Prediction of the glass transition temperature of polymers: A model based on the principle of corresponding states

The application of corresponding state principles to describe the properties of polymers is implicit in many of the fundamental studies of polymeric behavior. The seminal works of Prigogine, Hildebrand, Eyring, Flory, Gibbs, and DiMarzio in which multidimensional lattice representations and refined statistical mechanical approaches have been used are the basis for much of today's understanding of the thermodynamic behavior of polymers and their solutions. In this work the lattice energy of a polymer is defined in terms of reduced molecular parameters, and it is assumed that all polymers with the same functional form for their lattice energies will be in corresponding states. A reduced second order transition temperature is defined relative to a characteristic temperature T* = sϵ*/2kv* c, where the molecular parameters refer to the properties of the repeating segments of the polymer chain. Equations are derived that express the effects of molecular weight, plasticization, degree of crosslinking, and copolymerization on the second order (i.e., glass) transition temperature. In their limits, the equations are shown to reduce in form to equations derivable from free volume theory. They are also used to analyze successfully a variety of glass transition temperature data available in the literature on homogeneous uncrosslinked and crosslinked polymers, plasticized polymers, and random copolymers.