Ab initio molecular dynamics simulation of proton hopping in a model polymer membrane

We report the results of ab initio molecular dynamics simulations of a model Nafion polymer membrane initially equilibrated using classical molecular dynamics simulations. We studied three hydration levels (λ) of 3, 9, and 15 H₂O/SO₃^- corresponding to dry, hydrated, and saturated fuel cell membrane, respectively. The barrier for proton transfer from the SO₃^--H₃O⁺ contact ion pair to a solvent-separated ion pair decreased from 2.3 kcal/mol for λ = 3 to 0.8 kcal/mol for λ = 15. The barrier for proton transfer between two water molecules was in the range from 0.7 to 0.8 kcal/mol for the λ values studied. The number of proton shuttling events between a pair of water molecules is an order of magnitude more than the number of proton hops across three distinct water molecules. The proton diffusion coefficient at λ = 15 is about 0.9 × 10^-5 cm²/s, which is in good agreement with experiment and our previous quantum hopping molecular dynamics simulations.