Diffusion of H through Pd membranes: Effects of non-ideality

H diffusion constants, D H, have been obtained from steady-state fluxes through Pd membranes with the downstream side maintained at p H 2 ≈ 0. Good linearity of plots of H flux versus (1/ d), where d is the thickness, attests to H permeation being bulk diffusion controlled in this temperature (423–523 K) and p H 2 range (≤0.2 MPa). D H values have been determined at constant p up and also at constant H content. H fluxes through Pd membranes with three different surface treatments have been investigated (polished (unoxidized), oxidized and palladized) in order to determine the effects of these pre-treatments. The palladized and oxidized membranes give similar D H values but the polished membranes give values about 12% lower. For diffusion in a concentration gradient J = − D H ∗ ( c H/ RT)(d μ H/d x) is the proper equation for the flux, where c H is the H concentration, rather than Fick's first law, J = − D H(d c H/d x), where D H and D H ∗ are the concentration-dependent and -independent diffusion constants. D H ∗ can be obtained from D H using the thermodynamic factor, D H ( c H ) = D H ∗ ( ∂ ln p H 2 1 / 2 / ∂ ln c H ) T = D H ∗ f ( c H ) . In the commonly employed situation, where there is a large difference in concentrations between the upstream and downstream sides of a membrane, the thermodynamic factor varies with distance through the membrane and this should be allowed for in obtaining D H ∗ . Procedures are given and utilized to determine D H ∗ from D H( c H) when there is a large concentration gradient through the membrane. Activation energies for diffusion, E D( c H), have been determined. E D is found to increase with c H, which is attributed to the thermodynamic factor.