The friction coefficient of a Lennard-Jones fluid from the random force autocorrelation function determined as a memory function by molecular dynamics calculations

A recent molecular dynamics (MD) study showed that the friction coefficient of a simple fluid is obtainable by the integral over the autocorrelation function (ACF) of the total force of a Brownian-type particle. The results indicated that mass ratios 50M/m200 of the massive and the light particle suffice to yield accurate friction coefficients. Complementarily, we calculate the random force ACF of the light particle, which is the memory function force of the ACF of the velocity apart from a constant factor, for all the states of the Lennard-Jones system investigated previously. A detailed comparison is presented of the memory function, the total force ACF of the fluid particle, and the total force ACF of the massive particle. The MD results confirm quantitatively our theoretical predictions: (i) on a time scale corresponding to the dynamics of the massive particle the total force ACF of that particle approximates well the memory function, while there are slight differences between them on a short time scale, (ii) the total force ACF of the liquid particle deviates significantly from the memory function already after extremely short time and is thus completely useless for the determination of the friction coefficient, (iii) using the total force ACF of a heavy particle for the determination of the friction constant with mass ratios ofM/m=50 up to 200, the pseudo plateau value of the time integral is often not very noticeable, as the memory function is only approximated and the total force ACF of the massive particle has a negative part at medium times. In those cases the integration has to be extended to include the negative part.