Thermodynamic description of geometrical confinement. Application to the glassy state and the glass transition of amorphous polymers

Based on the analysis of the geometrical confinements and the interactions between neighbor segments in polymeric systems, besides the quasi-lattice model used in Gibbs–DiMarzio entropy theory, an alternative theoretical method was developed here to investigate the thermodynamic aspect of the glassy state and the glass transition of amorphous polymers. A glass forming process through solvent evaporation from amorphous polymer-good solvent system was investigated, and the functional relationship between the glass transition temperature (Tg) and Kauzmann temperature (TK) at which configurational entropy equals zero was derived. The ratio Tg/TK=e1/4 was also deduced as a good approximation for a large amount of glassy polymers. The ratio is consistent with the empirical result Tg/TK=1.30±8.4%, which was proposed by Adam and Gibbs. The theoretical method presented here was also applied to investigate the compositional variation of glass transition temperatures; equations, which are consistent with experiments, were also derived.