Free Volume, Viscosity and the Glass Transition

The relationship between viscosity and the Tg has been described by various empirical and semi-empirical equations. Two of 

These equations can be related to one another by assuming the free volume is proportional to the coefficient of thermal expansion, a, near T0 [i.e., Vf a(T- 7J,)]. (There is also the WLF equation, which we will get into later in Chapter 13, Mechanical and Rheological Properties.) 

The characteristic temperature, T0, is usually located about 30-70°C below the experimentally measured Tg and in various thermodynamic theories it represents an equilibrium value. We will not discuss these theories, but the existence of such a thermodynamic transition remains in dispute, with some arguing that the T is purely a kinetic phenomenon. Certainly, the experimentally observed quantity is kinetic in character. One manifestation of this is the shift in T 

Another important manifestation of the kinetic character of the Tg is the process of 

FIGURE 10-59 Schematic plots of specific volume versus temperature showing how the T varies with cooling rate. 

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