Theory of Anisotropic Diffusion of Entangled and Unentangled Polymers in Rod-Sphere Mixtures

We present a microscopic self-consistent theory for the long-time diffusion of infinitely thin rods in a hard sphere matrix based on the simultaneous dynamical treatment of topological uncrossability and finite excluded volume constraints. Distinctive regimes of coupled anisotropic longitudinal and transverse diffusion are predicted, and steric blocking of the latter leads to a tube-like localization transition largely controlled by the ratio of the sphere diameter to rod length and tube diameter. For entangled polymers, in a limited regime of strongly retarded dynamics a "doubly renormalized" reptation law is predicted where the confinement tube is compressed and longitudinal motion is partially blocked. At high sphere volume fractions, strong suppression of rod motion results in dynamic localization in the unentangled regime. The present advance provides a theoretical foundation to treat differential mobility effects and flexible chain dynamics in diverse polymer-particle mixtures.