Achievable boundary conditions in potentiostatic and galvanostatic hydrogen permeation through palladium and nickel foils

Two popular electrochemical methods for the investigation of the permeability of metal membranes to atomic hydrogen are critically discussed. In the potentiostatic (P) method, hydrogen is generated at constant potential at the entrance face; in the galvanostatic (G) method, it is generated at constant current. In both, the concentration at the exit face of the membrane is zero. The boundary condition at the entrance face usually taken to correspond with these experiments is either that the surface concentration is constant (the C case) or that the flux of hydrogen entering the membrane is constant (the F case). It is pointed out that the widespread assumptions that use of the P technique guarantees the C boundary condition, and that use of the G technique guarantees the F condition, are incorrect. The boundary condition actually established depends on the relative rates of the various steps involved in hydrogen evolution at the entrance face and its diffusion through the membrane. Experimental work on ca. 25 μm thick nickel and palladium, which supports this contention, is described. The F boundary condition is readily established by the G experiment on palladium, but the C condition cannot be established by the P experiment. The converse is true for nickel. These differences are explained in terms of the greater solubility and diffusivity of hydrogen in palladium as compared with nickel. An extended potentiostatic experiment, termed the Pf experiment, is described. In the Pf experiment, all the potentiostatically generated hydrogen enters the membrane. The currents passing at both faces of the membrane are measured during permeation, and also as they decay after the potential of the entrance face is switched to that of the exit face, causing hydrogen to diffuse out of both sides of the membrane. The Pf experiment is shown to work well with thin palladium membranes, and to provide crosschecks on the diffusivity of hydrogen. The diffusion coefficient of hydrogen in nickel is sensitive to the thermal history of the metal. Decay transients give some evidence for the existence of hydrogen traps in both nickel and palladium. The potential of the entrance face during G experiments on either metal is not related to the surface concentration of hydrogen by the Nernst equation. It is concluded that a full analysis of the permeation transients obtained by P or G experiments should be made to establish the boundary conditions actually created by the experimental procedure. Some previously published permeation work is critically examined in the light of this conclusion.