The molecular dynamics simulations of the damping matrices in a Lennard-Jones fluid and testing of the two-relaxation time models for the memory function

Abstract

We have carried out the molecular dynamics simulations (MD) for the velocity autocorrelation functions (vacf), the acceleration autocorrelation functions, and the damping matrices in a Lennard-Jones fluid. Seven state conditions, from low densities (ρ*=ρσ3=0.3) to high densities (ρ*=0.85) and from low temperatures (T*=kT/ε=0.73, σ and ε being the Lennard-Jones parameters) to high temperatures (T*=5.2) were investigated. The values of the damping matrices Kn(t=0), n=1,2,3,4, and 5 in the continued fraction representation of the memory kernel, as given by Mori, were obtained directly from the MD via a seventh order backward difference algorithm. These Kn(0) increase rapidly in magnitude as the order increases. They also show strong temperature dependence, but weak density dependence. These damping matrices are used to test the empirical models proposed to represent the memory functions for the velocity autocorrelation. We test some commonly used memory function models with two relaxation times, one representing the short time binary collision effects and the other the long time hydrodynamic effects. It is discovered that in the single dynamic variable autocorrelation approach adopted here none of the empirical models tested perform well in reproducing the MD vacf at intermediate to long times. We attribute this to the lack of mode–mode coupling contributions.

Theory of transport coefficients of simple fluids

“…For the memory function we have proposed a sech(6t) form, the parameters of which have been determined using the frequency sum rules. The validity of the SA and the low-order decoupling approximation used in obtaining the numerical results of the frequency sum rules have been checked by performing some MD calculations and comparing our results with already existing MD data (Lee andChung 1982, Toxvaerd 1984). The error involved owing to these approximations in the total frequency sum rules has been found to be insignificant.…”

“…From table 1 we find that the error involved in V by using SA is not significant. In order to see the effect of the SA and low-order decoupling approximation on the numerical values of d2 and d3, we compare our results in table 2 with already existing MD data of Lee and Chung (1982) and Toxvaerd (1984). We have used theoretically generated g ( r ) (Sung and Chandler 1974) for our calculations.…”

“…The results obtained from equations ( 14) and ( 20) are shown as broken curves, whereas V(t) obtained using equations ( 14) and ( 23) are shown as full curves in figure 2 for six thermodynamic states. The MD results (Kushick andBerne 1973, Lee andChung 1982) are represented as full circles. It can be seen from figure 2 that the results obtained using equation (20) (first stage of the continued fraction) for f(o) are in good agreement with MD data at low temperatures and high densities.…”

“…In the present work, the validity of the SA and low-order decoupling approximation used in obtaining the numerical results of the frequency sum rules has been checked by performing some MD calculations and using already existing MD data (Lee andChung 1982, Toxvaerd 1984). The errors involved in numerical values of sum rules due to these approximations have been found to be not very significant.…”

“…Figure 2. Variation in the normalised VAC function V(t) with time t" = t(E/ma2) obtained for six thermodynamic states: -, results obtained from equation (14) and (23); ---, results from equations (14) and (20); 0, MD results(Kushick and Berne 1973, Lee andChung 1982).…”