Polymers and composites
Which correctly describes the idea of time–temperature superposition in polymer viscoelasticity?
- ARaising the temperature has the same effect as measuring over longer times (lower frequencies)
- BRaising the temperature has the same effect as measuring faster, over shorter times (higher frequencies)
- CViscoelastic properties depend only on temperature, so changing the time scale or frequency of the measurement leaves the modulus unchanged
Show answer and explanation
Answer: A. Raising the temperature has the same effect as measuring over longer times (lower frequencies)
Molecular motion in polymers is faster at higher temperatures, so relaxations that occur in a short time at high temperature take a long time at low temperature. Relaxation modulus curves measured at different temperatures can therefore be shifted along a logarithmic time axis to overlap into a single composite curve (the master curve). In other words, raising the temperature has the same effect as measuring at longer times (lower frequencies). The amount of shift (the shift factor) is described by the WLF equation near Tg and by an Arrhenius-type expression well below Tg. Using this principle, long-term creep and stress relaxation at room temperature can be predicted from short tests at high temperature.