Exponents for the Pressure Dependence of Hydrogen Permeation through Pd and Pd−Ag Alloy Membranes

Abstract

A frequently employed boundary condition for H permeation of membranes is p down ≈ 0 and, for this case, the flux is given by J = ( KD H / d ) p up n, where K is a constant and d is the membrane thickness. Values of n can then be obtained from slopes of plots of ln J against ln p up . When the H solution is ideal, n = 0.5, and D H is concentration-independent, but when the H solution is nonideal, i.e., when the H atoms interact, n ≠ 0.5 and D H is concentration-dependent. An equation is derived for n, which includes the effects of nonideality of H on both D H and the solubility. The terms in this equation for n can be obtained from the appropriate equilibrium H 2 isotherms for Pd or its alloys. Good agreement is found between the derived values of n and the experimental values for the pressure dependence of H 2 permeation through Pd, Pd 0.77 Ag 0.23, and Pd 0.50 Ag 0.50 membranes. By comparing experimental n ≠ 0.50 values to those calculated from the equilibrium isotherms, a decision can be made about whether bulk diffusion is the slow step.