Temporal scaling ansatz for viscoelastic behavior

This section presents an ansatz that predicts functional forms for viscoelastic properties. The temporal scaling ansatz was originally applied to the loss modulus G (w)(3). Extensions treat the storage modulus G ( y) and shear thinning 

The approach here is fundamentally unlike some other approaches found in the literature. The ansatz does not reason from a molecular picture of a polymer solution. No assumption is made as to the nature of the dominant interactions 

Because the ansatz does not invoke a detailed molecular picture, its predictive powers are restricted. The approach yields the functional dependence of various viscoelastic parameters on frequency or shear rate. The price exacted for the simplicity of derivation is that the ansatz is fundamentally unable to predict numerical values for functional parameters, let alone predict the dependence of those parameters on solvent quality, polymer concentration, or molecular weight. The ansatz is thus substantially noncommunicating with treatments of polymer viscoelasticity that invoke detailed microscopic models of polymer dynamics, such as the models of Bird, etal.(4,5), Graessley(6,7), or Raspaud, etal. S). 

The five primary steps of the derivation are (1) extension of the renormalization group derivation of the hydrodynamic scaling model for Ds to treat the zero-shear viscosity t], (2) description of the experimental phenomenology of r] c), 

Equation 13.2, including numerical values for a and v, has been(lO) derived from a hydrodynamic scaling description via a positive-function renormalization 

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