Abstract
We consider a shallow rectangular well of nematic liquid crystal subject to weak anchoring on the sides of the well. By considering weak anchoring instead of infinitely strong anchoring, we are able to analyze nematic equilibria in the well without the need to exclude point defects at the corners, as done in previous work in the area. For relatively weak anchoring, we are able to derive analytic expressions for the director alignment angle in terms of an infinite series of modes, involving roots of a transcendental equation. The analytic forms of the director configuration are then used to calculate critical anchoring strengths at which uniform and distorted director structures exchange stability. We also consider the asymptotic behavior of the director structure and energy for very strong anchoring. We show that in both cases-for the transitions from uniform to distorted states and the limit of infinitely strong anchoring-the approximate analytic expansions agree very well with corresponding numerical calculations of the full model.
Highlights
Liquid crystals are liquids in which there is some degree of orientational ordering of the constituent molecules
These molecules, often elongated organic compounds, arrange in such a way that an average orientation of one of the principle molecular axes may be defined [1]. This average molecular orientation is termed the director and is denoted mathematically by the unit vector n(x, t), an orientation that may vary in both space and time [2]
One alternative mathematical description uses both the average molecular orientation and a measure of the order about that average orientation, the general form of which leads to an analysis in terms of a second-order tensor Q, termed the orientation tensor or the Q tensor [3]
Summary
Liquid crystals are liquids in which there is some degree of orientational ordering of the constituent molecules. We consider a shallow rectangular well of nematic liquid crystal, but instead of imposing infinite planar anchoring on the boundaries of the well, we introduce weak planar anchoring through a Rapini–Papoular [5] surface energy at each boundary. This allows us to carry out an analysis of the director configuration equilibria in the well without the need to exclude point defects at the corners of the rectangle, in other words, avoiding the problems faced in [20]. We show that the asymptotic expansions agree very well with numerical calculations
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