DIFFUSION AND INTERACTION IN GELS AND SOLUTIONS .3. THEORETICAL RESULTS ON THE OBSTRUCTION EFFECT

A new theory for the diffusion of a spherical solute in a network, e.g., a polymer gel or solution, is presented. The distribution of spaces in the network is used to evaluate a frequency function giving the weights of cylindrical cells with different radii. Once the frequency function is known, the effective diffusion coefficient can be calculated, numerically or analytically, from the local diffusion coefficients given by the solution of Fick's first law in the cylindrical cell model. The predictions are compared with Brownian dynamics simulations, literature data, and results from our own experiments. It is found that the theory can successfully predict the diffusion of solutes in both flexible and stiff polymer systems. One result is that the diffusion of a solute is faster in a system of flexible polymers than in a system of stiff polymers. A crucial parameter is the ratio p/a, where p is the persistence length of the polymer and a is its radius. It is shown that the space distribution given by Ogston can be used to give a qualitative description of the hindrance when p/a > 10. However, in this case a quantitative prediction can also be made by the analytical theory presented here. When p/a < 10, a numerical calculation of the solute diffusion can be carried out. Thus, the approach in this paper leads to a theory with a wide range of applications.