Deformable homeotropic nematic droplets in a magnetic field

Abstract

We present a Frank-Oseen elasticity theory for the shape and structure of deformable nematic droplets with homeotropic surface anchoring in the presence of a magnetic field. Inspired by recent experimental observations, we focus on the case where the magnetic susceptibility is negative, and find that small drops have a lens shape with a homogeneous director field for any magnetic-field strength, whereas larger drops are spherical and have a radial director field, at least if the magnetic field is weak. For strong magnetic fields the hedgehog configuration transforms into a split-core line defect that, depending on the anchoring strength, can be accompanied by an elongation of the tactoid itself. We present a three-dimensional phase diagram that shows the tactoid shape and director field for a given anchoring strength, tactoid size, and magnetic-field strength. Our findings rationalize the different shapes and structures that recently have been observed experimentally for nematic droplets found in dispersions of gibbsite platelets in two types of solvent.

Electric-field-induced shape transition of nematic tactoids

“…For comparison, under a 1T magnetic field, large V 2 O 5 tactoids are aligned along the field and are slightly elongated, with an aspect ratio increasing by only about 10%, without any change of their bipolar structure [2]. In a similar way, the axial ratio of lens-like tactoids formed by gibbsite platelets only slightly varies (by ∼30%) under a 1T magnetic field [20], in good agreement with theoretical models [7,20].…”

“…These nematic droplets have characteristic shapes that have already been the subject of several theoretical studies [2][3][4][5][6][7][8] and experiments on systems such as vanadium pentoxide (V 2 O 5 ) [2,9], carbon nanotubes [10,11], rodlike viruses [12,13], F-actin in cells [14], chromonic liquid crystals [15], and cellulose nano-crystals [16][17][18]. These investigations showed that the typical tactoid shapes, for example the so-called spindle-like shape with a bipolar director field (see the right inset in Fig.…”

A Landau-de Gennes theory for hard colloidal rods: Defects and tactoids

“…Finally, we remark that the hedgehog defect can be unstable towards a ring disclination or a split core defect, as was found for thermotropic LdG theory [46]. For hard rods the split core defect has been realized by applying an external magnetic field [49]. Ring disclinations, however, are expected not to occur in hard-rod systems, because, in contrast to molecular systems, we have K 11 K 33 .…”

Effect of Electric Fields on the Director Field and Shape of Nematic Tactoids

“…Indeed, the surface free energy for x 1 would require a term proportional to an area that scales as r 2 rather than the Rr that is valid for x ≥ 1. Similar arguments hold for the elastic and Coulomb terms [32,58,59].…”

“…Theoretical studies of Kaznacheev et al [26,27] and Prinsen et al [28][29][30] have revealed that the boojums are by and large virtual, situated outside of the droplet in an extrapolated director field pattern, and that the director field is almost always incompletely or quasi bipolar [4,26,28,[31][32][33]. The smaller the droplet, the further the virtual boojums move away from the poles of the droplets and the more strongly the director field resembles that of a spatially uniform director field that represents its ground state.…”