Gibbs-DiMarzio thermodynamic theory

However, the conformation statistics in Flory s treatment gives the conformational free energy, rather than the conformational entropy adapted in the Gibbs-DiMarzio theory. In addition, W was calculated with respect to the fully ordered state therefore. In W = 0 simply implies the return to the fully ordered state, rather than frozen in a disordered state. Furthermore, reflects the static semi-flexibility, while the glass transition should be related with the d3mamic semi-flexibility of polymer chains. Therefore, fundamental assumptions of the Gibbs-DiMarzio thermodynamic theory are misleading. 

We have replaced the idea of second order phase transition postulated by the Gibbs-DiMarzio theory, yet retained its successful features. Tr is treated as the thermodynamic anomaly at which the most stable hole configuration is reached under the close packing of holes and flex bonds. 

Thus, the Miller theory has trivial thermodynamics. Starting from the Gibbs-DiMarzio theory, one arrives at the Miller theory by setting Ae = U and z — 2 = 2 in Eq. (4-8) and by assuming that the conformation of one chain imposes no thermodynamic constraints which limit the possible conformations of other chains. 

A quite different approach is adopted in the statistical mechanical theory expounded by Gibbs and DiMarzio. They considered that the rotating unit could exist in two stable conformations (which might correspond to the trans and gauche conformers discussed earher), separated by a standard state energy difference, AE°, called the flex energy. Using the techniques of statistical thermodynamics, they calculated the partition of the units between these two forms. In theory, the... 

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