The Complete Jamming Landscape of Confined Hard Discs

TL;DR

This paper provides an exact analysis of the complete jamming landscape for confined hard discs, revealing how local arrangements and geometric frustration influence packing density and structural order.

Contribution

It introduces a comprehensive method to describe all jammed states of confined hard discs using transfer matrix, linking structural order with packing density.

Findings

Configurational entropy and equation of state derived for jammed packings.

Structural randomness varies non-monotonically with packing density.

Properties of equilibrium liquid relate closely to the jamming landscape.

Abstract

An exact description of the complete jamming landscape is developed for a system of hard discs of diameter $\sigma$, confined between two lines separated by a distance $1+\sqrt{3/4} < H/\sigma < 2$. By considering all possible local packing arrangements, the generalized ensemble partition function of jammed states is obtained using the transfer matrix method, which allows us to calculate the configurational entropy and the equation of state for the packings. Exploring the relationship between structural order and packing density, we find that the geometric frustration between local packing environments plays an important role in determining the density distribution of jammed states and that structural "randomness" is a non-monotonic function of packing density. Molecular dynamics simulations show that the properties of the equilibrium liquid are closely related to those of the landscape.