Dynamic Slowing-Down and Nonexponential Decay of the Density Correlation Function in Soft-Sphere Supercooled Liquids

Molecular dynamics simulations were carried out for supercooled soft-sphere liquids. The computed density correlation function shows a clear nonexponential decay in intermediate times, as the liquid-glass transition is approached. The overall time dependence of the correlation function can be fitted by a stretched function of the type: exp [-( t / t 0 ) α ], where the exponent α varies from 1, in stable liquids, down to about 0.5, in the vicinity of the liquid-glass transition. The average correlation time < T >=(1/α) G (1/α) t 0 ( G ( x ) being the gamma function) can be reasonably fitted by a scaling law of the type: \({}T{}{∝}(g-)-θ\), where \(\) is a coupling constant, the suffix g denotes the glass transition, and the exponent θ varies from about 2 to 5, depending on wave number k . The wave number dependence of the correlation function is discussed.