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 previously 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.

KEYWORDS:

• Chromonic liquid crystals
• twist cell
• quartic twist theory
• nematic elasticity
• frustrated ground state
• non-uniform distortions

Acknowledgments

We are grateful to an anonymous reviewer of an earlier version of this paper for their suggestions, which have improved our work. Both authors are members of the Italian Gruppo Nazionale per la Fisica Matematica, which is part of INdAM, the Italian Institute for Advanced Mathematics.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1. Tactoids are elongated, cylindrically symmetric shapes with pointed ends as poles.

2. It is nothing but what others would call a cholesteric twist.

3. It was shown in [38] that a double twist can, for example, be attained exactly on the symmetry axis of cylinders enforcing degenerate planar anchoring on their lateral boundary.

4. Equation (29a) is equivalent to equation (1) of [15], provided in the latter one corrects the typo that made appear $(\mathit{X}sin\mathit{\tau }/\sqrt{1+X^2}{)}^2$ as $(sin\mathit{\tau }/\sqrt{1+X^2}{)}^2$. Moreover, a perfectly equivalent form of (29b) would be the following,

$I_{\mathrm{\perp }}^{\mathrm{m}\mathrm{a}\mathrm{x}}\left(\mathrm{\Omega }\right)=\left(1-\frac{{\mathrm{\Omega }}^2}{{\tau }^2}\right){sin}^2\mathrm{\Omega }+{\left(cos\mathrm{\Omega }sin\tau -\frac{\mathrm{\Omega }}{\tau }sin\mathrm{\Omega }cos\mathit{\tau }\right)}^2.$