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 Landau-deGennes 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 have not been reported so far. These new structures are longitudinal ($N_{LP}$) and transverse ($N_{TP}$) periodic waves where the polarization field being periodic in one dimension stays parallel and perpendicular, respectively, to the wave vector. The other two phases have all characteristic features of the twist-bend nematic phase ($N_{TB}$) and the splay-bend nematic phase ($N_{SB}$), but their fine structure appears more complex than that considered so far. The presence of molecular chirality converts nonchiral $N_{TP}$ and $N_{SB}$ into new $N_{TB}$ phases. Interestingly, the nonchiral $N_{LP}$ phase can stay stable even in the presence of intrinsic molecular chirality. Exemplary phase diagrams provide further insights into the relative stability of these new modulated nematic structures.