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 o n 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 poten tial due to inter action with the solvent molecules and the pendant side ch ains. The corresponding probability density is derived through solution of the Liouville equation, and this probability density is then used to comput e the friction tensor for the hydronium ion. The conventionally derived con tinuum-model friction coefficient is then "corrected' with the effective fr iction coefficient computed in this model, and then the corresponding proto n diffusion coefficient is calculated. For a Nafion(R) membrane pore with s ix water molecules associated with each fixed anionic site (a total of 36 s ites) and experimentally estimated pore parameters, the model predicts a pr oton diffusion coefficient of 5.05 x 10(-10) m(2) s(-1). A similar calculat ion for a pore containing 13 water molecules/SO3- resulted in a diffusion c oefficient of 8.36 x 10(-10) m(2) s(-1). Both of these theoretically calcul ated values are in good agreement with experimentally measured diffusion co efficients. (C) 2000 The Electrochemical Society. S0013-4651(99)06-060-7. A ll rights reserved.