Twist-bend nematic drops as colloidal particles: Electric instabilities

The mesogen 1,''7''-bis(4-cyanobiphenyl-4'-yl)heptane (CB7CB), doped with a small quantity of an amphiphilic compound, is examined in its biphasic state in which twist-bend nematic (N_{TB}) drops are dispersed in the isotropic fluid. Various flexoelectric and electrokinetic responses of small drops in their escaped-radial-like (ER) geometry, and also of larger ones with parabolic focal conic defects, are discussed. A pair of confocal parabolas with their axes along the applied low-frequency electric field undergo periodic dimensional changes so as to contribute flexoelectrically to free-energy reduction. In an ER droplet, the same result is achieved by periodic relocations of the hedgehog core. Sine-wave fields of low frequency and high voltage excite patterned states near zero-voltage crossings and homeotropic alignment at peak voltages. ER drops also exhibit electrohydrodynamic effects; in relatively weak fields, they undergo translatory motion with a velocity that is a quadratic in the field strength; the drift, which occurs over a very wide frequency range, extending from dc to MHz region, is enabled by radial symmetry breaking that their off-centered geometry entails; and the drift direction reverses across a critical frequency. In high fields, vortical flows occurring within an ER N_{TB} drop become discernible. The hydrodynamic effects are discussed based on the Taylor-Melcher leaky dielectric model.