A theory of the molecular-mass dependence of glass transition temperatures for polydisperse homopolymers

Abstract

Arbitrary distributions of finite molecular-mass homopolymers are treated as one-phase solutions of chain ends and high polymers in order to derive an entropie relation for the dependence of their glass transition temperatures on the number-average degree of polymerization. Absolute predictions of this equation from high molecular-mass and dimer properties are found to be in good agreement with dilatometric transition temperatures for polystyrene. The theoretical equation is generalized to allow for the characterization of chain ends by properties other than those of dimers. An initial approximation to the entropic expression is obtained by neglect of the difference between chain-end and high-polymer transition increments of heat capacity. Two subsequent approximations arise from a series expansion of logarithmic functions. In order of decreasing accuracy these three approximations are: a new form of the Ueberreiter-Kanig equation, a logarithmic expression, and a new form of the Fox-Flory relation.