Physical Origin of the Mass Dependence of Glass Transition Temperature and Fragility of Polymer Liquids

Recently, there has been great interest in the prediction of the glass transition temperature Tg and fragility of polymer materials in connection with the need for utilizing these material parameters to guide materials design and characterization. Most of these studies have involved empirical correlations of Tg and fragility with various thermodynamic and structural properties in the absence of a validated predictive theoretical framework. In the present paper, we first focus on the variation of Tg and fragility of polymer materials with molecular mass (M) calculated from the generalized entropy theory (GET), a synthesis of the lattice cluster theory of polymer thermodynamics with the Adam–Gibbs model relating the structural relaxation time to the fluid configurational entropy density Sc, and determined from molecular dynamics simulations of a coarse-grained polymer melt having variable chain stiffness. In addition to providing predictions of the M variation of both Tg and fragility for variable chain rigidity, molecular structure, and intermolecular interaction strength, the GET provides novel insights into the physical origin of changes in these parameters in terms of the magnitude of Sc in its high temperature athermal state, Sc*, where relaxation is nearly Arrhenius. The calculation of Sc* based on an analytic theory is notably a unique capability of the GET. We show that the observed trends can be understood by analogy with crystallization and equilibrium polymerization transitions, where Sc* influences the melting temperature and the self-assembly transition sharpness in a similar fashion, as found correspondingly in the GET for Tg and fragility. Basic experimental trends in Tg and fragility with varying M are reproduced by both the GET calculations and simulation results, offering a new theoretical framework for predicting Tg and fragility for various applications. In contrast to the conventional free volume model, our theoretical framework provides a new interpretation of the M dependence of Tg and fragility in terms of frustrated packing of polymers, arising from the constraint of chain connectivity.