Shear-induced textural transitions in flow-aligning liquid crystal polymers

The equations of nematodynamics are formulated, solved, and used to model textural transformations in sheared thermotropic flow-aligning nematic polymers. The solutions are classified and characterized using analytical, scaling, and numerical methods. It is found that as the shear rate increases, the pathway between an oriented nonplanar state and an oriented planar state is through texture formation and coarsening. The two shear-rate dependent dimensionless numbers that control the texture formation and coarsening process are Ericksen Er and Deborah De numbers. The emergence of texture is independent of the Deborah number, and occurs at Er=10⁴. As the shear rate increases and Er>10⁴ the first texture that arises is a defect lattice. Further increases of the shear rate bring De close to 1, ignite the coarsening processes, and replace the defect lattice with a defect gas. The smallest texture length scale lₜ occurs at the defect lattice-defect gas transition. In the defect lattice regime the texture length scale decreases with increasing shear rate as lₜ∝( ̇ \.γ-a)^-1/2, while in the defect gas regime it increases as ${l}ₜ{∝}({ ̇ \.{}{}}{{γ}}{-}b√{({ ̇ \.{}{}}{{γ}}{-}a)}{-}c{)}^{{-}1}.$ Finally when $De>2,$ an oriented monodomain state emerges, and the texture vanishes since coarsening overpowers defect nucleation. It is found that the texture transition cascade $unorientedmonodomain{⇒}defectlattice{⇒}defectgas{⇒}orientedmonodomain$ is remarkably consistent with the experimentally observed textural transitions of sheared lyotropic nematic polymers.