Selection rules and a new model for stable topological defect arrays in nematic liquid crystal

Jieh-Wen Tsung^1*, Ya-Zi Wang¹, Sheng-Kai Yao¹, Shih-Yu Chao¹

¹Department of Electrophysics, National Yang Ming Chiao Tung University, Hsinchu, Taiwan

* Presenter:Jieh-Wen Tsung, email:jiehwen.tsung@nycu.edu.tw

Creation of a topological defect array in liquid crystals has been a notable focus in recent years, because the defect array can be utilized as precision optics, templates of self-assembled microstructures, and elastomer actuators. So far, the defect arrays are created intuitively by trial and error. Systematic rules to arrange defects into stable long-ranged arrays are in demand. A new model of two-dimensional square and hexagonal defect array was developed based on experimental results. Two-dimensional defect arrays with various lattice structures (square and hexagonal), various defect shapes (radial or circular) and various lattice constants (pixel size) are generated by pixelated patterned electrodes in home­otropic nematic liquid crystal (NLC) cells. Orientation of NLC around a topological defect is expressed by the equation, ψ= sφ+φ₀ , where ψ, s, φ and φ₀ are the director spatial phase, topological charge, azimuthal angle and a spatial phase shift, respectively. The results verify the two selection rules, 1) The total s must be zero, 2) φ₀ must be a constant throughout the array, and a new model is established. The model is generalized for defect crystals and quasicrystals. A crystal is the periodic repetition of a unit cell. A stable defect crystal must have minimum free energy, and the arrangement of the defects must obey the topological conservation laws. By solving the Euler–Lagrange equation of the director field of a unit cell and by integrating the topological rules into the boundary conditions, the director field of a defect crystal can be easily obtained. A large variety of defect crystals and quasicrystals are derived. The lattices are rectangular, triangular, square, pentagonal, and hexagonal. The defects can be either radial or vortex-like. The nematic and vector orders are both considered. The collection of defect crystals is presented as a catalog. The suggested cell structure and switching modes are summarized.

Keywords: topological defect, nematic liquid crystal, long-range order