Sorption with plasticization.
Example 1, case of high dry diffusion speed and a moderate speed of relaxation (or plasticization) :

It may be the case of carbon dioxide in polymers just under the glass transition. The diffusion coefficients in the dry part of the polymer and in the plasticized part are not very different. The sorption kinetic curve likes a fickian one with an initial linear part at short times if one uses a square root of time scale, and an equilibrium plateau at long times. The measurement of the initial slope leads to a good estimation of the diffusion coefficient.