Bridging scales in disordered porous media by mapping molecular dynamics onto intermittent Brownian motion

Abstract

Owing to their complex morphology and surface, disordered nanoporous media possess a rich diffusion landscape leading to specific transport phenomena. The unique diffusion mechanisms in such solids stem from restricted pore relocation and ill-defined surface boundaries. While diffusion fundamentals in simple geometries are well-established, fluids in complex materials challenge existing frameworks. Here, we invoke the intermittent surface/pore diffusion formalism to map molecular dynamics onto random walk in disordered media. Our hierarchical strategy allows bridging microscopic/mesoscopic dynamics with parameters obtained from simple laws. The residence and relocation times – tA, tB – are shown to derive from pore size d and temperature-rescaled surface interaction ε/kBT. tA obeys a transition state theory with a barrier ~ε/kBT and a prefactor ~10−12 s corrected for pore diameter d. tB scales with d which is rationalized through a cutoff in the relocation first passage distribution. This approach provides a formalism to predict any fluid diffusion in complex media using parameters available to simple experiments.