Viscoelastic frequency dependence shear stress relaxation

We tiu-n from the frequency-dependent shear modulus and viscosity considered above to the time-dependent relaxation modulus. As mentioned in the previous section, we focus on the linear viscoelastic domain, in which the shear stress a t) depends linearly on the velocity gradient g(t) [2]. The relaxation modulus G(t) is now implicitly introduced through a relation between... 

The classical viscoelastic properties are the dynamic shear moduli, written in the frequency domain as the storage modulus G ( y) and the loss modulus G a>), the shear stress relaxation function G t), and the shear-dependent viscosity j (k). Optical flow birefringence and analogous methods determine related solution properties. Nonlinear viscoelastic phenomena are treated briefly in Chapter 14. 

The shift factor ap can be used to combine time-dependent or frequency-dependent data measured at different pressures, exactly as ap is used for different temperatures in Section A above, and with a shift factor ar,p data at different temperatures and pressures can be combined. It is necessary to take into account the pressure dependence of the limiting values of the specific viscoelastic function at high and low frequencies, of course, in an analogous manner to the use of a temperature-dependent Jg and the factor Tp/Topo in equations 19 and 20. The pressure dependence of dynamic shear measurements has been analyzed in this way by Zosel and Tokiura. A very comprehensive study of stress relaxation in simple elongation, with the results converted to the shear relaxation modulus, of several polymers was made by Fillers and Tschoegl. An example of measurements on Hypalon 40 (a chlorosulfonated polyethylene lightly filled with 4% carbon black) at pressures from 1 to 4600 bars and a constant temperature of 25°C... 

This square-root dependence on tw is a fundamental featme of linear chains in the Rouse model. The shear modulus at intermediate frequencies is a signature of the internal, intra-chain dynamics, which is determined by the topology of the GGS. As stressed before, the viscoelastic relaxation forms can be expressed through the relaxation spectrum H r), see Eq. 27. Here one finds [3] ... 

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