Dynamical Instability Causes the Demise of a Supercooled Tetrahedral Liquid

Abstract

We investigate the relaxation mechanism of a supercooled tetrahedral liquid at its limit of stability using isothermal isobaric (NPT) Monte Carlo simulations. In similarity with systems which are far from equilibrium but near the onset of jamming (O’Hern et al. in Phys Rev Lett 93:165702, 2004), we find that the relaxation is characterized by two time-scales: the decay of long-wavelength (slow) fluctuations of potential energy is controlled by the slope $[\partial (G/N)/\partial \phi ]$ of the Gibbs free energy (G) at a unique value of per particle potential energy $\phi = \phi _{{\tiny mid}}$. The short-wavelength (fast) fluctuations are controlled by the bath temperature T. The relaxation of the supercooled liquid is initiated with a dynamical crossover after which the potential energy fluctuations are biased towards values progressively lesser than $\phi _{{\tiny mid}}$. The dynamical crossover leads to the change of time-scale, i.e., the decay of long-wavelength potential energy fluctuations (intermediate stage of relaxation). Because of the condition [$\partial ^2 (G/N)/\partial \phi ^2 = 0$] at $\phi = \phi _{{\tiny mid}}$, the slope $[\partial (G/N)/\partial \phi ]$ has a unique value and governs the intermediate stage of relaxation, which ends just after the crossover. In the subsequent stage, there is a relatively rapid crystallization due to lack of long-wavelength fluctuations and the instability at $\phi _{{\tiny mid}}$, i.e., the condition that G decreases as configurations with potential energies lower than $\phi _{{\tiny mid}}$ are accessed. The dynamical crossover point and the associated change in the time-scale of fluctuations is found to be consistent with the previous studies.