Sorption with plasticization
It may be the case of solvent molecules in vitreous polymers. During the sorption process, the membrane has got three zones, two plascticized ones saturated by solvent molecules near the membrane faces and a completly dried one in the center of the membrane. The two fronts of plasticization progress slowly in direction to the center of the membrane. Thus, the concentration profile shows two symetrical drops of concentration. The concentration near the center of the membrane is quiet nil while the concentration profile is almost flat in the plasticized parts. The sorbed mass increases linearly with time as it is noticeable on the kinetic curve drawed with a linear scale of time. Thus, the kinetic curve drawed with a square root of time scale does not allow to estimate any diffusion coefficient by the use of Fick law. Therefore the half-sorption time is proportional to the inverse of the relaxation speed.
Example 3, case of very low (also nil) dry diffusion speed, very low speed of plasticization (relaxation) speed and long (or infinite) lifetime of plasticized sites :