Thermodynamics of the glass-rubber transition

To consider the nature of the glass mbber transition on a thermodynamic basis, we should first compare this transition with melting. The melting point is a first-order transition, Tg could be mentioned a second-order transition. 

The quantity G, the (Gibbs) free enthalpy, plays a predominant role in the thermodynamic treatment of transitions. 

U = internal energy, e.g. as a result of the attraction forces between molecules T = absolute temperature, 

With each type of transition, AG = 0, in other words the G(T) curves for both phases intersect, and slightly below and above the transition temperature the free enthalpies are equal. The various derivatives of the free enthalpy may, however show discontinuities. With a first-order transition such as melting, this is the case with with the first derivatives like V and S and also with H. 

With melting the volume differs at both sides of the melting point a jump AV in volume occurs, which is a jump in the first derivative of G after p at constant T. Also a jump AH occurs in the enthalpy (the heat of melting), as well as a jump AS in entropy. 

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Staverman (1966) and Breuer and Rehage (1967) extensively discussed the thermodynamics of the glass-rubber transition. They concluded that it is not a real second-order transition, mainly because the glassy state is not completely defined by the normal state variables p, V and T. 

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