Phase behavior and characterization of heptamethyltrisiloxane-based de Vries smectic liquid crystal by electro-optics, x rays, and dielectric spectroscopy

A heptamethyltrisiloxane liquid crystal (LC) exhibiting $I–\mathrm{Sm}{A}^{*}–\mathrm{Sm}{C}^{*}$ phases has been characterized by calorimetry, polarizing microscopy, x-ray diffraction, electro-optics, and dielectric spectroscopy. Observations of a large electroclinic effect, a large increase in the birefringence ($\mathrm{\Delta }n$) with electric field, a low shrinkage in the layer thickness (∼1.75%) at 20 °C below the $\mathrm{Sm}{A}^{*}–\mathrm{Sm}{C}^{*}$ transition, and low values of the reduction factor (∼0.40) suggest that the $\mathrm{Sm}{A}^{*}$ phase in this material is of the de Vries type. The reduction factor is a measure of the layer shrinkage in the $\mathrm{Sm}{C}^{*}$ phase and it should be zero for an ideal de Vries. Moreover, a decrease in the magnitude of $\mathrm{\Delta }n$ with decreasing temperature indicates the presence of the temperature-dependent tilt angle in the $\mathrm{Sm}{A}^{*}$ phase. The electro-optic behavior is explained by the generalized Langevin-Debye model as given by Shen et al. [Y. Shen et al., Phys. Rev. E 88, 062504 (2013)]. The soft-mode dielectric relaxation strength shows a critical behavior when the system goes from the $\mathrm{Sm}{A}^{*}$ to the $\mathrm{Sm}{C}^{*}$ phase.

Figure 1

Schematic representation of (a) conventional $\mathrm{Sm}A$–$\mathrm{Sm}C$ (rigid-rod model) and (b) de Vries $\mathrm{Sm}A$–$\mathrm{Sm}C$ (diffuse-cone model) phase transition. Here, $z$ is the layer normal; $n$ is the molecular long axis orientation; θ is the angle between $n$ and $z$; $d_C$ and $d_A$ are the layer spacings in $\mathrm{Sm}C$ and $\mathrm{Sm}A$ phases, respectively.

Figure 2

(a) Molecular structure of the LC material $\mathrm{MS}{\mathrm{i}}_3\mathrm{MR}11$, phase sequences, and the transition temperatures ( °C) with enthalpies (J/g, in square brackets). (b) Optimized molecular geometry of $\mathrm{MS}{\mathrm{i}}_3\mathrm{MR}11$. The arrow in Fig. 1 shows the direction of the molecular dipole moment (3.562 D). (c) DSC cooling and heating curves obtained at the rate of $10{}^{\circ }\mathrm{C}\mathrm{mi}{\mathrm{n}}^{-1}$. The transition temperatures are obtained from the cooling cycle under the quasiequilibrium condition at a rate of $\sim 1^{\circ }\mathrm{C}\mathrm{mi}{\mathrm{n}}^{-1}$ using polarizing microscopy. $I=\mathrm{isotropic}\mathrm{state}, \mathrm{Cry}=\mathrm{crystalline}\mathrm{state}$.

Figure 3

Optical textures of ${\mathrm{MSi}}_3\mathrm{MR}11$ in (a) $\mathrm{Sm}{A}^{*}$, 5 °C above the $\mathrm{Sm}A–\mathrm{Sm}{C}^{*}$ transition, $T_{AC}$, and (b) $\mathrm{Sm}{C}^{*}$ (0.4 °C below $T_{AC}$), phases. The dark regions in the texture correspond to homeotropically aligned LC molecules.

Figure 4

Temperature dependence of the normalized optical film thickness, plotted as circles. Birefringence as squares, plotted as a function of temperature on the right-hand side. Measurements of the birefringence are carried out in the absence of external field on a 3-µm planar cell under cooling from the isotropic state. The coexistence region shown by two vertical dotted lines, where the two phases coexist, is the signature of the first-order phase $\mathrm{Sm}{A}^{*}–\mathrm{Sm}{C}^{*}$ phase transition. In this narrow temperature range, if all the layers were to be in the $\mathrm{Sm}{C}^{*}$ alone, the optical film thickness would have shown a small linear drop-off with temperature.

Figure 5

(a) Measured values of the birefringence as a function of the electric field are fitted to the generalized Langevin-Debye model (solid lines) [21]; (b) the field-induced optical tilt (experimental values in symbols) are fitted to this model (solid lines). Data points for the orientational distribution function (ODF) shown in Fig. 6 are marked here in (b). (c) The local dipole moment $p_0$ obtained from $\mathrm{\Delta }n$ and ${\theta }_{\mathrm{App}}$ fits plotted as a function of the reduced temperature. The solid lines are the best fits to the power law equation for the total dipole moment $p_0\left(T\right)=A/{\left(T–T_{AC}\right)}^{\gamma }$; γ is the power law exponent. The divergence of $p_0\left(D\right)$ at $T=T_{AC}$ is a clear evidence of de Vries nature of the $\mathrm{Sm}A$ phase.

Figure 6

The orientation distribution function $f\left(\theta ,\phi \right)$ of $\mathrm{MS}{\mathrm{i}}_3\mathrm{MR}11$ at a temperature of $T={\left(T_{AC}+0.8\right)}^{\circ }\mathrm{C}$ for various values of electric field strengths: (a) 0 V/µm (black); (b) 1.14 V/µm (blue, slanted); (c) 4.17 V/µm (red, like a long fan). $X-Y$ is the smectic layer plane and $Z$ is directed along the layer normal. Electric field is applied (normal to the plane of the paper) along the $Y$ direction which lies in the smectic layer.

Figure 7

Representative x-ray diffraction patterns of ${\mathrm{MSi}}_3\mathrm{MR}11$ in (a) $\mathrm{Sm}{A}^{*}$ phase (1.2 °C above the $T_{AC}$) and (b) $\mathrm{Sm}{C}^{*}$ phase (17.5 °C below the $T_{AC}$). Inset of (b) depicts the $\mathrm{Sm}{C}^{*}$ structure.

Figure 8

(a) Temperature dependence of the layer spacing determined from the x-ray diffraction. A comparison of the results of the layer thickness from the freestanding film experiment (red solid line) and the layer thickness from the x-ray results as discrete points (circles) are given in the inset. Both curves in the inset are normalized. (b) The representative azimuthal intensity distribution $I$(φ) of the wide-angle reflection centered at 4.6 Å in the $\mathrm{Sm}{A}^{*}$ (open circles) and in the $\mathrm{Sm}{C}^{*}$ (open squares) phases. The solid black line in $\mathrm{Sm}{A}^{*}$ is a single Gaussian fit ($\mathrm{FWHM}=64$), while in $\mathrm{Sm}{C}^{*}$, it is the sum of two Gaussian fits (dashed lines) with $\mathrm{FWHM}=36$.

Figure 9

The orientational distribution functions in the $\mathrm{Sm}{A}^{*}$ phase determined from the experimentally measured $I$(φ) (solid line) and the simulation (red dashed line), using molecular fluctuations $\langle \beta \rangle ={23}^{\circ }$ and the tilt angle $\alpha ={25}^{\circ }$.

Figure 10

Spontaneous polarization $P_S$ vs ($T–T_{AC}$) measured on a 4-µm planar cell under cooling from the isotropic state. A triangular-waveform voltage of $50{\mathrm{V}}_{\mathrm{pk}-\mathrm{pk}}$ at a frequency of 152 Hz is used in the experiment. $P_0=56.9\mathrm{nC}\mathrm{c}{\mathrm{m}}^{-2}$. The exponent $\beta$ in this figure and section 3c is unrelated to earlier defined $\beta$ in section 3b on x-ray diffraction.

Figure 11

(a) The three-dimensional (3D) plot of temperature-dependent dielectric loss spectra (ε") for a 10-μm planarly aligned cell in the frequency range 1 Hz–10 MHz. The dielectric measurements are carried out on the sample under cooling from the isotropic state. Temperature is stabilized to ±0.05 °C and the applied voltage in the experiment is fixed as $0.1{\mathrm{V}}_{\mathrm{rms}}$. (b) The dielectric relaxation strength Δε and the relaxation frequency $f_R$ for both the Goldstone (GM) and soft (SM) modes are plotted as a function of the reduced temperature. The temperature range where the two phases coexist is shown by a set of vertical dotted lines close to the transition temperature.

Figure 12

Reagents and conditions: (a) 11-bromo-1-undecene, ${\mathrm{K}}_2\mathrm{C}{\mathrm{O}}_3$, DMF; (b) $\mathrm{NaN}{\mathrm{O}}_2$, HCl, ${\mathrm{H}}_2\mathrm{O}$, 0 °C; (c) DMAP, DCC, THF; (d) 1,1,1,3,3,5,5-heptamethyltrisiloxane, Karstedt's catalyst, THF.

Figure 13

Chemical Formula of compound T1.

Figure 14

Chemical Formula of compound T2.

Figure 15

Chemical Formula of compound T3.

Figure 16

Chemical Formula of compound ${\mathrm{MSi}}_3$-MR11.