Simulation of self-diffusion of point-like and finite-size tracers in stochastically reconstructed Vycor porous glasses

摘要

Aim of the present study is to simulate self-diffusion in three-dimensional images of reconstructed Vycor porous glass, which have the same statistical content as the actual material in terms of porosity and autocorrelation function. Effective diffusivities are determined from a step-by-step random walk process at different porosities and diffusion regimes. In all cases, the effective diffusivity curves show a sharp decreases below 20% porosity and drop to zero below a porosity of about 15%, a value suggested independently from the theory of spinodal decomposition. Comparison between the computed and experimental diffusivity values obtained in the Knudsen regime, shows a relative difference of less than 6%. Additional simulations in the molecular diffusion regime are performed using inert tracers of finite size. In these simulations, a transition is found in the value of diffusivity from a high value at small time scales, to a lower constant value achieved at large times. The time at which this crossover takes place corresponds to a mean-square displacement value whose square root is roughly equal to the average pore radius of the material. Comparison between computed and experimental results taken from the literature, shows very good agreement, as in the case of point-like tracer diffusion. Thus, the reconstructed Vycor is shown to represent properly not only structural properties such as porosity and correlation function, but also dynamic properties such as effective diffusivity of inert gas molecules of various sizes.