Viscoelasticity free volume theory, glass transition

The free volume theory originated some years later than the lubricity and the gel theories, when the evolution of different properties of polymers as a function of temperature, specific volume, thermal expansion coefficients, or viscosity was attempted to be explained.The relationships between these properties and some variables corresponding to polymer stracture, such as molecular weight or terminal groups content, the presence of another monomer and, of course, the presence of plasticizers, was also explained. For plasticized polymers the theory attempted to explain the diminution of the glass transition temperature with the plasticizer content. This theory is a contribution of different authors, but it was postulated by Fox and Floiy. The theory is still being used to explain some properties of plasticized polymers, i.e., viscoelastic properties. ... 

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. 

The glass transition phenomenon has been the object of many molecular theories, that of Ferry [29], further developed by Bueche [30], on the free volume concept being widely accepted in the polymer field. The volume occupied by a chain of amorphous polymer consists partly of free space, i.e., the volume excluded by the movements of segments about their equilibrium position. As shown in Fig. 1.8, the temperature coefficient for the polymer volume at constant pressure dV dT)p is higher for the viscoelastic state (curve b) than for the glassy state (curve a), and it changes abruptly at Tg this is the mathematical definition of the glass transition temperature. It can also be defined as the... 

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