Metastability and Crystallization in Hard-Sphere Systems

Abstract

We present results of large-scale molecular dynamics simulations of hard sphere systems at values of the volume fraction $\ensuremath{\varphi}$ along the disordered, metastable branch of the phase diagram up to random close-packing ${\ensuremath{\varphi}}_{c}$. By quantifying the degree of local order, we determine the necessary conditions to obtain a truly random system, enabling us to compute the pressure carefully along the entire metastable branch. Near ${\ensuremath{\varphi}}_{c}$ we show that the pressure scales as $({\ensuremath{\varphi}}_{c}\ensuremath{-}\ensuremath{\varphi}{)}^{\ensuremath{-}\ensuremath{\gamma}}$, where $\ensuremath{\gamma}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ and ${\ensuremath{\varphi}}_{c}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.644\ifmmode\pm\else\textpm\fi{}0.005$. Contrary to previous studies, we find no evidence of a thermodynamic glass transition and find that after long times the system crystallizes for all $\ensuremath{\varphi}$ above the melting point.