The discovery of thermotropic biaxial nematic phase in bent-core mesogens, have engendered interest in these systems. Also, it undergoes optical switching about 100 times faster than conventional uniaxial nematic liquid crystal. Azo-substituted bent-core compounds, A131 and A103, were investigated as both offer an opportunity to observe their structures and phase transitions from the uniaxial nematic (Nu) to biaxial nematic (Nb) phase and from Nb to the underlying smectic-C (SmC) phase.;Plank-like molecular systems are also expected to form Nb phase. Chromonic liquid crystals formed by aqueous solutions of plank-like dye molecules are interesting for their unique self-assembly and structural evolution. They have applications in optical element, coloring in food and textiles, and etc. Both systems were investigated with synchrotron x-ray scattering, polarizing optical microscopy, and differential scanning calorimetry.;Temperature dependence of d-spacing and positional order correlations along the director clearly mark the phase boundaries where Nu-Nb transition was approximately 27° below the clearing point. Positional order correlation length of A131 increased from 1.5 in Nu to 3.3 molecular lengths in Nb phase, before it jumps by a factor of at least 5 in SmC phase. The lack of large discontinuous changes in the structural parameters and the subtle signatures in heat capacity establish the second order nature of Nu-Nb and Nb-SmC phase transitions.;The chromonic system investigation results provide quantitative information of structural properties in nematic and columnar mesophases. We studied water solutions of (achiral) sunset yellow dye and (chiral and achiral) dihydrochloride salts of perylenebis-dicarboxydiimide. Positional order correlation lengths measurements, parallel and perpendicular to the aggregate axis, revealed that they increase with concentration and decrease with temperature. Temperature dependence of correlation lengths yielded the scission energy to be 1.8 (+/-0.1) x10-20J and 1.5 (+/-0.08) x10-20J in the nematic and columnar phases. The aggregates' small aspect ratio (2.5) is inconsistent with the Onsager model for the formation of an orientationally ordered phase, which strongly suggests more complicated aggregate-shape than simple cylindrical objects as postulated by Laventovich, et al.
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