Dynamic Mechanical Properties

In steady laminar shearing flow at a constant shear rate, one can define three material functions: viscosity and the two normal stress differences. These have been considered in Chapters 3 – 5 . One can also generate time-dependent, especially periodic, flows. These are the subject of the current chapter. It is common practice to expose a polymer sample to a sinusoidal strain in a shearing flow and to measure the resulting stress response. If the strain amplitude is small, the stress is also sinusoidal, with a component that is in phase with the strain and a component that is out of phase with the strain. The former component represents storage of energy and leads to the definition of the storage modulus, G ′, while the latter component represents dissipation of energy and leads to the definition of the loss modulus, G ″. These are called dynamic mechanical properties, and their magnitude depends on the temperature and the applied frequency. G ′ is an elastic effect, like N 1 , but, unlike in the case of N 1 , material structure does not change during measurement. Thus, small amplitude oscillatory shear (SAOS) measurements reveal information only on the equilibrium state of the polymer sample. These results are useful for “fingerprinting” the material and for developing constitutive equations for polymeric fluids; the polymer structure and compositional sensitivity of these measurements also make them practically useful. When the strain amplitude is increased, the stress response ceases to be sinusoidal and becomes nonlinear. Interpreting the results of these large amplitude oscillatory shear (LAOS) experiments is less straightforward and is highly mathematical, but these results have theoretical, to build constitutive equations, as well as practical, to build structure–property relations, utility. Temperature dependence of the SAOS measurements has been a useful tool in practice, due to its sensitivity to structural and compositional factors.