Viscoelastic spectrum structural-relaxation times

For polyacrylamide there are two rheological effects which can be explained in terms of its random coil structure. Firstly, it was discussed above that polyacrylamide is much more sensitive than xanthan to solution salinity and hardness. This is explained by the fact that the salinity causes the molecular chain to collapse, which results in a much smaller molecule and hence in a lower viscosity solution. The second effect which can be explained in terms of the polyacrylamide random coil structure is the viscoelastic behaviour of this polymer. This is shown both in the dynamic oscillatory measurements and in the flow through the stepped capillaries (Chauveteau, 1981). When simple models of random chains are constructed, such as the Rouse model (Rouse, 1953 Bird et al, 1987), the internal structure of these bead and spring models gives rise to a spectrum of relaxation times, Analysis of this situation shows that these relaxation times define response times for the molecule, as indicated in the simple Maxwell model for a viscoelastic fluid discussed above. Thus, because of the internal structure of a flexible coil molecule, one would expect to observe some viscoelastic behaviour. This phenomenon is discussed in much more detail by Bird et al (1987b), in which a range of possible molecular models are discussed and the significance of these to the constitutive relationship between stress and deformation rate and deformation history is elaborated. 

It is well known that the linear viscoelastic properties of polymer melts and concentrated solutions are strong function of molecular structure, average molecular mass and molecular mass distribution (MWD). The relaxation time spectrum is a characteristic quantity describing the viscoelastic properties of polymer melts. Given this spectrum, it is easy to determine a series of rheological parameters. The relaxation time spectrum is not directly accessible by experiments. It is only possible to obtain the spectrum from noisy data. 

As stated previously, the maximum relaxation time becomes infinite approaching the gel point. Specifically evaluating gelation from the viewpoint of dynamic structure requires measurements for infinite time. Also, the strain y must be very close to zero to avoid damage on the crosslinks, because the crosslink density of the networks at the gel point is extremely small. In practice, when the gel point is studied by viscoelastic property measurements, it is assumed that all relaxation modes will appear in the relaxation spectrum [31]. Under this hypothesis, the stress relaxation modulus G t) can be expressed as G t) t L The exponential rule will also apply for the complex modulus. That is. 

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