NMR studies of molecular ordering and molecular dynamics in a chiral liquid crystal with the $\mathrm{Sm}{C_{\alpha }}^{*}$ phase

Molecular dynamics of the antiferroelectric liquid crystal 4′-(octyloxy)biphenyl-4-carboxylate2-fluoro-4-[(octyl-2-yloxy)carbonyl]phenyl (abbreviated as D16) was investigated using different nuclear magnetic resonance (NMR) techniques. D16 molecules form a smectic-${C_{\alpha }}^{*}$ phase $\left(\mathrm{Sm}{C_{\alpha }}^{*}\right)$ in an extremely wide temperature range (∼10 °C). Due to a small tilt of the molecules, this phase is characterized by short switching times, important for new photonic applications. The proton spin-lattice relaxation times were measured in isotropic (Iso), smectic-$A$ ($\text{Sm}A)$, and $\mathrm{Sm}{C_{\alpha }}^{*}$ phases over a wide frequency range of five decades, with conventional and fast field-cycling NMR techniques. This approach allowed a comparison of the essential processes of molecular dynamics taking place in these phases. On the basis of NMR relaxometry measurements, we present a description of the motional behavior of liquid crystal molecules forming $\mathrm{Sm}{C_{\alpha }}^{*}$. Pretransitional effects were observed in wide temperature ranges in both the isotropic and $\text{Sm}A$ phases in D16. The ${}^1\mathrm{H}$ fast field-cycling NMR measurements were supplemented with NMR diffusometry and ${}^{19}\mathrm{F}$ NMR spectroscopy.

Figure 1

The structural formula of the D16 mesogen; diameter of the molecule $d=5\AA$ and length $l=35\AA$.

Figure 2

The ${}^{19}\mathrm{F}$ NMR spectra (a) and the gradient map of the signal intensity (b) in D16 presented as a function of temperature; $\delta -$ chemical shift.

Figure 3

The temperature dependence of the change in spin-spin coupling constant, $C_{\mathrm{FH}}$.

Figure 4

The temperature dependence of the orientational order parameter, $S$, in the $\text{Sm}A$ phase and $\mathrm{Sm}{C_{\alpha }}^{*}$ phase of D16 determined from the ${}^{19}\mathrm{F}$ NMR measurements; the dashed line was obtained from the fit to the Haller equation.

Figure 5

Temperature dependence of the tilt angle θ in $\mathrm{Sm}{C_{\alpha }}^{*}$ phase of D16 determined from the ${}^{19}\mathrm{F}$ NMR measurements.

Figure 6

${}^1\mathrm{H}$ NMR spectra recorded as a function of temperature in D16 at a magnetic field of 11.74 T, $\delta -$ chemical shift.

Figure 7

Normalized experimental spin echo signal attenuation as a function of magnetic field gradient and model fitting curves observed in the isotropic phase of D16 at 135 °C as explained in the text. $D_{\mathrm{i}}$ and $D_{\mathrm{a}}$, denote the molecular diffusion constants, respectively, for the isotropic process occurring outside the clusters (dash blue curve) and the anisotropic one associated with the molecules within the clusters (dash-dot green curve). The solid red line is the best fit of the biexponential Eq. (3) to the experimental points (circles).

Figure 8

The relaxation dispersion profiles of proton spin-lattice relaxation rate $1/T_1$ in D16 at various temperatures including three different LC phases.

Figure 9

Temperature dependence of $1/T_1$ at Larmor frequency 10 kHz and 500 MHz in the isotropic, $\text{Sm}A$, and $\mathrm{Sm}{C_{\alpha }}^{*}$ phases of D16. The dashed lines are a guide to the eye.

Figure 10

Schematic illustration of different molecular motions in the system under investigation in the isotropic phase $(\mathrm{R}-\text{rotations}$ or reorientations, $\mathrm{S}{\mathrm{D}}_{\mathrm{a}},\mathrm{S}{\mathrm{D}}_{\mathrm{i}}-\text{anisotropiclike}$ and isotropic translational self-diffusions inside and outside the clusters, respectively; $\mathrm{OPF}-\text{order}$ parameter fluctuations) in the isotropic phase of D16.

Figure 11

Local $(\mathrm{R}-\text{rotations}$ or reorientations, $\mathrm{SD}-\text{translational}$ self-diffusion) and collective $(\mathrm{LU}-\text{layer}$ undulations, $\mathrm{TDF}-\text{tilt}$ direction fluctuations) molecular processes observed in the smectic phases of D16.

Figure 12

Experimental data (symbols) and calculated model fitting curves (solid lines) obtained for the best model fit as explained in the text in the isotropic phase (Iso) of D16 at 125 °C; individual relaxation processes (dashed lines) are marked as molecular rotations or reorientations (R), translational self-diffusion inside $\mathrm{S}{\mathrm{D}}_{\mathrm{a}}$ and outside the clusters $\left(\mathrm{S}{\mathrm{D}}_i\right)$, and order parameter fluctuations (OPF).

Figure 13

Experimental data (symbols) and calculated model fitting curves (solid lines) obtained to the best model fit as explained in the text in the smectic-$A$ phase ($\text{Sm}A)$ of D16 at two temperatures: 115 °C (a), 65 °C (b); relaxation processes (dashed lines) are molecular rotations (R), translational self-diffusion $\left(\mathrm{S}{\mathrm{D}}_{\mathrm{a}}\right)$, layer undulations (LU), and tilt direction fluctuations (TDF).

Figure 14

Experimental data (symbols) and calculated model fitting curves (solid line) obtained for the best fit of the model as explained in the text in the $\mathrm{Sm}{C_{\alpha }}^{*}$ phase of D16 at 55 °C; relaxation processes (dashed lines) are molecular rotations or reorientations (R), translational self-diffusion $\left(\mathrm{S}{\mathrm{D}}_{\mathrm{a}}\right)$, layer undulations (LU), and tilt direction fluctuations (TDF).

Figure 15

Temperature dependence of the diffusion coefficient in the isotropic phase and principal diffusion coefficients in the LC state of D16; the self-diffusion values in smectic phases were obtained from the model fits; the red dot-dashed line and blue dashed line are calculated assuming the CM model [48]. For the group of points that fulfil the Arrhenius law (black solid lines) the fitting parameters are presented in the Supplemental Material [23] Eq. (S14).

Figure 16

Temperature dependencies of the low cut-off frequency of LU and TDF processes in the smectic phase of D16: values obtained from the model fits (points: ${\mathit{\nu }}_{\mathrm{cm}}^{\mathrm{LU}}-$ circles, ${\mathit{\nu }}_{\mathrm{cm}}^{\mathrm{TDF}}-$ squares), the best fits of empirical equations to the presented points (solid line); see the Supplemental Material [23] Eqs. (S15) and (S16).

Figure 17

Temperature dependencies of $A^{\mathrm{LU}}$ and $A^{\mathrm{TDF}}$ in the smectic phase in D16: values obtained from the model fits (points: $A^{\mathrm{LU}}-\text{circles},A^{\mathrm{TDF}}-\text{squares})$, the best fits of empirical equations to the presented points (lines); see the Supplemental Material [23] Eqs. (S17) and (S18).

Figure 18

Temperature dependencies of the correlation times of rotations around the short ${\tau }_{\mathrm{x}}$ and long ${\tau }_{\mathrm{z}}$ molecular axis in isotropic and smectic phases; solid line are fits made using the Arrhenius temperature dependencies; see the Supplemental Material [23] Eq. (S19) and Table S2.