Nematic twist-bend phase in an external field

The response of the nematic twist-bend (N-TB) phase to an applied field can provide important insight into the structure of this liquid and may bring us closer to understanding mechanisms generating mirror symmetry breaking in a fluid of achiral molecules. Here we investigate theoretically how an external uniform field can affect structural properties and the stability of N-TB. Assuming that the driving force responsible for the formation of this phase is packing entropy, we show, within Landau-de Gennes theory, that N-TB can undergo a rich sequence of structural changes with the field. For the systems with positive anisotropy of permittivity, we first observe a decrease of the tilt angle of N-TB until it transforms through a field-induced phase transition to the ordinary prolate uniaxial nematic phase (N). Then, at very high fields, this nematic phase develops polarization perpendicular to the field (Np+). For systems with negative anisotropy of permittivity, the results reveal new modulated structures. Even an infinitesimally small field transforms N-TB to its elliptical counterpart (N-TBe), where the circular base of the cone of the main director becomes elliptic. With stronger fields, the ellipse degenerates to a line, giving rise to a nonchiral periodic structure, the nematic splay-bend (N-SB), where the two nematic directors are restricted to a plane. The three structures-N-TB, N-TBe, and N-SB-with a modulated polar order are globally nonpolar. But further increase of the field induces phase transitions into globally polar structures with nonvanishing polarization along the field's direction. We found two such structures, one of which is a polar and chiral modification of N-SB, where splay and bend deformations are accompanied by weak twist deformations (N*(SBp)). Further increase of the field unwinds this structure into a polar nematic (Np-) of polarization parallel to the field.