Order reconstruction in inverse twisted nematic cell with an applied electric field

Order reconstruction in an inverse twisted nematic (ITN) liquid crystal cell with an applied electric field is investigated based on Landau–de Gennes theory and the two-dimensional finite-difference iterative method. Twice eigenvalue exchange in three-axis layer configuration, thrice eigenvalue exchange in four-axis layer configuration, and negative order parameter uniaxial twisted state exist in this cell, which can be described by the order parameter tensor Q in equilibrium state. The twice eigenvalue exchange also has two degenerate configurations with reduced electric field E from 0.8 to 2.8 in 10ξ cell (ξ is the biaxial correlation length). Moreover, two critical cell gaps d c ⁎ ⁎ = 7 ξ and d c ⁎ = 12 ξ are included in the study of the ITN cell. When d ≤ d c ⁎ ⁎ , only the eigenvalue change state exists. When d ≥ d c ⁎ , only a positive order parameter uniaxial twisted state exists near the threshold electric field. When d c ⁎ ⁎ d d c ⁎ , a negative order parameter uniaxial twisted state exists near the threshold electric field. Comparison of the eigenvalue exchange solutions of different cell gaps of 5ξ, 10ξ, and 20ξ shows that smaller cell gap can inhibit the complexity of the eigenvalue exchange solution and reduce the number of axis layers. This research provides a theoretical basis for the change of multi-axis layer defect and promotes the concept of eigenvalue exchange.