The van Hove distribution function for Brownian hard spheres: dynamical test particle theory and computer simulations for bulk dynamics

TL;DR

This paper introduces a dynamical density functional theory approach to compute the van Hove distribution function for Brownian hard spheres, validating it against simulations and exploring implications for glassy dynamics.

Contribution

It presents a novel DDFT-based method to calculate the van Hove function by modeling self and distinct particles as a binary mixture, validated with simulations.

Findings

Good agreement with simulations at low and intermediate densities.

The free energy landscape develops a minimum at higher densities.

Implications for slow and glassy dynamics are discussed.

Abstract

We describe a test particle approach based on dynamical density functional theory (DDFT) for studying the correlated time evolution of the particles that constitute a fluid. Our theory provides a means of calculating the van Hove distribution function by treating its self and distinct parts as the two components of a binary fluid mixture, with the `self' component having only one particle, the `distinct' component consisting of all the other particles, and using DDFT to calculate the time evolution of the density profiles for the two components. We apply this approach to a bulk fluid of Brownian hard spheres and compare to results for the van Hove function and the intermediate scattering function from Brownian dynamics computer simulations. We find good agreement at low and intermediate densities using the very simple Ramakrishnan-Yussouff [Phys. Rev. B 19, 2775 (1979)] approximation for the excess free energy functional. Since the DDFT is based on the equilibrium Helmholtz free energy functional, we can probe a free energy landscape that underlies the dynamics. Within the mean-field approximation we find that as the particle density increases, this landscape develops a minimum, while an exact treatment of a model confined situation shows that for an ergodic fluid this landscape should be monotonic. We discuss possible implications for slow, glassy and arrested dynamics at high densities.