Hydration-Controlled Coupling of Water Polarization and Proton Transport in Nafion Under External Electric Fields

We use molecular dynamics simulations at a fixed cell volume (canonical, NVT, and ensemble) to study hydrated Nafion at hydration levels λ=3,9,15 under external electric fields. At zero field, the static dielectric constant of the aqueous subsystem, obtained from water dipole fluctuations, grows with hydration, from ϵ≈2.9 at λ=3 to ϵ≈17.2 at λ=15; because the single-molecule dipole is unchanged, this enhancement is cooperative, reflecting dipolar correlations that build up as the aqueous domains percolate. Under an applied field, the fluctuation formula no longer defines an equilibrium dielectric constant, so we characterize the response through the polarization itself: the collective water dipole orients along the field already at low fields, while its magnitude ⟨Mz⟩ saturates gradually, on a field scale that grows with hydration. This polarization build-up is accompanied by a reorganization of the first H₃O⁺-SO₃(H) coordination shell and by a crossover from diffusive to drift-dominated proton transport. These signatures shift together to higher fields as hydration increases, consistent with a common controlling variable: electrostatic screening by the added water. Because volume is held fixed across λ, the results characterize this coupling at controlled density rather than at each hydration's equilibrium swelling volume.