Semi-Dilute Dumbbells: Solutions of the Fokker–Planck Equation

Spring bead models are commonly used in the constitutive equations for polymer melts. One such model based on kinetic theory—the finitely extensible nonlinear elastic dumbbell incorporating a Peterlin closure approximation (FENE-P)—has previously been applied to study concentration-dependent anisotropy with inclusion of mean-field term account intermolecular forces dilute solutions background profiles weak shear and elongation. These investigations involved solution Fokker–Planck equation second moment. In this paper, we extend analysis include effects large elongation beyond Hookean regime. Further, is solved probability density function which permits computation any macroscopic variable, allowing direct comparison predictions molecular dynamics simulations. It was found that if concentration at equilibrium taken into account, FENE-P gives qualitatively correct predictions, although over-shoot extension infinitely case significantly underpredicted.