Robert Repnik

Physics of defects in nematic liquid crystals

Liquid-crystal phases are typical examples of soft and complex materials that exhibit an abundance of different phenomena. In this paper we present some of our results contributing to the understanding of the physics of defects in nematic liquid crystals. The examples presented exhibit many features that are also of interest for other branches of physics. We describe nematic point defects, the annihilation dynamics of a defect and anti-defect pair, and the coarsening dynamics of a dense pattern of defects after a sudden symmetry-breaking phase transition.

Symmetry breaking in nematic liquid crystals: analogy with cosmology and magnetism

Universal behavior related to continuous symmetry breaking in nematic liquid crystals is studied using Brownian molecular dynamics. A three-dimensional lattice system of rod-like objects interacting via the Lebwohl-Lasher interaction is considered. We test the applicability of predictions originally derived in cosmology and magnetism. In the first part we focus on coarsening dynamics following the temperature driven isotropic-nematic phase transition for different quench rates. The behavior in the early coarsening regime supports predictions made originally by Kibble in cosmology. For fast enough quenches, symmetry breaking and causality give rise to a dense tangle of defects. When the degree of orientational ordering is large enough, well defined protodomains characterized by a single average domain length are formed. With time subcritical domains gradually vanish and supercritical domains grow with time, exhibiting a universal scaling law. In the second part of the paper we study the impact of random-field-type disorder on a range of ordering in the (symmetry broken) nematic phase. We demonstrate that short-range order is observed even for a minute concentration of impurities, giving rise to disorder in line with the Imry-Ma theorem prediction only for the appropriate history of systems.

Controlled nanoparticle targeting and nanoparticle-driven nematic structural transition

We study experimentally and theoretically controlled targeting of specific nanoparticles (NPs) to different regions within nematic liquid crystal. Using a simple mesoscopic Landau-de Gennes-type model in terms of a tensor nematic order parameter, we demonstrate a general mechanism which could be exploited for controlled targeting of NPs within a spatially nonhomogeneous nematic texture. Furthermore, we experimentally demonstrate using polarising microscopy that even a relatively low concentration of localised appropriate NPs could trigger a nematic structural transition. A simple estimate is derived to account for the observed transition.

Mixtures of Nanoparticles and Liquid Crystal Phases Exhibiting Topological Defects

We study theoretically mixtures of liquid crystals (LCs) and nanoparticles (NPs) at a mesoscopic level. Orientational LC ordering is given in terms of a tensor order parameter. We estimate conditions which favor or disfavor phase separation. We show under which conditions topological defect could be exploited as trapping centers for nanoparticles. Influence of Defect Core Replacement mechanism on phase stability of a structure possessing topological defect is demonstrated.

Development of Some Natural Science Competences in Undergraduate Study by Training Visualization Skills on Subject Liquid Crystal Phases and Structures

Understanding physical phenomena often requires a comprehensive imagination of the subject. Visualization software uses two main approaches for presenting three-dimensional (3D) physical systems in two dimensions (2D): 3D virtual simulation (3D view) or 2D cross-sections (2D view). We focused on liquid crystals (LCs) in our comparative study of comprehension of both views for two groups of students: unfamiliar and familiar with LCs. We found that students with experiences in this field prefer the use of 2D view while other students are significantly worse in interpretation of 2D views.

Sudden Isotropic-Nematic Phase Transition Within a Plan-Parallel Cell

ABSTRACT We study the nematic structure of a liquid crystal confined within a plan-parallel cell following the temperature driven isotropic-nematic phase transition quench. The Lebwohl-Lasher lattice model is used. The kinetics of the system is followed via Brownian molecular dynamics, enabling us to reach macroscopic time scales. In the simulation we assume that at one confining plate the nematic pattern becomes imprinted and frozen in after the phase transition. We study the main features of resulting nematic equilibrium structures.

Smectic ordering of octylcyanobiphenyl confined to control porous glasses

We performed an x-ray scattering study of the smectic A (SmA) ordering of the liquid crystal 8CB (octylcyanobiphenyl) confined to a control porous glass with a typical void radius R = 0.2 µm. The voids were either nontreated or covered with silane. The results reveal a strong influence of spatial restriction and surface treatment on the temperature evolution of smectic ordering. The observations are qualitatively reproduced using the Landau-Ginsburg approach.

Chapter Eight - Defects in Planar Cell Polarity of Epithelium: What Can We Learn from Liquid Crystals?

Epithelial tissues are structured and highly organized monolayers of cells with many different tissue-specific functions. Ordering of epithelium cells in living tissues relies on spatially and temporally regulated cell behavior and is of vital importance for their functioning. The underlying mechanisms that govern the development of the tissue architecture and morphogenesis rely on planar cell polarity signaling pathways. Mutations and other disruptions of these pathways were found to cause developmental defects, leading to failures in lung branching or kidney development, for example, and are also involved in cancer cell migration. Here, we investigate how these defects affect the spatial arrangement and orientation of epithelium cells, giving special attention to tissue reorganization during development. For the characterization of the resulting polarized cytoarchitectures, we make use of methods developed in the field of liquid crystal (LC) research. In fact, epithelial tissues possess typical features of liquid crystalline systems albeit exhibiting a different local symmetry. Therefore, tools developed in the LC research community can be successfully applied for the description of the overall epithelial tissue topology and its orientational order. We additionally discuss and hypothesize the possibilities of using nanoparticles for structural defect stabilization and its application.

Mixtures Composed of Liquid Crystals and Nanoparticles

The past decade has witnessed an increased interest in the study of mixtures [1–3] of various soft materials and nanoparticles. A characteristic feature of a nanoparticle is that at least one of its dimensions is limited to between 1 and 100 nm. It is of interest to find combinations where each component introduces a qualitatively different behavior into the system. Such systems are expected to play an important role in the emerging field of nanotechnology and also in composites with extraordinary material properties.

Liquid Crystals and Development of Natural Science Competences

Understanding physical phenomena in education often requires a good three-dimensional (3D) imagination. Visualization software mainly uses either active 3D virtual simulations or static two-dimensional cross-sections for presenting real physical systems. We performed a comparative study of students’ comprehension of both visualization approaches in the field of fundamental liquid crystal (LC) phases. We also developed a mechanical teaching tool—three boxes with wooden rods attached on vertical strings, in order to simulate the transitions between LC phases. We found that both the software and mechanical visualizations are efficient for representation of LC phases as well as training natural science competences.