Glass: Kohlrausch exponent, fragility, anharmonicity

Abstract

The thermodynamical and mechanical properties of (fragile and strong) glass are modeled based on a generalised activation energy relationship log( τ ) = ΔG ( β )/RTn(T') process of glass-forming liquids. This cooperative process involves 1/n(T') elementary β motions of activation Gibbs energy ΔG ( β ) dependent on the equivalent temperature T', the temperature of the liquid in equilibrium having the volume of the glass, function of temperature and aging conditions. From this modified VFT law the relaxation of any properties (V , H , stress, creep) can be calculated and approximated by the Kohlrausch function. This model predicts consistency relationships for: a) the temperature (and aging time) variation of the Kohlrausch exponent; b) the temperature dependence of the stabilisation time domain of strong and fragile glass; c) the linear relation between the activation parameters (E (*) energy, S (*) entropy, V (*) volume) of the α and β transition. The Lawson and Keyes (LK) relations are recalled and it is shown that these relations (somewhat equivalant to the compensation law or Meyer-Neldel rule) are observed generally in glass. Morever the (macroscopic) ratios ΔH/ΔV observed during aging or after a temperature jump and the (microscopic) ratio E (*)/V (*) are found equal to κγ (κ compressibily, γ Grüneisen parameter), in agreement with the LK predictions. From various experiments and in agreement with predictions of this model we conclude that the Grüneisen parameter γ ( B ) (pressure derivative of the bulk modulus) and the Mean Square Displacement (MSD) characterising the anharmonicity of solids (and liquids) are the main parameters which govern the relaxation properties of the glass state. Linear relations between the parameters γ ( B ), the fragility m, and the Kohlrausch exponent n ( g ) at T ( g ) are explained. These correlations underscore a strong relationship between the fragilty of glass formers and the extent of the anharmonicity in the interatomic interactions.