How can a change in molecular structure affect the relative stability and structural properties of the twist-bend nematic phase (N_TB)? Here we extend the mean-field model¹ (C. Greco, G. R. Luckhurst and A. Ferrarini, Soft Matter, 2014, 10, 9318) for bent-shaped achiral molecules, to study the influence of arm molecular biaxiality and the value of the molecule's bend angle on the relative stability of N_TB. In particular we show that by controlling the biaxiality of the molecule's arms, up to four ordered phases can become stable. They involve local uniaxial and biaxial variants of N_TB, together with uniaxial and biaxial nematic phases. However, a V-shaped molecule shows a stronger ability to form stable N_TB than a biaxial nematic phase, where the latter phase appears in the phase diagram only for bend angles greater than 140° and for large biaxiality of the two arms.

A generalized Landau-de Gennes theory is proposed that comprehensively explains currently available experimental data for the heliconical twist-bend nematic (N_TB) 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 (N_U) 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 to demonstrate quantitative agreement between the calculated and experimentally determined temperature dependence of the pitch and conical angle in N_TB. Properties of order parameters also explain a puzzling lack of half-pitch band in resonant soft X-ray scattering. Another key findings of the model are predictions of I - N_TB and N_U - N_TB tricritical points and insight into biaxiality of N_TB.

One of the interesting questions related to bent-shaped materials is how structural chirality of the twist-bend nematic ( ) phase can respond to the presence of molecular chirality, with later being introduced through chiral centers incorporated in the molecules or chiral dopants. We study this problem using minimal coupling Landau-de Gennes theory of , supplemented by a term representing intrinsic molecular chirality. Relative stability and properties of cholesteric ( ), chiral twist-bend nematic with heliconical structure ( ), and other homogeneous phases are studied. Besides nematic, chiral twist-bend nematic and cholesteric phases of vanishing global polarization, we find their polar analogues. In particular, a coupling between molecular chirality, alignment tensor and polarization fields can promote a globally polar and chiral twist-bend nematic ( ) with period comparable to that of .

What are the prerequisites for acquiring a stable twist-bend nematic phase (N_TB)? Addressing this question has led to the synthesis of a vast number of new compounds, concluding each time that the molecule's shape is one of the predominant factors. Inspired by the expanding knowledge of different achiral bent-shaped molecules forming a twist-bend nematic phase, we reinvestigate the interplay between a molecule's bend angle and a molecule's arms molecular biaxiality. Employing our previously developed generalized mean-field model, we explore more obtuse bend angles. We observe direct phase transition sequences between locally biaxial and uniaxial variants of N_TB, along with biaxial and uniaxial nematic phases. Additionally, we present a comprehensive overview of how phase diagrams evolve according to alterations in the value of the bend angle and the magnitude of biaxiality.