Structural properties of hard disks in a narrow tube

TL;DR

This study investigates the structural behavior of hard disks confined in narrow tubes, revealing a fluid-to-solid-like transition characterized by changes in pressure, correlations, and domain sizes, using exact and approximate analytical methods.

Contribution

It introduces an analytically solvable model for hard disks in narrow tubes, capturing the transition from fluid to solid-like order and analyzing pressure and correlation changes.

Findings

No true fluid-solid phase transition occurs.

Solid-like domains grow exponentially with pressure.

Approximate model closely matches the behavior of hard disks.

Abstract

Positional ordering of a two-dimensional fluid of hard disks is examined in such narrow tubes where only the nearest-neighbor interactions take place. Using the exact transfer-matrix method the transverse and longitudinal pressure components and the correlation function are determined numerically. Fluid-solid phase transition does not occur even in the widest tube, where the method just loses its exactness, but the appearance of the dramatic change in the equation of state and the longitudinal correlation function shows that the system undergoes a structural change from a fluid to a solid-like order. The pressure components show that the collisions are dominantly longitudinal at low densities, while they are transverse in the vicinity of close packing density. The transverse correlation function shows that the size of solid-like domains grows exponentially with increasing pressure and the correlation length diverges at close packing. It is managed to find an analytically solvable model by expanding the contact distance up to first order. The approximate model, which corresponds to the system of hard parallel rhombuses, behaves very similarly to the system of hard disks.