Charlotte G. Slaughter

The three adjacent drop geometries for (a) sessile–sessile merging, (b) sessile–suspended or mixed merging, and (c) suspended–suspended merging.

We observe the formation of stable, magnetic field induced, alignment inversion walls, also called Helfrich walls, in nematic liquid crystals (NLCs) confined to a toroidal droplet with tangential anchoring at the boundaries. Walls are rare in NLCs due to their high energy compared to lower-dimensional defect structures. However, we find that Helfrich walls naturally form, transform, and migrate in this unconventional toroidal setting, generating intricate director-field configurations due to the interplay of confining geometry and external fields. Interestingly, the presence and number of point defects in the zero field nematic configuration of the toroid influences the types of walls that arise. In the absence of point defects, splay-bend walls emerge. By contrast, when a point defect pair exists on the toroidal surface, a wall not previously classified by Helfrich, and that involves both twist and splay-bend distortions, forms, and transforms. Our experiments and numerical simulations enable the quantification and elucidation of the physics behind the formation and transformation of these wall structures, extending the class of walls that were believed to occur in NLCs.

We deploy optical microscopy with and without an applied magnetic field to characterize the three-dimensional morphology and measure the line tension of twist disclinations in twisted nematic liquid crystal (LC) sample cells. Twist disclinations are generated by quenching the LC, 5CB (4-cyano-4’-pentylbiphenyl), into the nematic phase; 5CB is confined between substrates with in-plane anchoring directions perpendicular to one another. The disclinations form loops separating domains of opposite twist handedness. Many segments of these loops are pinned to the substrates, and the ends of some pinned segments connect to free disclination segments that penetrate into the bulk nematic. We use confocal microscopy to measure the profiles of these free disclinations and test theoretical predictions about their shape, yielding a lower bound of $\sim$32 nm for the disclination core radius. We then use an applied magnetic field to deform the free disclinations into circular arcs whose curvature increases with magnetic field strength and depends on the field-induced energy difference between opposite twist domains. The line tension of the disclinations is derived from an energy-balance equation that relates disclination curvature to magnetic field. The measured line tension increases logarithmically with sample cell thickness; it ranges from 75 to 200 pN in samples with thickness spanning from 6 to 27 $\mu$m. In total, the investigation introduces new non-invasive methodologies for studies of defects in LCs, and it provides new information about the line tension and character of isolated twist disclinations, thereby testing theory and laying experimental foundation for the study of ensembles of disclinations.