POLYFLOW - Validity of Cox-Merz and Gleissle empirical rules?
For some polymers, it is possible to extract non-linear viscosity data from linear measurements or from transient measurements at low shear rate. For this, we respectively apply the Cox-Merz and Gleissle empirical rules. To what extend are they valid?
Since these rules are empirical, they are not proven from theory. They are however observed for several materials. A typical example here shows the validity from the point of view of the model. For this, a six-mode viscoelastic model is considered, for which the parameters are available in a paper by B. Debbaut and H. Burhin, J. Rheol., 46/5 (2002) 1155-1176.
The attached figure Cox_Merz.jpg shows the linear properties of the model, together with the actual shear viscosity and the modulus of the complex viscosity obtained by applying the Cox-Merz rule.
The attached figure Gleissle.jpg shows transient viscosity curves vs. time, calculated for various shear rates. The figure also shows the actual steady shear viscosity and modulus of complex viscosity, respectively vs. the reciprocal shear rate and the reciprocal frequency.
The present figures show a good agreement, which may be typical for polyolefins. The comparison will not always work that fine; this depends on the melt.