Glass transition Gibbs-DiMarzio theory

Fig. 6. The hole formation energy 2ajk), the barrier to internal rotation (/de/fi) and the glass transition temperature vs. compoafdon for NaPOjijCa(PO, counterion copolymers (2 /ft) and (Aelk) calculated from the Gibbs-DiMarzio theory at 10% intervals. T, points experimental...

Figure 5-8. Molecular weight trends in the glass transition temperature trends in cyclic and linear oligomers of poly(dimethyl siloxane), and the comparison of these data with the prediction of the Gibbs-DiMarzio theory. [Reprinted with permission from E. A. DiMarizio and C. M. Guttman, Macromolecules, 20, 1403 (1987). Copyright 1987, American Chemical Society]...

There are rival theories of the glass transition the Gibbs Dimarzio theory assumes that the configurational entropy of the chains approaches zero at Tg. Other researchers prefer a mode coupling theory (MCT), based on the dynamics of density fluctuations. However, it is difficult to extract a simple physical meaning from the complex equations that describe correlations between density fluctuations. Neither theory, at its current state of development, is particularly useful in understanding the properties of glassy polymers. 

QUANTITATIVE EVALUATION OF THE GIBBS-DIMARZIO THEORY OF THE GLASS TRANSITION FOR POLYSTYRENE... 

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. 

A basis for the effects described above can be developed in terms of the Gibbs-DiMarzio theory of the glass transition, using the following two postulates (4). 

Another interesting aspect of the Gibbs-DiMarzio " " theory is that it predicts an effect of deformation on the glass transition temperature due to changes in the entropy of the system upon straining the network. For uniaxial extension, the result in terms of the small-strain modulus G, measured at a temperature Tq, is ... 

The entropy theory of the glass transition was developed by Gibbs and DiMarzio and by Adams and Gibbs to describe polymeric systems. By mixing the polymer links with holes or missing sites on a lattice to account for thermal expansion as in a lattice gas model, they could determine the entropy of mixing and the configurational entropy of the polymer. They found a second-order transition at a temperature They then pointed... 

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