The molecular stress function (MSF) model in rheology

Abstract

The molecular stress function (MSF) model is an integral constitutive equation introduced more than two decades ago. It is based on the time-deformation separability principle. The time contribution encloses the linear viscoelastic information, which can be provided by the phenomenological models or any molecular theory. The deformation contribution is defined in the MSF model as a strain measure describing the orientation and the stretch of the strands of the chain as independent processes. The orientation is described by the second-order tensor of the Doi-Edwards model, considering the independent alignment assumption. The stretch is taken into account by the molecular stress function, the main characteristic being that it is included inside the integral and it is the solution of an evolution equation. Since its proposal, the MSF model has been used to describe quantitatively the non-linear rheology of a broad variety of materials such as rubbers, linear and long-chain branched polymer melts and blends of polydisperse samples relevant to the industry. Nearly, monodisperse systems in solution and melt states have also been studied in samples with different structures like linear, bidisperse blends with linear components, combs and pom-pom molecules. Predictions have been obtained for a variety of deformations like uniaxial, equibiaxial and planar extensional flow as well as for steady, medium and large amplitude oscillatory and exponential shear flow. The quantitative description of polymer melts in transient elongation is crucial for numerical simulations. Therefore, the MSF model has been applied to perform finite element simulations for different processes and freesurface deformations, due to its flexibility, reliability and reduced number of material parameters. The integral constitutive equation and its physical interpretation remains the same since it was first published. The evolution equation of the molecular stress function is material dependent because it considers different molecular mechanisms occurring in different structures. Given its importance to rheology, it is the objective of this contribution to review the antecedents, physical basis and applications of the MSF model.