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

A frequently employed boundary condition for H permeation of membranes is p(down) approximate to 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 In J against In 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 not equal 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 not equal 0.50 values to those calculated from the equilibrium isotherms, a decision can be made about whether bulk diffusion is the slow step.