Double mode of sorption.
It may be the case of gas molecules such nitrogen or oxygen in olefinic polymers. Strong interaction sites may be induced by some impurities. The absolute energy of sorption on strong interaction sites may be lightly higher than in other parts of the membrane. The kinetic sorption curve likes a fickian kinetics with an initial linear part at short times if using a square root of time scale and an equilibrium plateau at long times. The concentration of trapped molecules on Langmu´r sites is low. The measurement of the initial slope leads to a good estimation of the diffusion coefficient.
Example 1, Case of a low concentration of Langmu´r sites and weak interactions :