Search for microscopic and macroscopic biaxiality in the cybotactic nematic phase of new oxadiazole bent-core mesogens

The possibility of biaxial orientational order in nematic liquid crystals is a subject of intense current interest. We explore the tendencies toward local and global biaxial ordering in the recently synthesized trimethylated oxadiazole-based bent-core mesogens with a pronounced asymmetric (bow-type) shape of molecules. The combination of x-ray diffraction and optical studies suggests that the biaxial order is expressed differently at the short- and long-range scales. Locally, at the scale of a few molecules, x-ray-diffraction data demonstrate biaxial packing. However, above the mesoscopic scale, the global orientational order in all three compounds is uniaxial, as evidenced by uniform homeotropic alignment of the nematic phase which is optically tested over the entire temperature range and by the observations of topological defects induced by individual and aggregated colloidal spheres in the nematic bulk.

Figure 1

Chemical structures and phase diagrams of the ODBP bent-core nematic (BCN) liquid crystals (a) OC4-Ph(mono2MeODBP), (b) OC4-2MePh(mono2MeODBP), and (c) OC4-2MePh(mono3MeODBP); Cr, $N$, and $I$ represent crystal, nematic, and isotropic phases, respectively.

Figure 2

(a), (c), and (e) The XRD patterns measured with $\mathbf{B}$ parallel to the x-ray beam and fits of the corresponding radial intensity profiles (averaged over a π azimuthal angle) with (b) two or (d) and (f) three Voigt line shapes: (a) and (b) BCN $\mathbf{1}$ at $155{}^{\circ }\mathrm{C}$, (c) and (d) BCN $\mathbf{2}$ at $100{}^{\circ }\mathrm{C}$, and (e) and (f) BCN $\mathbf{2}$ at $30{}^{\circ }\mathrm{C}$. $p_0$ is the peripheral scattering of the small-angle region.

Figure 3

Schematic drawing of the molecular ordering within a cybotactic cluster: $\mathbf{k}$ indicates the normal to the smectic plane (purple); $\mathbf{n}, \mathbf{m}$, and $\mathbf{l}$ are the three orthogonal molecular directors; and $d_1$ and $d_2$ are the intermolecular distances in the plane normal to $\mathbf{n}$ (gray).

Figure 4

Orientation of the transverse molecular directors $\mathbf{m}$ and $\mathbf{l}$ in $N_b$ with $\mathbf{n}$ perpendicular to the drawing: transverse directors aligned by (a) an external field or (c) randomly distributed in the plane orthogonal to $\mathbf{n}$. The ellipses represent micron-sized domains (each one consisting of uniformly aligned nanometer-sized cybotactic clusters) where the orientation of the molecular director is spontaneously uniform. (b) and (d) Corresponding WA diffraction patterns. The latter would be indistinguishable from that of a composite $N_u$ comprised of randomly oriented nanometer-sized biaxial clusters.

Figure 5

Azimuthal intensity profiles of the WA peaks shown in the fits of Fig. 2: peak $p_1$ of BCN $\mathbf{1}$ at $155{}^{\circ }\mathrm{C}$ (curve a), peaks $p_1$ (curve c) and $p_2$ (curve d) of BCN $\mathbf{2}$ at $100{}^{\circ }\mathrm{C}$, and peaks $p_1$ (curve b) and $p_2$ (curve e) of BCN $\mathbf{2}$ at $30{}^{\circ }\mathrm{C}$. The gap at ${270}^{\circ }$ is due to the shadow of the beamstop.

Figure 6

The POM textures of BCNs $\mathbf{1}$–$\mathbf{3}$ in (a)–(c) SE5661 and (d)–(f) RM-SE5661 cells of $h=1.3\mu \mathrm{m}$. The left column is with BCN $\mathbf{1}$ at $T=160.0{}^{\circ }\mathrm{C}$, the central column is with BCN $\mathbf{2}$ at $T=95.0{}^{\circ }\mathrm{C}$, and the right column is with BCN $\mathbf{3}$ at $T=120.0{}^{\circ }\mathrm{C}$. Here P and A indicate the polarization of the polarizer and analyzer, respectively.

Figure 7

Optical properties of the homeotropic RM-SE5661 cells filled with BCNs $\mathbf{1}$–$\mathbf{3}$ and the standard $N_u$ mixture E7. (a) Optical retardance ${\mathrm{\Gamma }}_H$ vs temperature $T$ in cells of thickness $h=1.3\mu \mathrm{m}$, (b) ${\mathrm{\Gamma }}_H$ vs cell thickness $h$ for the temperatures presented in the figure, and (c) effective in-plane birefringence $\mathrm{\Delta }{n}_{\mathrm{eff}}={\mathrm{\Gamma }}_H/h$ as a function of $h$ at selected temperatures. Data were recorded upon cooling within the $N$ phase, including the supercooled $N$ region.

Figure 8

(a) Scheme of the director configuration around a sphere with tangential alignment placed in a planar $N_u$ cell; note two point-defect boojums at the poles. (b) Hypothetical configuration of the main and secondary directors around a similar sphere placed in an $N_b$ cell. Note two disclination lines, which are formed by the secondary director $\mathbf{m}$, emerging from the poles. (c)–(h) The POM textures of isolated glass spheres and their clusters in the planar $N$ cells ($h=20\mu \mathrm{m}$) at the temperatures indicated in the figures for (c) and (d) BCN $\mathbf{1}$, (e) and (f) BCN $\mathbf{2}$, and (g) and (h) BCN $\mathbf{3}$. Here P, A, and ${\mathbf{n}}_0$ represent the polarization of the polarizer and analyzer and the overall director set by the rubbing direction, respectively.