Structure-sensitive bend elastic constants between piconewton and subnanonewton in diphenylacetylene-core-based liquid crystals

Elastic constants in liquid crystals are known to be in the range of pico- and several-tens piconewton (pN). We report herein that a bend elastic constant, $K_{33}$, remarkably varies depending on a slight modification of the chemical structure in an analogous series of calamitic liquid crystals. In contrast to the record-high bend elastic constants (hundreds pN or sub-nN) reported previously in a compound with an azo linkage, analogous compounds with tolan and ester linkages show several-tens pN and pN, respectively. X-ray diffraction studies of these compounds reveal that smectic-like layer structures $\left(cybotacticclusters\right)$ are formed in the nematic phase of only the homologous compounds with an azo linkage, certifying the idea that the existence of cybotactic clusters strongly enhances $K_{33}$. Two theoretical considerations were made: (1) Based on molecular conformation calculation, flat molecules that have high torsional potential energy, such as the one with an azo linkage, easily pack to form cybotactic clusters. (2) Theoretical estimation was made of how much cluster volume ratio is necessary to give about 100-times-larger $K_{33}\mathrm{s}$.

Figure 1

Chemical structures of liquid-crystalline materials used in our previous [10] and present works with their phase behaviors. Numbers indicated are transition temperatures in ${}^{\circ }\mathrm{C}$. The letter string, $nd$, is an abbreviation for not determined.

Figure 2

Bend elastic constant $\left(K_{33}\right)$ of all LC materials as a function of temperature $T-T_{\mathrm{I}-\mathrm{N}}$ in the N phase.

Figure 3

Birefringence of all LC materials as a function of temperature $T-T_{\mathrm{I}-\mathrm{N}}$ in the N phase.

Figure 4

X-ray diffraction patterns in the N phase of (a) p-oxyAzo3, (b) p-oxyAzo4, (c) p-oxyTolan5, and (d) p-oxyEster5. $\beta$-scans are also shown in the insets.

Figure 5

Potential energies of the four linking groups as a function of the internal rotation (dihedral) angle between two phenyl groups at the positions indicated by arrows.

Figure 6

The bend deformation is localized to the regions (thin lines) between two cybotactic groups. Within the cybotactic group the orientation of the director is constant (thick lines). $\Delta \phi$ is the bend deformation over the region of width $\lambda$ between two cybotactic groups, each of width ${\xi }_c$.

Figure 7

The smectic correlation length and the area of the x-ray peak corresponding to the cybotactic group as a function of temperature in nematic phase of p-oxyAzo5.