#### Document Type

Article

#### Publication Date

2005

#### DOI

10.1137/040618187

#### Publication Title

Multiscale Modeling and Simulation

#### Volume

4

#### Issue

4

#### Pages

1280-1304

#### Abstract

Nematic, or liquid crystalline, polymer (LCP) composites are composed of large aspect ratio rod-like or platelet macromolecules. This class of nanocomposites exhibits tremendous potential for high performance material applications, ranging across mechanical, electrical, piezoelectric, thermal, and barrier properties. Fibers made from nematic polymers have set synthetic materials performance standards for decades. The current target is to engineer multifunctional films and molded parts, for which processing flows are shear-dominated. Nematic polymer films inherit anisotropy from collective orientational distributions of the molecular constituents and develop heterogeneity on length scales that are, as yet, not well understood and thereby uncontrollable. Rigid LCPs in viscous solvents have a theoretical and computational foundation from which one can model parallel plate Couette cell experiments and explore anisotropic structure generation arising from nonequilibrium interactions between hydrodynamics, molecular short- and long-range elasticity, and confinement effects. Recent progress on the longwave limit of homogeneous nematic polymers in imposed simple shear and linear planar flows [R. G. Larson and H. Ottinger,* Macromolecules*, 24 (1991), pp. 6270-6282], [V. Faraoni, M. Grosso, S. Crescitelli, and P. L. Maffettone, *J. Rheol*., 43 (1999), pp. 829-843], [M. Grosso, R. Keunings, S. Crescitelli, and P. L. Maffettone, *Phys. Rev. Lett.* 86 (2001), pp. 3184-3187], [M. G. Forest, Q. Wang, and R. Zhou, *Rheol. Acta*, 43 (2004), pp. 17-37], [M. G. Forest, Q. Wang, and R. Zhou, *Rheol. Acta*, 44 (2004), pp. 80-93], [M. G. Forest, Q. Wang, R. Zhou, and E. Choate, *J. Non-Newtonian Fluid Mech*., 118 (2004), pp. 17-31], [M. G. Forest, R. Zhou, and Q. Wang, *Phys. Rev. Lett.*, 93 (2004), 088301] provides resolved kinetic simulations of the molecular orientational distribution. These results characterize anisotropy and dynamic attractors of sheared bulk domains and underscore limitations of mesoscopic models for orientation of the rigid rod or platelet ensembles. In this paper, we apply our resolved kinetic structure code [R. Zhou, M. G. Forest, and Q. Wang, *Multiscale Model. Simul*., 3 (2005), pp. 853-870] to model onset and saturation of heterogeneity in the orientational distribution by coupling a distortional elasticity potential (with distinct elasticity constants) and anchoring conditions in a plane Couette cell. For this initial study, the flow field is imposed and the orientational distribution is confined to the shear deformation plane, which affords comparison with seminal [T. Tsuji and A. D. Rey, *Phys. Rev. E* (3), 62 (2000), pp. 8141-8151] as well as our own mesoscopic model simulations [H. Zhou, M. G. Forest, and Q. Wang, *J. Non-Newtonian Fluid Mech*., submitted], [H. Zhou and M. G. Forest, *Discrete Contin. Dyn. Syst. Ser. B,* to appear]. Under these controlled conditions, we map out *the kinetic phase diagram of spatiotemporal attractors of a Couette cell film i*n the two-parameter space of Deborah number (normalized shear rate) and Ericksen number (relative strength of elasticity potentials). © 2005 Society for Industrial and Applied Mathematics.

#### Original Publication Citation

Forest, M. G., Zhou, R., & Wang, Q. (2005). Kinetic structure simulations of nematic polymers in plane couette cells. II: In-plane structure transitions. *Multiscale Modeling and Simulation, 4(*4), 1280-1304. doi:10.1137/040618187

#### Repository Citation

Forest, M. Gregory; Zhou, Ruhai; and Wang, Qi, "Kinetic Structure Simulations of Nematic Polymers in Plane Couette Cells. II: In-plane structure transitions" (2005). *Mathematics & Statistics Faculty Publications*. 13.

http://digitalcommons.odu.edu/mathstat_fac_pubs/13