Elastic continuum theory: Fully understanding of the twist-bend nematic phases

TL;DR

This paper develops an elastic continuum theory to fully understand the twist-bend nematic phase, predicting phase transition behavior and nanoscale pitch consistent with experimental observations.

Contribution

It introduces a symmetry-based elastic energy model for the twist-bend nematic phase, revealing its stability and phase transition characteristics.

Findings

Identifies the elastic parameters governing the phase stability.

Predicts a second order phase transition driven by a new elastic parameter.

Matches the predicted nanoscale pitch with experimental data.

Abstract

The twist-bend nematic phase, $N_{\rm TB}$, may be viewed as a heliconical molecular arrangement in which the director $\bf n$ precesses uniformly about an extra director field, $\bf t$. It corresponds to a nematic ground state exhibiting nanoscale periodic modulation. To demonstrate the stability of this phase from the elastic point of view, a natural extension of the Frank elastic energy density is proposed. The elastic energy density is built in terms of the elements of symmetry of the new phase in which intervene the components of these director fields together with the usual Cartesian tensors. It is shown that the ground state corresponds to a deformed state for which $K_{22} > K_{33}$. When the elastic free energy is interpreted in analogy with the Landau theory, it is demonstrated the existence of a second order phase transition between the usual and the twist-bend nematic phase, driven by a new elastic parameter playing a role similar to the one of the main dielectric anisotropy of classical nematics and being closely related to the bulk compression modulus representing the pseudo-layers of twist-bend nematic phases. A phase transition and the value of the nanoscale pitch are predicted in accordance to experimental results.