Study of the α and β relaxations in a supercooled fluid via molecular-dynamics simulations

Incoherent scattering function (self-part of the density autocorrelation function) F_s(k, t) is computed by molecular-dynamics (MD) simulation in supercooled fluids of binary soft-sphere mixtures. The full density autocorrelation function F(k, t) was also computed. It is found that F_s(k, t)'s at various temperatures and wavenumbers can be fitted over a wide range of time steps (at least over three orders of the decay) by a Williams-Watts stretched exponential function F_s(k, t) = A exp[ -(t/t₀)^β], where A, β and t₀ are adjustable parameters. Significant dynamical behaviours are also presented for mean square displacements and non-Gaussian parameters. With results obtained from different system size, N = 500 and N = 4000 a significant size dependence is suggested. Generalized susceptibility χ(k, ω) and dynamical structure factor S(k, ω) are also computed over a wide range of ω (over five orders) using a new algorithm for the numerical integrations. Computational results are presented for the imaginary part of the generalized susceptivility, χ′(k, ω), which indicates both α and β peaks in such spectra for the first time by the present MD computation. The present MD results are in good agreement with the predictions of the trapping diffusion model, which we have previously proposed for the glass transition.