Self-Consistent-Field Theory of Viscoelastic Behavior of Inhomogeneous Dense Polymer Systems

By combining the self-consistent-field (SCF) model and a reptation model, we propose a unified molecular model to explicitly account for dynamics of chain conformation in studying fast polymeric fluid flows in which the polymer chains can be severely stretched and the fluid can even become inhomogeneous. In the governing equations of the unified model, we directly couple the probability distribution function P(u;s,r) of the tangent vector u ≡ dR(s)/ds at the sth segment at position r, with the statistical weight, Q(s,r;s′,r′), of the subchain between sth and s′th segments at the positions of r and r′, respectively. The polymeric stress responses under flow condition can be readily calculated from the second moment of P(u;s,r), A(s,r) ≡ 〈≡〉 ≡ ∫uuP(u;s,r) du. The model was first validated in homogeneous simple shear flow. The quantitative agreements between the polymeric stresses evaluated by this novel method and the results of the reptation theory have been found. The model was then tested in a case study of grafted polymer melt brushes under strong shear flow. Our results demonstrate that the unified model provides a very promising way for modeling highly nonlinear polymer fluid flow, and it can also overcome the difficulty of the standard SCF technique when it is applied to highly nonequilibrium systems.