Twist–Bend Nematic Phase from the Landau–de Gennes Perspective

Abstract

Generalized Landau–de Gennes theory is proposed that comprehensively explains currently available experimental data for the heliconical twist–bend nematic (NTB) phase observed in liquid crystalline systems of chemically achiral bent-core-like molecules. A bifurcation analysis gives insight into possible structures that the model can predict and guides in the numerical analysis of relative stability of the isotropic (I), uniaxial nematic (NU), and twist–bend nematic phases. An estimate of constitutive parameters of the model from temperature variation of the nematic order parameter and the Frank elastic constants in the nematic phase enables us to demonstrate quantitative agreement between the calculated and experimentally determined temperature dependence of the pitch and conical angle in NTB. Properties of order parameters also explain a puzzling lack of a half-pitch band in resonant soft X-ray scattering. Other key findings of the model are predictions of I–NTB and NU–NTB tricritical points and insight into biaxiality of NTB.

In silico study of liquid crystalline phases formed by bent-shaped molecules with excluded-volume type interactions

“…As pointed by Shamid et al 58 , the effective K 33 constant can become negative below a certain critical temperature, when the coupling of polarization with bend deformation is introduced, supporting the assumption that N TB is inherently polar. The phase can be also understood via geometrical reasoning 15,16,26,64 . For curved spherocylinders, one can predict a correct relation between molecule bend angle, pitch p and conical angle θ matching the spherocylinder curvature with an integral curve of a director field n 42 .…”

“…All this makes LCs formed by BSMs, per se, a riveting field to explore both from experimental and theoretical points of view 15,16,18,[22][23][24][25][26] . In particular, substantial efforts were undertaken to decipher how the molecule's structure influences the emergence of individual mesophases 21,27,28 .…”

On the effect of capillarity and polarity in colloidal suspensions of nanoparticles

“…We show that the N SB phase has a periodic spatially modulating S(z). By contrast with existing LdG theories for thermotropics [54,135,138,167], our theory provides a natural coupling between orientational and positional order. The spatially modulated scalar order parameter S in the N SB phase thus yields a one-dimensional density modulation, such that the N SB phase has actually the key characteristics of a smectic rather than a nematic phase.…”

“…In this Chapter we have employed the LdG theory introduced in Chapter 4 of this thesis for lyotropic colloidal suspensions of bent rods, to investigate the effect of spatial distortions in the nematic director field on the density of the twist-bend and splay-bend nematic phases. In contrast with the existing Oseen-Frank theories [50,51,53], our theory allows us to analyze the spatial dependence of the nematic order parameter S, in addition to that of the nematic director field n. Moreover, by contrast with LdG theories for thermotropic liquid crystals [54,135,138,167], our theory provides a natural coupling between S and the particle density ρ. We show that the N SB phase is characterized by a spatially modulated S(z), and hence by a onedimensional density modulation ρ(z).…”

“…The nematic order parameter S is not involved in the Oseen-Frank theories of Dozov [51] and Selinger [53], while it has been assumed spatially constant in LdG theories for thermotropics [138,167]. Analogously we have assumed S spatially constant in Chapter 4.…”