In
this communication, we propose a different approach for analyzing
linear viscoelastic relaxation data that is more faithful to the underlying
physics and naturally accommodates the thermorheological complexity
that is observed in glass-forming polymers. Specifically, the linear
viscoelastic behavior was evaluated for a diglycidyl ether of bisphenol-A
epoxy cured with 4,4′-methylenedianaline with a glass transition
temperature (T
g) of 101.5 °C. The
dynamic storage and loss moduli were measured from 10–2 to 101.7 Hz for 19 temperatures between 90 and 180 °C.
The experimental window was extended by two orders of magnitude using
stress relaxation experiments for temperatures between 90 and 112.5
°C. The G′ and G″responses
for this single-phase polymer are thermorheologically complex, thus
precluding the construction of master curves via time–temperature
superposition. The traditional method of determining the relaxation
spectrum implicitly assumes a constant spectral density where the
spectral strength changes with the relaxation time. An alternative
approach presented herein is to assume that individual spectral contributions
have a constant strength where the spectral density changes. This
alternative approach is in better agreement with the physics of dielectric
relaxation and readily accounts for thermorheological complexity.
Using this new approach, a relaxation map of how the individual relaxation
times change with temperature has been developed, which is the only
relaxation information that can be rationally extracted from viscoelastic
isotherms. The relaxation map for the bisphenol-A epoxy shows a smooth
transition between the high temperature α+ process, the main
α transition, and the excess wing, where none of the relaxation
regions exhibit Arrhenian behavior.