A test of the timescale separation in solutions containing interacting Brownian-type particles

Abstract

Theoretical work has shown that the timescale separation required for the application of the Smoluchowski, Fokker-Planck and Langevin equations to interacting Brownian particles in concentrated liquid solutions may not exist. In particular, it was suggested that the current autocorrelation function of the Brownian particles may not decay sufficiently quickly in comparison with the intermediate scattering function at appropriate wave vectors. Here, molecular dynamics (MD) calculations are performed for hard-soft-sphere liquid solutions containing Brownian-type particles of large mass and volume. The mass and volume ratio are varied systematically. The MD results indicate the following: (i) for solutions of equally sized particles, the current autocorrelation function of the massive particles decreases sufficiently quickly compared with the intermediate scattering function, thus ensuring timescale separation; (ii) massive particles of large volume diluted among light and small particles show a time decay of the current autocorrelation function, which approaches that of the intermediate scattering function. However, the similarity of the two correlation functions reduces with increasing mass ratio. Hence, for asymptotic conditions timescale separation can be expected.