Inherent Structure Landscape of Hard Spheres Confined to Narrow Cylindrical Channels

TL;DR

This paper develops an analytical model to explore the inherent structure landscape of hard spheres confined in narrow cylindrical channels, revealing hierarchical organization and predicting packing properties across densities.

Contribution

The study extends previous models to provide a detailed analytical description of jammed packings and their landscape for confined hard spheres, including hierarchical basin structures.

Findings

Hierarchical organization of jammed states with low barriers.

Model accurately predicts geometric properties of large packings.

Insight into probability distribution of helical section lengths.

Abstract

The inherent structure landscape for a system of hard spheres confined to a hard cylindrical channel, such that spheres can only contact their first and second neighbours, is studied using an analytical model that extends previous results [Phys. Rev. Lett. 115, 025702 (2015)] to provide a comprehensive picture of jammed packings over a range of packing densities. In the model, a packing is described as an arrangement of $k$ helical sections, separated by defects, that have alternating helical twist directions and where all spheres satisfy local jamming constraints. The structure of each helical section is determined by a single helical twist angle, and a jammed packing is obtained by minimizing the length of the channel per particle with respect to the $k$ helical section angles. An analysis of a small system of $N=20$ spheres shows that the basins on the inherent structure landscape associated with these helical arrangements split into a number of distinct jammed states separated by low barriers giving rise to a degree of hierarchical organization. The model accurately predicts the geometric properties of packings generated using the Lubachevsky and Stillinger compression scheme ($N=10^4$) and provides insight into the nature of the probability distribution of helical section lengths.