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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.

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The excess proton mobility in water has attracted scientific attention for more than a century. Detailed theoretical concepts and models are also presently in strong focus in efforts toward understanding this ubiquitous phenomenon. In the present report, we discuss a theoretical framework for rationalizing the excess proton mobility, based on computer simulations, theory of proton transfer (PT) in condensed media, and analysis of classical proton conductivity experiments over broad temperature ranges. The mechanistic options involved are (i) classical hydrodynamic motion of the hydronium ion (H 3 O +), (ii) proton transfer from hydronium to a neighboring water molecule, and (iii) structural diffusion of the Zundel complex (H 5 O 2 +), the processes all controlled by orientational fluctuations or hydrogen bond breaking in neighboring hydration shells. Spontaneous conversion of excess proton states between Zundel and hydrated hydronium states and between hydrated and bare hydronium states are the crucial parts of the scheme. A comparison between experimental data and molecular dynamics (MD) simulations shows that prototropic structural diffusion is determined by comparable contributions of the Zundel and hydrated hydronium states. The temperature dependent mobility is, moreover, determined not only by activation free energies of the three different acts of charge transfer, but also by labile equilibria between the different PT clusters. The proton conduction mechanisms of the three clusters are brought into the framework of quantum mechanical PT theory in condensed media. Both the nature of the elementary act and the reaction coordinates are, however, different for the two types of PT clusters. The corresponding rate constants are calculated and compared with MD simulations. Within the framework of PT theory we can also identify the nature of the kinetic deuterium isotope effect in the strongly interacting proton donor and acceptor groups in the clusters. The views and models introduced may carry over to PT in more composite, heterogeneous, and confined environments such as in polymer electrolyte membrane systems.