Dynamics of localized particles from density functional theory

TL;DR

This paper critically examines the assumptions of dynamical density functional theory (DDFT) for colloidal systems, revealing unphysical self-interactions and limitations in modeling localized particles, especially in confined geometries.

Contribution

The study identifies the source of unphysical predictions in DDFT and proposes schemes to incorporate tagged densities, highlighting fundamental limitations in current formulations.

Findings

Unphysical self-interactions cause overly fast relaxation in DDFT.

Canonical functionals do not improve predictions for many-particle systems.

DDFT predicts delocalized particle densities in confined systems, conflicting with Brownian dynamics.

Abstract

A fundamental assumption of the dynamical density functional theory (DDFT) of colloidal systems is that a grand-canonical free energy functional may be employed to generate the thermodynamic driving forces. Using one-dimensional hard-rods as a model system we analyze the validity of this key assumption and show that unphysical self-interactions of the tagged particle density fields, arising from coupling to a particle reservoir, are responsible for the excessively fast relaxation predicted by the theory. Moreover, our findings suggest that even employing a canonical functional would not lead to an improvement for many-particle systems, if only the total density is considered. We present several possible schemes to suppress these effects by incorporating tagged densities. When applied to confined systems we demonstrate, using a simple example, that DDFT neccessarily leads to delocalized tagged particle density distributions, which do not respect the fundamental geometrical contraints apparent in Brownian dynamics simulation data. The implication of these results for possible applications of DDFT to treat the glass transition are discussed.