIII/II reactions and a more recently identified14 factor: ion-pairing of the reactants. The former effect is indirectly supported by strong evidence13 for solvent dynamics control of the rate of the heterogeneous (electrode surface) CoIII/II reaction. Ion-pairing effects are suggested, also indirectly, by recent experiments14 demonstrating that a substantial level of ion-pairing occurs between [Co(bpy)3]2+ and sulfonated counterions (and to a lesser extent, perchlorate counterions) in ether solvents. Values of the thermal activation prefactor kEX0 (Table 1) give insight into the adiabaticity of electron transfers in the melts. The precursor complex formation constant KA is ca. unity,15 so kEX0 ≈ κν. Adiabatic electron transfers (highly coupled reactant/ product potential energy surfaces) give κν ≈ 1012-1013 s-1 for adiabatic reactions;4a κν is smaller for nonadiabatic (low electronic coupling of reactant/product potential energy surfaces) electron transfers.3 Table 1 shows that the electron transfer reactions in the semisolid melts are nearly adiabatic. This interpretation of a reasonably strong electron donor/acceptor coupling is supported by recent observations16 of optically driven intermolecular electron transfers in mixed valent melts of similar structure. Physical and Ionic Characteristics. A premise of the electron transfer dynamics part of this study was that the physical properties of the chosen melts be quite similar so as to inspectsinsofar as possiblesvariations in electron transfer dynamics solely due to the counterion versus ligand-tailed structure of the melts. We inspect these physical properties next. From density measurements,8 the center-to-center metal complex distances (δ) are not very different in the counterion and ligand-tailed melts. Differential scanning calorimetry plots (see Supporting Information, Figure S2) for both melt varieties are nearly superimposable and display similar glass transition temperatures (TG, Table 1); i.e., thermal properties are nearidentical. The DSC data also confirm a molten state over the experimental voltammetry temperature range. Room-temperature viscosities17 are also similar for ligand- and counterion-tailed Co complex melts (η, Table 1). Ionic conductivities and activation plots thereof (Figure 4) are almost identical except for the Co-Lig-tailed melt, which is more conductive by ca. 10-fold. Activation plots for ionic conductivity (Figure 4) and fluidity (Figure S3 of Supporting Information) are curved, as expected for polymeric systems.18 Curvature has been seen in ligand-tailed melts;2a,b physical transport processes are strongly coupled to the segmental motions of the polyether units. These observed similarities between the counterion- and ligand-tailed melts support the premise that the ethylene oxide (EO) content of the melts is the key to similar physical properties; recall our strategy of choosing melts with “equaltail content” for study. This maxim may be useful in gauging the synthesis of redox polyether hybrids for physical property content.3 We next test an empirical model for the “equal-tail content” notion, based on the premise that “free volume” is controlled by EO content. Free Volume. In the materials described here, amorphous molten salts are generated from normally crystalline metal complexes by combining them with short ethylene oxide
Dickinson et al.
Figure 4. Activation plot of ionic conductivity for undiluted CoIICI-tailed melt (2) and RuII-CI-tailed melt (b); regression lines near room temperature give activation energies in Table 1.
oligomers. We have observed elsewhere that the melts, while polymer-like in terms of, for example, viscosity, have the nonpolymer-like property of becoming less viscous as the polyether chainlength2a or number of chains2b is increased, at least in the realm of short chainlengths. This characteristic implies that the melt physical properties, DPHYS and viscosity (η), might be quantified in terms of the volume fraction (Vf) of polymer chain present. We hypothesize that the free volume content of the material is proportional to the amount of introduced polyether chain (in the form of both chain length and number of chains). According to free volume theory, diffusivity is exponentially related to the inverse of the free volume, 1/Vf,19 and DPHYS and viscosity are inversely related according to the Stokes-Einstein equation.20 Figure 5 (top) shows that plots of both ln DPHYS (9, 2, b) and ln η (0, O) versus 1/Vf are indeed linear (and of opposite slope sign). The DPHYS and η data used in the figure are from this and previous work2a,21 on a variety of Co bipyridine complexes in which differing polyether chainlengths have been investigated. Ligands tailed with ethylene oxide (b, O) and propylene oxide (2) oligomers, and counterions tailed with ethylene oxide (9, 0) oligomers are represented in the plots and fall into three different, but linear, segments. The two segments (b, 9) for the ethylene oxide oligomer tails are not very different. The volume fraction Vf in Figure 5 (top) was calculated by dividing the product of the number of repeat units in the oligomer and the unit’s molar volume constant22 by the molar volume of the melt. A plot using a more exact calculation of Vf (accounting for free volume contributions from other parts of the structure, using “group molar volume constants”22) is shown in Figure 5 (bottom). There the ethylene oxide-tailed ligandattached and counterion-attached data (b, 9) fall nearly onto a single line, while the propylene oxide oligomers comprise a separate correlation. Despite the undoubted presence of experimental uncertainties in the DPHYS and viscosity data, the trends with polyether volume fraction seem to be conclusive and show that the “equal-tail content” concept has an underlying physical basis. This relation should be valuable in anticipating DPHYS and viscosity values of new members of a redox polyether hybrid melt series, with a given redox grouping. Whether such
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J. Phys. Chem. B, Vol. 103, No. 50, 1999 11033
Figure 5. Relationship between physical diffusion (DPHYS, closed symbols)/viscosity (η, open symbols) and free volume, proportional to 1/volume fraction of polymer (Vf), for a variety of cobalt tris-bipyridine melts: [Co(bpy(CO2[C2O]nCH3)2)3]2+(ClO4-)2 (b, O, and n ) 3, 7.2, 11.8), [Co(bpy)32+](CH3[C2O]n-BzSO3-)2 (9, 0, and n ) 3, 7.2, 11.8), [Co(bpy(CO2[C2CH3O]nCH3)2)3]2+(ClO4-)2 (2 and n ) 3, 2, 50/50 mixture of 2 and 1). Top: volume fraction determination based on number of repeat units in tail. Bottom: volume fraction determination incorporating values for specific group contributions.23
a correlation would hold across structurally different redox groupings has not been tested. Migration and Ion Pairing. The analysis of DAPP given above is simplified in that migration effects are not considered. We do that next, with some uncertainties being inserted into the electron self-exchange rate constants as a result. Migration comes in two flavors, ionic and electronic. The former refers to an ionic reactant being measurably transported (in addition to its physical diffusion) by the ionic charge flow accompanying (to maintain electroneutrality) electrolysis. Ionic migration is unimportant when the transference number,23 tM, of the ionic reactant is small, which is usually ensured by adding an inert “supporting electrolyte.” That measure, as we have explained previously,2a is not available in semisolid melts, at least for the typical LiClO4 electrolyte, because that dissolved electrolyte exerts a serious perturbation of the melt’s physical and electrontransfer properties.24 Electronic migration arises in the presence of a substantial iRUNC potential drop across the electrode diffusion layer; the potential gradient thus developed accelerates electron hopping and increases the observed DE and kEX. Electronic migration becomes significant when the ratio of counterion and electron diffusion coefficients (DCION/DE) be-
comes much less than unity. Cases of both forms of migration occurring simultaneously are uncommon but known,25 and the theory is quite complex. Inspection for the presence of these two forms of migration requires an estimation of the diffusion coefficient, DCION, of the melt’s electroinactive counterion, which is the ClO4- ion in M-Lig-tailed melts (M ) Co, Ru) and the polyether-tailed 2-sulfobenzoate counteranion in M-CI-tailed melts. As before,2a,b,24 we estimate DCION from measured ionic conductivities and DPHYS of the CoII complex melts, using the Nernst-Einstein equation:26
σION )
F2 2 D C + zCo2DPHYSCCo] [z RT CION CION CION
(4)
where σION is ionic conductivity, and z and C are charge and concentration of counterion (CION) and Co complex, respectively. Because of recent experiments14 revealing strong ionpairing of sulfonated counterions in the ligand-tailed metal complex melts, the present calculations (unlike those previous2a,b,24) assume a 1:1 ion-pairing so that in the CoII complex melt zCo ) +1 (not +2) and the unassociated counterion
11034 J. Phys. Chem. B, Vol. 103, No. 50, 1999 concentration CCION is halved. This assumption produces DCION values (Table 1) about 5-fold larger than otherwise. (For example, DCION ) 7.6 × 10-13 cm2/s if no ion-pairing is assumed.) It is unsurprising that the counterion diffusivity DCION of the tailed counterion is about 6-fold smaller than that of the smaller perchlorate ion. Calculated transference numbers, tM, given in Table 1 show that ionic migration is a minor effect in the Co,Ru-CI-tailed melts (where tM, while not zero, is small) and is absent in the Co-Lig-tailed melt. Calculated DCION/DE ratios27 on the other hand, show that electronic migration effects should be present in both Co,Ru-CI-tailed and Co-Lig-tailed melts, implying that the kEX given in Table 1 overestimates the actual rate constant. For the CoII/I reaction in the Co-CI-tailed complex, an electronic migration correction (using a theory27 for systems with fixed redox sites and freely mobile counterions, thus an approximation here) produces a (25 °C) rate constant kEX,COR ) 7 × 104 M-1 s-1 or about 4-fold smaller than the Table 1 result. For the RuIII/II reaction in the Ru-CI-tailed melt, the correction is a factor of about 5-fold. However, applying the electronic migration correction over a range of temperatures produces activation plots exhibiting vastly increased barrier energies and somewhat implausible preexponential factors (for the Co-CI-tailed complex, for example, EA,ET,COR ) 61 kJ/ mol and kEX0 ≈ 4 × 1015 M-1 s-1). This behavior generates concern about the efficacy of applying the fixed-site electronic migration theory27 to the present materials. This concern is heightened by the result of applying the electronic migration theory to DCION and DCION/DE values calculated assuming28 no ion-pairing exists in the melt, whereby for the Co-CI-tailed complex, EA,ET ) 75 kJ/mol and an unrealistic kEX0 ≈ 5 × 1017 M-1 s-1. For this reason, we have chosen to leave the Table 1 kEX and activation results for the CoII/II reaction in the Co-CItailed complex and the RuIII/II reaction in the Ru-CI-tailed melts as uncorrected values, with uncertainties of the rough magnitude stated above. (In the previous data2a given in Table 1 for the Co-Ligtailed melt, no ion-pairing was assumed (the counterion there is perchlorate) and an electronic migration correction gave a smaller, 3-fold factor, decrease in the rate constant of the CoII/I electron transfer reaction.) The above calculations reveal an uncertainty in translating experimental DAPP results in the counterion-tailed melts into electron self-exchange rate constants. While the counterion-tailed melts are more synthetically accessible, they are revealed to bring the burden of a greater migration effect to DAPP results and indicate a need to seek tactics to ameliorate their slowed DCION properties. These uncertainties do not, however, remove a principal conclusion of this paper, namely, that the earlier hypothesis of an inner-sphere contribution to the electron transfer barrier energy that arises from polyether chain attachment to the redox moiety (i.e., as in Co-Lig-tailed melts) must be discarded. In fact, relocation of the chains from the redox structure to the counterion has only a minimal effect on the characteristic propertiessboth electron transfer and physical transportsof these hybrid melts, not a substantial lowering of the activation barrier energy as the above hypothesis would have predicted. Acknowledgment. This research was supported in part by a grant from the Department of Energy, Division of Basic Sciences.
Dickinson et al. Supporting Information Available: Three figures displaying Cottrell plots, differential scanning calorimetry data, and activation plot for fluidity of Co-CI-tailed melt. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) (a) Terrill, R. H.; Murray, R. W. Molecular Electronics; Jortner, J., Ratner, M. A., Eds.; IUPAC Series Chemistry for the 21st Century; Blackwell Science: Oxford, U.K. 1997. (b) Terril, J.; Hatazawa, T.; Murray, R. W. J. Phys. Chem. 1995, 99, 16676. (c) Postlethwaite, T. A.; Samulski, E. T.; Murray, R. W. Langmuir 1994, 10, 2064. (d) Jernigan, J. C.; Surridge, N.; Zvanut, M. E.; Silver, M.; Murray, R. W. J. Phys. Chem. 1989, 93, 4620. (e) Oliver, B. N.; Egekeze, J.; Murray, R. W. J. A. Chem. Soc. 1988, 110, 2321. (2) (a) Williams, M. E.; Masui, H.; Long, J. W.; Malik, J.; Murray, R. W. J. Am. Chem. Soc. 1997, 119, 1997. (b) Masui, H.; Murray, R. W. Inorg. Chem. 1997, 36, 5118. (c) Long, J. W.; Velasquez, C. S.; Murray, R. W. J. Phys. Chem. 1996, 100, 5492. (d) Velasquez, C. S.; Hutchinson, J. E.; Murray, R. W. J. Am. Chem. Soc. 1993, 115, 7896. (e) Longmire, M. L.; Watanabe, M.; Zhang, H.; Wooster, T. T.; Murray, R. W. Anal. Chem. 1990, 62, 747. (f) Pinkerton, M. J.; LeMest, Y.; Zhang, H.; Watanabe, M.; Murray, R. W. J. Am. Chem. Soc. 1990, 112, 3730. (3) Dickinson, E. V.; Williams, M. E.; Hendrickson, S. M.; Mzsui, H.; Murray, R. W. J. Am. Chem. Soc. 1999, 121, 613. (4) (a) Marcus, R. A.; Sutin, N. Biochim. Biophys. Acta 1985, 811, 2001. (b) Marcus, R. A.; Siddarth, P. In Photoprocesses in Transition Metal Complexes, Biosystems, and Other Molecules; Kochanski, E., Ed.; Kluwer Acadmic Publishers: Dorhrecht, The Netherlands, 1992. (c) Sutin, N. Acc. Chem. Res. 1982, 15, 275. (d) Sutin, N. Prog. Inorg. Chem. 1993, 30, 441. (5) Taylor, J. R. An Introduction to Error Analysis, The Study of Uncertainties in Physical Measurements; Oxford University Press: Oxford, U.K., 1982. (6) Buttry, D. A.; Anson, F. C. J. Am. Chem. Soc. 1983, 105, 685. (7) (a) Dahms, I. J. Phys. Chem. 1968, 72, 362. (b) Ruff, I.; Friedrich, V. J. J. Phys. Chem. 1971, 75, 3297. (8) (a) In this paper, as in ref 2a, δ is taken as the average or equilibrium center-to-center separation between metal complexes and is calculated from the melt density. δ is ordinarily taken6,7 as the distance between the redox reactants at the instant of electron transfer, which can be less than the equilibrium δ. However, the Co-Lig-tailed complexes appear to have motion within the polyether tail shell that achieves close contact between the metal complexes on a time scale shorter than that of the electron-transfer reaction, since electron transfer rate constants are independent2a,24 of the chain lengths of the polyether tails. Thus, the rate constant kEX in these melts is thought to represent a “contact” reaction, while the equilibrium δ is the appropriate distance representing the overall charge displacement from the contact electron transfer and ensuing motion of the complexes within their polyether shells. Additionally, the difference between equilibrium and contact δ in the present case is only ca. 1.5 Å. (b) Density F, metal complex concentration C, and center-to-center spacing δ for Co-CI-tailed, CoLig-tailed, Ru-CI-tailed and Ru-Lig-tailed are 1.35 g/cm3, 0.85 M, and 12.5 Å; F ) 1.35 g/mol, C ) 0.723 M, δ ) 13.2 Å; F ) 1.37 g/mol, C ) 0.84 M, δ ) 12.5 Å; F ) 1.42 g/mol, C ) 0.936 M, δ ) 12.1 Å, respectively. (9) i ) nFAD1/2C/(π1/2t1/2) where i ) current, n ) number of e-, A ) area of electrode, D and C are the diffusion coefficient and concentration of electroactive species, respectively. (10) (a) Wightman, R. M. Anal. Chem. 1981, 53, 1125A. (b) Kovach, P. M.; Lowry, C.; Peters, D. G.; Wightman, R. M. J. Electroanal. Chem. 1985, 185, 285. (11) (a) Sutin, N.; Brunschwig, B. S.; Cretuz, C.; Winkler, J. R. Pure Appl. Chem. 1988, 60, 1817. (b) Newton, M. D.; Sutin, N. Annu. ReV. Phys. Chem. 1984, 35, 437. (12) (a) Our estimations2 of outer-sphere barrier energies have been based on dielectric constant data for polyether media. Determination12b of the optical dielectric constant for an example redox polyether hybrid gave a constant within 10% of the polyether-alone value. (b) Ritchie, J. Unpublished results, UNC, 1999. (13) Williams, M. E.; Crooker, J. C.; Pyati, R.; Lyons, L. J.; Murray, R. W. J. Am. Chem. Soc. 1997, 119, 10249. (14) (a) Williams, M. B. University of North Carolina at Chapel Hill. Unpublished results, 1999. (b) Sulfonated counterions ion-pair to ligandtailed metal complexes much more strongly than perchlorate counterions. (15) KA is derived from4d KA ) 4πNAjr2δrj/103 where the center-to-center distance jr is taken as that for the Co-Lig-tailed complex, 13.2 Å, and δrj is taken3d as 0.8 Å. (16) Ritchie, J. Manuscript in preparation. (17) These materials behave as Newtonian fluids; i.e., measured viscosity does not vary with shear rate. (18) (a) Gary, F. M. Solid Polymer Electrolytes, Fundamentals and Technological Applications; VCH Publishers: New York, 1991. (b)
Polyether Hybrid Salts MacCallum, J. R.; Vincent, C. A. Polymer Electrolyte ReViews; Elsevier Applied Science: Oxford, U.K., 1989; Vols. 1 and 2. (19) (a) Watanabe, M.; Longmire, M. L.; Murray, R. W. J. Phys. Chem. 1990, 94, 2615. (b) Cohen, M. H.; Turnbull, D. J. Chem. Phys. 1959, 31, 1164. (20) D ) kT/(6πηRH) where k is Boltzmann’s constant and RH is the hydrodynamic radius of a diffusion molecule in the following reference. Atkins, P. W. Physical Chemistry, 5th ed.; W. H. Freeman & Co.: New York, 1990; p 849. (21) Crooker, J. C. University of North Carolina at Chapel Hill. Unpublished results, 1997. (22) Van Krevelen, D. W.; Hoftyzer, P. J. Properties of Polymers: Their Estimation and Correlation with Chemical Stucture; Elsevier Scientific Publishing Company: Amsterdam, 1976.
J. Phys. Chem. B, Vol. 103, No. 50, 1999 11035 (23) (a) tM ) DM/(∑DM,DCION). (b) Bard, A. J.; Faulkner, L. R. Electrochemical Methods: Fundamental and Applications; John Wiley & Sons: New York, 1980; p 66, 124. (24) Williams, M. E.; Lyons, L. J.; Long, J. W.; Murray, R. W. J. Phys. Chem. B 1997, 101, 7584. (25) Norton, J. D.; Anderson, S. A.; White, H. S. J. Phys. Chem. 1992, 96, 3. (26) Reference 18, p 850. (27) Andrieux, C. P.; Saveant, J.-M. J. Phys. Chem. 1988, 92, 6761. (28) Additionally, assuming ion-pairing is negligible produces much larger values of tM (0.68 and 0.93 for the Co,Ru-CI-tailed complexes, respectively), meaning that both ionic and electronic migration effects should be present.
