Using microelectrochemical techniques, our laboratory has explored selfexchange-based electron transport in a variety of mixed-valent polymeric media. The transport rate is measured as the electron diffusion coefficient, D,, or the self-exchange rate constant k,, . The basic variables for electron transport in mixed-valent polymer materials include: ( a ) the physical mobility of the counterions of the polymer that migrate due to electroneutrality requirements, ( b ) the physical diffusion coefficient, Dphy\, of the monomeric or polymeric oxidized and reduced molecular sites or ions relative to the rate of electron hopping or tunnelling between donor/acceptor pairs, ( c ) the observational timescale relative to these mobilities which provides the distinction between transient and steady-state experiments, and ( d ) the chemical environment of the polymer, whether dry and solvent-free or contacted by solvent vapour or liquid. Experimental strategies and results are presented for the measurement of rates of ion diffusion, D , , in N,-dry and solvent-wetted mixed valent polymers. I n a dry, mixed-valent osmium complex polymer, the electron-transport rate measured under steady-state conditions, where no ion transport occurs concurrently, is much faster than the diffusion rate of the ion as estimated in a transient electrolysis experiment. In a solvent-wetted osmium complex polymer, the electron-transport rate measured under transient conditions is much slower than that of the ion which was measured under steady-state conditions. These circumstances allow isolation of individual processes and are interpreted as giving electrontransport rates not strongly influenced by macroscopic ion-transport rates. Cyclic voltammetry of [Co(bpy),]*+ and of Li+TCNQ-in dry poly(ethy1ene oxide) polymer electrolyte solvents exhibits differing measured diffusion coefficients, Dapp, for the oxidation us. the reduction of each compound, reflecting the coupling of physical diffusion and electron self-exchange transport. Microdisc electrode voltammetry of solutions of a synthesized ferrocene mono-tagged poly(ethy1ene oxide) in a polymer solvent of comparable molecular weight gives Dapp values smaller than those for ferrocene monomer dissolved in the same polymer solvent. The Dapp in the former case measures the self-diffusion rate of a linear chain polymer within a linear chain polymer solvent. Measurability of this rate has implications for assumptions about diffusive mobility of redox molecules attached to polymer chains.
The dynamics of electrical-field-driven solid-state electron transfers between Os(II) and Os(III) sites in the 1:1 mixed-valent redox polymer poly [Os(III/II)(bpy)2(vpy)2] (C104)2 3 (bpy = bipyridine; vpy = vinylpyridine) are described. The nonlinear molecular conductivity of the polymer is modeled as an experimentally controllable intersite free energy gradient imposed by the electrical field. Electron self-exchange rates are analyzed as a function of free energy and temperature from 83 to 295 K with both classical and semiclassical electron-transfer theories. The analysis shows that room-temperature electron transfers lie near the high-temperature limit of classical behavior with a thermal barrier of 7-8 kcal/mol, but those at lowered temperature exhibit non-Arrhenius behavior and involve a nuclear tunneling mechanism. A single-frequency vibronic model gives 250 cm"1 as the vibrational energy and ca. 7 cm"1 as the electronic coupling term HAB. We derive an apparent intersite reaction free energy that is 3-8 times larger than those estimated from the applied voltage bias £ divided by the number of monolayers of osmium complex sites in the film. This effect may arise from imperfections in contacting electrodes to discussions with Professor R. P. Buck (UNC), Professor E. A. Irene (UNC), S. Feldberg (Brookhaven), and C. E. D. Chidsey (Bell Labs) are gratefully acknowledged.Registry No. Poly[Os(III/II)(bpy)2(vpy)2] (C104)2 5, 106762-37-2; Pt,
Recent theory has shown that, in transient electrochemical oxidation or reduction of a redox polymer film, electroneutrality coupling between concurrently transported electrons and counterions in the polymer film can enhance the rate of electron-hopping transport as expressed by the apparent electron diffusion coefficient De,app. We have investigated this problem in the redox polymers poly[Os(2,2'-bipyridine)z(N-(4-pyridyl)cinnamamide)z12+ (poly-I), poly[Os(2,2'-bipyridine)2(4-~inylpyridine)2] 2+ (poly-11), and poly[Os(4-viny1-4'-methyl-2,2'-bipyridine)312+ (poly-111) by measuring and comparing the diffusion coefficients (DcJ of C1-counterions in the cationic polymer films to the transient chronoamperometric (De,app) and steady-state (De) electron diffusion coefficients. At room temperature, the ratio u = Dion/Dc is 1.25,0.16, and 0.076 for the three redox polymers, respectively. According to the electroneutrality coupling theory, the coupling effect is insignificant in poly-I films at room temperature, with and without dilution of the Os centers by copolymerized R u complexes, but at lowered temperature, assuming u -0, coupling in poly-I has a substantial effect. Electroneutrality coupling in poly-I11 films enhances the room temperature chronoamperometric over the ("true") steady-
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