Eur. Phys. J. E (2006) 20: 71-79
https://doi.org/10.1140/epje/i2005-10120-9

Regular Article

Annihilation of nematic point defects: Pre-collision and post-collision evolution

¹ Regional Development Agency Ltd., Lendavska 5a, 9000, Murska Sobota, Slovenia
² Laboratory of Physics of Complex Systems, Faculty of Education, University of Maribor, Koroška 160, 2000, Maribor, Slovenia
³ Jožef Stefan Institute, Jamova 39, 1000, Ljubljana, Slovenia
⁴ Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000, Ljubljana, Slovenia

^* e-mail: milan@rra-mura.si

Received: 11 December 2005
Accepted: 27 March 2006
Published online: 2 May 2006

Abstract

The annihilation of the nematic hedgehog and anti-hedgehog within an infinite cylinder of radius R is studied. The semi-microscopic lattice-type model and Brownian molecular dynamics are used. We distinguish among the i) early pre-collision, ii) late pre-collision, iii) early post-collision, and iv) late post-collision stages. In the pre-collision stage our results agree qualitatively with the existing experimental observations and also continuum-type simulations. The core of each defect exhibits a ring-like structure, where the ring axis is set perpendicular to the cylinder symmetry axis. For ξ⁽⁰⁾ _d/(2R) > 1 the interaction between defects is negligible, where ξ⁽⁰⁾ _d describes the initial separation of defects. Consequently, the defects annihilate within the simulation time window for ξ⁽⁰⁾ _d/(2R) < 1. For close enough defects their separation scales as ξ_d (t _c - t)^0.4±0.1, where t_c stands for the collision time. In elastically anisotropic medium the hedgehog is faster than the anti-hedgehog. In the early pre-collision stage the defects can be treated as point-like particles, possessing inherent core structure, that interact via the nematic director field. In the late pre-collision stage the cores reflect the interaction between defects. After the collision a charge-less ring structure is first formed. In the early post-collision stage the ring adopts an essentially untwisted circular structure of the radius ξ_r. In the late post-collision stage we observe two qualitatively different scenarios. For μ = ξ_r/R < μ_c ∼ 0.25 the ring collapses leading to the escaped radial equilibrium structure. For μ > μ_c the chargeless ring triggers the nucleation growth into the planar polar structure with line defects.