Effect of polydispersity on diffusion in random obstacle matrices

The dynamics of tracers in disordered matrices is of interest in a number of diverse areas of physics such as the biophysics of crowding in cells and cell membranes, and the diffusion of fluids in porous media. To a good approximation the matrices can be modeled as a collection of spatially frozen particles. In this Letter, we consider the effect of polydispersity (in size) of the matrix particles on the dynamics of tracers. We study a two dimensional system of hard disks diffusing in a sea of hard disk obstacles, for different values of the polydispersity of the matrix. We find that for a given average size and area fraction, the diffusion of tracers is very sensitive to the polydispersity. We calculate the pore percolation threshold using Apollonius diagrams. The diffusion constant, D, follows a scaling relation D∼(φ _c- φ _m)μ ^-β for all values of the polydispersity, where φ _m is the area fraction and φ _c is the value of φ _m at the percolation threshold.