Elastic constants and orientational viscosities of a bent-core nematic liquid crystal

Using a combination of dynamic light scattering and Freedericksz transitions induced in applied magnetic and electric fields, we have determined the absolute magnitudes of the Frank elastic constants and effective orientational viscosities of the bent-core nematic liquid crystal, 4-chloro-1,3-phenylene bis 4-[4’-(9-decenyloxy)benzoyloxy] benzoate. At a fixed temperature $2\hspace{0.5em}{}^{ˆ}$C below the isotropic-nematic transition, we find $K_{11}=3.1\times {10}^{-12}$ N, $K_{22}=0.31\times {10}^{-12}$ N, $K_{33}=0.88\times {10}^{-12}$ N, ${\eta }_{\mathrm{splay}}=1.1$ Pa s, ${\eta }_{\mathrm{twist}}=0.37$ Pa s, and ${\eta }_{\mathrm{bend}}=1.2$ Pa s. The unusual anisotropies of these parameters are discussed in terms of short-range, smectic-C-like correlations among molecules in the nematic phase.

Figure 1

Molecular structure of ClPbis10BB, and schematics of the sample geometries used in the light scattering (left) and Freedericksz transition (right) measurements.

Figure 2

Typical light scattering correlation functions taken on a homogeneously aligned, 10-$\mu$m-thick sample of ClPbis10BB at $T_{\mathit{NI}}-T=2\hspace{0.5em}{}^{ˆ}$C. Main figure, right: Result for pure splay + pure twist geometry, with $q_{\perp }=18\hspace{0.5em}700$ cm${}^{-1}$, $q_z=0$. The solid line passing directly through all the data points (open circles) is a fit to a double exponential decay, representing the two expected overdamped director modes. An additional line represents the best fit to a single exponential decay, which, as highlighted in the insets, does not accurately describe the data (solid dots). Main figure, left: Result for nearly pure bend geometry, with $q_z=49\hspace{0.5em}600$ cm${}^{-1}$, $q_{\perp }=2300\hspace{0.5em}$cm${}^{-1}$. The solid line is an accurate fit to a single exponential decay.

Figure 3

Dispersion of the relaxation rates associated with splay, twist, and bend fluctuations of the director in ClPbis10BB at $T_{\mathit{IN}}-T=2\hspace{0.5em}{}^{ˆ}$C. The slopes of the lines give the corresponding elastic constant to viscosity ratios.

Figure 4

Ratio of mode amplitudes, obtained from fitting of the correlation data in the splay + twist light scattering geometry for ClPbis10BB, plotted against the ratio of geometric factors calculated from Eq. (2) ($T_{\mathit{IN}}-T=2\hspace{0.5em}{}^{ˆ}$C). Slope gives the ratio of splay to twist elastic constants [see Eq. (6)].

Figure 5

Top panel: Effective dielectric constant of ClPbis10BB measured as a function of applied magnetic field $B$ in the “splay” Freedericksz geometry and for $T_{\mathit{IN}}-T=2\hspace{0.5em}{}^{ˆ}$C. The vertical axis intercept corresponds to the value of ${\epsilon }_{\perp }/{\epsilon }_0$. The solid line is a fit to Eq. (10) of the text. Bottom: Data for the phase shift $\Delta \varphi$ between ordinary and extraordinary components of polarized light transmitted through the sample as a function of applied $B$. The solid line is a fit to Eq. (8). The triangular symbols correspond to values of $\Delta \varphi$ where the intensity in Eq. (7) is a maximum.

Figure 6

Threshold magnetic field for splay-bend Freedericksz transition in ClPbis10BB determined as a function of voltage applied across the sample cell ($T_{\mathit{IN}}-T=2\hspace{0.5em}{}^{ˆ}$C). The $E$ and $B$ fields are parallel to each other and normal to the undistorted director. The solid line is a fit to Eq. (11) in the text.

Figure 7

Intensity of depolarized scattered light collected from the ClPbis10BB sample for small angles off the incident direction and plotted against applied magnetic field in the twist Freedericksz geometry. The dashed lines are used to estimate the threshold field for a twist distortion of the director. (Temperature $T_{\mathit{IN}}-T=2\hspace{0.5em}{}^{ˆ}$C.)