Fickian and non-Fickian diffusion in high polymer systems

Abstract

The normal and the anomalous diffusion in binary polymer solutions are considered. After a survey of the theory of diffusion it is demonstrated which criteria must be fulfilled so that the Fickian diffusion occurs. For transport between the solvent and a solution, or between two solutions, normal diffusion is found. Experimental results with polystyrene + solvent systems are given. With good solvents the diffusion coefficient increases strongly with increasing polymer concentration, passes through a maximum at medium concentrations and decreases by several decades at high polymer concentrations. This concentration dependence arises because the diffusion coefficient is not only a transport coefficient, but also contains a thermodynamic factor. With poor solvents, which show a phase separation of the polymer at low temperatures, the concentration dependence of the diffusion coefficient is even more complicated. With increasing concentration of polymer the diffusion coefficient first decreases, passes through a minimum and the increases again. In this case there is also a maximum at medium concentrations and a strong decrease at high polymer concentrations. The minimum for a binary system is located at the critical point of the system.

Normally ln D is a linear function of 1/T. Deviations from the linear course can be explained by the temperature dependence of the thermodynamic factor.

For anomalous diffusion the √t-relations are no longer valid, since the diffusion coefficient depends not only on concentration, but also explicitly on time. The anomalous diffusion is due to the fact that superimposed on the normal diffusion is another process. If a solvent penetrates into a glassy polymer, then relaxation processes are superimposed on the diffusion process. The polymer changes from the glassy state into a state of internal thermodynamic equilibrium. Experimentally the continuous range between the pure glassy polymer and the pure solvent can be divided into three parts of an open system. In the first and the third part only diffusion occurs, while in the second part diffusion and structural relaxation are superimposed.