Molecular dynamics simulation study of self-diffusion for penetrable-sphere model fluids

TL;DR

This study uses molecular dynamics simulations to analyze self-diffusion in penetrable-sphere fluids, comparing results with kinetic theory predictions and revealing effects of clustering and energy barriers on diffusion behavior.

Contribution

It provides a detailed comparison between simulation data and theoretical models for penetrable-sphere fluids, extending the Enskog theory to finite energy barriers.

Findings

Good agreement between theory and simulation for low to moderate energy barriers.

Clustering effects become significant at high densities and energy barriers.

Theoretical predictions are less accurate for dense, highly repulsive systems due to metastable clustering.

Abstract

Molecular dynamics simulations are carried out to investigate the diffusion behavior of penetrable-sphere model fluids characterized by a finite energy barrier $\epsilon$. The self-diffusion coefficient is evaluated from the time-dependent velocity autocorrelation function and mean-square displacement. Detailed insights into the cluster formation for penetrable spheres are gained from the Enskog factor, the effective particle volume fraction, the mean free path, and the collision frequency for both the soft-type penetrable and the hard-type reflective collisions. The simulation data are compared to theoretical predictions from the Boltzmann kinetic equation and from a simple extension to finite $\epsilon$ of the Enskog prediction for impenetrable hard spheres ($\epsilon\to\infty$). A reasonable agreement between theoretical and simulation results is found in the cases of $\epsilon^*\equiv \epsilon/k_BT=0.2$, $0.5$, and $1.0$. However, for dense systems (packing fraction $\phi>0.6$) with a highly repulsive energy barrier ($\epsilon^*=3.0$), a poorer agreement was observed due to metastable static effects of clustering formation and dynamic effects of correlated collision processes among these cluster-forming particles.