Electroconvection with and without the Carr-Helfrich effect in a series of nematic liquid crystals

Experimental electroconvection (EC) investigations on four homologs with negative dielectric anisotropy ${ϵ}_a$ and conductivity anisotropies ${\sigma }_a$ of various signs (the relative ${\widehat{\sigma }}_a={\sigma }_a∕{\sigma }_{\perp }$ ranges from $-0.6$ to $+0.3$) are reported. The homolog with positive conductivity anisotropy follows the predictions of the standard theoretical model, while the homolog with negative ${\sigma }_a$ shows a phenomenon, i.e., nonstandard electroconvection, not described by the Carr-Helfrich mechanism but manifesting in forms of stripes mainly parallel to the initial director, thus having a morphological similarity to the rolls of the standard EC. The remaining two homologs change the sign of their conductivity anisotropy with temperature that leads to a twofold character by crossing over from standard to nonstandard electroconvection. The patterns of both the standard and nonstandard EC have been characterized and compared.

Figure 1

The dielectric anisotropy ${ϵ}_a={ϵ}_{\Vert }-{ϵ}_{\perp }$ of (a) $\mathbf{5}∕\mathbf{8}$, (b) $\mathbf{8}∕\mathbf{7}$, (c) $\mathbf{10}∕\mathbf{4}$, and (d) $\mathbf{10}∕\mathbf{6}$ as a function of the relative temperature $T^{*}=(T-T_N)∕\left(T_{NI}-T_N\right)$ where $T_{NI}$ is the clearing point and $T_N$ is the lower temperature limit of the nematic range.

Figure 2

The normalized conductivity anisotropy ${\widehat{\sigma }}_a={\sigma }_a∕{\sigma }_{\perp }$ of $\mathbf{5}∕\mathbf{8}$ (solid squares), $\mathbf{8}∕\mathbf{7}$ (solid stars), $\mathbf{10}∕\mathbf{4}$ (triangles), and $\mathbf{10}∕\mathbf{6}$ (open circles) as a function of $T^{*}$.

Figure 3

The EC threshold voltage $U_c$ for $\mathbf{5}∕\mathbf{8}$ as a function of the frequency $f$ at three different temperatures. $\mathrm{CM}$, $\mathrm{DM}$, $\mathrm{NR}$, $\mathrm{OR}$, $\mathrm{tNR}$, and $\mathrm{tOR}$ denote the conductive mode, the dielectric mode, normal rolls, oblique rolls, traveling normal rolls, and traveling oblique rolls, respectively. The vertical dotted lines denote the Lifshitz points.

Figure 4

Comparison of the measured data (squares) and the linear stability fit (solid line) of the dependence of the threshold voltage $U_c$ (a) and the critical wave number $\mid {\mathbf{q}}_c\mid =\sqrt{q_x^2+q_y^2}$ (b) on $\omega {\tau }_0$ for $\mathbf{5}∕\mathbf{8}$, where $\omega =2\pi f$ and ${\tau }_0={ϵ}_0({ϵ}_{\perp }∕{\sigma }_{\perp })$ is the charge relaxation time. The dotted line marks the Lifshitz point. The experiments were carried out at ${80}^{\circ }\mathrm{C}$ ($T^{*}=0.86$).

Figure 5

Calculated ${\widehat{\sigma }}_a^c$ vs $\omega {\tau }_0$ above which the s-EC state exists for $\mathbf{10}∕\mathbf{6}$.

Figure 6

Comparison of the measured data (squares) and the theoretical predictions (solid line) for the dependence of the threshold voltage $U_c$ (a) and the critical wave number $\mid {\mathbf{q}}_c\mid =\sqrt{q_x^2+q_y^2}$ (b) on $\omega {\tau }_0$, for $\mathbf{10}∕\mathbf{6}$ at $88°\mathrm{C}$ $\left(T^{*}=0.8\right)$. The dotted line denotes the Lifshitz point.

Figure 7

Snapshot of the $\mathrm{ns}\text{−}\mathrm{EC}$ structure (OR, see the text for description) taken with crossed polarizers (a) and the corresponding intensity profile (b) along the white line for $\mathbf{10}∕\mathbf{6}$ at $T=85°\mathrm{C}$ $\left(T^{*}=0.4\right)$, $f=100\mathrm{Hz}$ $\left(\omega {\tau }_0=0.42\right)$, and $\epsilon =0.32$. The director is vertical as it is shown by the white arrow and it is parallel to one of the crossed polarizers.

Figure 8

Threshold voltage $U_c$ vs frequency $f$ of the structures observed in $\mathbf{10}∕\mathbf{6}$ at three different temperatures.

Figure 9

The dependence of the critical wave number $\mid {\mathbf{q}}_c\mid =\sqrt{q_x^2+q_y^2}$ and the obliqueness $\alpha =\arctan \left(q_x∕q_y\right)$ on $\omega {\tau }_0$ for $\mathbf{10}∕\mathbf{6}$ at $85°\mathrm{C}$ $(T^{*}=0.4)$, $87°\mathrm{C}$ $(T^{*}=0.66)$ and $88°\mathrm{C}$ $\left(T^{*}=0.8\right)$.

Figure 10

The threshold as a function of the frequency $U_c\left(f\right)$ for $\mathbf{8}∕\mathbf{7}$ at $T=72°\mathrm{C}$ $(T^{*}=0.14)$, $T=78°\mathrm{C}$ $(T^{*}=0.46)$ and $T=84°\mathrm{C}$ $(T^{*}=0.78)$.