Zero-shear rate viscosity from relaxation modulus

It is expected that the same picture that gives a good account of the linear viscoelastic behavior of polymer melts should also hold for semidilute and concentrated solutions. In the case of semidilute solutions some conclusions can be drawn from sealing arguments (19,3, p. 235). In this way, concentration dependence of the maximum relaxation time tmax the zero shear rate viscosity r Q, and the plateau modulus G% can be obtained, where t is the viscosity of the solvent. The relevant parameters needed to obtain Xmax as a function of concentration are b, c, N, kgT, and Dimensional analysis shows that... 

Masao Doi and Sam F. Edwards (1986) developed a theory on the basis of de Genne s reptation concept relating the mechanical properties of the concentrated polymer liquids and molar mass. They assumed that reptation was also the predominant mechanism for motion of entangled polymer chains in the absence of a permanent network. Using rubber elasticity theory, Doi and Edwards calculated the stress carried by individual chains in an ensemble of monodisperse entangled linear polymer chains after the application of a step strain. The subsequent relaxation of stress was then calculated under the assumption that reptation was the only mechanism for stress release. This led to an equation for the shear relaxation modulus, G t), in the terminal region. From G(t), the following expressions for the plateau modulus, the zero-shear-rate viscosity and the steady-state recoverable compliance are obtained ... 

The temperature dependence of D may be obtained from the zero shear-rate viscosity of the polymer in an indirect way. Both D and the zero shear-rate viscosity, Qq, are related through xd and hence the monomeric friction coefficient. One can obtain iJq from the stress relaxation modulus, G(t) > ... 

This expression allows the determination of the viscosity at zero shear rate from the time dependence of the relaxation modulus. 

For a viscoelastic material, the viscosity in the limit of zero-shear rate, the Newtonian viscosity, can be obtained from the integral of the stress relaxation modulus ... 

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