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1. Co-revolving topological defects in a nematic liquid crystal

   Susser, Adam L.; Kralj, Samo; Rosenblatt, Charles (November 2021, Soft Matter)

   A patterned surface defect of strength m = +1 and its associated disclination lines can decompose into a pair of surface defects and disclination lines of strength m = +1/2. For a negative dielectric anisotropy liquid crystal subjected to an applied ac electric field E , these half-integer defects are observed to wobble azimuthally for E > than some threshold field and, for sufficiently large fields, to co-revolve antipodally around a central point approximately midway between the two defects. This behavior is elucidated experimentally as a function of applied field strength E and frequency ν , where the threshold field for full co-revolution scales as ν 1/2 . Concurrently, nematic electrohydrodynamic instabilities were investigated. A complete field vs. frequency “phase diagram” compellingly suggests that the induced fluctuations and eventual co-revolutions of the ordinarily static defects are coupled strongly to—and driven by—the presence of the hydrodynamic instability. The observed behaviour suggests a Lehmann-like mechanism that drives the co-revolution. 

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2. Electric field-induced crossover from 3D to 2D topological defects in a nematic liquid crystal: Experimental verification

   https://doi.org/10.1039/c9sm01733j  

   Ferris, Andrew J.; Afghah, Sajedeh; Selinger, Jonathan V.; Selinger, Robin L.; Rosenblatt, Charles (January 2019, Soft Matter)

   A substrate was patterned with two pairs of half-integer strength topological defects, (+½, +½) and (+½, −½). In a sufficiently thick cell, a disclination line runs in an arch above the substrate connecting the two half integer defects within each pair. The director around the disclination line for the like-sign pair must rotate in 3D, whereas for the opposite-sign defect pair the director lies in the xy-plane parallel to the substrate. For a negative dielectric anisotropy nematic, an electric field applied normal to the substrate drives the director into the xy-plane, forcing the arch of the disclination line of the like-sign pair to become extended along the z-axis. For sufficiently large field the arch splits, resulting in two nearly parallel disclination lines traversing the cell from one substrate to the other. The opposite-sign defect pair is largely unaffected by the electric field as the director already already lies in the xy-plane. Experimental results are presented, which are consistent with numerical simulations. 

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3. Electric field driven reconfigurable multistable topological defect patterns

   https://doi.org/https://doi.org/10.1103/PhysRevResearch.2.013176  

   Harkai, S.; Murray, B.S.; Rosenblatt, C.; Kralj, S. (January 2020, Physical review research)

   Topological defects appear in symmetry breaking phase transitions and are ubiquitous throughout Nature. As an ideal testbed for their study, defect configurations in nematic liquid crystals (NLCs) could be exploited in a rich variety of technological applications. Here we report on robust theoretical and experimental investigations in which an external electric field is used to switch between predetermined stable chargeless disclination patterns in a nematic cell, where the cell is sufficiently thick that the disclinations start and terminate at the same surface. The different defect configurations are stabilized by a master substrate that enforces a lattice of surface defects exhibiting zero total topological charge value. Theoretically, we model disclination configurations using a Landau-de Gennes phenomenological model. Experimentally, we enable diverse defect patterns by implementing an in-house-developed atomic force measurement scribing method, where NLC configurations are monitored via polarized optical microscopy. We show numerically and experimentally that an “alphabet” of up to 18 unique line defect configurations can be stabilized in a 4 × 4 lattice of alternating s = ±1 surface defects, which can be “rewired” multistably using appropriate field manipulation. Our proof-of-concept mechanism may lead to a variety of applications, such as multistable optical displays and rewirable nanowires. Our studies also are of interest from a fundamental perspective. We demonstrate that a chargeless line could simultaneously exhibit defect-antidefect properties. Consequently, a pair of such antiparallel disclinations exhibits an attractive interaction. For a sufficiently closely spaced pair of substrate-pinned defects, this interaction could trigger rewiring, or annihilation if defects are depinned. 

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4. Geometry and mechanics of disclination lines in 3D nematic liquid crystals

   https://doi.org/10.1039/D0SM01899F  

   Long, Cheng; Tang, Xingzhou; Selinger, Robin L.; Selinger, Jonathan V. (March 2021, Soft Matter)

   null (Ed.)

   In 3D nematic liquid crystals, disclination lines have a range of geometric structures. Locally, they may resemble +1/2 or −1/2 defects in 2D nematic phases, or they may have 3D twist. Here, we analyze the structure in terms of the director deformation modes around the disclination, as well as the nematic order tensor inside the disclination core. Based on this analysis, we construct a vector to represent the orientation of the disclination, as well as tensors to represent higher-order structure. We apply this method to simulations of a 3D disclination arch, and determine how the structure changes along the contour length. We then use this geometric analysis to investigate three types of forces acting on a disclination: Peach–Koehler forces due to external stress, interaction forces between disclination lines, and active forces. These results apply to the motion of disclination lines in both conventional and active liquid crystals. 

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5. Trapping of isotropic droplets by disclinations in nematic liquid crystals controlled by surface anchoring and elastic constant disparity

   https://doi.org/10.1103/PhysRevE.109.064703  

   Haputhanthrige, Nilanthi P; Paladugu, Sathyanarayana; Lavrentovich, Maxim O; Lavrentovich, Oleg D (June 2024, Physical Review E)

   Na (Ed.)

   Linear defects such as dislocations and disclinations in ordered materials attract foreign particles since they replace strong elastic distortions at the defect cores. In this work, we explore the behavior of isotropic droplets nucleating at singular disclinations in a nematic liquid crystal, predesigned by surface photopatterning. Experiments show that in the biphasic nematic-isotropic region, although the droplets are attracted to the disclination cores, their centers of mass shift away from the core centers as the temperature increases. The shift is not random, being deterministically defined by the surrounding director field. The effect is explained by the balance of interfacial anchoring and bulk elasticity. An agreement with the experiment can be achieved only if the model accounts for the disparity of the nematic elastic constants; the so-called one-constant approximation, often used in the theoretical analysis of liquid crystals, produces qualitatively wrong predictions. In particular, the experimentally observed shift towards the bend region around a +1/2 disclination core can be explained only when the bend constant is larger than the splay constant. The described dependence of the precise location of a foreign inclusion at defect cores on the elastic and surface anchoring properties can be used in rational design of microscale architectures. 

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