Small-amplitude oscillatory shear defined

Small amplitude oscillatory shear is the method of choice for materials with very broad distributions of relaxation modes, such as materials near LST, and for materials which undergo change during the measurement. The dynamic moduli in Eq. 4-10 are defined by [10]... 

For a small amplitude oscillatory shearing flow, the strain is defined as,... 

In a dynamic experiment, a small-amplitude oscillatory shear is imposed to a molten polymer confined in the rheometer. The shear stress response of the polymeric system can be expressed as in Equation 22.14. In this equation, G and G" are dynamic moduli related to the elastic storage energy and dissipated energy of the system, respectively. For a viscoelastic fluid, two independent normal stress differences, namely, first and second normal stress differences can be defined. These quantities are calculated in terms of the differences of the components of the stress tensor, as indicated in Equation 22.15a and 22.15b, and can be obtained, for instance, from the radial pressure distribution in a cone-and-plate rheometer [5]. Some other experiments used in the determination of the normal stress differences can be found elsewhere [9, 22] ... 

In marked contrast to measurements of shear rheological properties, such as apparent viscosity in steady shear, or of complex viscosity in small amplitude oscillatory shear, extensional viscosity measurements are far from straightforward. This is particularly so in the case of mobile elastic liquids whose rheology can mitigate against the generation of well-defined extensional flow fields. 

Once the cross-linking temperature has been attained, add the second KBr disc to the top of the sample and apply pressure to define the sample thickness. If an aligned sample is desired a small, linear, oscillatory shear may be applied at this point (amplitude 5 mm, frequency 1 Hz). 

A sinusoidally varying shear strain rate with small amplitude, such that 721 = 721 cos cor, evokes a sinusoidally varying normal stress difference symmetry considerations because of the proportionality to 721, is predicted by the phenomenological models previously quoted.5 -54 jj,g oscillatory stress difference is superposed on a constant stress and both are proportional to 721 if 721 is small. The coefficient is now defined as the ratio (ai i — ff22)/(72i) - It is the sum of a constant term and two oscillating terms ... 

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