J. Phys. Chem. 1994, 98, 5127-5134
5127
Electric Field Driven Electron Self-Exchanges in Dry Nafion Containing Mixed-Valent Osmium Bipyridine Roger H. Terrill,? Paul E. Sheehan,t**Virginia C. Long,$ Sean Washburn,$ and Royce W. Murray’*? Kenan Laboratories of Chemistry and Department of Physics and Astronomy, University of North Carolina, Chapel Hill, North Carolina 27599- 3290 Received: January 21, 1994; In Final Form: March 12, 1994” Dry Nafion perfluorosulfonate ionomer films incorporating mixed-valent osmium(II/III) tris(4,4’-dimethyl2,2’-bipyridine) or osmium( II/III) tris(2,2’-bipyridine) are shown to be electronic conductors due to electron self-exchange (hopping) from Os(I1) to Os(II1) sites. Film conductivity is measured as a function of the product [Os(II)] [Os(III)] of site concentrations and conforms to the expected bimolecular rate law. Hopping currentvoltage curves are analyzed with a Marcus-based model and the dispersive transport model of Scher, Montroll, and Pfister. The activation energy for electron hopping is 44 f 3 kJ/mol, and the bimolecular rate constant is ca. 2 X lo3 M-l s-I. Exposure to water vapor increases both the ionic and electronic conductivity of the mixed-valent films. Infrared spectra of Os-containing films show evidence of ion pairing between sulfonate and osmium complexes. These observations are consistent with a model in which electron-hopping rates are limited by intersite hop distance in the rigid polymer matrix.
Polymerscontaining well-defined molecular electron donor and acceptor sites (fixed-site redox polymers) are a useful setting for the study of solid-state intermolecular electron transfers as well as a potentially important class of electronic conductors. This laboratory has described recent studies of electron transport in mixed-valent poly(viny1ferrocene)l and poly(viny1bipyridine) metal complexes,2“ in which the redox molecules form the polymer matrix and their respective counterions are monomeric. The present work inverts that relationship, using a polymeric counterion (theperfluorosulfonateionomer, Nafion) hosting the mixedvalent redox monomers, osmium tris(4,4’-dimethyl-2,2’-bipyridine, [ O ~ ( M e ~ b p y ) ~ ] 2 +and / ~ + osmium , tris(2,2’-bipyridine), [O~(bpy)3]~+/~+. The electrochemistry of redox polymer coatings on electrodes, including Nafion films, has been studied extensively4 in contact with electrolyte solutions; in such circumstance these materials act as mixed ionic and electronic conductors. In a series of investigations, we havel~3~4~7~8 sought to quench their characteristic ionic conductivity by eliminating contacts with fluid electrolyte solutions, by using lowered temperatures and/or fast experimental time scales, and in the present study, by use of a dried, polymeric counterion (Nafion) in which ionic conductivity arising from either the Nafion sulfonate groups or the cationic Os sites proves to be negligible at room temperature even at very long experimental time scales. We will describe the dynamics of the solid-state electron selfexchange, or “hopping” reaction, with rate constant kex:
where subscripts a and b denote metal site location in the polymer in thin, thoroughly dried, Os-loaded Nafion films sandwiched between metal electrodes. This condition quenches the usual ionic conductivity of Nafion and ensures that the film’s conductivity is solely electronic and not mixed ionic-electronic. The rates of reaction 1 obey the predicted biomolecular rate law, but are much slower than those previously determined2-8 for polymerphase Os complexes. Kenan Laboratories of Chemistry. Present address: Department of Chemsitry, Harvard University, Cambridge MA. i Department of Physics and Astronomy. Abstract published in Aduance ACS Abstracts, April 15, 1994. t
0022-3654/94/2098-5 127$04.50/0
The water-swollen perfluorosulfonate ionomer Nafion and its structural relatives are well-known as ion-exchange membranes and as polymer electrolytes for chlor-alkali cells9 and fuel cells.10 There have been numerous studies of charge transport in waterswollen Nafion f i l m ~ l l -that ~ ~ are contacted by electrolyte solutions, including measurements of electron self-exchange rates for the [O~(bpy)3]~+/~+, [Ru(bpy)3I2+P, and [C0(bpy)3]1+/~+ c o ~ p l e s ~ ~ - lwhen ~ , 2 2these cations are loaded as counterions into the Nafion films. These measurements have required untangling of the effects of ionicmobilities from those of the electron hopping, which can be a substantial complication.26 There have been, in contrast, few studies of dry Nafion films and none involving electronic transport. Ionic conductivity2I (by AC impedance) and ion pairingz7 (by 23Na N M R and IR spectra1)28-30 measurements conducted as a function of film hydration show that dry Nafion films with alkali metal cations (a) have extremely small ionic conductivities (AC as well as DC) and (b) exhibit strong ion pairing between the metal cation and Nafion sulfonategroups. These studies, indicating the reluctance of the dry perfluorosulfonate environment toward significant ionic mobility and/or carrier generation, are fully consistent with the electrical properties that we observe in dry Nafion films loaded with Os bipyridine complex counterions. The ionic conductivity of the latter films when dried in a gas stream is sufficiently low as to sustain nearly DC (ca. lC3Hz) electric fields up to 105 V/cm. Theobserved electronic and ionic conductivities rise upon film hydration. The absence of ionic conductivity in a dry Nafion film containing a mixed-valent redox counterion and sandwiched between metal electrode contacts has the following consequences: (a) there is no electrolysis a t the electrode-polymer interfaces and no associated development of concentration gradients of electron donor-acceptor sites that could drive electron self-exchanges like reaction 1;(b) as a result, a sustained electrical gradient can exist in the bulk of the mixed-valent polymer film, and reaction 1 occurs solely under its impetus; and (c) the free energy of reaction 1 can be systematically varied by controlling the applied potential bias. The latter aspect of the measurement gives insight into aspects of redox polymer electron self-exchanges that had not been previously6J1-25discerned with mixed ionic/ electronic conduction experiments, notably details of the bimolecular rate law and the existence of a dispersion in the electrontransfer kinetics. 0 1994 American Chemical Society
-ierriii et ai.. -3.
5128 The Journal of Physical Chemistry, Vol. 98, No. 19, I994
Models of Analysis of Electron-Transfer Kinetics. Currents obser~edl,3.~,~,3la.32 for electrical gradient-driven electron-hopping rise exponentially with applied potential bias, limited only by ultimate dielectric breakdown of the polymer film. Our analysis of the Nafi~n/[(Os(bpy)~] system employs two models for the hopping reaction. One is a modifiedl-3~49~ Marcus33-36 free energyrate relation,
where k,, is self-exchange rate constant, d the film thickness, and A thecontacting electrodearea; C,and C,are respectively electron acceptor and donor concentrations, PE is applied voltage, p (ideally = 1) is an empirical fitting parameter employed because the current-potential curves rise more steeply than classical Marcus theory predicts, and intersite distance 6 is estimated using a cubic packing model in which Ct = C, + C,,and 6 = [CtNa]-1/3.The two RHS terms in eq 2 represent downfield and upfield electron hops, necessary because, although the overall gradient AE/d is large, the intersite gradient AE6/d is small. For example, for 6 = 1.6 nm, and AE/d = 105 V/cm; the intersite driving force is only 16 mV, about 40% less than kT298. In the limit of low AE (Le., (pFGAE)/(2dRT)
