A Phenomenological Description of Case-II Diffusion in Polymeric Materials

In several glassy polymer-solvent systems the observed initial uptake of solvent is linear in time. A sharp front moving at a constant velocity v0 divides the polymer into two regions: ahead of the front the solvent concentration is low and the polymer is still glassy, while behind it the concentration is high and the polymer has been plasticized. Here a simple description of this process is presented. It is based on the idea that the slow plasticization kinetics sets an upper limit for the flux of solvent into the glassy region. Our description predicts that the front velocity will crossover to the usual 1/√t behaviour at t ≈ τ1 = D1/v02 (here D1 is the diffusion coefficient for solvent in the plasticized region) and that an induction time (whose duration depends on the value of the diffusion coefficient D0 in the glassy region) will precede the establishment of the front.