Generalized entropy theory investigation of the relatively high segmental fragility of many glass-forming polymers†

Abstract

We utilize the generalized entropy theory (GET) of glass formation to address one of the most singular and least understood properties of polymer glass-forming liquids in comparison to atomic and small molecule liquids—the often relatively high fragility of the polymer dynamics on a segmental scale, m_s. Based on this highly predictive framework of both the thermodynamics and segmental dynamics in terms of molecular structure, polymer backbone and side-group rigidities, and intermolecular interaction strength, we first analyze the relation between m_s and the ratio, , where S_c is the configurational entropy density of the polymer fluid, equals S_c at the onset temperature T_A for non-Arrhenius relaxation, and T_g is the glass transition temperature at which the structural relaxation time τ_α equals 100 s. While the reduced activation energy estimated from an Arrhenius plot (i.e., differential activation energy) normalized by k_BT_g is determined to be not equal to the actual activation energy, we do find that an apparently general nonlinear relation between m_s and holds to a good approximation for a large class of polymer models, . The predicted ranges of m_s and are consistent with experimental estimates for high molecular-mass polymer, oligomeric, small molecule, and atomic glass-forming liquids. In particular, relatively high values of m_s are found for polymers having complex monomer structures and significant chain stiffness. The variation of m_s with molecular mass, chain stiffness, and intermolecular interaction strength can be traced to the variation of , which is shown to provide a measure of packing frustration defined in terms of the dimensionless thermal expansion coefficient and isothermal compressibility. The often relatively high fragility and large extent of cooperative motion are found in the GET to derive from the often relatively large packing frustration in this class of polymer glass-forming liquids. Finally, we also develop a tentative model of the “dynamical segmental relaxation time” based on the GET, in which the polymers on a coarse-grained scale are modeled as strings of structureless “beads”, as assumed in the Rouse and reptation models of polymer dynamics.