Ternary liquid crystalline mixture showing broad antiferroelectric smectic C$_A$* and glassy hexatic smectic X$_A$* phases
A ternary liquid crystalline mixture was designed to obtain a tilted hexatic smectic phase in the glassy state. Structural, electro-optic, and dielectric properties of the mixture are investigated, and selected measurements are also performed for its pure components. In particular, the electron density profile perpendicular to smectic layers is determined from the X-ray diffraction data and compared to the results of density functional theory calculations both for the mixture and pure components. Comparison of the experimental smectic layer spacing and tilt angle in the mixture allows us to assess whether molecular dimerization is likely to occur. On the mesoscopic scale, the helical pitch is determined in the SmC$_A$* phase of the mixture, and selective reflection of light is observed under a polarizing microscope in the SmC*, SmC$_A$*, and SmX$_A$* phases. The glass transition in the smectic X$_A$* phase is observed in calorimetric results. At the same time, the dielectric spectra do not directly reveal the primary $\alpha$-process, although the secondary $\beta$- and $\gamma$-processes are detected. Overall, the results show that the ternary mixture stabilizes a broad SmC$_A$* phase and enables vitrification of the hexatic SmX$_A$* phase, while the structural data suggest a change in the molecular organization between the SmC* and SmC$_A$* phases.