Couplings between the cooperatively rearranging regions of the Adamndash;Gibbs theory of relaxations in glasshyphen;forming liquids

摘要

The Adamndash;Gibbs theory of relaxation for glasshyphen;forming liquids is based on an ensemble of independent and equivalent cooperatively rearranging regions (CRRrsquo;s). In this work we extend the Adamndash;Gibbs theory by incorporating the mutual interactions between the CRRrsquo;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 timehyphen;dependent factor. The new combined theory predicts a stretched exponential relaxation function and modifies the Adamndash;Gibbs parameters for the temperature dependence of the relaxation time making them functions of the stretched exponent bgr;. 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 1minus;bgr; atTgand the rapidity of the temperature variation of bgr;. 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,nhyphen;propanol, butanediolhyphen;1,3, and sorbitol.