On the heterophase liquid thermodynamics and cooperative dynamics

Abstract

The thermodynamics and cooperative dynamics of heterophase liquid states is considered taking into account frustration and volumetric interaction of the solid-like uctuons . It is found that the glass transition temperature range is scaled by difference of the frustration parameter and mean energy of the volumetric interaction. A model of the cooperative relaxation with nite cooperatively rearranging domains is considered. The ctitious Kauzmann and Vogel-Fulcher temperatures are determined. It is found that they are close to a proper ac- curacy. Correlation of the temperatures of glass transition, Vogel-Fulcher and iideali glass transition (as it is determined in the mode coupling model) is considered too. The heterophase uctuations model (HPFM) is based on the idea of heterophase structure of glass forming liquids (1{5). Consecutive consideration shows that in a heterophase state (HPS), molecular clusters (uctuons) of specied short-range order (SRO) are statistically signican t en- tities rather than single molecules. As a result, the supramolecular interactions determine the thermodynamics and dynamics of the glass forming liquids. Equation for the free energy of HPS is deduced within the framework of HPFM taking into account frustration and volumetric interaction of the uctuons (5, 6). The model of the cooperative relaxation dynamics of HPS developed in (2, 3) describes the -relaxation rate in terms of the free energy. The developed theory is a proper base for the analysis of experimental data on thermodynamics, structure and cooperative relaxation of the glass-forming liquids (2{4). The Vogel-Fulcher and Kauzmann temperatures (TVF and TK) (7{9) and the temperature of the \ideal" glass transition determined within the framework of the mode-coupling model (TMCT) (10, 11) are in use at the analysis and rationalization of experimental data. At TK the extrapolated entropy of liquid becomes equal to that of crystal or, in other words, the congurational entropy of liquid is going to zero. In (9, 12) it is assumed that a critical point is located at Kauzmann temperature, TK < Tg while TVF is the assumed singular point of the cooperative relaxation (7, 8). The relaxation time at this point is exp (TK=(T TK)). The empiric Vogel-Fulcher formula was obtained by Adam and Gibbs in a theoretical model (13). They connected the size of the cooperatively rearranging domain with the congurational entropy of liquid. The size increases with the congurational entropy decrease while at TK it goes to innit y. As a result, TK is a singular point of the cooperative relaxation and TK = TVF. Though TK and TVF are not accessible for a direct observation, the formulas obtained in Gibbs-DiMarzio and Adam-Gibbs (AG) models (along with the empiric denition by Kauzmann) make it possible to rationalize and t the experimental data on the liquid congurational entropy and relaxation cooperative rates. Determination of TMCT is given in terms of the basic relations of thermodynamic and dynamic properties of glass-forming liquids under special assumptions (10, 11). The predicted \ideal" glass transition has not been observed yet but this model and its consequences have been under consid-