Primitive chain network simulation of elongational flows of entangled linear chains: Role of finite chain extensibility

摘要

For entangled linear monodisperse polymers, uniaxial elongational flow behavior was examined with the primitive chain network (PCN) simulation, which was originally formulated for a network of Gaussian chains bound by sliplinks but was modified in this study to properly take into account the finite extensibility of actual chains. On an increase of the elongational rate ε? from the terminal relaxation frequency 1/τ_d (at equilibrium) to the Rouse relaxation frequency 1/τ_R, the original and modified simulations gave an indistinguishable steady state elongational viscosity η_E that almost scaled as ε?~(-1/2). On a further increase of ε? > 1/τ_R, η_E obtained from the original PCN simulation diverged to infinity (as noted also for the unentangled Rouse chains). In contrast, η_E deduced from the modified simulation increased but did not diverge with increasing ε? > 1/τ_R (similarly to the behavior of FENE dumbbells). This feature of the modified PCN simulation, i.e., hardening to a finite (nondiverging) level, mimicked the η_E data of entangled semidilute solutions, which naturally reflected the finite extensibility of actual chains. Analysis of the simulation results suggested that the power law behavior (η_E ～ ε?~(-1/2)) at 1/τ_d< ε? < 1/τ_R is related to reduction of the entanglement density and the corresponding reduction of chain tension, while the hardening (upturn of η_E at ε? > 1/τ_R) results from stretch of the chain (eventually approaching full stretch), thus shedding light on the behavior of semidilute solutions. Nevertheless, the modified simulation did not describe the behavior of entangled melts, i.e., η_E ～ ε?~(-1/2) even at ε? > 1/τ_R. A factor missing in the modified simulation is discussed in an attempt to elucidate, from a molecular point of view, the difference between entangled solutions and melts.