β-relaxation in supercooled liquids

For the dynamics within the β-relaxation region, the mode-coupling theory for supercooled liquids predicts as the simplest generic possibility for the correlation functions φ (t) = f + hc_σg(t/t_σ). Here f and h are time-independent quantities specifying the variables under discussion and c_σ, t_σ are scales that depend sensitively on the separation, σ, from the glass-transition singularity. g is a master function specified completely by the exponent parameter λ, which can be evaluated from the structure factors. The result describes, for examples, the crossover from the critical decay law g(t/t_σ≪1)σ1/t^a to the von Schweidler law g(t/t_gs≫1)∝ -t^b. Under special conditions there may be another region of fractal decay, φ ∝-t^a, which causes the β-peaks. The latter is given asymptotically by the Cole-Cole law. The results of the theory are in good agreement with some experiments.