On the calculation of diffusion coefficients in confined fluids and interfaces with an application to the liquid-vapor interface of water

摘要

We propose a general methodology for calculating the self-diffusion tensorfrom molecular dynamics for a liquid with a liquid-gas or liquid-solidinterface. The standard method used in bulk fluids, based on computing the meansquare displacement as a function of time and extracting the asymptotic lineartime dependence from this, is not valid for systems with interfaces or forconfined fluids. The method proposed here is based on imposing virtual boundaryconditions on the molecular system and computing survival probabilities andspecified time correlation functions in different layers of the fluid up to andincluding the interfacial layer. By running dual simulations, one based on MDand the other based on Langevin dynamics, using the same boundary conditions,one can fit the Langevin survival probability at long times to the MD computedsurvival probability, thereby determining the diffusion coefficient as afunction of distance of the layers from the interface. We compute the elementsof the diffusion tensor of water as a function of distance from the liquidvapor interface of water. Far from the interface the diffusion tensor is foundto be isotropic, as expected, and the diffusion coefficient has the value$D\approx$ .22\AA$^2$/psec in agreement with what is found in the bulk liquid.In the interfacial region the diffusion tensor is axially anisotropic, withvalues of $D_{\parallel}\approx$. 8\AA$^2$/psec and $D_{\perp}\approx$.5\AA$^2$/psec for the components parallel and normal the interface surfacerespectively. We also show that diffusion in confined geometries can becalculated by imposing appropriate boundary conditions on the molecular systemand computing time correlation functions of the eigenfunctions of the diffusionoperator corresponding to the same boundary conditions.