Past exam of the materials science course of the University of Cambridge / 2018 / Paper 1 / 6 / d / Solution

Within the rubbery regime, viscosity usually decreases as temperature increases, because segmental rearrangement becomes easier. The spring's entropic contribution generally increases approximately with absolute temperature at fixed effective network density, so $k$ tends to increase modestly under that assumption.

Consequently $\tau =\eta /k$ decreases. The storage-modulus crossover moves to larger squared frequency,and the high-frequency plateau moves upward if $k$ increases. The warmer curve in the figure illustrates those two changes. At intermediate frequencies the reduced relaxation time can lower the storage modulus even though its eventual plateau is higher; there is no requirement that the entire curve move upward.

These trends assume the same rubbery material state and no degradation, crystallization or change in effective network density. Close to other transitions the simple entropic-spring and viscosity picture needs modification.