Structure-correlated diffusion anisotropy in nanoporous channel networks by Monte Carlo simulations and percolation theory

Nanoporous silicon consisting of tubular pores imbedded in a silicon matrix has found many technological applications and provides a useful model system for studying phase transitions under confinement. Recently, a model for mass transfer in these materials has been elaborated [Kondrashova et al., Sci. Rep. 7, 40207 (2017)], which assumes that adjacent channels can be connected by “bridges” (with probability p bridge) which allows diffusion perpendicular to the channels. Along the channels, diffusion can be slowed down by “necks” which occur with probability p neck. In this paper we use Monte-Carlo simulations to study diffusion along the channels and perpendicular to them, as a function of p bridge and p neck, and find remarkable correlations between the diffusivities in longitudinal and radial directions. For clarifying the diffusivity in radial direction, which is governed by the concentration of bridges, we applied percolation theory. We determine analytically how the critical concentration of bridges depends on the size of the system and show that it approaches zero in the thermodynamic limit. Our analysis suggests that the critical properties of the model, including the diffusivity in radial direction, are in the universality class of two-dimensional lattice percolation, which is confirmed by our numerical study.