Gibbs-di Marzio theory

Moacanin, J., Simha, R., Some consequences of the Gibbs-Di Marzio theory of the glass transition. The Journal of Chemical Physics, 45(3), pp. 964-967 (1966). 

A theoretical derivation based on the Gibbs-Di Marzio (1958) theory of the glass transition leads to the conclusion that for the series of poly(alkyl methacrylates)... 

One must be carefiil here because one can prove too much. The entropy theory of glasses, also called the Gibbs-Di Marzio (GD) theory, is a theory of equilibrium thermodynamic quantities only, it is not a theory of the kinetics of glasses. Polymer viscosities do in fact get so large at the glass transition that the relaxation times in the material equal and exceed the time scale of the experiment. At such temperatures one should not expect to have a perfect prediction of the various thermodynamic quantities. It is sensible to suppose that our predictions should not accord perfectly with experiment in these high viscosity regions. 

Theory must account for these properties of fluids, their temperature dependence, the glass transition, and the properties of the amorphous solid. The two most widely accepted theories are the entropy theory, as formulated by Gibbs and Di Marzio (1958), Gibbs (1960), and Adam and Gibbs (1965), and the free-volume theory as developed by Eyring (1936), Fox and Flory (1950), Williams, Landel and Ferry (1955), Cohen and Turnbull (1959), and Turnbull and Cohen (1961, 1970). 

The entropy theory is the result of a statistical mechanical calculation based on a quasi-lattice model. The configurational entropy (S, ) of a polymeric material was calculated as a function of temperature by a direct evaluation of the partition function (Gibbs and Di Marzio (1958). The results of this calculation are that, (1) there is a thermodynamically second order liquid to glass transformation at a temperature T2, and 2), the configurational entropy in the glass is zero i.e. for T > T2, => 0 as T... 

Gibbs and Di Marzio [23,24] proposed that the dilatometric Tg is a manifestation of a true equilibrium second-order transition at the temperature T2. In a further development, Adams and Gibbs [21] have shown how the WLF equation can then be derived. On their theory, the frequency of molecular jumps is given by... 

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