The phenomena of dielectric saturation in the water domains of polymer electrolyte membranes

A statistical mechanical formalism is presented for the calculation of the thermodynamic property of the permittivity of the water in the water and ion containing domains of polymer electrolyte membranes, with particular emphasis on the polarization. The present work differs from previous work in that the electric field due to the dissociated acidic groups (i.e. –SO3H) of the polymer is included in the expression of the total Hamiltonian of the system. With this important consideration we compute the dielectric constant of the water in a fully hydrated Nafion membrane and show that there exists a central region within the pores where the water is similar to bulk water (i.e. ε=80) but as the pore walls are approached the water becomes increasingly more bound.