Relaxation of glasses: The Kohlrausch exponent

Relaxation of glasses is analyzed in the framework of the generalized Vogel–Fulcher–Tamann law. In this model the relaxation times of the cooperative and individual motions (α and β) verify the relation log τα(T,T′) = 1/n(T,T′) log τβ(Τ) . In the glass state the equivalent temperature T′ is the temperature of the liquid (at equilibrium) which has the volume of the glass, T′ is then the function of the aging time and of the experiment time. In the liquid state (T = T′), n(T) ~ T − T0 is the Kohlrausch exponent (T0 is the Vogel temperature). In the glass state the parameter, n(T,T′), is a function of the aging time and temperature, of the rheological parameters of the liquid (WLF constants C1 and C2) and of the expansion coefficients of the liquid and glass states. The Kohlrausch exponents deduced from the properties below Tg (volume, creep, stress relaxation) are deduced from the generalized VFT model.