# Mechanisms to Splay-Bend Nematic Phases

## TL;DR

This paper explores theoretical mechanisms, flexoelectricity and bond orientational order, to explain the formation of two-dimensional splay-bend nematic phases, highlighting flexoelectricity as a viable explanation.

## Contribution

It demonstrates that flexoelectricity can induce splay-bend phases, while bond orientational order is unlikely due to symmetry and chirality constraints.

## Key findings

- Flexoelectricity can produce splay-bend phases with various modulations.
- Bond orientational order is ruled out as a basic mechanism due to symmetry considerations.
- Flexoelectric coupling is a viable mechanism for splay-bend phase formation.

## Abstract

While twist-bend nematic phases have been extensively studied, the experimental observation of two dimensional, oscillating splay-bend phases is recent. We consider two theoretical models that have been used to explain the formation of twist-bend phases -- flexoelectricity and bond orientational order -- as mechanisms to induce splay-bend phases. Flexoelectricity is a viable mechanism, and splay and bend flexoelectric couplings can lead to splay-bend phases with different modulations. We show that while bond orientational order circumvents the need for higher order terms in the free energy, the important role of nematic symmetry and phase chirality rules it out as a basic mechanism.