Nonstandard electroconvection in a bent-core nematic liquid crystal

We characterize three nonstandard electrohydrodynamic instabilities in nematic liquid crystals composed of bent-core molecules. In addition to their shape, another important attribute of this material is that the anisotropy in the electrical conductivity changes sign as the frequency of the applied electric field changes. These instabilities do not appear to fit within the standard model for electroconvection. The first instability creates a pattern with stripes parallel to the initial director orientation, with a wavelength about equal to the separation of the cell plates. The next is the previously reported prewavy instability. The third instability is optically and dynamically identical to the prewavy instability, but is distinguished by different threshold behavior.

Figure 1

Schematic chemical structure of 4-chloro-1,3-phenylene bis4-[$4^{\prime }$ - (9-decenyloxy)benzoyloxy]benzoate.

Figure 2

(Color online) Example of the variation of the measured capacitance and conductance with magnetic field, at a temperature of $70°\mathrm{C}$.

Figure 3

This figure shows $[\sigma \left(H\right)-{\sigma }_{\perp }]∕{\sigma }_{\perp }$, where $\sigma \left(H\right)$ is the (nearly) parallel component measured in the Freedericksz state with $H=10.9\mathrm{kG}$, which is well above the Freederickz field, calculated to be $4.8\mathrm{kG}$. ${\sigma }_a$ is negative from $1\mathrm{Hz}$ to roughly $1500\mathrm{Hz}$, positive for $1500\to 8100\mathrm{Hz}$, and then negative again up to the end of the measurement at $100\mathrm{kHz}$. These measurements were made on the $25\text{−}\mu \mathrm{m}$ sample at $70°\mathrm{C}$.

Figure 4

Threshold curve for a $15\text{−}\mu \mathrm{m}$ sample at $75°\mathrm{C}$ in the $V\text{−}\log \left(f\right)$ plane. Below $28\mathrm{Hz}$ parallel stripes (PS) are observed. From $28\text{to}1000\mathrm{Hz}$ a wide stripe pattern (PW2) is seen. The region from $1000\text{to}5000\mathrm{Hz}$ does not show any EC (ER). Above $5000\mathrm{Hz}$ another wide stripe pattern (PW1) is observed. Regions are separated by solid lines. The inset shows PS threshold versus frequency to better demonstrate the linearity of the threshold curve in this region.

Figure 5

(Color online) (a) PS at $12\mathrm{Hz}$ and $28{\mathrm{V}}_{\mathit{rms}}$. (b) PS and PW2 coexisting at $26\mathrm{Hz}$ and $32{\mathrm{V}}_{\mathit{rms}}$. (c) PW2 at $200\mathrm{Hz}$ and $48{\mathrm{V}}_{\mathit{rms}}$. (d) Turbulent state at $5\mathrm{Hz}$ and $32{\mathrm{V}}_{\mathit{rms}}$, which is well above threshold at this frequency. Images were taken with a $15\text{−}\mu \mathrm{m}$ sample at $75°\mathrm{C}$ with crossed polarizers that were rotated $\sim 15°$ with respect to the vertical direction in the picture. Length scale represents $100\mu \mathrm{m}$ in each picture. In (a) and (b) the rubbing direction of the cell plates is in the vertical direction in the picture. In (c) and (d) the rubbing direction is in the horizontal direction in the picture.

Figure 6

(a) $V_{\mathit{th}}$ versus frequency in the PS regime. Solid triangles, solid circles, and open circles represent data at 70, 75, and $77°\mathrm{C}$, respectively. (b) Temperature dependence of $V_{\mathit{th}}$ at $20\mathrm{Hz}$ in the PS regime. The clearing point is at $78.2°\mathrm{C}$. Both measurements were made on a $15\text{−}\mu \mathrm{m}$ sample.

Figure 7

The linear fits (solid lines) to $1∕V_{\mathit{th}}\left(f\right)$ for PW2 (at low $f$) and PW1 (at high $f$) at $75°\mathrm{C}$ indicate that an ER exists even as $V_{\mathit{th}}\left(f\right)\to \infty$.

Figure 8

(Color online) Frequency dependence of the threshold voltages for PW1 and PW2. Squares, circles, and triangles represent $V_{\mathit{th}}$ at 70, 75, and $77°\mathrm{C}$, respectively. The solid, dashed, and dash-dotted lines mark the frequencies where the sign of of ${\sigma }_a$ changes at 70, 75, and $77°\mathrm{C}$, respectively. These measurements were made on a $25\text{−}\mu \mathrm{m}$ cell. $V_{\mathit{th}}\left(T\right)$ for PW1 shows a strong temperature dependence, while $V_{\mathit{th}}\left(T\right)$ for PW2 shows only a slight temperature dependence compared to PW1.

Figure 9

Temperature dependence of threshold voltages for the prewavy regimes. Solid triangles represent $V_{\mathit{th}}\left(T\right)$ for PW2 at $200\mathrm{Hz}$; open circles represent $V_{\mathit{th}}\left(T\right)$ for PW1 at $12000\mathrm{Hz}$. The clearing point is at $77.8°\mathrm{C}$. Both measurements were made on a $25\text{−}\mu \mathrm{m}$ sample.

Figure 10

Example of the wavy pattern, which is seen in the center region of the image, at $30\mathrm{kHz}$ and $55{\mathrm{V}}_{\mathit{rms}}$. Image taken with a $10\text{−}\mu \mathrm{m}$ sample at $70°\mathrm{C}$ between crossed polarizers that were rotated $\sim 15°$ with respect to the vertical direction in the picture. The rubbing direction of the cell plates is in the horizontal direction of the picture; the length scale represents $100\mu \mathrm{m}$.

Figure 11

(a) Wavelength as a function of $\epsilon$ at $20\mathrm{kHz}$ for PW1. (b) Wavelength as a function of frequency at $25{\mathrm{V}}_{\mathit{rms}}$ for PW1. (c) Wavelength as a function of $\epsilon$ at $200\mathrm{Hz}$ for PW2. (d) Wavelength as a function of frequency at $25{\mathrm{V}}_{\mathit{rms}}$ for PW2. In all charts the solid triangles and the open circles represent the pattern achieved by slowly varying and by quickly varying the voltage, respectively. All measurements were made on a $10\text{−}\mu \mathrm{m}$ sample at $70°\mathrm{C}$.

Figure 12

(Color online) Examples of the two main types of dislocations which form in the prewavy regions. (a) The stripes appear to split apart. (b) The stripes appear to cross over or twist around each other. Both images taken at $20\mathrm{kHz}$ after quickly moving from $0\text{to}30{\mathrm{V}}_{\mathit{rms}}$ with a $10\text{−}\mu \mathrm{m}$ sample at $70°\mathrm{C}$ between crossed polarizers that were rotated $\sim 15°$ with respect to the vertical direction in the picture. The rubbing direction of the cell plates is in the horizontal direction in the pictures; the length scales represent $100\mu \mathrm{m}$.

Figure 13

(Color online) The “knitting” instability at $40\mathrm{kHz}$ and $35{\mathrm{V}}_{\mathit{rms}}$. It is produced by abruptly raising the voltage from one of the prewavy states. Image taken with a $10\text{−}\mu \mathrm{m}$ sample at $70°\mathrm{C}$ between crossed polarizers that were rotated $\sim 15°$ with respect to the vertical direction in the picture. The rubbing direction of the cell plates is in the horizontal direction in the picture; the length scale represents $100\mu \mathrm{m}$.

Figure 14

Maxima of the azimuthal director modulation measured at $20\mathrm{kHz}$ and $70°\mathrm{C}$. The solid triangles and the open circles show the director angle found by slowly varying and by quickly varying the voltage, respectively. The solid line shows the fit to Eq. (1) with ${\varphi }_0=22.4°$ for the case where the voltage was slowly varied. The inset shows that the goodness of the fit can be better demonstrated by manipulating Eq. (1) to the form ${\varphi }^2={({\varphi }_0∕V_{\mathit{th}})}^2{V}^2-{\varphi }_0^2$, which more clearly shows the linear relation between ${\varphi }^2$ and $V^2$. Again, this was done for the case where the voltage was slowly varied. The fact that the $\varphi$ values saturated at higher voltages made it difficult to discern the point where the quadratic behavior ended, so there is an amount of uncertainty introduced into the fit of the straight line depending on how many data points are used.