A statistical mechanical model of proton and water transport in a proton exchange membrane

We present here a mathematical model that focuses on the computation of the effective friction coefficient of an hydronium ion in a water-filled pore of a proton-exchange membrane (PEM) with a nonuniform charge distribution on the walls of the pore. The total Hamiltonian is derived for the hydronium ion as it moves through the hydrated pore and is affected by the net potential due to inter action with the solvent molecules and the pendant side chains. The corresponding probability density is derived through solution of the Liouville equation, and this probability density is then used to compute the friction tensor for the hydronium ion. The conventionally derived continuum-model friction coefficient is then "corrected' with the effective friction coefficient computed in this model, and then the corresponding proton diffusion coefficient is calculated. For a Nafion(R) membrane pore with six water molecules associated with each fixed anionic site (a total of 36 sites) and experimentally estimated pore parameters, the model predicts a proton diffusion coefficient of 5.05 x 10(-10) m(2) s(-1). A similar calculation for a pore containing 13 water molecules/SO3- resulted in a diffusion coefficient of 8.36 x 10(-10) m(2) s(-1). Both of these theoretically calculated values are in good agreement with experimentally measured diffusion coefficients. (C) 2000 The Electrochemical Society. S0013-4651(99)06-060-7. All rights reserved.