Framework for liquid crystal based particle models

Abstract

Uniaxial nematic liquid crystal of ellipsoid-like molecules can be represented using director field n(x) of unitary vectors. It has topological charge quantization: integrating field curvature over a closed surface S, we get 3D winding number of S → S 2 , which has to be integer -getting Gauss law with built-in missing charge quantization if interpreting field curvature as electric field. In recent years there were experimentally observed various types of long-range interactions for such localized topological configurations, including Coulomb-like. This article proposes a general skyrmion-like mathematical framework to extend this similarity with particle physics to biaxial nematics: additionally recognising intrinsic rotation of uniaxial nematic, having 3 distinguishable axes -e.g. allowing to construct hedgehog configuration with one of 3 axes: with the same topological charge, but different energy/mass -getting similarity with 3 leptons. The proposed approach recreates electromagnetism for them with builtin charge quantization and field regularization to finite energy, also suggesting unification of EM with GEM (gravitoelectromagnetism) approximation of general relativity by just extending from 3 distinguished axes in 3D space, to 4 in 4D spacetime.

Qualitatively and Quantitatively Different Configurations of Nematic–Nanoparticle Mixtures

“…The case shown in Figure 2a penalises only the interfacial free energy contribution because the LC order is essentially spatially homogeneous and, consequently, it does not, on average, accommodate the homeotropic anchoring condition. Consequently, the total free energy penalty of this state is estimated by [2,40] 𝐹 ~4𝜋𝑅 𝑊 (12) where we use Equation (10) and 𝑊~𝑤𝑆. In the competing state shown in Figure 2b, the homeotropic surface anchoring condition is fulfilled.…”

“…These could enable numerous applications, particularly in photonics, sensitive detectors, and memory devices, to mention some of them [ 5 , 7 ]. Furthermore, such systems often exhibit diverse universal features [ 8 , 9 , 10 , 11 , 12 , 13 ] and could be exploited as relatively easy and cheap experimentally accessible testing grounds to study different open problems in physics.…”

Stable Assemblies of Topological Defects in Nematic Orientational Order

“…Gained knowledge might shed light on behavior of their analogs in related systems, which are otherwise hardly experimentally accessible. 7 Landau-type modeling of symmetry-breaking phase transitions introduces order parameter fields describing order in the broken phase. In general, an order parameter field consists of two qualitatively different components: 8 amplitude fields and phase fields.…”

“…10,15−20 Furthermore, a rich pallet of existing LC phases possesses analogs of almost all physical phenomena. For example, smectic A (SmA) configurations bear some resemblance to superconductors 21 and Abrikosov lattices, 22 coarsening dynamics of defect structures in a fast enough isotropic−nematic (I−N) quenches provides clues of the early universe evolution, 15,23 and studies of topological defects 7,10,16,17,24 and knots 18,20 in LCs give insight into particle-like excitations in nature.…”