We measured the splay (K11) and bend (K33) elastic constants in the nematic phase of a bent-core liquid crystal. In the vicinity of the nematic-isotropic transition temperature K33 is proportional to the square of the order parameter. In the nematic range K11 increases monotonically with decreasing temperature, whereas K33 is practically independent of temperature and is smaller than K11 . K33 exhibits a pretransitional slow divergence toward the transition temperature to the smectic phase and becomes slightly larger than K11. The small K33 is explained on the basis of strong coupling of the bent shape of the molecules with the bend distortion.

Chiral mesophases in achiral bent-shaped molecules have attracted particular attention since their discovery in the middle 1990s, not only because of their homochirality and polarity, but also due to their unique physical/physicochemical properties. Here, the most intriguing results in the studies of such symmetry-broken states, mainly helical-nanofilament (HNF) and dark-conglomerate (DC) phases, are reviewed. Firstly, basic information on the typical appearance and optical activity in these phases is introduced. In the following section, the formation of mesoscopic chiral superstructures in the HNF and DC phases is discussed in terms of hierarchical chirality. Nanoscale phase segregation in mixture systems and gelation ability in the HNF phase are also described. In addition, some other related chiral phases of bent-shaped molecules are shown. Recent attempts to control such mesoscopic chiral structure and the alignment/confinement of HNFs are also discussed, along with several examples of their fascinating advanced physical properties, i.e. huge enhancement of circular dichroism, electro- and photo-tunable optical activities, chirality-induced nonlinear optics (second-harmonic-generation circular difference and electrogyration effect), enhanced hydrophobicity through the dual-scale surface morphological modulation, and photoconductivity in the HNF/fullerene binary system. Future prospects from basic science and application viewpoints are also indicated in the concluding section.

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