Ion and water transport in a nafion(circle R)membrane pore: a statistical mechanical model with molecular structure

摘要

With the well established importance of the coupling of water and protons through electroosmotic drag in operating PEFCs we present here a derivation of a mathematical model that focuses on the computation of the mobility of an hydronium ion through an arbitrary cylindrical pore of a PEM with a non-uniform 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 effected by the net potential due to interaction with the solvent molecules and the pendant side chains. The corresponding probability density is derived through solution of the Liouville equation. This probability density is then used to compute the friction tensor for the hydronium ion. We find two types of contributions: (a) due to the solvention interactions for which we adopt the conventional continuum model; (b) due to the interaction between the pendant charges and the hydronium ion. The latter is a new rersult and displays the role of the non-uniform nature of the charge distribution on the pore wall.