Anisotropic molecular diffusion in confinement I: Transport of small particles in potential and density gradients

TL;DR

This paper develops a model to spatially resolve anisotropic diffusion coefficients near interfaces by analyzing local crossing times and drift effects, validated through molecular dynamics simulations of water in bulk and confined environments.

Contribution

It introduces a novel analytic method to determine spatially dependent, anisotropic diffusion coefficients at interfaces, accounting for local drift effects.

Findings

Demonstrates anisotropic diffusion at interfaces.

Reveals spatial variations in diffusivity related to interface structuring.

Validates the model with molecular dynamics simulations.

Abstract

Hypothesis: Diffusion in confinement is an important fundamental problem with significant implications for applications of supported liquid phases. However, resolving the spatially dependent diffusion coefficient, parallel and perpendicular to interfaces, has been a standing issue. In the vicinity of interfaces, density fluctuations as a consequence of layering locally impose statistical drift, which impedes the analysis of spatially dependent diffusion coefficients even further. We hypothesise, that we can derive a model to spatially resolve interface-perpendicular diffusion coefficients based on local lifetime statistics with an extension to explicitly account for the effect of local drift using the Smoluchowski equation, that allows us to resolve anisotropic and spatially dependent diffusivity landscapes at interfaces. Methods and simulations: An analytic relation between local crossing times in system slices and diffusivity as well as an explicit term for calculating drift-induced systematic errors is presented. The method is validated on Molecular Dynamics simulations of bulk water and applied to simulations of water in slit pores. Findings: After validation on bulk liquids, we clearly demonstrate the anisotropic nature of diffusion coefficients at interfaces. Significant spatial variations in the diffusivities correlate with interface-induced structuring but cannot be solely attributed to the drift induced by local density fluctuations.