Proton-decoupled deuterium NMR study of an asymmetric liquid crystal dimer having two nematic phases

Proton-decoupled deuterium NMR spectra were obtained for an asymmetric liquid crystal dimer 1-(4-cyanobiphenyl-4′-yloxy)-6-(4-cyanobiphenyl-4′-yl)hexane (CB6OCB) containing a single -${\mathrm{CD}}_2$- group. The sample has two nematic liquid crystal phases: a twist-bend nematic, $N_{TB}$, at the lowest temperature followed by a uniaxial nematic, $N_U$, on increasing the temperature. Proton decoupling reduces the linewidths of the peaks in the deuterium spectrum from kHz to $\sim 100\mathrm{Hz}$, enabling quadrupolar splittings, $\mathrm{\Delta }\nu$, to be obtained with enhanced precision as well as the dipolar coupling between deuterium nuclei within the ${\mathrm{CD}}_2$ group, hence enhancing the information content.

Figure 1

Structure and atomic labeling of the asymmetric liquid crystal dimer CB6OCB.

Figure 2

Helical twist of local directors, n (red) about the helix axis h in $N_{TB}$ phase. Local directors lie on the surface of a cone and make a constant angle, ${\theta }_0$,with h.

Figure 3

Location of axes ($xyz$) in the biphenyl-${\mathrm{CH}}_2$ fragment of CB6OCB. Axis $y$ is normal to $xz$ plane.

Figure 4

The 76.77-MHz spectra of deuterium in CB6OCB-${\mathrm{d}}_2$ in $N_U$ phase at 385 K: (a) without and (b) with proton decoupling at 25 kHz of rf power.

Figure 5

Simulated ${}^2\mathrm{H}$ spectra of two equivalent deuterium nuclei with $q$, component of quadrupolar coupling tensor along the liquid crystal director, $\mathit{n}$. (a) opposite in sign to $D$, the dipolar coupling, and (b) the same sign. Simulations were made with a program written in SpinDynamica [8].

Figure 6

The 76.77-MHz ${}^2\mathrm{H}–\left\{{}^1\mathrm{H}\right\}$ spectra of CB6OCB-$d_2$ recorded at intervals of 1 K starting at 382 K when the sample is in the $N_U$ phase followed by spectra in $N_{TB}$ phase. The ${}^2\mathrm{H} \pi /2$ pulse was $4.625\mu \mathrm{s}$. ${}^1\mathrm{H}$ decoupling at 25 kHz of rf power, during the whole acquisition time of 13.95 ms. Spectra were acquired with 1585 complex points and are processed with 16 384 complex points and an exponential window function with 5 Hz of line broadening.

Figure 7

Simulation of ${}^2\mathrm{H}$ spectra recorded at 381 K in $N_{TB}$ phase. Spectra are symmetric about their center and only the high-frequency side of the spectrum is shown. Nonequivalent deuterium nuclei have $q_1=–40040\mathrm{Hz}, q_2=–38641\mathrm{Hz}$, and $D=–137\mathrm{Hz}$ (top) and $+137\mathrm{Hz}$ (bottom).

Figure 8

Temperature variation of $q$ in $N_U$ ($•$) phase, $q_1$ ($\circ$) and $q_2$ (×), and their mean (Δ) in $N_{TB}$ phase.

Figure 9

Temperature variation of $D$ in $N_U$ and $N_{TB}$ phases for CB6OCB-$d_2$. Spectra were recorded manually in two different experiments, the first from the isotropic phase to 389 K in 2 K steps and the second from 386 K in 1 K steps.

Figure 10

Dependence, on temperature for CB6OCB-$d_2$, of order parameters $S_{\mathrm{CD}}$ ($•$) in $N_U$ phase. For $N_{TB}$ phase the two values of $q_1$ and $q_2$ yield two values, $S_{\mathrm{CD}1}$ ($\circ$) and $S_{\mathrm{CD}2}(\times )$, and their mean, $S_{\mathrm{CD}}\left(\mathrm{mean}\right)$ (Δ). In $N_U$ phase, ${}^2\mathrm{H}$ nuclei in ${\mathrm{CD}}_2$ group are symmetrically equivalent and there is just one measured value of $D$ at each temperature and hence just one value ($\blacksquare$) for $S_{\mathrm{DD}}$ order parameter. In $N_{TB}$ phase, two values for $D$ at each temperature could be measured, but these are equal within experimental error and just their average value is shown for $S_{\mathrm{DD}}$ ($\square$).

Figure 11

Local axes ($abc$) with $a$ in the plane defined by C37, H41, and H42, and bisecting the angle $\angle 41,37,42=2\varphi$. Axis $c$ is normal to the plane defined by C28, C37, and C38.

Figure 12

Values of $S_{\mathrm{aa}}$ ($•$) together with $S_{\mathrm{CD}}$ ($•$) and $S_{\mathrm{DD}}$ ($\blacksquare$) in $N_U$ phase.

Figure 13

Dependence on temperature, $T$, of $S_{zz}$ obtained from ${}^{13}\mathrm{C}$ chemical-shift anisotropies in CB6OCB [5] ($•$) and from dipolar coupling between deuterons in CB6OCB-$d_2$ ($\circ$).

Figure 14

$S_{zz}=-2S_{\mathrm{DD}}$ ($•$) compared with a Haller plot ($\circ$) with $\gamma =0.12$ and $S_{zz}\left(0\right)=0.735, T_{\mathrm{NI}}^{*}=428\mathrm{K}$.

Figure 15

Tilt, ${\theta }_{\mathrm{tilt}}$, of the director away from direction of applied magnetic field obtained for CB6OCB-$d_2$ using $S_{zz}=-2S_{\mathrm{DD}}$ and a Haller plot with $\gamma =0.12$ and $S_{zz}\left(0\right)=0.735$ with $T_{\mathrm{NI}}^{*}=428\mathrm{K}$.

Figure 16

Tilt, ${\theta }_{\mathrm{tilt}}$, of the director from direction of applied magnetic field obtained from difference between values of $S_{zz}=-2S_{\mathrm{DD}}$($\circ$) compared with values ($•$) derived previously [5] from ${}^{13}\mathrm{C}$ chemical-shift anisotropies.