Mesoscale Simulation of Proton Transport in Proton Exchange Membranes

R Jorn and GA Voth, JOURNAL OF PHYSICAL CHEMISTRY C, 116, 10476-10489 (2012).

DOI: 10.1021/jp300040w

Previous efforts to model proton transport through fuel cell membranes have largely focused on disparate length scales: molecular dynamics at the atomistic level and fuel cell stack engineering approaches at the macroscale. A new multiscale approach to bridge these extremes is proposed in this work which combines concepts from coarse-grained (CG) modeling with smoothed particle hydrodynamics (SPH) to capture the qualitative morphology and transport behavior of a proton exchange membrane at the length scale of tens of nanometers. This method allows for connection to atomistic simulations via the inclusion of transport coefficients from molecular dynamics and coarse-grained forces derived for the polymer backbone, side chain, proton, and water interactions. Information pertaining to macroscopic conductivity is obtained by volume averaging based on the flux and chemical potential fields within the membrane. Proton transport is effectively coarse-grained via introduction of a composition variable associated with each interacting site which carries the field information. By combining this technique with local electrostatics and coordinate dependent diffusion constants, the effects of double layer formation within the water pores and the influence of proximity to sulfonate groups on transport is recovered. The combined CG-SPH method is validated and subsequently applied to an equilibrated hydrated Nafion structure with a box length of 40 nm. The resulting conductivities calculated for the material agree very well with trends from experiment and provide insight into the complex interplay of morphology, proton distribution, and diffusion coefficients at a length scale that can be expanded beyond feasible atomistic molecular dynamics simulations to capture the effects of mesoscopic morphology on proton conduction.

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