Backflow-Induced Asymmetric Collapse of Disclination Lines in Liquid Crystals

Abstract

We present experiments where opposed pairs of planar parallel disclination lines of topological strength s 1 move due to their mutual attraction. Our measurements show that their motion is clearly asymmetric, with 1 defects moving up to twice as fast as ÿ1 ones. This is a clear indication of backflow, given the intrinsic isotropic elasticity of our system. A phenomenological model is able to account for the experimental observations by renormalizing the orientational diffusivity estimated from the velocity of each defect. DOI: 10.1103/PhysRevLett.95.027801 PACS numbers: 61.30.Jf, 61.30.Hn, 61.72.Lk, 83.80.Xz Topological defects were first postulated in order to explain the plasticity of metals. Then, they were proved to be essential for understanding phase transitions, disordered systems, frustrated media, convective instabilities, as well as some biological shapes, etc. In real systems, defects interact, leading to complex dynamics that often result in the annihilation of pairs of defects of opposite signs. Such phenomena arise, for instance, during solid recrystallization, but they can similarly be observed in liquid crystals where they are much easier to study experimentally.In nematic (or cholesteric) liquid crystals, defects are disclination lines that break locally the orientational order. Their motion induces a distortion of the director field, starting at the defect core and propagating diffusively in the bulk. Early analysis assumed that the dynamical director field was the same as under static conditions at all times [1]. This quasistatic approximation leads to a logarithmic divergence of the calculated total dissipated energy, which requires one to introduce a cutoff length at large distances from the core of the defect. Ryskin and Kremenetsky [2] later showed that this characteristic length comes out naturally from the dynamic equations and is of the order of the orientational diffusivity divided by the velocity of the defect. This length defines an active zone around the defect in which the quasistatic approximation is valid. On the other hand, liquid crystals flow as liquids. One thus may expect that defect motion, which is mainly due to an inplace rotation of the director, is affected by hydrodynamics (the so-called backflow effects). Recent numerical simulation in two dimensions [3] of the annihilation of two planar disclination lines of strengths s 1=2 in nematics have confirmed this point. It was found numerically that backflow breaks the symmetry of the collapse dynamics between defects, even in isotropic elasticity, the 1=2 defect moving faster than the ÿ1=2 one. A similar conclusion was reached in simulations for the collapse of 1 disclinations in smectic-C films [4]. These results are consistent with the analysis by Kats et al. [5] who found that positive disclinations always exert a stronger influence on the flow velocity than negative ones.There has been some experimental work dealing with the interaction between parallel disclination lines. Most of it has involved statistical studies...

Interaction between a disclination and a uniaxial–isotropic phase interface in a nematic liquid crystal

“…For time-dependent processes, the dissipative forces associated with disclination and interface kinetics may strongly influence disclination-interface interactions. Results of Toth et al [8] and Oswald and Ignes-Mullol [9] demonstrating that the propagation speeds of disclinations strongly depends their topological strengths lead one to expect that disclinations of different strengths may approach a uniaxial-nematic phase interface at different rates. To explore such phenomena one might study the full dynamical equations of Cermelli et al [19].…”

“…The observed speed asymmetry in defect-defect annihilation was attributed to backflow arising from coupling between the director and velocity fields. Later Oswald and Ignes-Mullol [9] experimentally observed the asymmetry in the attractive motion of two disclinations with strengths +1 and −1. The authors qualitatively explained their results using a semi-phenomenological model which, to account for backflow effects, allows the defect mobility to depend on the defect strength.…”

Antipersistent behavior of defects in a lyotropic liquid crystal during annihilation

“…It is also known that defect and anti-defect present an anisotropic behavior when approaching each other, the defect usually moves faster than the anti-defect [35][36][37][38][39]. This last aspect has been recently addressed both, experimentally and numerically, by Dierking et al [40], for umbilical defects in a thermotropic liquid crystal under applied electric field.…”

Probing Elastic Anisotropy from Defect Dynamics in Langmuir Monolayers

“…In general, elastic anisotropy (inequality of the elastic constants) and hydrodynamic effects arising from defect motion (backflow) play a role in explaining this asymmetry. In fact, the latter is dominant in the context of bulk liquid crystals [1][2][3][4], thus hindering the possibility to develop a simple method to quantitatively relate material elasticity to defect dynamics, which would be an interesting alternative to traditional methods of determining the elastic constants [5,6]. We address here the somewhat opposite scenario by studying defect dynamics in Langmuir monolayers spread at the air-water interface [7].…”