title: Elastic continuum theory: towards understanding of the twist-bend nematic phases.
abstract: The twist-bend nematic phase, N_{TB}, may be viewed as a heliconical molecular arrangement in which the director n precesses uniformly about an extra director field, 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}. In the framework of the model, the phase transition between the usual and the twist-bend nematic phase is of second order with a finite wave vector. The model does not require a negative K_{33} in agreement with recent experimental data that yield K_{33}>0. A threshold is predicted for the molecular twist power below which no transition to a twist-bend nematic may occur.
authors.affiliation: Department of Applied Science and Technology, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.
authors.forename: G
authors.initials: G
authors.lastname: Barbero
authors.affiliation: Departamento de Física, Universidade Estadual de Maringá, Avenida Colombo, 5790-87020-900 Maringá, Paraná, Brazil.
authors.forename: L R
authors.initials: LR
authors.lastname: Evangelista
authors.affiliation: Departamento de Física, Universidade Estadual de Maringá, Avenida Colombo, 5790-87020-900 Maringá, Paraná, Brazil.
authors.forename: M P
authors.initials: MP
authors.lastname: Rosseto
authors.affiliation: Universidade Tecnológica Federal do Paraná, Campus Apucarana, Rua Marcílio Dias 635, 86812-460 Apucarana, Paraná, Brazil.
authors.forename: R S
authors.initials: RS
authors.lastname: Zola
authors.affiliation: Solid State Section, Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 157 84, Greece.
authors.forename: I
authors.initials: I
authors.lastname: Lelidis