Analogy between the twist-bend nematic and the smectic A phases and coarse-grained description of the macroscopic N_TB properties

ABSTRACT

The twist-bend nematic, N_TB, has unusual elastic properties. Contrary to the usual nematic, the N_TB director n is spontaneously distorted, resulting in a heliconical structure with small period and doubly degenerate handedness. Different models have been proposed so far, and are still actively debated, to describe the N_TB properties on the microscopic scale. On the macroscopic scale, we propose a symmetry-based analogy between the N_TB and the SmA* phases. Introducing a complex order parameter, we write the macroscopic N_TB energy by analogy with the de Gennes’ SmA* description. By coarse graining, based on the elastic-instability local model, we calculate the macroscopic elastic constants and characteristic lengths in terms of a few Frank-like elastic coefficients. We discuss the inverse elastic anisotropy of the N_TB phase, compared with the SmA*, and its impact on the structure of the N_TB defects. We extend the coarse-grained (CG) model to investigate the macroscopic response to electric fields, and the surface anchoring alignment and the microscopic distortions of the N_TB phase. Finally, we suggest the existence of a N_TB analogue of the twist grain boundary phase TGB_A, with a penetration of the twist field in the bulk through a network of screw dislocations of the N_TB pseudo-layers.

GRAPHICAL ABSTRACT

KEYWORDS:

• Twist-bend nematic
• smectic A analogy
• coarse-grained theory
• TGB phase

Acknowledgements

We acknowledge fruitful discussions with Geoffrey R. Luckhurst and Patrick Davidson and a financial support by the grant ANR-15-CE24-0012BESTNEMATICS of Agence Nationale de la Recherche, France.

Additional information

Funding

This work has been financially supported by the Agence Nationale de la Recherche, France [Grant Number ANR-15-CE24-0012BESTNEMATICS].