Orientational order of a ferroelectric liquid crystal with small layer contraction

We present spectroscopic and optical studies of a non-layer-shrinkage ferroelectric liquid crystal DSiKN65. The orientational order parameters $S$, measured with respect to the smectic layer normal using IR spectroscopy on a sample aligned homeotropically, does not exhibit any significant variation between the smectic-$A^{\ast }$ and smectic-$C^{\ast }$ phases. In contrast the birefringence of a planar homogenous sample abruptly increases at the smectic-$A^{\ast }$ to smectic-$C^{\ast }$ transition. This suggests a general increase in the orientational order, which can be described by the orientational order parameters $S^{\prime }$ defined with respect to the director. Simultaneous increase of $S^{\prime }$ and the director tilt $\Theta$ may explain the low shrinkage of smectic layers, which is consistent with recent theoretical models describing the smectic-$A^{\ast }$ to smectic-$C^{\ast }$ transition for such materials.

Figure 1

Molecular structure of DSiKN65 (a) and a region of its IR spectrum of stretching vibrations well-localized within the molecular core (as listed in Table ); solid line-experimental spectrum, dashed line-theoretical spectrum obtained using the density functional theory (for details see the text).

Figure 2

(Color online) (a) Schematic of the experimental arrangement. Orientation of the director $\mathbf{n}$ in the laboratory reference system $XYZ$ shown for two typical phases: $\text{Sm}{A}^{\ast }$ and $\text{Sm}{C}^{\ast }$. Arrows indicate the direction of the IR beam. Please, note that the IR beam is not polarized, hence the tilting direction (the azimuthal angle) of the director does not matter. Also shown example IR transition dipole moments parallel and perpendicular to the long molecular axis. (b) Definitions of angular coordinates $\beta$ and $\gamma$ specifying the orientation of an IR transition dipole moment $\mu$ in the molecular reference system $xyz$. For details see the text.

Figure 3

(Color online) (a) IR absorbance normalized with respect to the isotropic phase vs temperature for three absorption bands; squares-phenyl ring stretching $1605{\text{cm}}^{-1}$, triangles-nitrophenyl ring stretching $1620{\text{cm}}^{-1}$, red stars-carbonyl stretching $1735{\text{cm}}^{-1}$ (b) Orientational order parameters vs temperature; squares-$S$ determined using band $1605{\text{cm}}^{-1}$, triangles-$S$ determined using band $1620{\text{cm}}^{-1}$, red stars-$D$. Note that in the range of $\text{Sm}{A}^{\ast }$ phase $S=S^{\prime }$.

Figure 4

(Color online) Smectic layer spacing $d$ vs temperature: measured on cooling (circles), expected from the optical tilt (triangles); orientational order parameter $S$ (squares).

Figure 5

Two alternative transition scenarios (represented by arrows) from $\text{Sm}{A}^{\ast }$ to $\text{Sm}{C}^{\ast }$ phase shown in terms of changes in the orientational distribution functions with polar and azimuthal angles in a single layer. The upper part represents the pure de Vries scenario and shows the corresponding diffuse-cone distribution of molecules in the $\text{Sm}{A}^{\ast }$ phase (a) (see also Lagerwall et al. [26]). The transition to $\text{Sm}{C}^{\ast }$ phase (b) proceeds as ordering of the azimuthal angles of molecules. In the lower part of the figure, the orientational distribution in the $\text{Sm}{A}^{\ast }$ phase is conventional (c), but very broad (with very low orientational order, $S=0.5$). Following the transition to $\text{Sm}{C}^{\ast }$ phase the director tilts and the orientational order increases. For details on the distribution functions see the Appendix.

Figure 6

(Color online) Birefringence of DSiKN65 vs temperature. Lower curve (circles)—without an external field, upper curve (squares)—with a $5\text{V}/\mu \text{m}$ bias. Helix is mostly unwound by surfaces in $\text{Sm}{C}^{\ast }$ phase in the absence of external field.

Figure 7

IR spectrum of DSiKN65 in $\text{Sm}{A}^{\ast }$ phase $\left(53°\text{C}\right)$, divided by a spectrum in isotropic phase. Parallel bands $\left(\beta <54.7°\right)$ point down, perpendicular bands point up. The lower values of $A/A_0$, reflect the closeness on average of the transition dipole moments to the smectic layer normal.