Correlation of glass transition temperature and molecular weight: A model based on the principle of corresponding states

The molecular weight dependence of the glass transition temperatures of polystyrene, polyα-methyl styrene, polyisopropylα-methyl styrene, polymethylmethacrylate, polyvinylchloride, poly-isobutylene, polyisoprene, and poly-N-octadecylmaleimide is described by an equation developed from the Principle of Corresponding States. A statistical analysis is used to test the adequacy of the equation, and it is shown that from a statistical point of view the three molecular parameters, S_e/S_m, ε/ε, and C_e/C_m, characterizing, respectively, the ratios of contact area, lattice energy, and segmental mobility of end groups relative to repeating segments along the chain, will adequately describe the data. It is also shown that in one limit the equation reduces to the well-known Ueberreiter-Kanig result, which for most cases is a good first approximation to the data. The molecular weight-T_G data were used to estimate the depression of the glass transition temperature of polystyrene and polymethylmethacrylate by a series of plasticizers. It was concluded that in the absence of important changes in the molecular structure within a homologous series of polymers, the Principle of Corresponding States can be employed to describe the molecular weight dependence of glass transition temperature over the entire range of available data.