Diffusion with discontinuous swelling. V. Type II diffusion into sheets and spheres

Type II diffusion into uniform spheres (radius R) and sheets (thickness 2l) is calculated under the assumption that the glass-gel boundary proceeds at a constant velocity v from the surface towards the interior of the sample, that the diffusion coefficient D_g in the glass is constant and that the diffusion coefficient D_r of the rubbery gel is so much higher than vR or vl that practically no sorbate gradient is needed for the transport through the gel of the sorbate. The diffusion process is completed when this boundary reaches the center of the sample. The concentration profile of the sorbate in the glassy matrix in front of the boundary varies with time and velocity v. It does not, however, influence the boundary propagation velocity. Hence the often observed increase of the rate of the weight gain just at the end of the diffusion process is not considered at all. The relative weight gain of the sample W(t)/W_∞ as a function of time is the only quantity usually measured. From the ordinate intercept A and the initial slope B of the plot of W(t)/t^1/2W_∞ vs. t^1/2, one can calculate the characteristic transport properties, i.e., the diffusion coefficient D_g of the glass and the velocity v of the glass–gel boundary.