Figure 6: The chemical potential of hydrogen in MoO₃ on Pd-membranes can be considered to be nearly constant, although the hydrogen concentration varies going from Pd high pressure feed through the membrane to the top of the MoO₃ surface.

The concentration in a material depends on the hydrogen solubility in the bulk of the membrane setup, and on the chemisorption enthalpy on its surfaces (as sketched by a simplified energy potential diagram). However, the chemical potential is balanced by the corresponding entropy terms, so that it is continuous. This is perfectly true for equilibrium conditions. The membrane works in quasi-equilibrium. However, because of the low desorption probability of H₂ from MoO₃ due to the high activation barrier, while absorption of hydrogen on the feed side is facilitated by the small activation energy of hydrogen dissociation on Pd, this quasi-equilibrium is near to equilibrium. In kinetic experiments as performed here, quasi-equilibrium is reached within a finite time, which depends on the amount of hydrogen absorbed in the bulk of the membrane (depicted by grey lines). The right graph shows the time dependence of the pressure at the feed side, which can be converted into the amount of hydrogen entering the membrane, and the pressure on the UHV side. A linear decrease of the feed pressure (corresponding to a constant UHV-pressure) is indicative of a constant flux through the membrane, which is reached within 500 s. See ref. 30 for more details.