Quantitatively Connecting Experimental Time-Temperature-Superposition-Breakdown of Polymers near the Glass Transition to Dynamic Heterogeneity via the Heterogeneous Rouse Model

Abstract

Polymers near the glass transition temperature Tg often exhibit a breakdown of time-temperature-superposition (TTS), with chain relaxation times and viscosity exhibiting a weaker temperature dependence than segmental relaxation times. The origin of this onset of thermorheological complexity has remained unsettled and a matter of debate. Here we extend the Heterogeneous Rouse Model (HRM), which generalizes the Rouse model to account for dynamic heterogeneity, to make predictions for the relaxation modulus G(t) and complex modulus G*($\omega$) of unentangled polymers near Tg. The HRM predicts that G(t) and G*($\omega$) exhibit enhanced effective scaling exponents in the Rouse regime in the presence of dynamic heterogeneity, with a more rapid decay from the glassy plateau emerging as the system becomes more dynamically heterogeneous on cooling. This behavior is predicted to emerge from a strand-length dependence of the moment of the segmental mobility distribution probed by chain dynamics. We show that the HRM predictions are in good accord with experimental complex modulus data for polystyrene, poly(methyl methacrylate), and poly(2-vinyl pyridine). The HRM also predicts the onset of distinct temperature dependences among chain scale quantities such as terminal relaxation time and viscosity in our experimental systems, apparently resolving one of the most significant standing objections to a heterogeneity-based origin of TTS-breakdown. The HRM thus provides a generalized theory of the chain-scale linear rheological response of unentangled polymers near Tg, accounting for the origin of TTS-breakdown at a molecular mechanistic level. It also points towards a new strategy of inferring the dynamic heterogeneity of glass-forming polymeric systems based on the temperature-evolution of modified scaling in the Rouse regime.