Correlation between the secondary β-relaxation time at Tg and the Kohlrausch exponent of the primary α-relaxation

A correlation between the logarithm of the secondary β-relaxation time, log[τβ(Tg)], and the Kohlrausch exponent, (1−n), of the primary α-relaxation correlation function exp[−(t/τα)1−n] has been found in glass-forming materials in general. I was guided to this finding by the coupling model based on the similarity of some secondary β-relaxation to the primitive α-relaxation of the model. The logarithm of the primitive α-relaxation time at Tg,log[τ0(Tg)], calculated according to the coupling model from the observed α-relaxation at Tg, is exactly correlated with the Kohlrausch exponent. A similar, although inexact, correlation between log[τβ(Tg)] and (1−n) is thus expected and found. Furthermore, the experimental values of τβ(Tg) are remarkably close in order of magnitude to τ0(Tg) for many glass-formers as anticipated.