Orientational order in liquid crystals by combining ${}^2\text{H}$ and ${}^{13}\text{C}$ nuclear magnetic resonance spectroscopy and density functional theory calculations

Structural and orientational order properties of the liquid crystal $4,4^{\prime }$-bis-heptyl-azoxybenzene (HAB) have been obtained in its nematic and smectic-$A$ phases by simultaneously analyzing several observables extracted from ${}^2\text{H}$ and ${}^{13}\text{C}$ nuclear magnetic resonance (NMR) spectra, i.e., ${}^2\text{H}$ quadrupolar, ${}^2\text{H}\text{−}{}^1\text{H}$ and ${}^{13}\text{C}\text{−}{}^2\text{H}$ dipolar couplings, as well as ${}^{13}\text{C}$ chemical shift anisotropy. ${}^{13}\text{C}$ experiments required the application of high-resolution solid-state NMR techniques like ${}^1\text{H}$ high-power decoupling and cross polarization, as well as the independent determination of chemical shift tensors by means of density functional theory (DFT) calculations, here performed taking into account the effect of the anisotropic medium by the polarizable continuum model method. The approach, consisting in the simultaneous analysis of all the ${}^2\text{H}$ and ${}^{13}\text{C}$ experimental data to derive orientational order parameters, and in the use of geometrical parameters determined by DFT methods, allows more detailed and reliable results to be obtained with respect to the traditional approach based on the sole analysis of ${}^2\text{H}$ experiments.

Figure 1

Molecular structure and labeling of atoms of HAB and HAB-${\mathbf{d}}_{\mathbf{4}}$ and axis systems used in the orientational order analysis.

Figure 2

Selection of ${}^2\text{H}$ NMR spectra of HAB-${\mathbf{d}}_{\mathbf{4}}$.

Figure 3

Experimental (symbols) and calculated (lines) ${}^2\text{H}\text{−}{}^1\text{H}$ (squares) and ${}^{13}\text{C}\text{−}{}^2\text{H}$ (triangles) dipolar splittings and ${}^2\text{H}$ quadrupolar splittings (circles) of HAB-${\mathbf{d}}_{\mathbf{4}}$ as a function of temperature. Full and empty symbols and solid and dashed lines refer to deuteria on ring A and B, respectively.

Figure 4

${}^{13}\text{C}$ CP NMR spectra of (a) HAB and (b) HAB-${\mathbf{d}}_{\mathbf{4}}$ recorded under proton decoupling at, from top to bottom, 341, 337, 331, 327, 321, and 311 K.

Figure 5

Experimental (symbols) and calculated (lines) ${}^{13}\text{C}$ chemical shifts of carbons in position 1 (circles), 2,6 (squares), 3,5 (up triangles), and 4 (down triangles) of the aromatic rings of HAB as a function of temperature. Full and empty symbols and solid and dashed lines refer to deuteria on ring A and B, respectively.

Figure 6

Best fit principal order parameter $S_{zz}^d$ (full circles) and biaxiality $S_{xx}^d-S_{yy}^d$ (empty circles) values of HAB as a function of temperature.