Modeling velocity autocorrelation functions of confined fluids: A memory function approach

Abstract

Velocity autocorrelation functions ͑VACF͒ of a fluid confined in a slit pore have been modeled using the memory equation. Models for the VACF are based on both the truncation and analytic closure approximations of the Mori's continued fraction representation. The performance of the models is evaluated for gas to liquid-like pore densities and pore widths which accommodate one to four atomic layers. In all cases we compare the predictions from the models with the VACF obtained from molecular dynamics simulations. The truncation models predict an oscillatory behavior for the in-plane VACF with better agreement at lower densities. Among the analytical closure models we observe that the sech model applied at the first level of closure is not only able to capture the short-time dynamics but is also seen to give the best predictions to the in-plane diffusivities at liquid-like pore densities. Although the minima in the VACFs are captured accurately by the sech model, the subsequent plateau regions in the VACF typically observed in confined systems are not predicted. This aspect is due to the slower relaxation of the actual memory kernel, which is not captured by the model. Predictions of the in-plane diffusivities using different levels of analytic closure have been compared with diffusivities obtained from the simulations.

The role of fluid-wall interactions on confined liquid diffusion using Mori theory

“…The numerical calculations for the sum rules V 2 and V 42 given by Eqs. (23), (25), (28), (30), and (36)- (39) are carried out by using the Gauss-quadrature method. The radial distribution function for fluid-fluid interaction as well as for fluid-wall interaction was taken to be same as that of bulk fluid.…”

“…23 Our theoretical results are found to provide more insight into the dynamics of confined fluid. It is found that our approach consistently provides good results for the velocity auto correlation function in the parallel direction, whereas in the perpendicular direction deviations from simulation results are found to increase with decrease in width of the channel.…”

“…In the present work, we consider the hyperbolic secant memory function which has been proposed 45 for bulk fluids and found to provide good results including confined fluids. 23 The expression for memory function is given by…”

“…18,23 In all of these studies, the interaction between the fluid molecules and wall molecules has been found to play a crucial role, specifically in determining the dynamics and static properties near the wall. There exist theoretical studies 22,36 which incorporate the effect of the wall on the dynamics of the fluid particles.…”

“…[14][15][16][17] Recent studies suggest that the transport properties of fluid in confined nanogeometries show anisotropic behavior. [18][19][20][21][22] The self-diffusivity of fluids confined in various nanogeometries, such as slit shaped nano-pores, [23][24][25][26] cylindrical nanotube, 27,28 and carbon nanotube [29][30][31][32][33] have been widely investigated using molecular dynamics simulation. It is observed that the mobility of particles in a nano pore is maintained even in pore widths as small as two times of size of particles.…”