Diffusion in glassy polymer membranes submitted to induced stresses - Grzywna, Z. J.; Stolarczyk, J. (Polimery, 2022)
Diffusion is described in terms of phenomenology to approach a large class of phenomena involving diffusion medium-diffusing substance interactions that are very difficult (if not impossible) to describe on the molecular level, e.g., processes in which diffusion-induced stresses modify the diffusion itself. This feedback mechanism appears in the diffusion of hydrogen at high pressures through Pd/Pt membranes and in glassy polymers (e.g., MeOH in poly(methyl methacrylate)). Case II of diffusion is approached characterized by the diffusive front of the penetrant that separates the penetrated polymer into two phases, the glassy phase ahead, and the rubbery phase behind the front, and by a linear mass uptake of polymer at early sorption stages. A phenomenological model of diffusion in glassy polymers is presented that incorporates the stress gradient in the diffusive flux equation and offers the equation providing for the generation of, and relaxation from, the viscoelastic stress (eqns. 12 and 15). The equation was solved numerically for a wide range of functional parameters and two types of the diffusive front were identified. One type occurs when there is no phase transition of the glassy into the rubbery polymer (temperatures T < Tg or penetrant concentration too low). Stresses are then formed behind the front; they act according to the concentration gradient (Figs. 3-6). The other type occurs when there is phase transition and stresses are formed ahead of the front to produce an effective barrier to penetrant molecules (Figs. 7, 8). A special role is played by the front precursor, i.e., a small amount of the penetrant that fills chain interstices to produce stresses and thus to form a strong diffusive front (Figs. 9-11, Table 1).