Determination of the friction coefficient of a Brownian particle by molecular-dynamics simulation

TL;DR

This study uses molecular dynamics simulations and the Kirkwood formula to accurately determine the friction coefficient of Brownian particles, revealing size-dependent asymptotic behavior in the force autocorrelation function.

Contribution

It introduces a systematic method to compute the friction coefficient from simulations and identifies size thresholds for reliable estimates.

Findings

Friction coefficient converges to a plateau for sufficiently large systems.

The minimal system size for convergence increases with particle size.

A reliable friction coefficient can be obtained from the plateau value.

Abstract

By using the Kirkwood formula, the friction coefficient of a solvated Brownian particle is determined from the integration on time of the autocorrelation function of the force that the solvent exerts on this particle. Extensive molecular dynamics simulations show that above a definite size of the studied systems the value of the integral defining the friction coefficient goes to a quasi constant value (a plateau) when the upper bound on time increases. The minimal value of the system size where the integral exhibits this asymptotic behavior, rises with the Brownian particle size. From the plateau, a reliable estimate of the friction coefficient is obtained.