Generalised technique for calculation of plane director profiles in bounded nematic liquid crystals

ABSTRACT

We propose an improved conformal mapping technique for analytical calculation of two-dimensional profiles of the nematic liquid crystal (NLC) director in a cell with a simply connected cross-sectional region. We consider the case of the strong anchoring and the piecewise constant director pretilt on the piecewise smooth curve which bounds the region. Obtained expressions for the director profile explicitly depend on the conformal mapping which maps the region onto the upper half plane of a complex plane. An advantage of our method in comparison with the standard conformal mapping technique is that it does not require the knowledge of the inverse mapping and the calculation of the integral in the Poisson formula. Proposed technique allows to take into account topological defects in the bulk of the NLC on the symmetry axis of the region. As an example of how the method can be used, we find an analytical expression for the director profile in a horizontal cylindrical groove partly filled with the NLC. We consider the case where a disclination line parallel to the axis of the groove occurs in the bulk of the NLC. The equilibrium position of the disclination line is found.

Graphical Abstract

KEYWORDS:

• Nematic liquid crystals
• conformal mapping technique
• topological defects
• cylindrical groove

Disclosure statement

No potential conflict of interest was reported by the authors.