Citation: Harkai, S.; Rosenblatt, C.; Kralj, S. Reconfiguration of Nematic Disclinations in Plane-Parallel Confinements. Crystals 2023, 13, 904. https://doi.org/10.3390/ cryst13060904 Academic Editor: Francesco Simoni Received: 20 April 2023 Revised: 23 May 2023 Accepted: 27 May 2023 Published: 1 June 2023 Copyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). crystals Article Reconfiguration of Nematic Disclinations in Plane-Parallel Confinements Saša Harkai 1, *, Charles Rosenblatt 2 and Samo Kralj 3,4 1 Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana, Slovenia 2 Department of Physics, Case Western Reserve University, Cleveland, OH 44106, USA; rosenblatt@case.edu 3 Department of Physics, Faculty of Natural Sciences and Mathematics, University of Maribor, 2000 Maribor, Slovenia; samo.kralj@um.si 4 Solid State Department, Jožef Stefan Institute, 1000 Ljubljana, Slovenia * Correspondence: sasa.harkai@fmf.uni-lj.si Abstract: We study numerically the reconfiguration process of colliding |m| = 1/2 strength disclina- tions in an achiral nematic liquid crystal (NLC). A Landau–de Gennes approach in terms of tensor nematic-order parameters is used. Initially, different pairs {m 1 , m 2 } of parallel wedge disclination lines connecting opposite substrates confining the NLC in a plane-parallel cell of a thickness h are imposed: {1/2,1/2}, {−1/2,−1/2} and {−1/2,1/2}. The collisions are imposed by the relative rotation of the azimuthal angle θ of the substrates that strongly pin the defect end points. Pairs {1/2,1/2} and {−1/2,−1/2} “rewire” at the critical angle θ (1) c = 3π 4 in all cases studied. On the other hand, two qualitatively different scenarios are observed for {−1/2,1/2}. In the thinner film regime h < h c , the disclinations rewire at θ (2) c = 5π 4 . The rewiring process is mediated by an additional chargeless loop nucleated in the middle of the cell. In the regime h > h c , the colliding disclinations at θ (2) c reconfigure into boojum-like twist disclinations. Keywords: liquid crystals; topological defects; disclinations; reconfiguration 1. Introduction Topological defects (TDs) appear at diverse natural scales [1], including in particle physics, condensed matter physics and cosmology. Their existence is enabled topologically, which is independent of systems’ microscopic details. In most cases, they exhibit localized singularities in the order parameter field that represent ordering in a symmetry-broken phase. Their essential properties are determined by topological charges that are topo- logical invariants [2]. The related topological charge conservation rules determine their transformations, including merging and decaying processes. TDs in uniaxial nematic liquid crystal [3] (NLC) phases and structures represent an ideal testbed to study diverse TDs. In particular, they exhibit a rich pallet of qualitatively different TD structures. Furthermore, TDs in NLCs could be relatively easily created, stabi- lized, manipulated and observed. The ordering within NLC configurations is commonly described by the nematic tensor order parameter Q. For the case of a uniaxial order, it is commonly expressed as Q = S(n  n − I/3) in terms of the nematic uniaxial scalar-order parameter S and the nematic director field n, and I stands for the unit tensor. The latter unit vector field points in the mesoscopic-scale local uniaxial LC direction and exhibits head-to-tail invariance (i.e., the states ±n are physically equivalent). The amplitude S reflects the degree of nematic order. If distortions are present, then the NLC could locally enter biaxial states. Consequently, the cores of TDs, where the NLC order experiences relatively strong spatial variations, generally exhibit a biaxial order [4–6]. Of interest are line defects in NLCs. Their key properties are described by a 2D topological charge m and a 3D topological charge q [7]. The former quantity is also termed the “winding number” or Frank index [3], which is determined by the total reorientation of Crystals 2023, 13, 904. https://doi.org/10.3390/cryst13060904 https://www.mdpi.com/journal/crystals