Volume relaxation, glass-forming

Sipp A. and Richet P. (2002) Equivalence of volume, enthalpy and viscosity relaxation kinetics in glass-forming silicate liquids. /. Non-Cryst. Solids 298, 202-212. 

Kakizaki, M., Anada, U. and Hideshima, T., Distribution of free-volume and dielectric alpha-relaxation in glass-forming liquid-mixtures, Jpn. J. Appl. Phys., Parti, 1995, 34, 3593. 

Paluch, M., Casalini, R., and Roland, C. M., Relative contributions of thermal energy and free volume to the temperature dependence of structural relaxation in fragile glass-forming liquids, Phys. Rev. B, 66, 092202-1 to 092202-3 (2002b). 

The fractional free volume f, which is the ratio of the free volume to the overall volume, occupies a central position in tr5nng to understand the molecular origins of the temperature dependence of viscoelastic response. The main assumption of the free-volume theory is that the fractional free volume assumes some universal value at the glass transition temperature. The Williams-Landel-Ferry (WLF) equation for the thermal dependence of the viscosity tj of polymer melts is an outgrowth of the kinetic theories based on the free volume and Eyring rate theory (35). It describes the temperature dependence of relaxation times in polymers and other glass-forming liquids above Tg (33-35). The ratio of a mechanical or dielectric relaxation time, Tm or ra, at a temperature T to its value at an arbitrary reference temperature To can be represented by a simple empirical, nearly universal function. 

To continue the a measiuement beyond the softening point requires that the supercooled glass-forming liquid be enclosed in containment such that volume change can be measured. But a above Mg is not usually relevant to the performance of a glass material in normal service since above Mg the glass melt cannot support sustained stress and undergoes viscous flow and stress relaxation. 

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