Structural Signatures of Vitrification in Hard Core Fluids

Computer simulations of hard spheres and disks are used to estimate the most probable cavity size, ${\xi }_{\mathrm{c}\mathrm{a}\mathrm{v}\mathrm{i}\mathrm{t}\mathrm{y}}$, and a ``rattle’’ size, $\xi_{\rm rattle}$, over which a particle can translate holding all other particles fixed. Both of these measures of free volume appear to extrapolate to zero at the random close packed density, ${\rho }_{\mathrm{r}\mathrm{c}\mathrm{p}}$, close to the density where extrapolations of the viscosity diverge. We also identify the onset of caging as the density at which cavities cluster. These results suggest that vitrification in hard core fluids can be viewed as a geometrical phenomenon, and that {\em local} free volume measures can identify the location of the onset of liquid-like dynamics, the complex dynamics of caged liquids, and vitrification.