A theory for the beta-relaxation process near the liquid-to-glass crossover

Abstract

The mode coupling theory for supercooled liquid dynamics finds a beta-relaxation regime on mesoscopic timeseales. It is caused by the interplay between nonlinear interadions of density fluctuations and phonon-assisted hopping transport. In this regime all correlation functions and spectra can be expressed in terms of a single ß-correlator G, which is a homogeneous function of lime and two relevant control parameters. It is specified by a single number, namely the exponent parameter. Eight regions can be identified, where the equation for G can be solved by series expansions. The various possibilities are discussed in comparison with representative numerical solutions. For temperatures T sufficiently above the critical value Tc hopping effects can be neglected and a stretched susceptibility minimum is found as a crossover from von Sehweidler decay to critical decay. For T near Tc hopping effects balance the cage effect and this results on logarithmic scales in a rather abrupt crossover from the high-frequency delta-peak tail to the critical spectrum. For T telow Tc there appears a frequency window between two knees in the susceptibility spectrum, where hopping effects suppress the enhanced fractal spectra. There occurs a crossover from Debye relaxation to white noise. The resulting susceptibility minimum in the strongly supercooled state exhibits a subtle power law dependence on the separation parameter T - Tc. The measurable features in the susceptibilily, such as position and strength of the minimum, are evaluated and shown to characterize transparently the liquid-to-glass crossover as caused by the underlying glass transition singularity.