Hydrogen chemical potentials and diffusion coefficients in hydrogen diffusion membranes

Numerical simulation of diffusivity of hydrogen in thin tubular metallic membranes affected by self-stresses

“…where E is the Young's modulus, E =100-200 GPa; is the Poisson's ratio, = 0:3-0.4; C0 is the concentration of H in M corresponding to nH = 1, C0 = 0:1-0:15 mol H cm −3 for materials used experimentally [1,2,[13][14][15][16][17][18][19][20][21][22][23][24][25][26]; L is the membrane thickness; z is the coordinate along the thickness direction, the upstream side is z = 0 (outer surface) and the downstream side is z = L (inner surface). The hydrogen ux has the form…”

“…The UHD phenomena, the time courses of pressure change in a tube during hydrogen absorption and interruption of steady di usion [1,2,[13][14][15][16][17][18][19][20][21][22][23][24] were demonstrated and interpreted by these theories. Besides these phenomena, it has been found that self-stresses lead to changes of apparent di usion coe cient (ADC) if traditional relations are applied in experiments [1,2,[13][14][15][16][17][18][19][20][21][22][23][24][25][26]. This is one of the reasons that ADCs of H in metal (alloy) hydrides di er from one work to another.…”

“…Since the discovery of the up-hill di usion (UHD) e ect in hydrogen permeable metals by Lewis et al [1], there has been much theoretical work concentrated on the aspects of stresses induced by the hydrogen (interstitials) di usion in metals (solids) [2][3][4][5][6][7][8]. However, the appropriate physical pictures of self-stress e ects in practical shapes of material have only been given recently [9][10][11][12].…”

Effects of self-stress on the hydrogen absorption into palladium hydride electrodes of plate form under galvanostatic conditions

“…Additionally, Lewis and coworkers showed that self-stresses are generated during the insertion and diffusion of hydrogen interstitials and that the consequent strain developed results in a force opposing the flux generated by diffusion (see Ref. [10][11][12][13][14][15][16][17][18][19][20] for palladium and palladium alloys). Contemporary theoretical treatments of these effects, based on thermodynamics of stressed solids, have been presented in a review paper by Li [21], in a series of works by Larché and Cahn [22][23][24], and other papers by Kandasamy [25,26], Baranowski [27], Simon and Grzywna [28] and Zoltowski [29].…”

Stress induced changes in hydrogen pressure in contact with tubular diffusion membrane

“…In other words, the hydrogen diffusion studies have both academic and technical interest. In the past, new sets of research data observed for hydrogen diffusion in tubular membranes of palladium and its alloys were published by Lewis and their collaborates (Lewis et al, 1983, 1987, 1988, Baranowski et al, 1989and Sakamoto et al,1996. The typical features of the observed time dependent changes of hydrogen pressure inside the tubular membrane due to the commencement of hydrogen diffusion either by gas adsorption or electrolysis are shown in Figures The observed diffusion of hydrogen against concentration gradient of hydrogen in the diffusion membrane (uphill diffusion) was explained by Kandasamy (Kandassmy 1988).…”