Phase transitions in a high magnetic field of an odd, symmetric liquid crystal dimer having two nematic phases, $N_{\mathrm{U}}$ and $N_{\mathrm{TB}}$, studied by NMR spectroscopy

Both ${}^1\mathrm{H}$ and ${}^{13}\mathrm{C}$ NMR spectra have been obtained in a static magnetic field of 23.5 T on a bent-shaped dimer molecule, $1^{\prime \prime },7^{\prime \prime }$-bis(4-cyanobiphenyl-4′-yl) nonane (CB9CB), which shows the sequence of liquid crystal phases twist-bend nematic, $N_{\mathrm{TB}}$, and uniaxial nematic, $N_{\mathrm{U}}$, before entering the isotropic phase. The ${}^1\mathrm{H}$ spectra are used to locate the temperature at which the sample melts to form a twist-bend nematic, $T_{Cr{N}_{\mathrm{TB}}}$, and then $T_{N_{U}I}$ when the isotropic phase is entered, both in a magnetic field of 23.5 T, and to compare these with those measured at the Earth's field. The differences between these transition temperatures are found to be zero within the error in their measurement, in stark contrast to previous measurements by Salili et al. [Phys. Rev. Lett. 116, 217801 (2016)]. In the isotropic phase in the presence of the field the sample exists in a paranematic phase in which the molecules of CB9CB are partially ordered. The ${}^1\mathrm{H}$ and ${}^{13}\mathrm{C}$ NMR spectra in the paranematic phase are used to measure the critical temperature T* below which this phase is unstable. The spectra are also used to study the structure, molecular orientational order, and distribution of molecular conformations in the paranematic phase.

Figure 1

Structure (top) and atomic labeling of the symmetric liquid crystal dimer CB9CB.

Figure 2

600-MHz ${}^1\mathrm{H}$ spectrum of CB9CB, acquired at 14.1 T. The spectrum scale is reported in ppm with respect to the TMS reference at 0.00 ppm.

Figure 3

Enlargements of the 1D ${}^1\mathrm{H}$ spectrum of CB9CB shown in Fig. 2. On the top of each peak the ${}^1\mathrm{H}$ assignment with the atomic positions of Fig. 1 is reported. To highlight the J coupling between peaks, the $x$ axis is reported in Hz with respect to the TMS reference at 0.00 Hz. The spectrum is processed with a Gaussian window function ($\mathrm{GB}=1.0$ and $\mathrm{LB}=–0.5$ Hz) to better detail the J-coupling fine structure.

Figure 4

150-MHz ${}^{13}\mathrm{C}$-{${}^1\mathrm{H}$} spectrum of CB9CB dissolved in $\mathrm{CD}{\mathrm{Cl}}_3$, acquired at 14.1 T. The spectral scale is reported in ppm with respect to the TMS reference at 0.00 ppm. On the top of each peak is the ${}^1\mathrm{H}$ assignment with the atomic positions of Fig. 1 reported.

Figure 5

250-MHz ${}^{13}\mathrm{C}\text{−}{}^{13}\mathrm{C}$ INADEQUATE spectrum of pure CB9CB at 23.5 T in the isotropic phase at 135 °C.

Figure 6

Assignment pathway of the ${}^{13}\mathrm{C}\text{−}{}^{13}\mathrm{C}$ INADEQUATE spectrum shown in Fig. 5. Three different enlargements (a)–(c) are reported. A red dotted line highlights the assignment pathway from one cross peak to another. Numbers report the assigned cross peaks with the positions given in Fig. 1.

Figure 7

1000-MHz ${}^1\mathrm{H}$ spectrum of CB9CB observed close to the melting point. The narrow peaks near the center of the spectra are from a proton impurity in the DMSO-$d_6$ sample which is contained in the inner, coaxial tube. Spectrum (a) was recorded at 83 °C when the sample is in the solid phase, and (b) at 85 °C when the sample is in the twist-bend nematic phase.

Figure 8

1000-MHz ${}^1\mathrm{H}$ spectra of CB9CB observed in the paranematic phase at 145 °C and 127 °C.

Figure 9

The growth in the doublet splitting on the peak from H28 and H29 as the transition to the nematic phase of CB9CB is approached in the paranematic phase. At 121.8 °C the sample shows spectra from both the paranematic and nematic phases with most of the sample being in the nematic. The spectrum for the nematic phase is not shown.

Figure 10

250-MHz ${}^{13}\mathrm{C}$ NMR spectra of CB9CB recorded in the paranematic phase in a field of 23.5 T.

Figure 11

The dependence of each value of $D_{\mathrm{CH}}^B$ on temperature for CB9CB observed in the paranematic phase with a magnetic field of 23.5 T. The solid lines show the best, least-squares fits of the experimental values to Eq. (19). The points are $\blacksquare$ C23; ◊ C25; ♦ C27; ▲ C26; □ C24; ▼ C8; • C9; ○ C4; △ C3.

Figure 12

Temperature dependence of $D_{28,29}^B$ (•) close to $T_{\mathrm{NI}}$ for CB9CB at a field of 23.5 T. The solid line shows the best fit to Eq. (18).

Figure 13

Bent- and Z-shaped mesogens.

Figure 14

The variation of ($T_{\mathrm{NI}}-T^{*}$) with $\mathrm{\Delta }{S}_{\mathrm{NI}}/R$ the change in entropy at $T_{\mathrm{NI}}$ for the mesogens in Table 5. The straight line passing through the origin is a least-squares, linear fit to the data.

Figure 15

(a) 1000-MHz ${}^1\mathrm{H}$ and (b) 250-MHz ${}^{13}\mathrm{C}$ spectra at a field of 23.5 T for selected regions of the spectrum measured for CB9CB at 395.0 K.

Figure 16

The site dependence of $D_{{\mathrm{C}}_{\mathrm{i}}\mathrm{H}}^B$ for CB9CB in the paranematic phase at 395.0 K.

Figure 17

The cyanobiphenyl-$\mathrm{C}{\mathrm{H}}_2$ fragment. The axes xyz are fixed in the alkylated ring with $x$ and $z$ in the ring plane.

Figure 18

Fragment interaction parameters ${\varepsilon }_{i,j}$ used for CB9CB when comparing the observed values of $D_{\mathrm{i},\mathrm{j}}^B$ with those calculated by the AP method.

Figure 19

The probabilities $P^B\left(n\right)$ of the 17 most populated conformers in the nonane spacer of CB9CB predicted to exist by the DFT calculations in the magnetic-field-induced paranematic phase at 395.0 K.