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Title:Impact of curvature on nematic topological defects
Authors:ID Mesarec, Luka (Author)
ID Kralj, Samo (Mentor) More about this mentor... New window
ID Iglič, Aleš (Co-mentor)
Files:.pdf DOK_Mesarec_Luka_2018.pdf (23,66 MB)
MD5: BB8CA0E0D05F209D5F88AFF51A3C8E0C
PID: 20.500.12556/dkum/6774b995-1ef4-4466-8a08-287652c16f84
 
Language:English
Work type:Doctoral dissertation (mb31)
Typology:2.08 - Doctoral Dissertation
Organization:FNM - Faculty of Natural Sciences and Mathematics
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
Year of publishing:2018
Publisher:L. Mesarec]
Source:[Maribor
PID:20.500.12556/DKUM-69191 New window
UDC:532.783(043.3)
COBISS.SI-ID:23697672 New window
NUK URN:URN:SI:UM:DK:PYDKTRFO
Publication date in DKUM:09.03.2018
Views:1572
Downloads:126
Metadata:XML RDF-CHPDL DC-XML DC-RDF
Categories:FNM
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Secondary language

Language:Slovenian
Title:Vpliv ukrivljenosti na nematične topološke defekte
Abstract:Topološki defekti se v naravi pogosto pojavijo ob zveznih faznih prehodih z zlomom simetrije. Zaradi njihovega topološkega izvora so glavne značilnosti topoloških defektov neodvisne od mikroskopskih lastnosti sistema. Topološki defekti imajo močan vpliv na številne lastnosti snovi in pomembno vlogo v nekaterih tehnoloških aplikacijah, zato obstaja interes, da odkrijemo enostavne in robustne mehanizme, ki kontrolirajo prostorsko porazdelitev in število toploških defektov v različnih sistemih. V fiziki je vse bolj popularna teorija, da za opis narave ne potrebujemo koncepta delcev, temveč lahko vse pojave opišemo s polji. Če ta teorija drži, potem bi lahko topološki defekti igrali vlogo osnovnih delcev. Primeren in dostopen sistem za raziskovanje topoloških defektov so nematični tekoči kristali. V doktorski disertaciji bomo predstavili numerično raziskavo topoloških defektov znotraj efektivno dvodimenzionalnih zaprtih površin, za katere je značilen nematični orientacijski red dolgega dosega. Znani primeri takšnih sistemov so tekočekristalne lupine in različne biološke membrane. V doktorskem delu analiziramo vpliv zunanje in notranje ukrivljenosti na položaje topoloških defektov v dvodimenzionalnih nematičnih lupinah. Pri modeliranju nematične urejenosti uporabimo Landau-de Gennesov formalizem, za izračun oblike lupin v primeru bioloških membran pa Helfrichov model spontane ukrivljenosti. V doktorski disertaciji smo vpeljali mehanizem izničitve efektivnega topološkega naboja, ki nam omogoča napovedovanje lokacije topoloških defektov in določitev pogojev za formacijo novih parov (defekt, antidefekt). S pomočjo elektrostatske analogije in mehanizma izničitve efektivnega topološkega lahko ocenimo kritične pogoje za formacijo novih parov (defekt,antidefekt). V doktorskem delu smo prikazali, da lahko s spreminjanjem relativnega volumna urejenih lupin na relativno enostaven način preklapljamo med kvalitativno različnimi strukturami. V doktorski disertaciji smo razvili teoretični model membrane eritrocitov z uporabo hibridnega Helfrich-Landau pristopa, kjer poleg upogibne energije membrane upoštevamo tudi orientacijski red v membrani. Ugotovili smo, da lahko nematična urejenost (predvsem, kadar upoštevamo vpliv zunanje ukrivljenosti) spremeni ravnovesne oblike zaprtih membranskih struktur. Pokazali smo, da se območje stabilnosti diskocitnih oblik v faznem diagramu močno razširi, kadar upoštevamo orientacijsko urejenost v prisotnosti zunanje ukrivljenosti.
Keywords:Topološki defekti, nematični tekoči kristali, biološke membrane, nematične lupine, Landau-de Gennesov formalizem, topološki naboj, nanodelci, Gaussova ukrivljenost, elektrostatska analogija, notranja ukrivljenost, zunanja ukrivljenost, tvorba kristalov, relativni volumen


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