(103h) How to Quantify Spatial Variations in Diffusivity in Molecular Dynamics Simulations.

The structure and function of many materials are strongly impacted by confinement as the properties of confined states of matter can deviate considerably from their bulk counterparts. At a fundamental level, confinement breaks the translational symmetry of materials, and makes all thermodynamic, structural and transport properties functions of position. Furthermore, transport properties usually become anisotropic (or direction-dependent) upon confinement. Characterizing such anisotropy and spatial variations is critical to understanding and engineering the behavior of materials whose properties are modulated by confinement. To this end, computational studies of confined materials have focused on ways of characterizing such spatial variations. This is a straightforward task for static properties, or mechanical observables that can be unambiguously calculated for each configuration, as their profiles can be readily computed via spatial binning of the simulation box. Such an approach cannot, however, be rigorously applied for dynamical properties such as transport coefficients as they can only be estimated from autocorrelations of mechanical observables, and there is no natural binning approach that can systematically capture spatial variations in such autocorrelations. For instance, diffusivity within bulk materials can be readily computed either from the mean-squared displacement (MSD) or using the velocity autocorrelation function (VACF). Both approaches break down, however, in the case of confined materials since no direct correspondence exists between any ad hoc notions of local MSD or VACF and the solutions of the Smoluchowski equation that governs anisotropic position-dependent diffusion.

In this work, we propose a generalized estimator for the position-dependent diffusivity tensor. We first validate this estimator by applying it to ensembles of trajectories generated via a stochastic differential equation (SDE) solver. We then apply this method to two systems, pure liquid within a slit pore and a supported film of a binary glass-forming liquid and obtain diffusivity profiles that yield autocorrelation functions that are consistent with those attained from MD simulations. Our approach can potentially provide a framework for characterizing position-dependent and anisotropic diffusivities in confocal microscopy experiments and molecular simulations.