Unusual polarity-dependent patterns in a bent-core nematic liquid crystal under low-frequency ac field

Electric-field-induced patterns of diverse morphology have been observed over a wide frequency range in a recently synthesized bent-core nematic (BCN) liquid crystal. At low frequencies (up to ∼25 Hz), the BCN exhibited unusual polarity-dependent patterns. When the amplitude of the ac field was enhanced, these two time-asymmetrical patterns turned into time-symmetrical prewavylike stripes. At ac frequencies in the middle-frequency range (∼50–3000 Hz), zigzag patterns were detected whose obliqueness varied with the frequency. Finally, if the frequency was increased above 3 kHz, the zigzag pattern was replaced by another, prewavylike pattern, whose threshold voltage depended on the frequency; however, the wave vector did not. For a more complete characterization, material parameters such as elastic constants, dielectric permittivities, and the anisotropy of the diamagnetic susceptibility were also determined.

Figure 1

Structural formula and phase sequence of the 2,5-bis(4-(difluoro(4-nonylphenyl)methoxy)- phenyl)-1,3,4-oxadiazole $\left(9\mathrm{P}\text{−}{\mathrm{CF}}_2\mathrm{O}\text{−}\mathrm{ODBP}\right)$ BCN compound.

Figure 2

Representative snapshots of the low-frequency ac voltage driven oblique roll pattern. (a) $\mathrm{O}{\mathrm{R}}^{+}$ near onset in the positive half period; (b) no pattern around the zero crossing of the voltage; (c) $\mathrm{O}{\mathrm{R}}^{-}$ near onset in the negative half period. All snapshots are of $100\mu \mathrm{m}\times 100\mu \mathrm{m}$ size. The white arrows indicate the initial director ${\mathbf{n}}_0$; the polarizer direction is vertical. (d) Temporal dependence of the pattern contrast and of the applied voltage within one full period. The symbols denote the time instants when the snapshots were taken. $f=12\mathrm{Hz},U=8.3\mathrm{V},T=97{}^{\circ }\mathrm{C}$.

Figure 3

Representative snapshots of the low-frequency ac voltage driven oblique roll pattern. (a) $\mathrm{O}{\mathrm{R}}^{+}$ in the positive half period; (b) $\mathrm{O}{\mathrm{R}}^{-}$ in the negative half period. Both snapshots are of $100\mu \mathrm{m}\times 100\mu \mathrm{m}$ size. The white arrows indicate the initial director ${\mathbf{n}}_0$, the polarizer direction is vertical. (c) Temporal dependence of the pattern contrast and of the applied voltage within one full period. The symbols denote the time instants when the snapshots were taken. $f=5\mathrm{Hz},U=8.0\mathrm{V},T=97{}^{\circ }\mathrm{C}$.

Figure 4

Frequency dependence of the threshold voltages of $\mathrm{O}{\mathrm{R}}^{\pm }$ and PWsec (see text later). The patterns are observed up to the critical frequency $f_{\mathrm{c}1}$. $T=97{}^{\circ }\mathrm{C}$.

Figure 5

Frequency dependence of (a) the dimensionless wave number $q*$, and (b) the obliqueness angle $\left|\alpha \right|$ enclosed by ${\mathbf{q}}_{\mathrm{c}}$ and ${\mathbf{n}}_0$ for $\mathrm{O}{\mathrm{R}}^{\pm }$ and PWsec. $T=97{}^{\circ }\mathrm{C}$.

Figure 6

Representative snapshots of the low-frequency ac voltage driven prewavy pattern. (a) PWsec in the positive half period; (b) PWsec around the zero crossing of the voltage; (c) PWsec in the negative half period. All snapshots are of $100\mu \mathrm{m}\times 100\mu \mathrm{m}$ size. The white arrows indicate the initial director ${\mathbf{n}}_0$, the polarizer direction is vertical. (d) Temporal dependence of the pattern contrast and of the applied voltage within one full period. The symbols denote the time instants when the snapshots were taken. $f=12\mathrm{Hz},U=10.0\mathrm{V},T=97{}^{\circ }\mathrm{C}$.

Figure 7

Transformation of $\mathrm{O}{\mathrm{R}}^{\pm }$ into PWsec; a time evolution following a jump of the voltage at $t=0$ from $U=0.0\mathrm{V}<U_{\mathrm{PWsec}}$ to $U=10.5\mathrm{V}\gtrsim U_{\mathrm{PWsec}}$. The system requires more than $100t_0$ to change from the initial $\mathrm{O}{\mathrm{R}}^{\pm }$ to the final PWsec state. $f=6\mathrm{Hz},T=97{}^{\circ }\mathrm{C}$. All snapshots are of $124\mu \mathrm{m}\times 124\mu \mathrm{m}$ size. The white arrows indicate the initial director ${\mathbf{n}}_0$, the polarizer direction is vertical.

Figure 8

Transformation of $\mathrm{O}{\mathrm{R}}^{\pm }$ into PWsec during gradual, slow voltage increase. $f=12\mathrm{Hz},T=97{}^{\circ }\mathrm{C}$. The smaller snapshots are of $100\mu \mathrm{m}\times 100\mu \mathrm{m}$, the bigger ones are of $200\mu \mathrm{m}\times 200\mu \mathrm{m}$ size. The white arrows indicate the initial director ${\mathbf{n}}_0$, the polarizer direction is vertical.

Figure 9

Representative snapshots of the medium frequency ac voltage driven oblique roll (ZZ) pattern. (a) $f=50\mathrm{Hz},U=7\mathrm{V}$; (b) $f=1000\mathrm{Hz},U=13\mathrm{V}$; (c) $f=2000\mathrm{Hz},U=20\mathrm{V}$. All snapshots are of $100\mu \mathrm{m}\times 100\mu \mathrm{m}$ size and are strongly contrast enhanced. The white arrows indicate the initial director ${\mathbf{n}}_0$, the polarizer direction is vertical. $T=97{}^{\circ }\mathrm{C}$.

Figure 10

Frequency dependence of (a) the threshold voltages $U_{\mathrm{c}}$, (b) the dimensionless wave numbers $q^{*}$ and (c) the angle $\left|\alpha \right|$ between the wave vector ${\mathbf{q}}_{\mathrm{c}}$ and ${\mathbf{n}}_0$ for the ZZ and the $\mathrm{O}{\mathrm{R}}^{\pm }$ patterns. The inset in (a) shows in more detail the neighborhood of the frequency gap $25\mathrm{Hz}<\mathrm{f}<50\mathrm{Hz}$, where no regular patterns could be observed. $\mathrm{T}=97{}^{\circ }\mathrm{C}$.

Figure 11

Snapshots of the ZZ pattern at various polarizer settings. If the polarizer (black arrows) is (a) parallel with or (b) perpendicular to ${\mathbf{n}}_0$ (white arrows), only a very weak pattern is visible. Maximum pattern contrast is obtained if (c) the polarizer is at 45° to ${\mathbf{n}}_0$. $f=250\mathrm{Hz},U=8\mathrm{V},T=97{}^{\circ }\mathrm{C}$. The images are of $100\mu \mathrm{m}\times 100\mu \mathrm{m}$ size.

Figure 12

Representative snapshots of the high-frequency ac voltage driven prewavy (PWprim) pattern. (a) $f=4\mathrm{kHz},U=45\mathrm{V}$; (b) $f=20\mathrm{kHz},U=53\mathrm{V}$; (c) $f=70\mathrm{kHz},U=82\mathrm{V}$. The image sizes are $100\mu \mathrm{m}\times 100\mu \mathrm{m}$. The white arrows indicate the initial director ${\mathbf{n}}_{\mathbf{0}}$, the black arrows correspond to the polarizer direction.

Figure 13

Frequency dependence of (a) the threshold voltage $U_{\mathrm{c}}$ and (b) the dimensionless wave number $q^{*}$ of the high-frequency prewavy (PWprim) pattern. $T=97{}^{\circ }\mathrm{C}$.