Surface anchoring energy of cholesteric liquid crystals

ABSTRACT

In this paper, we propose a suitable surface energy expression for cholesteric liquid crystals. We show that there exists a symmetry allowed term for chiral nematics that doesn’t appear in the traditional Rapini-Papoular surface energy form. We discuss some consequences of this new surface anchoring term.

KEYWORDS:

• Surface anchoring
• cholesteric liquid crystal
• symmetry
• chirality

Acknowledgments

Subsequent to this work, we became aware of a similar result by E.C. Gartland [5].

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. Totalitariansm has been adopted as a principle of physics; according to Gell-Mann ‘Everything not forbidden is compulsory.’ [6].

2. There is an additional higher-order term on $\mathbf{N}$, which is symmetry allowed and reads as, $\frac{1}{2}{q}_0{W}_{c2}{\epsilon }_{\alpha \beta \gamma }{Q}_{\mu \beta }{N}_{\mu }{N}_{\gamma }{N}_{\nu }{Q}_{\nu \alpha }^0$. In the uniaxial case, it is in the form of $\frac{1}{2}{q}_0{W}_{c2}{\stackrel{\mathbf{ˆ}}{\mathbf{n}}}^0\cdot (\stackrel{\mathbf{ˆ}}{\mathbf{N}}\times \stackrel{\mathbf{ˆ}}{\mathbf{n}})(\stackrel{\mathbf{ˆ}}{\mathbf{n}}\cdot \stackrel{\mathbf{ˆ}}{\mathbf{N}})({\stackrel{\mathbf{ˆ}}{\mathbf{n}}}^{\mathbf{0}}\cdot \stackrel{\mathbf{ˆ}}{\mathbf{N}})$. The existence of this term was pointed out to us by Jamie Taylor, after we posted the article on arXiv.

Additional information

Funding

This work was supported by the Office of Naval Research [ONR N00014-18-1-2624].