Biaxial Nematic Phase in Bent-Core Thermotropic Mesogens

A biaxial nematic phase had been predicted with $D_{2h}$ symmetry, wherein the mesogen’s long and short transverse axes are simultaneously aligned along the two orthogonal, primary and secondary directors, $\mathbf{n}$ and $\mathbf{m}$, respectively. The unique low-angle x-ray diffraction patterns in the nematic phases exhibited by three rigid bent-core mesogens clearly reveal their biaxiality. The results of x-ray diffraction can be readily reproduced by ab initio calculations that explicitly include the bent-core shape in the form factor and assume short-range positional correlations.

Figure 1

Molecular structure, phase sequence, and transition temperatures of samples $\mathit{A}$, $\mathit{B}$, and $\mathit{C}$. The arrows show the direction of the large ($\sim 4D$) transverse dipole moment.

Figure 2

The two dimensional XRD pattern in magnetic field ($\mathbf{H}$) aligned biaxial $N$ phase of sample $\mathit{A}$ at $195°\mathrm{C}$.

Figure 3

Two dimensional XRD patterns of sample $\mathit{B}$ aligned between two Be plates along the rubbing direction represented by $\mathbf{R}$ and the green arrows (a) at zero electric field and (b) with field applied perpendicular to the substrate. Small angle (shown magnified in middle panels) pattern changes to two diffuse arcs along $\mathbf{R}$ while large angle reflections remain unchanged. Intensity difference in the two arcs in (b) arises due to slight instrument misalignment. Schematics at the bottom represent the corresponding experimental situation and molecular orientation.

Figure 4

(a) Form factor calculated for a bent-cylindrical shape molecule. (b) Structure factor for the small angle reflection. The small angle x-ray pattern calculated from $f(\mathbf{q})\times S(\mathbf{q})$ in (c) the $q_x\mathrm{\text{−}}{q}_z$ plane and (d) the $q_y\mathrm{\text{−}}{q}_z$ plane for perfect biaxial order.