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

Abstract Owing to their complex pore morphology and strong surface heterogeneity, disordered nanoporous media possess a rich underlying diffusion landscape that gives rise to specific transport phenomena. The unique diffusion mechanisms in such heterogeneous, ultra-confining solids stem from restricted pore relocation and blurred, i.e. ill-defined, pore/surface boundaries. As a result, while the fundamentals of diffusion and transport in simple pore geometries are well-established, the case of fluids confined in such complex porous materials still challenges existing frameworks. Here, we invoke the intermittent surface/pore diffusion formalism to map molecular dynamics onto random walk in disordered nanoporous media. Our hierarchical strategy allows quantitatively bridging microscopic and mesoscopic dynamics with parameters obtained from simple physical laws. In more detail, the surface residence and relocation times - t_A, t_B - are shown to derive from pore size p and temperature-rescaled surface interaction ε/k_BT. On the one hand, t_A obeys a transition state theory with an adsorption free energy barrier ~ε/k_BT and a prefactor ~1ps corrected for pore curvature p. On the other hand, t_B scales with p which is rationalized through a cutoff in the relocation first passage distribution. Beyond fundamental implications, the present approach provides a robust formalism to predict diffusion for any fluid in complex nanoporous media using fluid and material parameters available to simple experiments.