A diagrammatic formulation of the kinetic theory of fluctuations in equilibrium classical fluids. VI. Binary collision approximations for the memory function for self correlation functions

TL;DR

This study evaluates various binary collision approximations for the memory function in dense Lennard-Jones fluids using computer simulations, revealing their strengths and limitations in predicting correlation functions across different timescales.

Contribution

The paper provides a systematic comparison of multiple binary collision approximations against simulation data, highlighting their accuracy and shortcomings in modeling fluid dynamics.

Findings

MGBE is accurate at short times but poor at intermediate times.

BCA is exact at zero time but diverges at long times.

STA reasonably predicts the SLCC but misses temperature dependence.

Abstract

We use computer simulation results for a dense Lennard-Jones fluid for a range of temperatures to test the accuracy of various binary collision approximations for the memory function for density fluctuations in liquids. The approximations tested include the moderate density approximation of the generalized Boltzmann-Enskog memory function (MGBE) of Mazenko and Yip, the binary collision approximation (BCA) and the short time approximation (STA) of Ranganathan and Andersen, and various other approximations derived by us using diagrammatic methods. The tests are of twotypes. The first is a comparison of the correlation functions predicted by each approximate memory function with the simulation results, especially for the self longitudinal current correlation function (SLCC). The second is a direct comparison of each approximate memory function with a memory function numerically extracted from the correlation function data. The MGBE memory function is accurate at short times but decays to zero too slowly and gives a poor description of the correlation function at intermediate times. The BCA is exact at zero time, but it predicts a correlation function that diverges at long times. The STA gives a reasonable description of the SLCC but does not predict the correct temperature dependence of the negative dip in the function that is associated with caging at low temperatures. None of the other binary collision approximations is a systematic improvement upon the STA. The extracted memory functions have a rapidly decaying short time part, much like the STA, and a much smaller, more slowly decaying part of the type predicted by mode coupling theory. Theories that use mode coupling commonly include a binary collision term in the memory function but do not discuss in detail the nature of that term. ...