Differential constitutive equations for polymer melts

A new mol. constitutive equation for a class of branched polymers was introduced by McLeish and Larson (J.Rheol. 42(1), 1998), the Pom-Pom model. Incorporating a Giesekus type of oriental diffusion in their differential form (which predicts zero N2) and writing it in a closed differential form for the stress tensor, results in a generalized differential constitutive equation. The nonlinear parameter related to the Giesekus part of the model accounts for a second normal stress difference. Linear parameters are fitted to data from dynamic measurements, and most of the nonlinear parameters to the transient uniaxial elongational data. It is demonstrated for different polymers that with this extended Pom-Pom model (EPP) a very good quant. agreement can be obtained over a wide range of well defined rheometric expts. for shear, uniaxial biaxial elongation, and reversed flow. This is exceptional and shows that the Pom-Pom model is a major step forwards in the field of viscoelastic constitutive equations