Non-Gaussian rotational diffusion in heterogeneous media

We employ a simple model for rotational diffusivity DR of dumbbells in porous media in order to study spatially heterogeneous and non-Gaussian dynamics at Fickian time scales. We obtain the distribution P(DR) of DR's of single dumbbells for both ergodic and nonergodic systems. When a pore percolating network disappears beyond the pore percolation transition and the rotational dynamics becomes nonergodic, each single dumbbell undergoes Gaussian rotational dynamics but with different DR, which depends solely on the local pore structure. We also construct a map of heterogeneous dynamic regions and illustrate that such seemingly Fickian but non-Gaussian dynamics could be understood as the linear combination of the Gaussian rotational displacement distribution functions of each dumbbell. With a percolating pore network, the rotational dynamics becomes ergodic, and P(DR) is a δ function at the average value of DR.