A kinetic theory and benchmark predictions for polymer-dispersed, semi-flexible macromolecular rods or platelets |
| |
Authors: | Jun LiMG Forest Qi Wang R Zhou |
| |
Institution: | a School of Mathematics, Nankai University, Tianjin, 300071, PR Chinab Department of Mathematics & Institute for Advanced Materials, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3250, United Statesc Department of Mathematics and NanoCenter, University of South Carolina, Columbia, SC 29208, United Statesd Department of Mathematics & Statistics, Old Dominion University, Norfork, VA 23529, United States |
| |
Abstract: | The goals of this paper are: to present a mean-field kinetic theory for the hydrodynamics of macromolecular high aspect ratio rods or platelets dispersed in a polymeric solvent; and, to apply the formalism to predict the impact due to a polymeric versus viscous solvent on the classical Onsager isotropic-nematic equilibrium phase diagram and on the monodomain response to imposed steady shear. The kinetic theory coupling between the nanoscale rods or platelets and the polymeric solvent is incorporated through a mean-field potential that reflects the enormous particle-polymer surface area and the particle-polymer interactions across this interfacial area. To determine predictions of this theory on the equilibrium and sheared monodomain phase diagrams, we present a reduction procedure which approximates the coupled Smoluchowski equations for the polymer chain probability distribution function (PDF) and the nano-particle orientational PDF in favor of a coupled system of equations for the rank 2 second-moment tensors for each PDF. The reduced model consists of an 11-dimensional dynamical system, which we solve using continuation software (AUTO) to predict the modified Onsager equilibrium phase diagram and the modified Doi-Hess shear phase diagram due to the physics of polymer-particle surface interactions. |
| |
Keywords: | Liquid crystal polymers Complex fluid mixtures Phase diagrams Kinetic theory |
本文献已被 ScienceDirect 等数据库收录! |
|