1. Reconfiguration of nematic disclinations in plane-parallel confinementsSaša Harkai, Charles Rosenblatt, Samo Kralj, 2023, izvirni znanstveni članek Opis: We study numerically the reconfiguration process of colliding |m|=1/2 strength disclinations in an achiral nematic liquid crystal (NLC). A Landau–de Gennes approach in terms of tensor nematic-order parameters is used. Initially, different pairs {m1,m2} 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<ℎc, 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>ℎc, the colliding disclinations at θ(2)c reconfigure into boojum-like twist disclinations. Ključne besede: liquid crystals, topological defects, disclinations, reconfiguration Objavljeno v DKUM: 28.03.2024; Ogledov: 100; Prenosov: 7 Celotno besedilo (7,16 MB) Gradivo ima več datotek! Več... |
2. Stable assemblies of topological defects in nematic orientational orderArbresha Hölbl, Luka Mesarec, Juš Polanšek, Aleš Iglič, Samo Kralj, 2023, izvirni znanstveni članek Opis: We considered general mechanisms enabling the stabilization of localized assemblies of topological defects (TDs). There is growing evidence that physical fields represent fundamental natural entities, and therefore these features are of interest to all branches of physics. In general, cores of TDs are energetically costly, and consequently, assemblies of TDs are unfavorable. Owing to the richness of universalities in the physics of TDs, it is of interest to identify systems where they are easily experimentally accessible, enabling detailed and well-controlled analysis of their universal behavior, and cross-fertilizing knowledge in different areas of physics. In this respect, thermotropic nematic liquid crystals (NLCs) represent an ideal experiment testbed for such studies. In addition, TDs in NLCs could be exploited in several applications. We present examples that emphasize the importance of curvature imposed on the phase component of the relevant order parameter field. In NLCs, it is represented by the nematic tensor order parameter. Using a simple Landau-type approach, we show how the coupling between chirality and saddle splay elasticity, which can be expressed as a Gaussian curvature contribution, can stabilize Meron TDs. The latter have numerous analogs in other branches of physics. TDs in 2D curved manifolds reveal that the Gaussian curvature dominantly impacts the assembling and stabilization of TDs. Furthermore, a strong enough curvature that serves as an attractor for TDs is a respective field that could be imposed in a fast enough phase transition. Assemblies of created TDs created in such a disordered environment could be stabilized by appropriate impurities. Ključne besede: topological defects, nematic liquid crystals, Gaussian curvature, topological charge Objavljeno v DKUM: 17.07.2023; Ogledov: 281; Prenosov: 8 Povezava na datoteko |
3. DIFFRACTION GRATINGS FORMED BY BENT-CORE LIQUID CRYSTALS IN THE TWIST – BEND NEMATIC PHASEMuhammad Ali, 2021, doktorska disertacija Opis: In this thesis, we study the structure and optical transmission properties of the twist-bend nematic liquid crystalline phase, made of bent dimers, confined in thin planar cells. Confinement leads to the formation of a periodic modulated structure, the formation of which is explained as follows. The twist-bend nematic phase is characterized by a heliconical modulation of the molecular long axes. Due to a short pitch of modulation (approximately 10 nm), the twist-bend nematic phase behaves as a pseudo-layered medium. At temperatures below the nematic – twist-bend nematic phase transition, the heliconical pitch and thus the thickness of the pseudo-layers reduces, which leads to a two-dimensional undulation of pseudo-layers in the direction perpendicular to the cell surfaces and along the surfaces. The undulated structure is responsible for a stripe texture observed under a polarizing microscope and acts as a diffraction grating.
We constructed theoretical models to predict the pseudo-layer structure of a confined twist-bend nematic phase and to describe the properties of light diffracted on such cells. The free energy of the two-dimensional pseudo-layer structure of the twist-bend nematic phase is expressed in terms of the nematic director field, by which we describe the direction of the heliconical axis, and a complex smectic order parameter, the gradient of which gives the direction of the layer normal. At first, we assume that pseudo-layers are perpendicular to the surfaces (bookshelf geometry) and find a stable structure by assuming an ansatz for the pseudo-layer displacement from the bookshelf geometry and then minimizing the free energy at a very strong and very weak surface anchoring. In this way a threshold condition for the onset of the modulated structure is obtained, as well as the amplitude and period of modulation. Next, we assume that, at the onset of the twist-bend nematic phase, pseudo-layers are formed at some angle (pre-tilt) with respect to the surface. We find that in both cases, the bookshelf and pre-tilted one, the calculated period of modulation far from the phase transition is always approximately twice the cell thickness, which agrees with experimental observations.
The properties of light diffracted by the spontaneously formed grating were studied both experimentally and theoretically. We measured the intensity and polarization properties of the first two orders of the diffracted light and the temperature dependence of the polarization of the second order diffraction peaks. To predict the observed properties of the diffracted light and to simplify the description of such gratings, we consider different preliminary models of a one-dimensional spatial variation of the optic axis, the direction of which is given by two angles. A transfer matrix method is used and a good agreement between the experimental and theoretical results is obtained. In a more comprehensive approach, we determine the spatial variation of the optic axis direction from the modeled structure. The electric field in the diffracted light is obtained by using the transfer matrix method and beam propagation method. In the case of a pre-tilt of the pseudo-layers and very strong surface anchoring both methods give good qualitative agreement with experimental results, only in the case of the temperature dependence of the second order diffraction peaks, a more complex beam propagation method is superior to the transfer matrix method.
The thesis is divided into three parts. In the first part, we focus on the physical properties of the twist-bend nematic phase and its structure in thin planar cells. In the second part, a continuum model is proposed and finally, the properties of diffracted light are discussed and theoretically predicted by using the beam propagation method and transfer matrix method. Ključne besede: Bent-dimer liquid crystals, twist-bend nematic phase, undulation of pseudo-layers, polarization, diffraction grating, beam propagation method, transfer matrix method. Objavljeno v DKUM: 21.10.2021; Ogledov: 1221; Prenosov: 85 Celotno besedilo (10,65 MB) |
4. Impact of curvature on nematic topological defectsLuka Mesarec, 2018, doktorska disertacija Opis: Topological defects (TDs) appear almost unavoidably in continuous symmetry breaking phase transitions. The topological origin makes their key features independent of systems' microscopic details; therefore TDs display many universalities. Because of their strong impact on numerous material properties and their significant role in several technological applications it is of strong interest to find simple and robust mechanisms controlling the positioning and local number of TDs. There are strong evidences that in physics the fields are fundamental entities of nature and not particles. If this is the case then topological defects (TDs) might play the role of fundamental particles. An adequate testing ground to study and gain fundamental understanding of TDs are nematic liquid crystals. We present a numerical study of TDs within effectively two dimensional closed soft films exhibiting in-plane orientational ordering. Popular examples of such class of systems are liquid crystalline shells and various biological membranes.
We analyze the impact of extrinsic and intrinsic curvature on positions of topological defects (TDs) in two-dimensional (2D) nematic films. We demonstrate that both these curvature contributions are commonly present and are expected to be weighted by comparable elastic constants. A simple Landau-de Gennes approach in terms of tensor nematic order parameter is used to numerically demonstrate impact of the curvatures on position of TDs on 2D ellipsoidal nematic shells. We introduce the Effective Topological Charge Cancellation mechanism controlling localised positional assembling tendency of TDs and the formation of pairs (defect,antidefect) on curved surfaces. Furthermore, we estimate a critical depinning threshold to form pairs (defect,antidefect) using the electrostatic analogy. Finally, we show how one could efficiently switch among qualitatively different structures by using a relative volume of ordered shells, which represents a relatively simple naturally accessible control parameter.
In doctoral thesis, we developed theoretical model of erythrocyte membrane by using a hybrid Helfrich-Landau type mesoscopic approach, taking into account in-plane membrane ordering. We demonstrate that the derived extrinsic membrane energy term, which strongly depends on the local orientations of the molecules, is essential for the predicted broadening of the range of the relative volumes corresponding to the stable discocyte shapes, which is otherwise very narrow if only intrinsic curvature energy term dominates. Ključne besede: Topological defects, Continuum fields, Nematic liquid crystals, Biological membranes, Nematic shells, Landau-de Gennes formalism, Topological charge, Nanoparticles, Gaussian curvature, Electrostatic analogy, Intrinsic curvature, Extrinsic curvature, Crystal growth nucleation, Relative
volume Objavljeno v DKUM: 09.03.2018; Ogledov: 2237; Prenosov: 237 Celotno besedilo (23,66 MB) |
5. Teaching complex fields of soft matter, proposal of a new liquid crystal analogyUroš Jagodič, Jacob Staines, Samo Kralj, Robert Repnik, 2014, izvirni znanstveni članek Opis: The key reason behind the richness of different structures and patterns displayed in nature is the universal mechanism of symmetry breaking. It shapes configurations at all length scales encountered in universe. Structures reached via symmetry breaking transitions are commonly described in terms of order parameter fields. One of the simplest systems where symmetry breaking concepts have already been explored in detail, are various liquid crystal (LC) phases. The reason behind this is rich variety of structures exhibited by LCs and their convenient experimental accessibility. Consequently, a wide spectrum of different theoretical tools have been developed in LCs. In this contribution the orientational ordering of housing block in San Francisco, which we choose as a typical large-city representative, was studied. Following nematic LC analogy we determine the local degree of ordering. The structural pattern of the city displays a domain-type pattern. The average degree of ordering within a domain strongly correlates with crime rate within it. Therefore, the results confirm an intuitive expectation that structures define properties. This model can be used as a helpful tool in education as it provides a way of understanding complex topics with the help of well-known every day phenomena. Ključne besede: education, liquid crystals, modelling, order parameter Objavljeno v DKUM: 19.12.2017; Ogledov: 1481; Prenosov: 81 Celotno besedilo (2,32 MB) Gradivo ima več datotek! Več... |
6. Patterns in symmetry breaking transitionsSamo Kralj, Robert Repnik, 2012, izvirni znanstveni članek Opis: It is now well accepted that we all have amazing capabilities in recognizing faces in a fraction of a second. This specific pattern recognition ability could be by appropriate training transferred to some other field of expertise. At the same time pattern recognition skills are becoming increasingly important survival strategy in the modern competitive world which faces information overload. In the paper we demonstrate an example of pattern-recognition type of lecturing modern physics. By using already absorbed knowledge and analogies we exploit our innate pattern recognition brain capabilities for more effective learning of new concepts in physics. Ključne besede: pattern recognition, universalities, liquid crystals, cosmology Objavljeno v DKUM: 15.12.2017; Ogledov: 1873; Prenosov: 141 Celotno besedilo (3,56 MB) Gradivo ima več datotek! Več... |
7. Symmetry breaking and structure of a mixture of nematic liquid crystals and anisotropic nanoparticlesMarjan Krašna, Matej Cvetko, Milan Ambrožič, 2010, izvirni znanstveni članek Opis: Orientational ordering of a homogeneous mixture of uniaxial liquid crystalline(LC) molecules and magnetic nanoparticles (NPs) is studied using the Lebwohl-Lasher lattice model. We consider cases where NPs tend to be oriented perpendicularly to LC molecules due to elastic forces. We study domain-type configurations of ensembles, which are quenched from the isotropic phase. We show that for large enough concentrations of NPs the long range uniaxial nematic ordering is replaced by short range order exhibiting strong biaxiality. This suggests that the impact of NPs on orientational ordering of LCs for appropriate concentrations of NPs is reminiscent to the influence of quenched random fields which locally enforce a biaxial ordering. Ključne besede: liquid crystals, nanoparticles, disorder, orientational order, quenched disorder, symmetry breaking Objavljeno v DKUM: 03.08.2017; Ogledov: 1384; Prenosov: 363 Celotno besedilo (447,84 KB) Gradivo ima več datotek! Več... |
8. Smectic A herringbone patternsSamo Kralj, Emmanuelle Lacaze, George Cordoyiannis, Zdravko Kutnjak, 2014, objavljeni znanstveni prispevek na konferenci Opis: Two qualitatively different SmA structures exhibiting herringbone-type layer patterns, to which we refer as the Defectless Smectic Herringbone (DSH) and the Dislocation Decorated Smectic Herringbone (DDSH) pattern are studied by a Landau-de Gennes-Ginzburg mesoscopic approach. Liquid crystal structures are described in terms of a nematic director field and a smectic complex order parameter. It is demonstrated that, in the proximity of the N-SmA phase transition, a melting of smectic layers could be realised even for relatively weakly-tilted smectic layers in DSH patterns (i.e. θt ≈ 100) for type I Sm4 phase. The width of melted region could be relatively large with respect to bulk values of the smectic characteristic lengths. In addition, a critical value of θt is determined at which a DDSH pattern is expected to appear. Ključne besede: liquid crystals, patterns, structural transitions Objavljeno v DKUM: 30.06.2017; Ogledov: 1875; Prenosov: 368 Celotno besedilo (1005,99 KB) Gradivo ima več datotek! Več... |
9. Effective topological charge cancelation mechanismLuka Mesarec, Wojciech Góźdź, Aleš Iglič, Samo Kralj, 2016, izvirni znanstveni članek Opis: Topological defects (TDs) appear almost unavoidably in continuous symmetry breaking phase transitions. The topological origin makes their key features independent of systems’ microscopic details; therefore TDs display many universalities. Because of their strong impact on numerous material properties and their significant role in several technological applications it is of strong interest to find simple and robust mechanisms controlling the positioning and local number of TDs. We present a numerical study of TDs within effectively two dimensional closed soft films exhibiting in-plane orientational ordering. Popular examples of such class of systems are liquid crystalline shells and various biological membranes. We introduce the Effective Topological Charge Cancellation mechanism controlling localised positional assembling tendency of TDs and the formation of pairs {defect, antidefect} on curved surfaces and/or presence of relevant “impurities” (e.g. nanoparticles). For this purpose, we define an effective topological charge Δmeff consisting of real, virtual and smeared curvature topological charges within a surface patch Δς identified by the typical spatially averaged local Gaussian curvature K. We demonstrate a strong tendency enforcing Δmeff → 0 on surfaces composed of Δς exhibiting significantly different values of spatially averaged K. For Δmeff ≠ 0 we estimate a critical depinning threshold to form pairs {defect, antidefect} using the electrostatic analogy. Ključne besede: topological defects, topological charge, numerical studies, orientational ordering, nematic liquid crystals, liquid crystalline shells, biological membranes, nanoparticles, Gaussian curvature, electrostatic analogy, annihilation, topology Objavljeno v DKUM: 23.06.2017; Ogledov: 1048; Prenosov: 337 Celotno besedilo (2,15 MB) Gradivo ima več datotek! Več... |
10. Impact of nanoparticles on nematic ordering in square wellsMitja Slavinec, Eva Klemenčič, Milan Ambrožič, Marjan Krašna, 2015, izvirni znanstveni članek Opis: Nematic liquid crystalline structures within square wells are studied numerically using both Lebwohl-Lasher lattice semimicroscopic and the Landau-de Gennes mesoscopic approach. At lateral boundary wall strong planar anchoring is enforced. The cell thickness h along the z Cartesian coordinate is assumed to be smaller than the characteristic square well size R. Using semimicroscopic modelling we restrict to effectively two-dimensional systems which we study in terms of the tensor nematic order parameter. We consider impact of appropriate nanoparticles (NPs) on nematic configuration for cases where R becomes comparable to the biaxial order parameter correlation length. In this case a star-like order reconstruction biaxial profile could be formed in absence of NPs. We demonstrate existence of a rich variety of different nematic structures, including topological defects, which are enabled by presence of appropriate NPs. Ključne besede: liquid crystals, nanoparticles, nematic ordering, square well, software simulation, visualization Objavljeno v DKUM: 14.06.2017; Ogledov: 1181; Prenosov: 365 Celotno besedilo (3,27 MB) Gradivo ima več datotek! Več... |