${}^{13}\mathrm{C}$ NMR study of the director distribution adopted by the modulated nematic phases formed by liquid-crystal dimers with odd numbers of atoms in their spacers

The orientational order of the molecules in the bent mesogen CB6OCB has been studied throughout the range of temperature stability of both the $N_{\mathrm{U}}$ and $N_{\mathrm{TB}}$ liquid-crystal phases by ${}^{13}\mathrm{C}$ NMR spectroscopy. These spectra provide local order parameters for the para axes of both of the nonequivalent cyanobiphenyl groups and show how they change on entering the twist-bend nematic phase. A key feature of the order parameters is a weak, but clear maximum in the temperature variation of the order parameter prior to the $N_{\mathrm{TB}}$ phase. This suggests that the directors in both the $N_{\mathrm{U}}$ and $N_{\mathrm{TB}}$ phases are tilted with respect to the magnetic field of the spectrometer. Significantly the conformational states of the spacer are comparable in both phases, although the low temperature nematic is chiral but not that at high temperature. It is proposed that the higher temperature, tilted phase could be the splay-bend nematic phase.

Figure 1

The formation of tilted directors (red) into a helix in the twist-bend nematic phase. The directors are at a constant tilt, or conical angle ${\theta }_0$, with respect to the helix axis.

Figure 2

Symmetric liquid-crystal dimers.

Figure 3

The nonsymmetric liquid-crystal dimer CB6OCB.

Figure 4

The symmetric liquid-crystal dimer DTC5C9.

Figure 5

The 150 MHz ${}^{13}\mathrm{C}-{\{}^1\mathrm{H}\}$ spectra of CB6OCB as a solution in $\mathrm{CDC}{\mathrm{l}}_3$ at 14 T (top) compared with a 125 MHz spectrum recorded at 11.7 T on the pure material in the isotropic phase at 429 K (bottom). The intense resonance at 77.23 ppm in the upper spectrum is from ${}^{13}\mathrm{C}$ nuclei in the solvent, and the broad resonance at $\sim 110\mathrm{ppm}$ in the bottom spectrum is from ${}^{13}\mathrm{C}$ in the spectrometer probe material. The two scales in ppm are the same, with the peaks at the highest frequencies made coincident. The spectrum in $\mathrm{CDC}{\mathrm{l}}_3$ solution was obtained by adding 1024 scans, acquired over a spectral window of 59.5 kHz, with an acquisition time of 1101.0 ms (65 536 complex points). The π/2 ${}^{13}\mathrm{C}$ pulse was 14.45 μs and the recycle delay was 8.899 s. ${}^1\mathrm{H}$ WALTZ-16 decoupling at 3.125 kHz was applied during acquisition. A weaker decoupling of about 0.95 kHz was applied during the recycle delay to increase the ${}^{13}\mathrm{C}$ polarization by ${}^1\mathrm{H}-{}^{13}\mathrm{C}$ cross relaxation. The spectrum was processed with 65 536 complex points and using an exponential window function of 2.0 Hz. The spectrum in the isotropic phase is the result of acquiring 192 scans, each with a spectral window of 50.0 kHz, and an acquisition time of 102.4 ms (5120 complex points). The π/2 ${}^{13}\mathrm{C}$ pulse was 5.0 μs and the recycle delay was 5.0 s. ${}^1\mathrm{H}$ SPINAL64 decoupling at 25.0 kHz was applied during acquisition. The spectrum was processed with 65536 complex points and using an exponential window function of 2.0 Hz.

Figure 6

Expansion of the 40−20 ppm region of the 150 MHz ${}^{13}\mathrm{C}-{\{}^1\mathrm{H}\}$ spectra of CB6OCB as a solution in $\mathrm{CDC}{\mathrm{l}}_3$ at 14 T and 298 K (top) compared with a 125 MHz spectrum recorded at 11.7 T on the pure material in the isotropic phase at 429 K (bottom). The peak labels in the $\mathrm{CDC}{\mathrm{l}}_3$ spectrum were obtained from 2D correlation experiments.

Figure 7

Expansion of the 100–170 ppm region of the ${}^{13}\mathrm{C}\text{−}{\{}^1\mathrm{H}\}$ spectra of CB6OCB as a solution in $\mathrm{CDC}{\mathrm{l}}_3$ at 14 T and 298 K (top) compared with the same spectrum recorded at 11.7 T on the pure material in the isotropic phase at 429 K (bottom). The peak labels in the $\mathrm{CDC}{\mathrm{l}}_3$ spectrum were obtained from 2D correlation experiments.

Figure 8

The 125 MHz ${}^{13}\mathrm{C}-{\{}^1\mathrm{H}\}$ spectra of aromatic carbons in CB6OCB in the isotropic phase at 429 K (top) compared with the spectrum at a temperature in the nematic phase at 394 K (bottom). The isotropic phase spectrum was obtained by adding 192 scans, acquired over a spectral window of 50.0 kHz, with an acquisition time of 102.4 ms (5120 complex points). The π/2 ${}^{13}\mathrm{C}$ pulse was 5.0 μs and the recycle delay was 5.0 s. ${}^1\mathrm{H}$ SPINAL64 decoupling at 25.0 kHz was applied during acquisition. The spectrum was processed with 65536 complex points and using an exponential window function of 2.0 Hz. The spectrum in the nematic phase (394 K) was acquired with a ${}^1\mathrm{H}-{}^{13}\mathrm{C}$ cross-polarization (CP) sequence adding up 96 scans, each with a spectral window of 31.25 kHz, and an acquisition time of 55.9 ms (1747 complex points). The π/2 ${}^1\mathrm{H}$ pulse was 5.0 μs, the CP contact time was 3.0 ms and the recycle delay was 5.0 s. The CP power levels were 38.3 kHz for ${}^1\mathrm{H}$ and 31.5 kHz for ${}^{13}\mathrm{C}$. Proton decoupling was applied using SPINAL64 with a rf field strength of 53.2 kHz during acquisition. The spectrum was processed with 16 384 complex points and using an exponential window function of 10.0 Hz.

Figure 9

The 150 MHz ${}^{13}\mathrm{C}-{\{}^1\mathrm{H}\}$ spectra of aliphatic carbons in CB6OCB in the isotropic phase at 429 K (top) at 14 T compared with the spectrum recorded at 125 MHz and at 11.7 T, and at a temperature in the nematic phase of 394 K (bottom).

Figure 10

Chemical shift anisotropies for C2 (○) and C45 ($•$) in the nematic and twist-bend nematic phases of CB6OCB as a function of temperature.

Figure 11

The 125 MHz ${}^{13}\mathrm{C}-{\{}^1\mathrm{H}\}$ spectra of carbons 2 and 45 in CB6OCB as the temperature is lowered from 387 K in the $N_{\mathrm{U}}$ phase (left column). The spectrum at 383 K shows peaks from both $N_{\mathrm{U}}$ (sharp) and $N_{\mathrm{TB}}$ (broad) phases. The sample froze at $\sim 376\mathrm{K}$, and was then heated from the solid back to 387 K and left for 20 min at each temperature before obtaining the spectra shown in the right column. The linewidths are shown alongside each set of peaks for each temperature.

Figure 12

Reference axes for the cyanobiphenyl groups in CB6OCB. For the hexyloxylated ring (biphenyl-O) the $z$ axis is parallel to the C1-C2 bond, and $x$ is in the plane defined by C1, C2, C3. Note that $z$ makes an angle of $\sim 4^{\circ }$ with the C-O bond [25, 26, 27]. For the hexylated ring (biphenyl-C) $z$ is along the C48-C45 bond, and $x$ is in the plane C48, C45, C44. The bond C37-C38 is parallel to $z$.

Figure 13

The PELF-NMR experiment.

Figure 14

${}^{13}\mathrm{C}-{}^1\mathrm{H}$ PELF-NMR spectrum at 11.7 T of the aromatic carbons in the nematic phase of CB6OCB at 394 K. The $F1$ axis has been adjusted to allow for the scaling factor of 0.47 introduced by the homonuclear refocusing sequence [22]. The spectrum was recorded at 11.7 T (125 MHz ${}^{13}\mathrm{C}$ Larmor frequency) on an Avance III Bruker spectrometer using a double resonance probe (static horizontal probe, 4-mm sample tube). The ${}^1\mathrm{H}$ and ${}^{13}\mathrm{C}\pi /2$ pulses were calibrated to be 2.5 and 5.0 μs each; $\mathrm{DUMBO}-1_{22}$ decoupling was applied at a rf field strength of 50 kHz (DUMBO cycle time of 60 μs). The contact time for the polarization transfer step was 2.5 ms using a 50%–100 % ramp of power on the ${}^1\mathrm{H}$ channel (with 36.8 kHz of maximum rf field strength) and a constant rf power of 23.7 kHz on the ${}^{13}\mathrm{C}$ channel. ${}^1\mathrm{H}$ SPINAL-64 decoupling was applied during acquisition with a rf field strength of 50 kHz. Up to 144 scans per increment were collected and added together, with 192 $t_1$ increments. The total acquisition times were 34.9 ms for the direct dimension and 12.3 ms for the $F1$ dimension. The recycle delay was 5.0 s with a total experiment time of 15 h.

Figure 15

${}^{13}\mathrm{C}-{}^1\mathrm{H}$ PELF-NMR spectrum at 11.7 T of the aliphatic carbons in CB6OCB at 394 K. The projections onto the $\mathit{F}\mathit{2}$ axis are at the positions of the ${}^{13}\mathrm{C}$ chemical shifts, with the assignment discussed in the text. The experimental parameters are reported in the caption of Fig. 14.

Figure 16

Temperature dependence of $S_{zz}$ for the para axes in the O-ring (○) and C-ring ($•$) of CB6OCB determined from the chemical shift anisotropies of the carbons C2 and C45.

Figure 17

Comparison of $S_{zz}\left(T\right)$ determined from the shift anisotropy of C45 ($•$) in biphenyl-C with values (○) calculated for the Haller function of Eq. (5) with $S_{aa}\left(0\right)=0.783$ and $\gamma =0.132$.

Figure 18

The temperature dependence of ${\theta }_0$, the tilt of the director away from the applied magnetic field, determined from $S_{zz}$ for the C-ring in CB6OCB ($\circ$) compared with values obtained by a similar method for DTC5C9 ($\times$) [15], and from the deuterium quadrupolar splittings in $\mathrm{CB}7\mathrm{CB}-d_4$ ($•$) (taken from [40]).

Figure 19

Torsional rotations about bonds in the $-\mathrm{O}{\left(\mathrm{C}{\mathrm{H}}_2\right)}_6-$ flexible spacer in CB6OCB.

Figure 20

The two minimum-energy structures for rotation through the dihedral angle ϕ(24) in CB6OCB.

Figure 21

Observed ($\circ$) values of ${}^1{D}_{\mathrm{CH}}$ for the chain carbon positions in the $N_{\mathrm{U}}$ phase of CB6OCB at 394 K, compared with values calculated ($•$) for the single, all-trans conformation. The assignment of ${}^1{D}_{\mathrm{CH}}$ at C24 is certain, while those for the other positions are made assuming that the chemical shifts are in the same order in the isotropic and $N_{\mathrm{U}}$ phase.

Figure 22

PELF spectra of the carbon nuclei in the hexyloxy chain in the $N_{\mathrm{U}}$ phase of CB6OCB at 394 K (a,b) compared with the $N_{\mathrm{TB}}$ phase at 377 K (c,d). The peak assignments are based on the chemical shifts for a sample in the isotropic phase. The $F1$ axis has been adjusted to allow for the scaling factor of 0.47 introduced by the homonuclear refocusing sequence.

Figure 23

Comparison of the values of ${}^1{D}_{\mathrm{CH}}$ observed along the chain at 394 K ($N_{\mathrm{U}}$) ($•$) and at 377 K ($N_{\mathrm{TB}}$) (○) for CB6OCB. The assignment of ${}^1{D}_{\mathrm{CH}}$ at C24 is certain, while those for the other positions are made assuming that the chemical shifts are in the same order in the isotropic and $N_{\mathrm{U}}$ phase. The additional, prochiral splittings at positions C25, C26, and C37 are shown by the red (gray) symbols ($•$): at these positions the open circles (○) are at the mean splittings.

Figure 24

The directors (red lines) in the splay-bend nematic phase vary in orientation in the range of $0\pm {\theta }_{\mathrm{SB}}$ in the $XZ$ plane.

Figure 25

The temperature dependence of the elastic constants in the nematic phase of the dimer DTC5C7. [Sebastián et al., Phys. Chem. Chem. Phys. 18, 19299 (2016). Reproduced with permission from the PCCP Owner Societies.]