Case-II diffusion in polymers. I. Transient swelling

Abstract

The swelling of a polymer glass by sorption of a small molecule penetrant is considered in a regime characterized by so-called case-II diffusion. Attention is focused on the polymer so that the swelling process can be investigated apart from diffusion. The model of Thomas and Windle (TW) is used to predict the surface swelling as a function of exposure time. This model assumes that the swelling is driven by the osmotic pressure which relaxes to zero as the surface penetrant volume fraction φs approaches its equilibrium value φe. The rate-controlling factor of the swelling process is the viscosity of the polymer η, which decreases with increasing surface sorption according to η=η0 exp(−mφ) where η0 is the viscosity of the unswollen polymer. For large values of M=mφe, φs is very small until a time τ is reached beyond which the swelling then accelerates rapidly towards its equilibrium value. This feature is absent if M<e. The time τ is estimated by asymptotic analysis. Rutherford backscattering spectrometry is used to investigate the surface swelling kinetics of polystyrene by iodohexane. The TW model tends to underestimate the swelling rate when φs is low and to overestimate it when φs is high. Nevertheless, the time for φs to approach its equilibrium value φe is approximated well by the TW model.