Relation between stretched-exponential relaxation and Vogel–Fulcher behavior above the glass transition

We point out a relationship between stretched-exponential relaxation, φ(t)=φ0 exp[−(t/τ)β], and the Vogel–Fulcher temperature dependence, τ=τ0 exp[A/(T−T0)], seen in many glasses near the glass transition. Recent experiments have shown that, in some glasses, the exponent β decreases as the temperature is lowered towards T0. Under rather nonrestrictive assumptions, this temperature dependence in φ(t) leads directly to Vogel–Fulcher behavior.