Sorption of a finite amount of swelling solvent in a glassy polymer

We study the time history of a diffusing front when a polymer is exposed to a finite amount of penetrant which becomes used up. A class of polymers is considered for which slow molecular relaxation occurs only at or near the glass-gel interface with instantaneous relaxation both ahead of and behind the progressing front. We show that the position of the penetrant front versus time undergoes a long smooth transition from standard Fickian t^1/2 behavior to exponential time decay onto a final equilibrium position attained when all the penetrant is used up.