Dynamics of a ±1/2 Defect Pair in a Confined Geometry

Abstract

This paper investigated the dynamics of a dipole of ± 1/2 parallel wedge disclination lines in a confined geometry, based on Landau-de Gennes theory. The behavior of the pair depends on the competition between two kinds of forces: the attractive force between the two defects, aggravating the annihilation process, and the anchoring forces coming from the substrates, inhibiting the annihilation process. There are three states when the system is equilibrium, divided by two critical thicknesses d c1 and d c2 (existing when r 0 ≤ 15 ξ , r 0 is the initial distance between the two defects), both changing linearly with r 0 . When the cell gap d ＞ d c1 , the two defects coalesce and annihilate. The dynamics follows the function of r ∝ ( t 0 -t ) α during the annihilation step when d is sufficiently large, relative to r 0 , where r is the relative distance between the pair and t 0 is the coalescence time. α decreases with the decrease of d or the increase of r 0 . The annihilation process has delicate structures: when r 0 ≤ 15 ξ and d ＞ d c2 or r 0 ＞ 15 ξ and d ＞ d c1 , the two defects annihilate and the system is uniaxial at equilibrium state; when r 0 ≤ 15 ξ and d c2 ＞ d ＞ d c1 , the two defects coalesce and annihilate, and the system is not uniaxial, but biaxial in the region where the defects collide. When d ≤ d c1 , the defects can be stable existence.