Diffusion with discontinuous swelling. IV. Type II diffusion into spherical particles

Abstract

AbstractIn the last few years some new features of the so‐called type II diffusion have been established which confirm the first theoretical description of such a material transport into a semi‐infinite glassy medium which at a certain concentration of the sorbate is transformed into a gel. The boundary between the glass and the gel progresses at a constant velocity into the interior of the sample thus yielding a linear term in the weight gain. The gradual establishment of the concentration profile in front of this boundary yields at the beginning a square root term in the weight gain. A detailed analysis of the extensive measurements of Hopfenberg, et al. of the diffusion of n‐hexane into extremely small polystyrene spheres demonstrates that the weight gain always starts with a square root of time term. In sufficiently large spheres this contribution is soon completely overridden by the term linear in time. The spherical geometry substantially modifies the concentration profile and the weight gain. In particular the weight gain divided by the square root of time vs the square root of time shows a maximum as soon as the geometrical factors prevail over the effect of the constant velocity progression of the boundary between the glass and the gel.