Molecular theory for moderately concentrated polymer solutions in shear flow

A molecular theory for the rheological properties of moderately concentrated polymer solutions is developed on the basis of a model of interacting dumbbells. The interaction is treated in a mean field approximation, leading to an effective one-particle potential and a Gaussian stationary distribution function. Various rheological functions such as birefringence, shear viscosity and first normal-stress coefficient for simple shear flow and the Trouton viscosity for simple extensional flow are calculated. Good qualitative agreement with experimental observations is found, especially at intermediate flow rates. It is predicted, for example, that the birefringence increases approximately linearly with shear rate at intermediate shear rates and that the concentration dependence of the gradient varies asc^1/2. The typical non-Newtonian behaviour is obtained for the shear viscosity. For small concentrations the onset of shear rate dependence decreases asc^–1/2. At intermediate shear rates an apparent power law is obtained with an exponent between – 0.5 and – 1.0, decreasing with concentration.