Nonlinear Stress Relaxation of Scarcely Entangled Chains in Primitive Chain Network Simulations

Abstract

Polymeric liquids exhibit a crossover from the nonentangled to entangled behavior on an increase of the molecular weight M. For example, it has been established that the zero-shear viscosity h0(M ) of non-entangled low-M chains is proportional to M as described by Rouse model, whereas h0(M ) of well-entangled high-M chains is proportional to M a with a = ~ 3.4. 2) Not only for the linear viscoelastic property, the crossover has been observed also for nonlinear viscoelasticity, specifically in the shear damping function h(g), where g is a magnitude of step shear strain. h(g ) is insensitive to M and close to the Doi-Edwards (DE) prediction for high-M chains. This universal damping behavior was classified by Osaki as the type-A behavior. In contrast, the g dependence of h(g) considerably weakens with decreasing M when M is below a critical value ~ 2Me (with Me being the entanglement molecular weight), as reported by Takatori et al. and Inoue et al. for polystyrene (PS) solutions and by Vega et al. for polystyrene (PS) melts. This weak damping was classified by Osaki as the type-B behavior. A couple of theoretical attempts has been made for explaining the origin of type-B damping behavior. Kapnistos et al. have reported a weak damping of h(g ) for scarcely entangled polymer deduced from their slip-spring model where a Rouse chain is confined in a tube shaped parabolic potential. The confinement is realized by some springs having one end anchored in space and the other end connected to the chain. The spring end connected to the chain slides along the chain backbone to mimic the entanglement. Kapnistos et al. reported that if the number of slip-springs on the chain, which reflects the number of entanglement per chain, is decreased, the strain dependence of h(g) is weakened. Since there is no damping in the limit of free Rouse chain, it is rather natural that the strain dependence of h(g ) becomes weaker when the number of springs on the chain becomes smaller. They discussed that their simulation results are consistent with those for comb polymers with a small number of backbonebackbone entanglements. Another explanation of the type-B behavior was given by Kharlamov et al. They derived the distribution function of the end-to-end vector of a whole chain Ree after the chain contraction along the primitive path, and then calculated the stress from the second moment of Nonlinear Stress Relaxation of Scarcely Entangled Chains in Primitive Chain Network Simulations