Short-range correlations seen in the nematic phase of bent-core liquid crystals by dielectric and electro-optic studies

Three bent-core nematic liquid crystals having the same core but with different terminal groups, short (C4) and long (C7,C9) tails, are investigated by dielectric and electro-optic contrast spectroscopic techniques. C4 shows sign reversal in the dielectric anisotropy $\Delta {\epsilon }^{\prime }$ as a function of both temperature and frequency, whereas C9 shows only negative $\Delta {\epsilon }^{\prime }$ in the entire mesophasic region. The behavior of C7 is intermediate of the two. Results of a dielectric study show that both C7 and C9 exhibit strong short-range polar correlations normal to the director. The correlation lengths of these interactions are found to be similar to those from the x-ray scattering. An increased hindered rotation for C9 compared to C4 moves the dielectric dispersion for ${\epsilon }_{\parallel }^{\prime }$ to much lower frequencies, such that C9 shows only negative $\Delta {\epsilon }^{\prime }$ over the entire temperature range.

Figure 1

Chemical structure of 4-cyanoresorcinol bisbenzoates. $n=4$, C4: $I$ 107 $N$; $n=7$, C7: $I$ 111 $N_{\text{cyb}C}$ 41 Cyb$C$ 25 Sm$C$; $n=9$, C9: $I$ 104 $N_{\text{cyb}C}$ 58 Cyb$C$ 50 Sm$C$. $N_{\text{cyb}C}$ is the nematic phase composed of Sm$C$-type cybotactic clusters and Cyb$C$ is a mesophase composed of elongated cybotactic clusters. The transitions temperatures ($T$/°C) are obtained during cooling [3].

Figure 2

Real part of dielectric permittivity of 4${}^{\prime }$-resorcinols (C4 and C9) for frequencies of 1 and 100 kHz vs $T^{*}$. ${\epsilon }_{\parallel }^{\prime }$, ${\epsilon }_{\perp }^{\prime }$ are shown as blue triangles and red circles, respectively. $T^{*}$ $=$ $T_{N-I}/T$. The red dotted vertical line represents the isotropic to the nematic transition temperature.

Figure 3

Relaxation frequency $f_{ij}\approx {\left(2\pi {\tau }_{ij}\right)}^{-1}$, and the dielectric strength ($\delta {\epsilon }_j$) obtained by fitting the measured permittivity data to the Havriliak-Negami equation, for planar (red triangles) and homeotropic cells (blue circles and squares) of C4. $f_{ij}$ and $\delta {\epsilon }_{ij}$ denote the relaxation frequency and the dielectric strength of the $i,j$th mode [16]. $T^{*}=T_{N-I}/T$. The solid lines indicate a fit to the M-M model. The black vertical dotted line indicates the isotropic-to-nematic transition.

Figure 4

Frequency-temperature plot of the transmittance for C4 in a planar cell of thickness 5 $\mu$m and $E=1.0$ V/$\mu$m; the color (shade) of the contour represents the transmittance level in arbitrary units. The lines are contours of constant transmittance. The crowded lines imply a sharp change in the transmittance through the cell, that is, a Freedericksz transition occurs due to a sign reversal in $\Delta {\epsilon }^{\prime }$ [13].

Figure 5

Comparison of static and theoretical permittivities of C4 (a), C7 (b), and C9 (c) using the M-M model (solid lines). The blue triangles and red circles indicate ${\epsilon }_{\parallel }$ and ${\epsilon }_{\perp }$, respectively. These are calculated by adding dielectric strengths for various processes to ${\epsilon }_{\infty }$. The blue (dark gray) and red (gray) lines denote calculated values of permittivity with ${\mu }_l^2/{\mu }^2=0.368$ and ${\mu }_t^2/{\mu }^2=0.632$, respectively. The vertical dotted line in (c) denotes the transition from $N_{\text{cyb}C}$ to Cyb$C$. We find $\beta =52.7^{\circ }$.

Figure 6

Cluster size $L=V^{1/3}$ compared to the x-ray scattering results $V^{1/3}={(\pi /6L_{\parallel }{L}_{\perp }^2)}^{1/3}$ ($L_{\parallel }$ and $L_{\perp }$ from Ref. [3]) and the line represents $n$, the number of interacting molecules as a function of reduced temperature ($T^{*}=T_{N-I}/T$).