Effects of Finite-size Ions and Relative Permittivity in a Nanopore Model of a Polymer Electrolyte Membrane

In this contribution, modified Poisson-Nernst-Planck equations are applied to study the distribution and flow of protons within cylindrical, water-filled nanopores of polymer electrolyte membranes (PEM). The model incorporates finite-size effects and an explicit expression for the relative permittivity. Due to the geometry, the problem decouples into a modified Poisson-Boltzmann equation in the radial direction and the Stokes equation in the axial direction. Ion saturation near pore walls, radial permittivity profiles, conductivity and water drag are properties of particular interest. Shortcomings and the usefulness of continuum models are elucidated and how these models might be employed to simulate macroscopic membrane properties.