A theoretical investigation of the influence of molecular relaxation and internal stress on diffusion in polymers

Abstract

AbstractRecent experiments have indicated that the diffusion properties of a penetrant‐polymer system may change with time as diffusion proceeds. It is thought that two possible explanations of these time effects are slow changes of polymer structure accompanying diffusion and internal stresses exerted by one part of the polymer sheet on another as it swells. Two theoretical models are set up in order to express these effects quantitatively. The first model is essentially that in terms of which mechanical and other properties of polymers are commonly discussed, involving the concept of an instantaneous change of diffusion coefficient when the concentration changes, followed by a slow drift toward an equilibrium value. The second model expresses the effect of stresses set up between the outer swollen layers and the unattacked center of a polymer sheet during sorption. These stresses are slowly relieved as the diffusion proceeds, leading to a time‐dependent diffusion coefficient. The main features of diffusion behavior are established by calculation and the models are shown to account for the various types of sorption and desorption curves observed experimentally under different conditions, e.g., for sheets of different thicknesses and for different ranges of penetrant concentration. As examples, sorption and desorption curves calculated from the first model are shown to agree reasonably well with experimental curves for the methylene chloride‐polystyrene system. The rate of sorption and of the associated change in area of the sheet are accounted for by the second model. The presence of internal stresses also provides an explanation for the observation that there may be an appreciable interval of time during which a thin sheet takes up more penetrant than a thicker one under corresponding conditions. On the other hand, it is the slow structural changes which cause the rate of sorption to be not always inversely proportional to the square of the thickness of the sheet. It is concluded that both polymer relaxation and internal stresses play a part in determining diffusion behavior. The particular experimental results examined can be accounted for if the half‐life of the slow structural changes is comparable with that of the sorption experiment itself, and if the internal stresses change the diffusion coefficient by a factor of two or three.