The cage effect in systems of hard spheres

TL;DR

This paper investigates how the cage effect influences the dynamics of dense hard sphere systems by analyzing displacement distributions and collective mechanisms, revealing non-local effects that delay correlation decay.

Contribution

It provides a detailed analysis of the cage effect's role in particle dynamics, highlighting the collective and non-local mechanisms that influence time correlation functions in hard sphere systems.

Findings

Caging induces non-local collective processes affecting displacement distributions.

Delay in correlation decay is linked to global conservation of displacement distributions.

Analysis distinguishes local and collective mechanisms in experimental and simulation data.

Abstract

The cage effect is generally invoked when discussing the delay in the decay of time correlation functions of dense fluids. In an attempt to examine the role of caging more closely we consider the spread of the displacement distributions of Brownian particles. These distributions are necessarily biased by the presence of neighbouring particles. Accommodation of this bias by those neighbours conserves the displacement distribution locally and presents a collective mechanism for exploring configuration space that is more efficient than the intrinsic Brownian motion. Caging of some particles incurs, through the impost of global conservation of the displacement distribution, a delayed, non-local collective process. This non-locality compromises the efficiency with which configuration space is explored. Both collective mechanisms incur delay or stretching of time correlation functions, in particular the particle number and flux densities. This paper identifies and distinguishes these mechanisms in existing data from experiments and computer simulations on systems of particles with hard sphere interactions.