What a twist cell experiment tells about a quartic twist theory for chromonics

Abstract

The elastic theory of chromonic liquid crystals is not completely established. We know, for example, that for anomalously low twist constants (needed for chromonics) the classical Oseen-Frank theory may entail paradoxical consequences when applied to describe the equilibrium shapes of droplets surrounded by an isotropic phase: contrary to experimental evidence, they are predicted to dissolve in a plethora of unstable smaller droplets. We proposed a quartic twist theory that prevents such an instability from happening. Here, we apply this theory to the data of two experiments devised to measure the planar anchoring strength at the plates bounding a twist cell filled with a chromonic liquid crystal; these data had before been interpreted within the Oseen-Frank theory. We show that the quartic twist theory affords a better agreement with the experimental data, while delivering in one case a larger value for the anchoring strength.

Figures (7)

• Figure 1: Schematic of a $\pi/2$ twist cell.
• Figure 2: Graphical solution of \ref{['eq:g_equation']}. The graph of $g_\lambda(\alpha,\delta)$ against $\delta$ is drawn for $\alpha=5$ and several values of $\lambda$. For $\lambda=0$, the red curve represents the graph of $g_0$ in \ref{['eq:g_0']}. The black straight line is the graph of $\frac{\pi}{2}-2\delta$, which has a single intersection with the graph of each $g_\lambda$.
• Figure 3: Plots showing how the root $\delta_0$ of \ref{['eq:g_equation']} depends on both $\lambda$ and $\alpha$
• Figure 4: Best fits of the data for the intensity ratio $R$ in Fig. 4 of collings:anchoring with the theoretical functions given by \ref{['eq:R_def']} and \ref{['eq:I_max_perp']} when the total twist angle $\Omega$ is delivered by \ref{['eq:total_twist']}. Red curve (classical quadratic theory): $\lambda=0$ and $\alpha$ is the only fitting parameter. Blue curve (quartic twist theory): $\lambda>0$ is set free and used as a fitting parameter alongside with $\alpha$. The quartic twist theory is apparently more successful than the quadratic theory. Quantitative estimates of the error are given for both curves in Appendix \ref{['sec:error']}.
• Figure 5: Best combined fits of the data for the scaled light intensities $I_\perp^\mathrm{min}$ and $I_\perp^{\mathrm{max}}$ in Fig. 2 of peng:patterning with the theoretical functions given by \ref{['eq:I_min_perp']} and \ref{['eq:I_max_perp']} when the total twist angle $\Omega$ is delivered by \ref{['eq:total_twist']}. Red curves (classical quadratic theory): $\lambda=0$ and $\alpha$ is the only fitting parameter. Blue curves (quartic twist theory): $\lambda>0$ is set free and used as a fitting parameter alongside with $\alpha$. Again, the quartic twist theory is more successful than the quadratic theory; further quantitative details are given in Appendix \ref{['sec:error']}.