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1. Splay-bend elastic inequalities shape tactoids, toroids, umbilics, and conic section walls in paraelectric, twist-bend, and ferroelectric nematics

   https://doi.org/10.1080/21680396.2024.2314305  

   Lavrentovich, Oleg D (January 2024, Liquid Crystals Reviews)

   Elastic constants of splay K_11, twist K_22, and bend K_33 of nematic liquid crystals are often assumed to be equal to each other in order to simplify the theoretical description of complex director fields. Here we present examples of how the disparity of K_11 and K_33 produces effects that cannot be described in a one-constant approximation. In a lyotropic chromonic liquid crystal, nematic droplets coexisting with the isotropic phase change their shape from a simply-connected tactoid to a topologically distinct toroid as a result of temperature or concentration variation. The transformation is caused by the increase of the splay-to-bend ratio K_11/K_33. A phase transition from a conventional nematic to a twist-bend nematic implies that the ratio K_11/K_33 changes from very large to very small. As a result, the defects caused by an externally applied electric field change the deformation mode of optic axis from bend to splay. In the paraelectric-ferroelectric nematic transition, one finds an inverse situation: K_11/K_33 changes from small to large, which shapes the domain walls in the spontaneous electric polarization field as conic sections. The polarization field tends to be solenoidal, or divergence-free, a behavior complementary to irrotational curl-free director textures of a smectic A. 

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2. Periodic splay Fréedericksz transitions in a ferroelectric nematic

   https://doi.org/10.1038/s41467-025-55827-9  

   Basnet, Bijaya; Paladugu, Sathyanarayana; Kurochkin, Oleksandr; Buluy, Oleksandr; Aryasova, Natalie; Nazarenko, Vassili G; Shiyanovskii, Sergij V; Lavrentovich, Oleg D (December 2025, Nature Communications)

   Abstract Electric field-induced splay of molecular orientation, called the Fréedericksz transition, is a fundamental electro-optic phenomenon in nonpolar nematic liquid crystals. In a ferroelectric nematic N_Fwith a spontaneous electric polarization$${{\bf{P}}}$$ $P$, the splay is suppressed since it produces bound electric charges. Here, we demonstrate that an alternating current (ac) electric field causes three patterns of N_Fpolarization. At low voltages,$${{\bf{P}}}$$ $P$oscillates around the field-free orientation with no stationary deformations. As the voltage increases, the polarization acquires stationary distortions, first splay and twist in a stripe pattern and then splay and bend in a square lattice of +1 and -1 defects. In all patterns,$${{\bf{P}}}$$ $P$oscillates around the stationary orientations. The stationary bound charge is reduced by a geometrical “splay cancellation” mechanism that does not require free ions: the charge created by splay in one plane is reduced by splay of an opposite sign in the orthogonal plane. 

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3. Structures, thermodynamics and dynamics of topological defects in Gay–Berne nematic liquid crystals

   https://doi.org/10.1039/D2SM01178F  

   Huang, Yulu; Wang, Weiqiang; Whitmer, Jonathan K.; Zhang, Rui (January 2023, Soft Matter)

   Topological defects are a ubiquitous phenomenon across different physical systems. A better understanding of defects can be helpful in elucidating the physical behaviors of many real materials systems. In nematic liquid crystals, defects exhibit unique optical signatures and can segregate impurities, showing their promise as molecular carriers and nano-reactors. Continuum theory and simulations have been successfully applied to link static and dynamical behaviors of topological defects to the material constants of the underlying nematic. However, further evidence and molecular details are still lacking. Here we perform molecular dynamics simulations of Gay–Berne particles, a model nematic, to examine the molecular structures and dynamics of +1/2 defects in a thin-film nematic. Specifically, we measure the bend-to-splay ratio K 3 / K 1 using two independent, indirect measurements, showing good agreement. Next, we study the annihilation event of a pair of ±1/2 defects, of which the trajectories are consistent with experiments and hydrodynamic simulations. We further examine the thermodynamics of defect annihilation in an NVE ensemble, leading us to correctly estimate the elastic modulus by using the energy conservation law. Finally, we explore effects of defect annihilation in regions of nonuniform temperature within these coarse-grained molecular models which cannot be analysed by existing continuum level simulations. We find that +1/2 defects tend to move toward hotter areas and their change of speed in a temperature gradient can be quantitatively understood through a term derived from the temperature dependence of the elastic modulus. As such, our work has provided molecular insights into structures and dynamics of topological defects, presented unique and accessible methods to measure elastic constants by inspecting defects, and proposed an alternative control parameter of defects using temperature gradient. 

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4. Topological transformations of a nematic drop

   https://doi.org/10.1126/sciadv.adf3385  

   Koizumi, Runa; Golovaty, Dmitry; Alqarni, Ali; Li, Bing-Xiang; Sternberg, Peter J.; Lavrentovich, Oleg D. (July 2023, Science Advances)

   Morphogenesis of living systems involves topological shape transformations which are highly unusual in the inanimate world. Here, we demonstrate that a droplet of a nematic liquid crystal changes its equilibrium shape from a simply connected tactoid, which is topologically equivalent to a sphere, to a torus, which is not simply connected. The topological shape transformation is caused by the interplay of nematic elastic constants, which facilitates splay and bend of molecular orientations in tactoids but hinders splay in the toroids. The elastic anisotropy mechanism might be helpful in understanding topology transformations in morphogenesis and paves the way to control and transform shapes of droplets of liquid crystals and related soft materials. 

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5. Conic sections in ferroelectric nematics: Experiments and mathematical modeling

   https://doi.org/10.1103/PhysRevResearch.6.043207  

   Kumari, Priyanka; Kurochkin, Olexandr; Nazarenko, Vassili G; Lavrentovich, Oleg D; Golovaty, Dmitry; Sternberg, Peter (November 2024, Physical Review Research)

   The domain structure of a fluid ferroelectric nematic is dramatically different from the domain structure of solid ferroelectrics since it is not restricted by rectilinear crystallographic axes and planar surface facets. We demonstrate that thin films of a ferroelectric nematic seeded by colloidal inclusions produce domain walls (DWs) in the shape of conics such as a parabola. These conics reduce the bound charge within the domains and at the DWs. An adequate description of the domain structures requires one to analyze the electrostatic energy, which is a challenging task. Instead, we demonstrate that a good approximation to the experimentally observed polydomain textures is obtained when the divergence of spontaneous polarization—which causes the bound charge—is heavily penalized by assuming that the elastic constant of splay in the Oseen-Frank energy is much larger than those for twist and bend. The model takes advantage of the fact that the polarization vector is essentially parallel to the nematic director throughout the sample. Published by the American Physical Society2024 

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