The influence of morphology on proton transport in proton exchange membranes (PEM) is studied at the mesoscale using smoothed particle hydrodynamics (SPH), a mesh-free particle method for solving continuity equations. By solving the Nernst–Planck equation for proton transport in lamellar, cylinder, and cluster morphologies, we find that the proton conductivity for cluster morphology is much lower than lamellar and cylinder morphology at all hydration levels. This suggests the porosity and tortuosity in PEM morphology can reduce proton transport significantly at the mesoscale. We also investigated the effect of including a position-dependent diffusion constant (PDDC) tied to the local morphology, which is usually ignored in studies of proton transport in confinement. We calculated the PDDC in lamellar PEM using both quantitative and phenomenological approaches. SPH calculations show that conductivities for PEM systems with a PDDC can vary compared with systems with uniform diffusion constant. Therefore, it is potentially important to take into account the inhomogeneity of transport coefficients when studying proton transport in anisotropic systems.
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