Hard disks confined within a narrow channel

TL;DR

This study uses inhomogeneous integral equation theory to analyze the equilibrium properties of hard disks confined in narrow channels, revealing accurate predictions of structural transitions and dimensional crossover behaviors.

Contribution

It demonstrates the high accuracy of the inhomogeneous Percus-Yevick integral equation in modeling confined hard disk systems and their structural transitions.

Findings

Accurately predicts the onset of zigzag structural transition at high packing.

Effectively models the dimensional crossover from 2D to quasi-1D confinement.

Shows the method's robustness in handling inhomogeneous two-body correlations.

Abstract

We employ inhomogeneous integral equation theory to investigate the equilibrium properties of hard disks confined to a channel of width $L$ by hard parallel walls. If the channel width is narrowed below two disk diameters, then the system enters a quasi one-dimensional regime for which the particles cannot move past each other. In the limit when $L$ is equal to one particle diameter the system reduces to the one-dimensional bulk along the center of the channel. We study first the dimensional crossover properties of the inhomogeneous Percus-Yevick (PY) integral equation as $L$ is reduced and then investigate the behaviour of a quasi one-dimensional system as the packing of the particles is increased for a fixed value of $L$. We find that the inhomogeneous PY equation is highly accurate for situations of quasi one-dimensional confinement and that it predicts the onset of a structural transition to a zigzag state at higher packing. The excellent performance of this integral equation method and the ease with which it handles confinement-induced dimensional crossover is a consequence of the improved resolution which comes from treating explicitly the inhomogeneous two-body correlation functions.