Mechanisms of Proton Conductance in Polymer Electrolyte Membranes M. Eikerling, †,‡ A. A. Kornyshev,* ,† A. M. Kuznetsov, § J. Ulstrup, | and S. Walbran † Institute for Materials and Processes in Energy Systems, Research Center “Ju ¨ lich” GmbH, D-52425 Ju ¨ lich, Germany, The A. N. Frumkin Institute for Electrochemistry, Russian Academy of Sciences, 117071 Moscow, Russia, and Department of Chemistry, The Technical UniVersity of Denmark, DK-2800 Lyngby, Denmark ReceiVed: September 5, 2000 We provide a phenomenological description of proton conductance in polymer electrolyte membranes, based on contemporary views of proton transfer processes in condensed media and a model for heterogeneous polymer electrolyte membrane structure. The description combines the proton transfer events in a single pore with the total pore-network performance and, thereby, relates structural and kinetic characteristics of the membrane. The theory addresses specific experimentally studied issues such as the effect of the density of proton localization sites (equivalent weight) of the membrane material and the water content of the pores. The effect of the average distance between the sulfonate groups, which changes during membrane swelling, is analyzed in particular, and the factors which determine the temperature dependence of the macroscopic membrane conductance are disclosed. Numerical estimates of the specific membrane conductivity obtained from the theory agree very well with typical experimental data, thereby confirming the appropriateness of the theoretical concepts. Moreover, the versatility of the models offers a useful and transparent frame for combining the analysis of both experimental data and the results of molecular dynamics simulations. I. Introduction The levels of research and development of new proton conductors as well as those currently available have increased dramatically over the past decade. 1-6 This activity has been driven by the booming demand for fuel cell technology, particularly for vehicles and portable applications. 7 These impose rather strict requirements on proton conductors, such as stable performance in the temperature range between 80 and 200 °C with a conductivity not lower than 0.1 S cm -2 , chemical, mechanical, and thermal stability, and impermeability to gases, methanol, and charge carriers other than protons. Some of these demands are met by the best currently available polymer electrolyte membranes such as Nafion, Aciplex, Flemion, and Dow membranes. These materials are essentially strong polymer acids. Exposed to water, they dissociate upon hydration into the immobile ionomer (anionic) groups residing on side chains of the polymer and free mobile protons in the aqueous solution. Thus, the free protons move through the hydrogen-bonded network of water molecules inside the poly- mer. Compared to solid state proton conductors, the major advantage of aqueous polymer electrolyte conductors is the high conductivity of 0.01-0.1 S cm -2 available at moderate tem- peratures. This is due to the high concentration of protons in water-filled pores and the high proton mobility. The mobility is facilitated by a “collective” character of the proton transfer, which is induced by configuration fluctuations of donor and acceptor water molecules; this mechanism is discussed further below and is the basis for the model of proton conduction addressed in this paper. The main reason for the facile proton transport in aqueous systems is, however, simple. No matter how many “excess” protons there are in the system, all of them become indistinguishable in the “sea” of the background protons of water. There are thus no “fixed” and “free” protons; they are interchangeable. A proton, mobile a moment ago, takes a rest to become a part of a water molecule. The privilege to run is then relayed to another proton, which was a part of this molecule or of other molecules clustered with the first one. It is the relay character typical of aqueous hydrogen-bonded systems which makes proton transport fast. While providing an environment for facile long-range proton transfer, aqueous-based membranes are also fraught with several disadvantages. One is the permeability to methanol, 8 which makes it hard to use them in direct methanol fuel cells. They are also, obviously, unstable at elevated temperatures (J100 °C), where electrocatalysis could otherwise run fast enough to consume all methanol at the anode so that the problem of methanol permeation would simply not arise. A third shortcom- ing is the electroosmotic effect: the transport of water induced by the classical migration of hydrated H 3 O + ions. This leads to dehydration of the anodic side of the membrane, and thus limits the current. 9 Last, but not least, is the prohibitive aspect of high cost for the best-performing polymer electrolyte membranes, such as Nafion and its derivatives. Progress in “dry” solid state proton conductors that offer high conductance without the listed deficiencies is, however, far from outclassing aqueous polymer electrolyte membranes in hydrogen energy technology. Theoretical and experimental efforts toward better understanding of membrane operation are therefore very * To whom correspondence should be addressed. E-mail: a.kornyshev@ fz-juelich.de. † Research Center “Ju ¨lich” GmbH. ‡ Present address: Materials Science Division, Los Alamos National Laboratory, P.O. Box 1663, MS D429, Los Alamos, NM 87545. § Russian Academy of Sciences. | The Technical University of Denmark. 3646 J. Phys. Chem. B 2001, 105, 3646-3662 10.1021/jp003182s CCC: $20.00 © 2001 American Chemical Society Published on Web 04/07/2001