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In deep supercooled liquids, particles get trapped in transient cages made upof 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. Firstwe show that the relationship between the average cage volume and thestructural relaxation time questions the existence of glass transition in hardsphere systems. Our observation suggests that the cage volume is zero at thetransition. Further we show that cage rearrangements are strongly coupled tothe single particle squared displacements. Additionally a cage can rearrange bylosing its neighbours with almost no change in particle displacements. Thepicture presented here also supports the complex scenarios of relaxation,dynamic heterogeneity and cooperative rearrangement.

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