  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.
