Monte Carlo simulation of self-avoiding lattice chains subject to simple shear flow. I. Model and simulation algorithm

Abstract

The efficient on-lattice Monte Carlo(MC) method is extended to simulate, for the first time, the simple shear flow of multiple macromolecular chains with self-avoiding walk (SAW) on a molecular level by introducing a pseudopotential to describe the flow field. This pseudopotential makes sense only for the potential difference associated with each local microrelaxational movement of a bead in the chain strictly defined by the four-site lattice model and bond fluctuation approach. The free-draining bead-spring model is thus investigated at low and high shear rates, and the resultant shear stress and first normal stress difference are obtained by statistics according to the sampled configurational distributions under flow. As the first paper of a corresponding series, the pseudopotential is checked in detail and confirmed by the simulation outputs for both a single SAW chain and multiple SAW chains in two dimensions. The simulated velocity profile is found to greatly satisfy the requirement of the simple shear flow unless the shear rate is unreasonably high. The material functions (apparent viscosity and first normal stress coefficient) show the shear-rate dependence at high shear rate, which is, in turn, explained by the large chain deformation on the microscopic origin. Both Newtonian regime and non-Newtonian regime are found in our on-lattice MC simulation. The nonlinear rheological behaviors at high shear rates revealed in this MC simulation agree with the experimental observations in literature for most polymers. On the other hand, the asymptotic behavior about the chain-length dependence of zero-shear viscosity can be reasonably explained by the present linear viscoelastic theory. Consequently, this paper puts forward a novel and unified simulation approach to study the chain conformation and chain dynamics under shear flow and the nonlinear viscoelasticity of polymeric fluids for both dilute and concentrated solutions or polymer melts.