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, $m_s$. We first analyze the relation between $m_s$ and the ratio, $S_c^*/ S_c(T_{\mathrm{g}})$. We find that an apparently general nonlinear relation between $m_s$ and $S_c^*/ S_c(T_{\mathrm{g}})$ holds to a good approximation for a large class of polymer models, $m_s \approx 7.9 \exp [0.6S_c^*/ S_c(T_{\mathrm{g}})]$. The predicted ranges of $m_s$ and $S_c^*/ S_c(T_{\mathrm{g}})$ 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 $S_c^*$, 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.