On a General Relation Involving the Glass Temperature and Coefficients of Expansion of Polymers

Treating the glass temperature TG of polymers as an iso-free volume state allows one to derive the result (αL—αG). TG=K1, a constant; or the approximate result αLTG=K2, another constant. The α's are the coefficients of cubical expansion for 100% amorphous polymer above and below TG. K1 is 0.113 for a wide variety of polymers differing in cohesive energy density, chain stiffness, and geometry. We thus have a general criterion for TG. K2 is 0.164. This latter relation combined with the principle of corresponding states, results in an expression for Tg as a function of cohesive energy density and chain rigidity. The polyalkyl methacrylates which have side-chain transitions below TG follow the first equation if αG is replaced by αG′, the expansion coefficient below the side-chain transition. Polymer-solvent systems are similar to the polyalkylmethacrylates. Two additional products, αL·TM and ΔCP·TG, where TM is the melting point of the polymer and ΔCP is the jump in specific heat at TG, are approximately constant.