X-ray and Raman scattering study of orientational order in nematic and heliconical nematic liquid crystals

The temperature dependence of the orientational order parameters $\langle P_2\left(\cos \beta \right)\rangle$ and $\langle P_4\left(\cos \beta \right)\rangle$ in the nematic ($N$) and twist-bend nematic $\left(N_{\mathrm{tb}}\right)$ phases of the liquid crystal dimer CB7CB have been measured using x-ray and polarized Raman scattering. The $\langle P_2\left(\cos \beta \right)\rangle$ obtained from both techniques are the same, while $\langle P_4\left(\cos \beta \right)\rangle$, determined by Raman scattering is, as expected, systematically larger than its x-ray value. Both order parameters increase in the $N$ phase with decreasing temperature, drop across the $N-N_{\mathrm{tb}}$ transition, and continue to decrease. In the $N_{\mathrm{tb}}$ phase, the x-ray value of $\langle P_4\left(\cos \beta \right)\rangle$ eventually becomes negative, providing a direct and independent confirmation of a conical molecular orientational distribution. The heliconical tilt angle α, determined from orientational distribution functions in the $N_{\mathrm{tb}}$ phase, increases to $\sim {24}^{\circ }$ at $\sim 15$ K below the transition. In the $N_{\mathrm{tb}}$ phase, $\alpha \left(T\right)\propto {(T^{*}-T)}^{\lambda }$, with $\lambda =0.19\pm 0.03$. The transition supercools by 1.7 K, consistent with its weakly first-order nature. The value of λ is close to 0.25 indicating close proximity to a tricritical point.

Figure 1

Schematic representation of the (a) calamitic nematic, $\mathcal{N}$; (b) cholesteric, Chol.; and (c) twist-bend nematic, $N_{\mathrm{tb}}$ phases of a molecule with bent shape. Here, arrows with $\mathit{n}$ represent the local director while $\mathcal{N}$ is the global director.

Figure 2

Temperature dependence of $\langle P_2\left(\cos \beta \right)\rangle$ and $\langle P_4\left(\cos \beta \right)\rangle$ in the nematic phases of CB7CB. (a) XRD taken at NSLS, (b) PRS. The lines are to guide the eye.

Figure 3

(a) Orientational distribution functions in the $N(t=0\mathrm{K})$ from Raman (blue solid line) and x-ray (red dotted line), and $N_{\mathrm{tb}}$ phases $(t=-15\mathrm{K})$ from Raman (blue dashed line) and x-ray (red dash-dot line) of CB7CB. (b) The ODF in the $N$ phase (green solid line) is sugarloaflike but its shape changes to diffuse cone (dashed magenta line) in the $N_{\mathrm{tb}}$ phase. The two black (dash-dot) curves are Gaussians fitted to the $N_{\mathrm{tb}}$ ODF. The separation between their centers, marked by solid vertical lines, is a measure of the cone, i.e., tilt, angle.

Figure 4

The heliconical tilt angle α in the $N_{\mathrm{tb}}$ phase of CB7CB as a function of $t^{*}=T^{*}-T$, where $T^{*}$ is the temperature at which $\alpha =0$. The curve is a single power law fit.

Figure 5

Raman spectra shown in (a,b), and peak intensities shown in (c,d) at different temperatures.

Figure 6

Optical texture of CB7CB in the $N_{\mathrm{tb}}$ phase.