Coarse-grained model of water diffusion and proton conductivity in hydrated polyelectrolyte membrane

Using dissipative particle dynamics (DPD), we simulate nanoscale segregation, water diffusion, and proton conductivity in hydrated sulfonated polystyrene (sPS). We employ a novel model [Lee et al. J. Chem. Theory Comput. 11(9), 4395-4403 (2015)] that incorporates protonation/deprotonation equilibria into DPD simulations. The polymer and water are modeled by coarse-grained beads interacting via short-range soft repulsion and smeared charge electrostatic potentials. The proton is introduced as a separate charged bead that forms dissociable Morse bonds with the base beads representing water and sulfonate anions. Morse bond formation and breakup artificially mimics the Grotthuss mechanism of proton hopping between the bases. The DPD model is parameterized by matching the proton mobility in bulk water, dissociation constant of benzenesulfonic acid, and liquid-liquid equilibrium of water-ethylbenzene solutions. The DPD simulations semi-quantitatively predict nanoscale segregation in the hydrated sPS into hydrophobic and hydrophilic subphases, water self-diffusion, and proton mobility. As the hydration level increases, the hydrophilic subphase exhibits a percolation transition from isolated water clusters to a 3D network. The analysis of hydrophilic subphase connectivity and water diffusion demonstrates the importance of the dynamic percolation effect of formation and breakup of temporary junctions between water clusters. The proposed DPD model qualitatively predicts the ratio of proton to water self-diffusion and its dependence on the hydration level that is in reasonable agreement with experiments.