Modulated nematic structures induced by chirality and steric polarization

What kind of one-dimensional modulated nematic structures (ODMNS) can form nonchiral and chiral bent-core and dimeric materials? Here, using the Landau–de Gennes theory of nematics, extended to account for molecular steric polarization, we study a possibility of formation of ODMNS, both in nonchiral and intrinsically chiral liquid crystalline materials. Besides nematic and cholesteric phases, we find four bulk ODMNS for nonchiral materials, two of which, to the best of our knowledge, have not been reported so far. These two structures are longitudinal $\left(N_{\text{LP}}\right)$ and transverse $\left(N_{\text{TP}}\right)$ periodic waves where the polarization field being periodic in one dimension stays parallel and perpendicular, respectively, to the wave vector. The other two phases are the twist-bend nematic phase $\left(N_{\text{TB}}\right)$ and the splay-bend nematic phase $\left(N_{\text{SB}}\right)$, but their fine structure appears more complex than that considered so far. The presence of molecular chirality converts nonchiral $N_{\text{TP}}$ and $N_{\text{SB}}$ into new $N_{\text{TB}}$ phases. Surprisingly, the nonchiral $N_{\text{LP}}$ phase can stay stable even in the presence of intrinsic chirality.

Figure 1

ODMNS predicted by the theory. Lengths of cuboid edges are proportional to the eigenvalues of $\mathbf{Q}+c\mathbf{I}$, where $\mathbf{I}$ is the unit matrix and $c$ is a constant, such that the isotropic state is represented by a cube. Red arrows represent $\mathbf{P}$ and the black arrow is the direction of $\mathbf{k}$.

Figure 2

Phase diagrams for $\rho =1$ and $B=1/\sqrt{6}$. Other coupling constants are indicated in each panel. Solid lines are obtained from numerical minimization while dashed curves are bifurcation temperatures from the isotropic phase. In panels (a) and (b) all phases are nonchiral, while in panel $\left(\mathrm{c}\right)$ all modulated phases are chiral. Despite nonzero intrinsic chirality in panel $\left(\mathrm{d}\right)$ there is a stable region of achiral modulated $N_{\mathrm{LP}}$ structure.