Linear viscoelasticity molecular weight dependences

The mean times t and tw will be called the number-average and weight-average relaxation times of the terminal region, and tw/t can be regarded as a measure of the breadth of the terminal relaxation time distribution. It should be emphasized that these relationships are merely consequences of linear viscoelastic behavior and depend in no way on assumptions about molecular behavior. The observed relationships between properties such as rj0, J°, and G and molecular parameters provides the primary evidence for judging molecular theories of the long relaxation times in concentrated systems. 

It appears that the formal theories are not sufficiently sensitive to structure to be of much help in dealing with linear viscoelastic response Williams analysis is the most complete theory available, and yet even here a dimensional analysis is required to find a form for the pair correlation function. Moreover, molecular weight dependence in the resulting viscosity expression [Eq. (6.11)] is much too weak to represent behavior even at moderate concentrations. Williams suggests that the combination of variables in Eq. (6.11) may furnish theoretical support correlations of the form tj0 = f c rjj) at moderate concentrations (cf. Section 5). However the weakness of the predicted dependence compared to experiment and the somewhat arbitrary nature of the dimensional analysis makes the suggestion rather questionable. 

V.R. Raju, E.V. Menezes, G. Marin, W.W. Graessley, and L.J. Fetters, "Concentration and Molecular Weight Dependence of Viscoelastic Properties in Linear and Star Polymers," Macromolecules, 1, 1668 (1981). 

At this point the reptation theory makes some strong predictions about the viscoelastic response in the linear regime, viz, the viscosity varies as and the ratio of Js°/Gn = 6/5 = 1.2. Note that the molecular weight dependence of the viscosity has already been discussed above, and recall that, experimentally, the viscosity varies as N -. In addition, the ratio is observed experimentally... 

Raju, V. R., Menezes, E. V., Marin, G., Graessley, W. W. Concentration and molecular weight dependence of viscoelastic properties in linear and star polymers. Macromol (1981) 14, pp. 1668-1676... 

Only a few non-linear viscoelastic properties have been studied with polymers of well-characterized structure. The most prominent of these is the shear-rate dependence of viscosity. Considerable data have now been accumulated for several polymers, extending over a wide range of molecular weights and concen-... 

Chemical gels, and perhaps physical gels also, show power-law frequency-dependences of the linear viscoelastic moduli G and G at the transition from sol to gel, and thus the spectrum can be characterized completely by a power law exponent n and a relaxation strength S, The constants n and S vary systematically with molecular weight of the prepolymer and with the ratio of prepolymer to cross-linker. 

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