Inhomogeneities and relaxation in supercooled liquids

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Abstract
Nonexponential relaxation in glass forming liquids has been attributed by Robertson and Donth to inhomogeneous distribution of small local regions. We show, based neither on free‐volume nor on configurational entropy theories that the correlation volume V of such inhomogeneous regions isR [ΔH* (1−x)/RT]2{k BT4 g Δκ Tg /〈 Δ2 ln τ〉}, where Δh* is the enthalpy of activation near the glass transition temperature T g , x is the Narayanaswamy–Gardon nonlinear parameter, Δκ Tg is the change in thermal conductivity at T g , 〈Δ2 ln τ〉, describes how wide is the spectrum of relaxation times, and k B and R are the Boltzmann and the gas constants, respectively. The correlation length does not diverge at T g . In fact, the correlation length at T g for B2O3, glycerol, and PVAc are found to be approximately 1.27, 0.91, and 1.53 nm, respectively. Our results indicate, in agreement with Moynihan and Schroeder, that characteristics of nonexponential relaxation in glass forming liquids may be due to inhomogeneous domains whose size are in the nanometer length scale.