DYNAMICALPHENOMENA INLIQUID-CRYSTALLINEMATERIALS

Abstract

▪ Abstract Recent progress in modeling and simulation of the flow of nematic liquid crystals is presented. The Leslie-Ericksen (LE) theory has been successful in elucidating the flow of low molar-mass nematics. The theoretical framework for the flow of polymeric nematic liquid crystals is still evolving; extensions of the Doi theory capture qualitative features of the flow of polymeric nematics in simple geometries, but these theories have not been shown to predict texture development in flow. Mesoscopic theories for textured materials based on spatial averaging capture only some qualitative features of nonrectilinear liquid-crystalline polymer flow. Interfacial effects in liquid-crystalline systems have begun to receive attention in the context of interfacial viscoelasticity and the dynamics of dispersed liquid-crystalline polymers in immiscible blends.

Linear viscoelasticity of textured carbonaceous mesophases

“…The elastic free energy density, F d, a nematic uniaxial liquid crystal material is given by: [5][6][7] (1)…”

“…For incompressible isothermal conditions the general conservation of linear and angular momentum are given by the follows equations: [5][6][7] (2) (3) where ρ is the density, v is the velocity vector, f is the body force per unit volume vector, σ σ σ σ σ is the total stress, ρ 1 is the moment of inertia per unit volume, G is the external director body force vector, g is the intrinsic director body force vector, and π π π π π is the director stress tensor. The following constitutive equations for the stress tensor and the director body force that describes anisotropic liquids was found using transversely isotropic tensor coefficients, which reflect the material symmetry: [5][6][7] (4) (5) (6) where, (7a,b,c) (8a,b,c) p is the pressure, I is the unit tensor, {α i : i=1, 2, 3, 4, 5, and 6}, are the Leslie viscosity coefficients that describes an anisotropic liquid, A is the rate of deformation tensor, N is the corotational derivative of the director vector, β β β β β is an arbitrary vector, "a" is an arbitrary scalar used to constrain the director (n) to be a unit vector, F d is the elastic free energy density known as Frank elasticity, γ 1 is the rotational viscosity, γ 2 is the irrotational torque coefficient, W is the vorticity tensor, and λ is the reactive parameter.…”

“…The theory most widely used to describe liquid crystalline system is that of EricksenLeslie, in which mass and linear momentum balance are coupled to angular momentum balance. [5][6][7] The latter is basically a torque balance in which viscous torques are balanced by elastic torques. The torque balance equation describes the spatio-temporal evolution of the average molecular orientation under the action of externally imposed flow fields.…”

“…[5][6][7] These materials are also elastic, such that spatial gradients of the average molecular orientation increases the energy. The three basic elastic storage modes for discotic nematics are splay, twist, and bend, and are shown in Figure 2.…”

“…The three basic elastic storage modes for discotic nematics are splay, twist, and bend, and are shown in Figure 2. [5][6][7] Therefore, any imposed processing flow creates through the balance between flow-induced orientation and elastic torques a unique texture that is defined by spatial characteristics of the director field such as orientation gradients, boundary layers, topological defects, and defect networks. The characterization and identification of liquid crystallinity is evaluated by polarized optical microscopy, since different textures correspond to different optical outputs.…”