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

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.