Glass transition in a soft-sphere model

Abstract

A molecular dynamics study of the glass forming properties of the inverse-twelfth-power soft-sphere model is reported. MD results in the equilibrium range for N=4000 are used to parametrize a six-term virial equation for the fluid and a three term anharmonic perturbation equation-of-state for the crystal, and thereby determine the excess entropy of the supercooled fluid. The hypothetical Kauzmann catastrophe temperature (Tk) of the extrapolated supercooled fluid corresponding to zero excess entropy is thus determined. When a 4000-particle system is cooled at a rate approximately 60 times slower than has previously been accomplished there is no evidence of crystal nucleation. On annealing the supercooled fluid for a very long time nucleation is apparent. The supercooled fluid equation-of-state data is fitted to a polynomial and the variation in heat capacity through the glass transition range is obtained. This yields an operational glass transition temperature Tgk, defined by the onset of kinetic retardation, and a limiting thermodynamic glass transition temperature (To). Both Tgk and To may be also observed from diffusion data and they coincide with those obtained from heat capacities to within the procedural uncertainties. Comparisons are made with the behavior of hard-sphere and Lennard–Jones systems in MD-glass formation. The results are consistent with the postulate of a thermodynamic transition at To, associated with vanishing self-diffusion and a limiting ground-state amorphous solid phase.