Defect Nucleation and Annihilation in Sheared Polymeric Liquid Crystals
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Defect Nucleation and Annihilation in Sheared Polymeric Liquid Crystals
Dana Grecov and Alejandro D. Rey Department of Chemical Engineering, McGill University, 3610 University Street, Montreal, Quebec, Canada H3A 2B2 ABSTRACT Shear–induced nucleation and annihilation of topological defects due to hydrodynamic instability in nematic liquid crystals is a phenomenon of both scientific interest and practical importance. We use a complete generalized non-linear second order tensor Landau-de Gennes model that takes into account short range order elasticity, long-range elasticity and viscous effects, to simulate the nucleation and annihilation of twist inversion walls in flow-aligning nematic polymers subjected to shear flow. Shearing a homogeneous nematic sample perpendicular to the director results in an linear instability that maybe symmetric at low shear rates, and antisymmetric at higher shear rates. At even higher shear rates the onset of nonlinearities results in the nucleation of a parallel array of twist inversion walls, such that asymmetry prevails. By increasing the shear rate the following director symmetry transition cascade is observed: symmetric antisymmetric asymmetric symmetric. The nucleation of the parallel array of twist inversion walls in the asymmetric mode is due to the degeneracy in reorientation towards the shear plane. The annihilation of twist walls is mediated by twist waves along the velocity gradient direction. Twist walls annihilate by three mechanisms: wall-wall annihilations, wallwall coalescence, and wall-bounding surface coalescence. The annihilation rate increases with increasing shear rate and at sufficiently high rates the layered structure is replaced by a homogeneously aligned system. The role of short range and long range elasticity on defect nucleation and annihilation is characterized in terms of the Deborah and Ericksen numbers. Close form solutions to approximated equations are used to explain the numerical results of the full Landau-de Gennes equations of nematodynamics.
INTRODUCTION Liquid crystalline materials have a wide range of technological applications such as as electro-optical displays (low molar mass liquid crystals) and high performance fibers (polymeric liquid crystals). Further improvements in the current understanding of their rheological behaviour is essential since a significant number of product and processing properties depend to a large extent on flow-induced orientation. The distinguishing features of the mechanical behavior can be summarized by stating that LC materials exhibit anisotropic, non-linear, viscoelastic behavior quite distinct from Newtonian viscous materials and from viscoelastic polymers. These differences arise because liquid crystals display various degrees of orientational order and because their elasticity has short and long range contributions, the latter arising from spatial gradients of the orientational order. A very well established mesoscopic model for liquid crystalline materials is based on the Landau-de Gennes f
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