Fourth-order nematic elasticity and modulated nematic phases: a poor man’s approach

ABSTRACT

We propose an extension of Frank-Oseen’s elastic energy for bulk nematic liquid crystals which is based on the hypothesis that the fundamental deformations allowed in nematic liquid crystals are splay, twist and bend. The extended elastic energy is a fourth-order form in the fundamental deformations. The existence of bulk spontaneous modulated or deformed nematic liquid crystal ground states is investigated. The analysis is limited to bulk nematic liquid crystals in the absence of limiting surfaces and/or external fields. The non deformed ground state is stable only when Frank-Oseen’s elastic constants are positive. In case where at least one of them is negative, the ground state becomes deformed. The analysis of the stability of the deformed states in the space of the elastic parameters allows to characterise different types of deformed nematic phases. Some of them are new nematic phases, for instance a twist – splay nematic phase is predicted. Inequalities between second-order elastic constants which govern the stability of the twist–bend, splay–bend, and splay–twist states are obtained. Their stability in respect to triple splay–bend–twist deformations is investigated.

Graphical Abstract

KEYWORDS:

• Elasticity
• achiral molecules
• twist-bend nematic
• splay-bend nematic
• splay-twist nematic
• splay-bend-twist nematic

Acknowledgements

GB was supported by the MEPhI Academic Excellence Project (agreement with the Ministry of Education and Science of the Russian Federation of 27 August 2013, project no. 02.a03.21.0005).

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by the Ministry of Education and Science of the Russian Federation [02.a03.21.0005].