1. History-dependent phase transition characterJuš Polanšek, Arbresha Hölbl, Szymon Starzonek, Aleksandra Drozd-Rzoska, Sylwester Rzoska, Samo Kralj, 2022, izvirni znanstveni članek Opis: We consider history-dependent behavior in domain-type configurations in orientational order that are formed in configurations reached via continuous symmetry-breaking phase transitions. In equilibrium, these systems exhibit in absence of impurities a spatially homogeneous order. We focus on cases where domains are formed via (i) Kibble-Zurek mechanism in fast enough quenches or by (ii) Kibble mechanism in strongly supercooled phases. In both cases, domains could be arrested due to pinned topological defects that are formed at domain walls. In systems exhibiting polar or quadrupolar order, point and line defects (disclinations) dominate, respectively. In particular, the disclinations could form complex entangled structures and are more efficient in stabilizing domains. Domain patterns formed by fast quenches could be arrested by impurities imposing a strong enough random-field type disorder, as suggested by the Imry-Ma theorem. On the other hand, domains formed in supercooled systems could be also formed if large enough energy barriers arresting domains are established due to large enough systems’ stiffness. The resulting effective interactions in established domain-type patterns could be described by random matrices. The resulting eigenvectors reveal expected structural excitations formed in such structures. The most important role is commonly played by the random matrix largest eigenvector. Qualitatively different behavior is expected if this eigenvector exhibits a localized or extended character. In the former case, one expects a gradual, non-critical-type transition into a glass-type structure. However, in the latter case, a critical-like phase behavior could be observed. Ključne besede: topological defects, domains, disorder Objavljeno v DKUM: 01.07.2024; Ogledov: 61; Prenosov: 2 Celotno besedilo (2,07 MB) Gradivo ima več datotek! Več... |
2. 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: 133; Prenosov: 7 Celotno besedilo (7,16 MB) Gradivo ima več datotek! Več... |
3. 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: 349; Prenosov: 17 Celotno besedilo (6,14 MB) Gradivo ima več datotek! Več... |
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: 2313; Prenosov: 237 Celotno besedilo (23,66 MB) |
5. Interplay between art and science in educationSamo Kralj, Boris Aberšek, Irena Kralj, 2014, izvirni znanstveni članek Opis: Music can be viewed as a structure formed by notes. Different structures in music have potential to yield enormously rich diversity of different melodies. Music is a typical example where a structure defines a property. Similar concepts could be also exploited in education, in presented case in nano-sciences, which are typical representatives of soft materials the structure of which can be strongly manipulated with local geometry and presence of appropriate nanoparticles. The objects of study, named also LC shells, will be exploited as basic unit elements for future soft colloidal crystals. A different arrangement of colloids within the crystal would result in different physical properties in a similar way as different packing of atoms results in different crystals made of real atoms. In presented research will be demonstrated, how relevant basic mechanisms in thin films of nematic liquid crystals could be explained in a classroom and used as a case study, also for explanation of many other physical properties. This research topic is still in its infancy. At this stage only various defect structures in relatively simple geometries (spherical and elliptical) will be analyzed. There is a need to find simple ways to control sensitively the valence of LC shells and in particular to develop strategies to assemble them in crystal structures of desired symmetry. This would allow tailoring specific optical dispersion relations or other physical property of interest and make new ways to teach different physical properties on the "music" based approach. Ključne besede: teaching strategies, music education, nanosciences, topological defects Objavljeno v DKUM: 15.12.2017; Ogledov: 1538; Prenosov: 94 Celotno besedilo (1,19 MB) Gradivo ima več datotek! Več... |
6. Vesiculation of biological membrane driven by curvature induced frustrations in membrane orientational orderingDalija Povše Jesenek, Šárka Perutková, Wojciech Góźdź, Veronika Kralj-Iglič, Aleš Iglič, Samo Kralj, 2013, izvirni znanstveni članek Opis: Membrane budding often leads to the formation and release of microvesicles. The latter might play an important role in long distance cell-to-cell communication, owing to their ability to move with body fluids. Several mechanisms exist which might trigger the pinching off of globular buds from the parent membrane (vesiculation). In this paper, we consider the theoretical impacts of topological defects (frustrations) on this process in the membranes that exhibit global in-plane orientational order. A Landau–de Gennes theoretical approach is used in terms of tensor orientational order parameters. The impact of membrane shapes on position and the number of defects is analyzed. In studied cases, only defects with winding numbers m = ±1/2 appear, where we refer to the number of defects with m = 1/2 as defects, and with m = –1/2 as anti-defects. It is demonstrated that defects are attracted to regions with maximal positive Gaussian curvature, K. On the contrary, anti-defects are attracted to membrane regions exhibiting minimal negative values of K. We show on membrane structures exhibiting spherical topology that the coexistence of regions with K > 0 and K < 0 might trigger formation of defect–anti-defect pairs for strong enough local membrane curvatures. Critical conditions for triggering pairs are determined in several demonstrative cases. Then the additionally appeared anti-defects are assembled at the membrane neck, where K < 0. Consequent strong local fluctuations of membrane constituent anisotropic molecules might trigger membrane fission neck rupture, enabling a membrane fission process and the release of membrane daughter microvesicles (ie, vesiculation). Ključne besede: structural transitions, topological defects, membrane microvesicles, membrane curvature, membrane fission, vesiculation Objavljeno v DKUM: 03.08.2017; Ogledov: 1273; Prenosov: 422 Celotno besedilo (4,92 MB) Gradivo ima več datotek! Več... |
7. Curvature-controlled topological defectsLuka Mesarec, Pavlo Kurioz, Aleš Iglič, Wojciech Góźdź, Samo Kralj, izvirni znanstveni članek Opis: Effectively, two-dimensional (2D) closed films exhibiting in-plane orientational ordering (ordered shells) might be instrumental for the realization of scaled crystals. In them, ordered shells are expected to play the role of atoms. Furthermore, topological defects (TDs) within them would determine their valence. Namely, bonding among shells within an isotropic liquid matrix could be established via appropriate nano-binders (i.e., linkers) which tend to be attached to the cores of TDs exploiting the defect core replacement mechanism. Consequently, by varying configurations of TDs one could nucleate growth of scaled crystals displaying different symmetries. For this purpose, it is of interest to develop a simple and robust mechanism via which one could control the position and number of TDs in such atoms. In this paper, we use a minimal mesoscopic model, where variational parameters are the 2D curvature tensor and the 2D orientational tensor order parameter. We demonstrate numerically the efficiency of the effective topological defect cancellation mechanism to predict positional assembling of TDs in ordered films characterized by spatially nonhomogeneous Gaussian curvature. Furthermore, we show how one could efficiently switch among qualitatively different structures by using a relative volume v of ordered shells, which represents a relatively simple naturally accessible control parameter. Ključne besede: topological defects, Gaussian curvature, self-assembling, crystal growth nucleation Objavljeno v DKUM: 20.07.2017; Ogledov: 1243; Prenosov: 453 Celotno besedilo (6,77 MB) Gradivo ima več datotek! Več... |
8. 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: 1098; Prenosov: 340 Celotno besedilo (2,15 MB) Gradivo ima več datotek! Več... |
9. Numerical study of membrane configurationsLuka Mesarec, Miha Fošnarič, Samo Penič, Veronika Kralj-Iglič, Samo Kralj, Wojciech Góźdź, Aleš Iglič, 2014, izvirni znanstveni članek Opis: We studied biological membranes of spherical topology within the framework of the spontaneous curvature model. Both Monte Carlo simulations and the numerical minimization of the curvature energy were used to obtain the shapes of the vesicles. The shapes of the vesicles and their energy were calculated for different values of the reduced volume. The vesicles which exhibit inplane ordering were also studied. Minimal models have been developed in order to study the orientational ordering in colloids coated with a thin sheet of nematic liquid crystal (nematic shells).The topological defects are always present on the surfaces with the topology of a sphere.The location of the topological defects depends strongly on the curvature of the surface. We studied the nematic ordering and the formation of topological defects on vesicles obtained by the minimization of the spontaneous curvature energy. Ključne besede: biological membranes, vesicles, spontaneous curvature model, Monte Carlo simulations, nematic shells, orientational ordering, topological defects Objavljeno v DKUM: 14.06.2017; Ogledov: 1219; Prenosov: 386 Celotno besedilo (4,38 MB) Gradivo ima več datotek! Več... |
10. Field induced memory effects in random nematicsAmid Ranjkesh Siahkal, Milan Ambrožič, Samo Kralj, T. J. Sluckin, 2014, izvirni znanstveni članek Opis: We studied numerically external field induced memory effects in randomly perturbed nematic liquid crystals. Random anisotropy nematic-type lattice model was used. The impurities imposing orientational disorder were randomly spatially distributed with the concentration p below the percolation threshold. Simulations were carried for finite temperatures, where we varied p, interaction strength between LC molecules, and impurities and external field B. In the {B, T} plane we determined lines separating short range—quasi long range and quasi long range—long range order. Furthermore, crossover regime separating external field and random field dominated regime was estimated. We calculated remanent nematic ordering in samples at B = 0 as a function of the previously experienced external field strength B. Ključne besede: liquid crystal, topological defects, random disorder Objavljeno v DKUM: 14.06.2017; Ogledov: 1240; Prenosov: 334 Celotno besedilo (2,15 MB) Gradivo ima več datotek! Več... |