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

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.