BETA-RELAXATION IN SUPERCOOLED LIQUIDS

For the dynamics within the beta-relaxation region, the mode-coupling theory for supercooled liquids predicts as the simplest generic possibility for the correlation functions PHI-(t) = f + hc-sigma-g(t/t-sigma). Here f and h are time-independent quantities specifying the variables under discussion and c-sigma, t-sigma are scales that depend sensitively on the separation, sigma, from the glass-transition singularity. g is a master function specified completely by the exponent parameter lambda, which can be evaluated from the structure factors. The result describes, for examples, the crossover from the critical decay law g(t/t-sigma << 1) proportional 1/t(a) to the von Schweidler law g(t/t-sigma >> 1) proportional - t(b). Under special conditions there may be another region of fractal decay, PHI proportional - t(a), which causes the beta-peaks. The latter is given asymptotically by the Cole-Cole law. The results of the theory are in good agreement with some experiments.