# Cage properties and its implication to the existence of glass transition in hard sphere systems

## TL;DR

This paper investigates the role of cage properties, defined via free volume, in hard sphere systems and questions the existence of a true glass transition based on cage volume behavior.

## Contribution

It introduces a geometrical cage definition using free volume and links cage volume to structural relaxation, challenging the traditional view of a glass transition in hard spheres.

## Key findings

- Cage volume approaches zero at the transition point.
- Cage rearrangements are linked to particle displacements.
- Cage loss can occur with minimal particle movement.

## Abstract

In deep supercooled liquids, particles get trapped in transient cages made up of neighbouring particles. Here we define a cage from a geometrical quantity, free volume, such that the free volume of a particle is the cage volume. First we show that the relationship between the average cage volume and the structural relaxation time questions the existence of glass transition in hard sphere systems. Our observation suggests that the cage volume is zero at the transition. Further we show that cage rearrangements are strongly coupled to the single particle squared displacements. Additionally a cage can rearrange by losing its neighbours with almost no change in particle displacements. The picture presented here also supports the complex scenarios of relaxation, dynamic heterogeneity and cooperative rearrangement.