Molecular shape, elastic constants and spontaneous twist in chiral and achiral nematics: insights from a generalised Maier–Saupe framework

ABSTRACT

Ordinary nematic liquid crystals have a uniform director field as ground state. However, there are relevant examples of spontaneously twisted nematic states, not only in chiral, but also in achiral materials. Different twist configurations can be found, with the director modulation along the twist axis, as in the cholesteric and in the twist-bend nematic phase, or perpendicular to it, as in blue phases and in skyrmion structures. Here, we develop a generalised Maier–Saupe theory to calculate the thermodynamic and elastic properties, included saddle-splay, of nematics made of particles whose shape can be described as a distorted rod. This turns out to be a powerful approach for screening the relation between the molecular shape and the formation of modulated nematic phases. Application to the paradigmatic models of banana-shaped and helical particles allows us to identify the role of distinct shape features, such as curvature and chirality, and the distinct mechanisms by which these promote twisted configurations.

GRAPHICAL ABSTRACT

KEYWORDS:

• Cholesteric
• twist-bend
• Maier-Saupe theory
• bent molecules
• molecular chirality
• reflection symmetry breaking

Acknowledgements

We acknowledge the CAPRI initiative (Calcolo ad Alte Prestazioni per la Ricerca e l’Innovazione, University of Padova Strategic Research Infrastructure Grant 2017) for HPC resources.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Notes

1. Different definitions of the saddle-splay contribution to the free energy density can be found in the literature [3–7], therefore attention must be paid when comparing numerical values from different sources.

2. Here molecules must be intended in general terms as the microscopic constituents of the systems, which may be low molar mass molecules, macromolecules and colloidal particles.

3. We call first, second and third the eigenvector associated with the eigenvalue having the largest, the intermediate and the smallest absolute value, respectively.

4. In other works [52,53] a negative sign is included in the definition of the chiral strength, $k_2^{\prime }=-k_2$, therefore the equilibrium wavenumber is obtained as $q_0=-k_2^{\prime }/K_{22}$.

5. It may be worth mentioning that in Ref. [53] a hypothetical twist-bend phase was investigated, characterised by the heliconical organisation of the (uniaxial) director of the longitudinal axes of helices. This phase is different from what is commonly denoted as the twist-bend nematic phase and was found to be unstable with respect to the cholesteric.