Diffusion in an array of immobile anisotropic obstacles: The influence of local orientation, bottlenecks, and free volume in absence of dead-ends

Obstacles (such as gel fibers) decrease the diffusion coefficient D of a particle. Several obstruction models have been proposed to predict how D depends on the fractional free volume f for a system with immobile obstacles. We investigate how the orientation of periodically distributed rod-shaped obstacles affects the 2D diffusion coefficient of different size particles when dead-ends are not present. We focus our attention on globally isotropic arrays of obstacles with different types of orientational order. Our Lattice Monte Carlo results show that the diffusion coefficient of a particle is sensitive to the way the gel fibers orient both locally and over large distances. When the obstacles are treated as Ising spins, D is directly related to the amount of disorder in the system with narrow bottlenecks playing a major role. When the obstacles are regrouped in large regular domains, on the other hand, D has only a weak dependence on domain size. Interestingly, we also observe that increasing f does not necessarily increase diffusivity; indeed, diffusivity is also influenced by the intrinsic tortuosity in the system. Our results show that local orientation, bottlenecks, fractional free volume and intrinsic tortuosity all play a role in determining the diffusivity of a particle in a globally isotropic system, thus implying that mean-field, free-volume models are not reliable when studying diffusion in complex media.