A Comprehensive Multi-Step Description of the Permeation of Hydrogen in a Dense Metal Membrane Over a Broad Temperature Range

Development of cheaper and more durable dense metal membranes are being sought for generation of pure hydrogen suitable for fuel cells from coal. Toward this end, we have developed a comprehensive multi-step model for describing permeation of hydrogen in such membranes. The various steps include: s₁) dissociative adsorption on the surface, followed by: s₂) solution and then: s₃) diffusion of hydrogen atoms within the bulk metal matrix, and finally: s₄) evolution from the bulk to the surface, and: s₅) associative desorption on the permeate side. 

The efficacy of the model is ascertained by first applying it to Pd and Pd-Cu membranes, for which much literature exists. Of course, for these membranes, typically Sieverts’ law is assumed, which is limited to high temperatures (> 300 ºC) and low hydrogen pressures, when diffusion (step, s₃) is controlling, and hydrogen concentration in bulk metal is low. Over a broader range of temperatures spanning the crystallographic phase-transition in the Pd-H and Pd-Cu-H systems, in fact, the slopes are very different at low and high temperatures, and also there is a pronounced peak in permeability in the intermediate temperature range. The latter behavior has not yet been theoretically explained. 

Our approach considers the 5-step network in analogy to an electrical circuit and describes well the permeation behavior of hydrogen in Pd and Pd-Cu membranes, including the peak at intermediate temperatures. Further, it can adequately describe the absorption isotherms of the metal-hydrogen system. A comparison of step resistances also allows a systematic reduction to a three-step (adsorption, diffusion, and desorption control) model that is adequate over a broad range of temperatures and pressures.