Anisotropic-Isotropic Transition of Cages at the Glass Transition

Characterizing the local structural evolution is an essential step in understanding the nature of glass transition. In this work, we probe the evolution of Voronoi cell geometry in simple glass models, and find that the individual particle cages deform anisotropically in supercooled liquid and isotropically in glass. We introduce an anisotropy parameter $k$ for each Voronoi cell, which mean value exhibits a sharp change at the mode-coupling glass transition $\phi_\mathrm{c}$. Moreover, a power law of packing fraction $\phi\propto q_1^{-d}$ is discovered in the liquid regime with $d>D$, in contrast to $d=D$ in the glass regime, where $q_1$ is the first peak position of structure factor, and $D$ is the space dimension. This power law is explained by the change of $k$. The active motions in supercooled liquid are spatially correlated with long axes rather than short axes of Voronoi cells. In addition, the dynamic slowing down approaching the glass transition can be well characterized through a modified free volume model based on $k$. These findings reveal that the nonagnostic structural parameter $k$ determines glassy dynamics and is effective in identifying the structure-dynamics correlations and the glass transition.