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

Abstract

Treating the glass temperature T_G of polymers as an iso‐free volume state allows one to derive the result (α_L—α_G). T_G=K₁, a constant; or the approximate result α_LT_G=K₂, another constant. The α's are the coefficients of cubical expansion for 100% amorphous polymer above and below T_G. 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 T_G. 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 T_G follow the first equation if α_G is replaced by α_G′, the expansion coefficient below the side‐chain transition. Polymer‐solvent systems are similar to the polyalkylmethacrylates. Two additional products, α_L·T_M and ΔC_P·T_G, where T_M is the melting point of the polymer and ΔC_P is the jump in specific heat at T_G, are approximately constant.