The Relationship between Time, Temperature, and Frequency

The loss modulus, representing the viscous nature of a material, is related to the real component of the complex viscosity, and the storage modulus, representing the elastic nature of the material, is related to the imaginary component. For an ideal liquid r will simply be the viscosity of the liquid and r will be zero. For an ideal solid r will be zero and r will be the ratio of the shear modulus to frequency. Thus, in DMA there is no real distinction between viscosity and modulus, and knowledge of either quantity along with the measurement frequency can be used to calculate the other. 

Dynamic viscosity data can be used to approximate the steady shear viscosity by taking advantage of an empirical relationship known as the Cox-Merz rule (Cox and Merz 1958), which relates the magnitude of the complex viscosity at frequency co to the steady shear viscosity at a shear rate y equal to co  

Dynamic viscosity measurements generally are easier to perform over a wide range of frequencies than are steady shear measurements over a wide range of shear rates, while steady shear viscosity is of more value in the analysis of polymer processing. Thus, the Cox-Merz rule is frequently assumed and t data are used in place of steady shear viscosity data. 

If an amorphous polymer is subjected to a stress relaxation experiment over a very long period of time, the modulus-log time curve will be similar to that shown in Fig. 5.11. There is a striking similarity in shape between the curves 

While there is a relationship between time and temperature, the theories of viscoelasticity (Ferry 1980) do not deal with the temperature dependence. However, there is an empirical relationship referred to as the time-temperature superposition (TTS) principle, which provides a useful, practical 

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