A Note for Kohlrausch-Williams-Watts Relaxation Function

Abstract

The Kohlrausch-Williams-Watts (KWW) relaxation function, F_KWW(t) = exp{-(t/τ_KWW)^β} with 0 < β ≤ 1 has been often utilized to describe relaxation processes in systems governed by cooperativity/coupling of molecules therein. Nevertheless, this function has not been well addressed in the general, phenomenological framework of linear relaxation phenomena, for which the relaxation function is expressed as F(t) = Σ_p g_pexp{-t/τ_p} with g_p and τ_p being the normalized intensity and characteristic time of pth (exponential) relaxation mode. In this study, the KWW function is analyzed to address this function in this general framework and derive analytical expressions of average relaxation times.