Gibbs free energy equation, glass transition

The glass transition is a second-order transition, that is, the second derivative of the free energy function. In comparison, a first-order transition, such as the melting of a material, is the first derivative of Gibbs free energy. The equation used to determine the glass transition is ... 

T Aa is seen to be a function of V only, and since, according to quite well established observations of Simha and Boyer this product is a constant for all polymers (10), eqn. (1) implies an iso-free volume glass transition state. In fact, using the empirical Simha-Boyer constant of 0.113 for T Aa, it is found that V = 0.025 at T, identical with the free volume estimated from tne WLF equation (11). The hole formation energy, E, in the Gibbs-DiMarzio treatment is a function of T alone and is directly proportional to the latter, as is seen in eqn. (2). 

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