Couplings between the cooperatively rearranging regions of the Adam–Gibbs theory of relaxations in glass-forming liquids

The Adam–Gibbs theory of relaxation for glass-forming liquids is based on an ensemble of independent and equivalent cooperatively rearranging regions (CRR’s). In this work we extend the Adam–Gibbs theory by incorporating the mutual interactions between the CRR’s. This is done by the method of the coupling scheme in which the transition rate for each independent CRR is slowed down by a time-dependent factor. The new combined theory predicts a stretched exponential relaxation function and modifies the Adam–Gibbs parameters for the temperature dependence of the relaxation time making them functions of the stretched exponent β. The model is applied to analyze specific heat and dielectric data of supercooled liquids. It is able to explain a previously proposed correlation of the increasing fragility of glass forming liquids with the size of 1−β at Tg and the rapidity of the temperature variation of β. The model also explains, in hydrogen bonded liquids, the correlation of the increasing fragility with the size of the basic molecular unit and/or the number of hydroxyl groups found by comparison of dielectric relaxations of glycerol, n-propanol, butanediol-1,3, and sorbitol.