1. DIFFRACTION GRATINGS FORMED BY BENT-CORE LIQUID CRYSTALS IN THE TWIST – BEND NEMATIC PHASEMuhammad Ali, 2021, doctoral dissertation Abstract: 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. Keywords: Bent-dimer liquid crystals, twist-bend nematic phase, undulation of pseudo-layers, polarization, diffraction grating, beam propagation method, transfer matrix method. Published in DKUM: 21.10.2021; Views: 433; Downloads: 39 Full text (10,65 MB) |
2. Impact of curvature on nematic topological defectsLuka Mesarec, 2018, doctoral dissertation Abstract: 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. Keywords: 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 Published in DKUM: 09.03.2018; Views: 1572; Downloads: 126 Full text (23,66 MB) |
3. Effective topological charge cancelation mechanismLuka Mesarec, Wojciech Góźdź, Aleš Iglič, Samo Kralj, 2016, original scientific article Abstract: 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. Keywords: topological defects, topological charge, numerical studies, orientational ordering, nematic liquid crystals, liquid crystalline shells, biological membranes, nanoparticles, Gaussian curvature, electrostatic analogy, annihilation, topology Published in DKUM: 23.06.2017; Views: 730; Downloads: 308 Full text (2,15 MB) This document has many files! More... |
4. Impact of nanoparticles on nematic ordering in square wellsMitja Slavinec, Eva Klemenčič, Milan Ambrožič, Marjan Krašna, 2015, original scientific article Abstract: 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. Keywords: liquid crystals, nanoparticles, nematic ordering, square well, software simulation, visualization Published in DKUM: 14.06.2017; Views: 832; Downloads: 329 Full text (3,27 MB) This document has many files! More... |
5. STABILITY AND METASTABILITY OF NEMATIC GLASSESAmid Ranjkesh Siahkal, 2014, doctoral dissertation Abstract: Structures exhibiting continuous symmetry breaking are extremely susceptible to various perturbations. The reason behind is the existence of Goldstone modes in the gauge
component of the order parameter describing broken symmetry. The so-called Larkin-Imry–Ma argument claims that even infinitesimally weak random field-type disorder destroys long range order (LRO) which would otherwise be present in the absence of random disorder. Furthermore, it claims that the system breaks into domain type configuration having short range order (SRO), where the characteristic domain size scales as ksi= W^-2/(4-d). Here W measures the strength of random field interaction and d is the dimensionality of space. However, some studies claim that structures with quasi long range order (QLRO) are established instead of SRO. The main focus of this doctor thesis is the character of nematic structures in the random field. I studied theoretically and numerically nematic structures that are obtained by continuous symmetry breaking in orientational degrees of freedom on
decreasing the temperature T, starting from the ordinary liquid, the so called isotropic phase. In particular, I investigated conditions for which the Larkin-Imry-Ma theorem holds true. So far statistical interpretations of such systems have typically used two different semi-
microscopic type models: i) the Random Anisotropic Nematic (RAN) and ii) the Sprinkled Silica Spin (SSS) model. The RAN model is a Lebwohl-Lasher (LL) model with nematic molecules locally coupled with uncorrelated random anisotropic field at each site, while the SSS model has a finite concentration of impurities frozen in random directions. I used a three dimensional (d = 3) model intermediate between SSS and RAN models, with finite
concentration p of frozen impurities, where p < pc (pc stands for the percolation threshold). The simulations were performed at different temperatures for temperature-quenched (TQH) and ﬁeld-quenched histories (FQH), as well as for temperature-annealed histories (AH). The
ﬁrst two of these limits represent extreme histories encountered in typical experimental studies. Numerically, I studied the impact of control parameters (T, p, W) and history of samples (TQH, FQH, AH) on structural properties of the system. Within the model I was varying p, temperature T, interaction strength W and also sample histories. From final configurations, I calculated orientational order parameters and two-point correlation
functions. Next, I estimated the size of the Larkin-Imry-Ma domains d. Finite size-scaling was also used to determine the range of the orientational ordering, as a function of W, p, T and sample history. The main results of my study are the following. In general, the system exhibited strong memory effects, indicating important role of history of samples. Furthermore, obtained results were relatively robust (from macroscopic point of view), indicating substantial energy barriers among competing states. On increasing the strength W, I typically obtained the following sequence of orders: LRO, QLRO, and SRO. For some concentrations p,however, SRO was absent. The crossover anchoring strength between QLRO and SRO strongly depends on history of samples, and it has the lowest values for TQH. From my simulations it follows that for the model used the Larkin-Imry-Ma argument holds only in limited range of model parameters. In most cases I obtain QLRO instead of SRO. However, in all structures there is imprint of Larkin-Imry-Ma domains, exhibiting scaling d 1/ (W2p) in the weak anchoring regime. This suggests that we do not have a “classical ” QLRO with algebraic decay with distance. Similar results were obtained in the studies of magnetic systems. Keywords: nematic liquid crystals, topological defect, order parameter, symmetry breaking, domains, Random field, larkin-Imry–Ma theorem, speroNematics Published in DKUM: 15.07.2014; Views: 1557; Downloads: 100 Full text (2,86 MB) |
6. Fingered core structure of nematic boojumsSamo Kralj, Riccardo Rosso, Epifanio G. Virga, 2008, original scientific article Abstract: Using the Landau-de Gennes phenomenological approach, we study the fine biaxial core structure of a boojum residing on the surface of a nematic liquid crystal phase. The core is formed by a negatively uniaxial finger, surrounded by a shell with maximal biaxiality. The characteristic finger's length and the shell's width are comparable to the biaxial correlation length. The finger tip is melted for topological reasons. Upon decreasing the surface anchoring strength below a critical value, the finger gradually leaves the bulk and it is expelled through the surface. Keywords: physics, liquid crystals, nematic crystals, line defects, surface phenomena Published in DKUM: 07.06.2012; Views: 1463; Downloads: 104 Link to full text |
7. Alignment of carbon nanotubes in nematic liquid crystalsPaul van der Schoot, Vlad Popa-Nita, Samo Kralj, 2008, original scientific article Abstract: The self-organizing properties of nematic liquid crystals can be used to aligncarbon nanotubes dispersed in them. Because the nanotubes are so much thinner than the elastic penetration length, the alignment is caused by the coupling of the unperturbed director field to the anisotropic interfacial tension of the nanotubes in the nematic host fluid. In order to relate the degree of alignment of the nanotubes to the properties of the nematic liquid crystal, we treat the two components on the same footing and combine Landau-deGennes free energies for the thermotropic ordering of the liquid crystal and for the lyotropic nematic ordering of carbon nanotubes caused by their mutually excluded volumes. The phase ordering of the binary mixture is analyzed as a function of the volume fraction of the carbon nanotubes, the strength of the coupling and the temperature. We find that the degree of ordering of the nanorods is enslaved by the properties of the host liquid and that it can be tuned by raising or lowering the temperature or by increasing or decreasing their concentration. By comparing the theory to recent experiments, we find the anchoring energy of multiwalled carbon nanotubes to be in the range from 10-10 to 10-7 N m-1. Keywords: liquid crystals, nematic crystals, molecular dynamics, stability, elasticity, carbon nanotubes Published in DKUM: 07.06.2012; Views: 1566; Downloads: 78 Link to full text |
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9. Finite-size effects on order reconstruction around nematic defectsSamo Kralj, Riccardo Rosso, Epifanio G. Virga, 2010, original scientific article Abstract: By use of the Landau-de Gennes phenomenological theory, we study the texture of a nematic liquid crystal confined within a hybrid cell. Precisely, we consider cylindrically symmetric solutions containing topological defects dictated by appropriate boundary conditions. We focus our attention on cells whose dimensions are comparable with the biaxial correlation length ▫$xi_b$▫. For such severe confinements the order reconstruction (OR) configuration could be stable. Its structural details reflect the balance among boundary-enforced frustration, elastic penalties, and finite-size effects. In particular, we analyze the interplay between finite-size effects and topological defects. We show that defects are always pinned to the negatively (planar) uniaxial sheet of the OR structure. The presence of a ring defect can dramatically increase the critical threshold below which the OR structure is stable. Keywords: physics, liquid crystals, nematic crystals, nematic defects, structural transitions Published in DKUM: 07.06.2012; Views: 1739; Downloads: 89 Link to full text |