Diffusion and interaction in gels and solutions. 4. Hard sphere Brownian dynamics simulations

Results from Brownian dynamics simulations of hard sphere diffusion in polymer networks of wormlike chains are presented. The influence of the size of the diffusing particles, the polymer concentration, the polymer radius, and the persistence length of the chains were investigated. The diffusion coefficients obtained in systems of stiff chains were compared to a theory [Macromolecules 24, 6024 (1991)]. The agreement between the simulation data and the theory was satisfactory, except for dense systems where the theory predicted somewhat too high diffusion coefficients. To account for the diffusion in systems of more flexible polymers, we derived a semiphenomenological theory based on ideas from the concept of fractals. By this approach we could show how the available volume fraction for particles in polymer networks scales with the particle radii. The scaling is not a power law, but instead is a stretched exponential, and is related to the local structure of the polymer chains. Finally, the inherent assumptions in the theoretical descriptions, e.g., the negligence of the hydrodynamic interactions, and the applicability of the theory to real polymer systems, are thoroughly discussed.