The glass transition in polydisperse polymers: contribution of mixing entropy

All polymerization processes give rise to polydisperse samples where the molecules exhibit a distribution of polymerization index, N. Due to the strong dependence of glass transition temperature, T_g, on N for small N, such polydispersity can potentially have a strong impact on the measured T_g values. Gibbs and DiMarzio 60 years ago (J. Chem. Phys.28, 373 1958) suggested that the T_g value of polydisperse samples is determined by the number average N of the sample “except for an ordinarily small correction” due to the excess mixing entropy. By considering mixtures of near oligomeric polystyrene with different compositions but the same number average molecular weight we can separate the entropic contribution due to chain ends from that of the chain mixing. We find that the measured T_g values of these mixtures has a significant composition dependence. We quantify this difference by considering the extra mixing entropy of the small chains. This analysis is also able to explain previously measured anomalies in bimodal mixtures of PS.