PHYSICAL REVIEW E 101, 012702 (2020) Coarse-grained model of the nematic twist-bend phase from a stable state elastic energy M. P. Rosseto and L. R. Evangelista Department of Physics, Universidade Estadual de Maringá, Avenida Colombo 5790, 87020-900 Maringá, Paraná, Brazil P. S. Simonário Department of Physics, Universidade Estadual de Maringá, Avenida Colombo 5790, 87020-900 Maringá, Paraná, Brazil and Department of Applied Mathematics, Universidade Estadual de Campinas, Rua Sérgio Buarque de Holanda 661, 13083-859 Campinas, São Paulo, Brazil R. S. Zola * Department of Physics, Universidade Estadual de Maringá, Avenida Colombo 5790, 87020-900, Maringá, Paraná, Brazil and Department of Physics, Universidade Tecnológica Federal do Paraná, Rua Marcílio Dias 635, 86812-460 Apucarana, Paraná, Brazil (Received 11 October 2019; published 3 January 2020) The twist-bend nematic (N TB ) phase is a doubly degenerated heliconical structure with nanometric pitch and spontaneous bend and twist deformations. It is favored by symmetry-breaking molecular structures, such as bent dimers and bent-core molecules, and it is currently one of the burgeoning fields of liquid-crystal research. Although tremendous advances have been reported in the past five years, especially in molecular synthesis, most of its potential applications are held back by the lack of a proper and definitive elastic model to describe its behavior under various situations such as confinement and applied field. In this work we use a recently proposed stable state elastic model and the fact that the mesophase behaves as a lamellar structure to propose a mesoscopic or coarse-grained model for the N TB phase. By means of standard procedures used for smectic and cholesteric liquid crystals, we arrive at a closed-form energy for the phase and apply it to a few situations of interest. The predicted compressibility for several values of the cone angle and the critical field for field-induced deformation agree well with recent experimental data. DOI: 10.1103/PhysRevE.101.012702 I. INTRODUCTION Despite having remarkable characteristics, such as spon- taneous twist and bend deformations, and presenting a dou- bly degenerated heliconical state with a nanometric pitch, the twist-bend nematic (N TB ) phase has drawn considerable attention not only for its unique features but also for the possibilities of new applications. From the experimental point of view, the existence of this mesophase has been reported in achiral bent dimers [1–6], trimers [7], rigid bent-core materials [8], and chiral dimers [9] and is quickly escalating to several other types of molecular shape that present some kind of bent structure [10]. A few publications have been dedicated to the probe and characterization of the mesophase [11–17] and also to the development of applications of the materials forming the N TB phase [18–21]. Many of the potential applications, however, lose their strength without a suitable model to describe the phase, espe- cially its elasticity. In fact, several of the recent studies still use the Frank energy and the corresponding elastic constants to describe or extrapolate their data. Although the N TB phase was first predicted theoretically years ago [22–24], the recently proposed models for the N TB elasticity are yet to prove their * Corresponding author: rzola@utfpr.edu.br strength. Among them, Frank- and Landau-like descriptions [25–29] and molecular approaches have been proposed [30], but a direct comparison of such models with experimental data has not been made. It has also been argued that flex- oelectricity is responsible for the N TB stability [31–33], but recent experimental evidence suggests flexoelectricity cannot explain, for example, the large compression modulus mea- sured [33]. On the other hand, due to the heliconical pitch (repeating itself structure), the N TB phase might be viewed as a pseudolayer medium [14,17]. It is therefore convenient to employ the coarse-graining method to model the mesophase in terms of pseudolayers’ deformations, which occur at length scales much larger than the pitch, rather than in terms of the molecular director. Challa et al. [14] used a smectic coarse-grained energy to interpret results of N TB subjected to a strong magnetic field. Meyer and Dozov [34,35] sug- gested that the N TB phase may be described as an effective chiral smectic-A phase. Parsouzi et al. [12] also presented a coarse-grained model which might be indirectly connected with the smectic-A phase. Shiyanovskii et al. [36], on the other hand, presented a coarse-grained energy that is derived from a nematic double-well potential, introducing the dependence on the cone angle, which does not occur in the smecticlike models. In this paper, we use the recently proposed energy [26] to derive its coarse-grained version for the N TB phase. The 2470-0045/2020/101(1)/012702(7) 012702-1 ©2020 American Physical Society