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Topological metadefects: tangles of dislocations
Abstract: The concept of topological defects is universal. In condensed matter, it applies to disclinations, dislocations or vortices that are fingerprints of symmetry breaking during phase transitions. Using as a generic example the tangles of dislocations, we introduce the concept of topological metadefects i.e. defects made of defects. We show that in cholesterics, dextrogyre and levogyre primary tangles are generated through the D2 -> C2 symmetry breaking from the coplanar dislocation pair called Lehmann cluster submitted to a high enough tensile strain. The primary tangles can be wound up individually into double-helices. They can also annihilate in pairs or associate into tangles of higher orders following simple algebraic rules.
Article published in Physical Review Letters (2023)
Generation of the dextrogyre primary tangle, driven by a tensile strain, from the Lehmann cluster: a) variation of the Peach-Koehler force with the gap thickness, b-e) overlapping instability of the Lehmann cluster, f) geometry of the Lehmann cluster, g-k) detailed views of the overlapping instability leading to the generation of the dextrogyre tangle.
Winding up of the primary tangle into a dextrogyre double helix by a growing tensile strain.
Abstract: We deal here with three metastable systems: 1- the dowser texture, 2- supertwisted cholesterics and 3- hypotwisted cholesterics. We outline remarkable properties of tropisms of the dowser texture stemming from its low symmetry and we show that, using setups called Dowsons Colliders, nematic monopoles can be nucleated, set into motion and brought into collisions in the dowser texture. Subsequently we point out that nucleation of dislocation loops occurs in cholesteric layers compressed or dilated between cylindrical mica sheets. Under compression, three modes of nucleation of dislocation loops have been identied: individual, serial and continuous. The serial mode generates dislocation nets made of L circular loops connected by C radial crossing into superloops. Similar superloops can also be generated under dilation. We analyse the topology of superloops in terms of the theory of knots and point out they can be reduced into the unknot by Reidemeister moves. In other words, superloops are multiply folded loops that can be continuously unfolded.
Keynote lecture of the ILCC2022. Published online in Liquid crystals on 24 April 2023.
Single and double dislocation loops generated in the individual nucleation mode.
Four dislocation loops generated in the serial mode. They are connected by crossings into one superloop
Complex net of dislocation loops connected by crossings
Arbitrary shape of the trefoil knot.
Knotted dislocation confined inside the cylinder/cylinder wedge.
Shape of the trefoil knot confined inside the cylinder/cylinder wedge.
The Geilo School 2022
Arne Skjetorp
Collisions of monopoles disclinations and dislocations
Submitted to Proceedings of the Geilo School 2022, to be published in EPJST.
Abstract: Motions and collisions of topological defects produced during symmetry breaking transitions is a crucial issue in cosmology and in condensed matter physics. Here, we deal with topological defects in nematics and cholesterics. Nematics may contain linear defects i.e. disclinations and point defects i.e. monopoles while cholesterics may contain linear defects of their 1D periodic order parameter, i.e. dislocations. The dowser texture appears as a natural universe of the nematic monopoles. They can be generated in it, set into motion and brought to collisions that may result in annihilation of pairs of monopoles. We show how to generate pairs of disclinations in twisted nematic cells by the isotropic-nematic transition in the presence of magnetic fields. When two such disclinations collide, i.e. enter into a contact at one point, an intercommutation or rewiring into a new pair of disclination can occur. We show how to bring these disclinations to collisions by means of an electric field and how to steer the rewiring by magnetic fields. For generation of dislocations in cholesteric we use a Grandjean-Cano wedge made of crossed cylindrical mica sheets. After their nucleation upon dilation, dislocation loops are growing along the meniscus and their lateral segments collide. Such a selfcollision of a dislocation can result in a trivial crossing or may produce a stable configuration called Lehman cluster.
Intercommutations of colliding disclinations.
Generation, motions and collision of monopoles.
Energy landscape of the cholesteric conned between the cylindrical mica sheets.
Selfcollision of an open dislocation loop.
Publication de la version française du livre collectif sur les cristaux liquides
Table des matières :
Chapitre 1: Optique singulière des défauts de cristaux liquides par Etienne Brasselet
Chapitre 2: Contrôle des microparticules avec des cristaux liquides par Chenhui Peng et Oleg Lavrentovich
Chapitre 3: Les effets thermomécaniques dans les cristaux liquides par Patrick Oswald, Alain Dequidt et Guilhem Poy
Chapitre 4: La physique de la texture furcelle par Pawel Pieranski et Maria Helena Godinho
Chapitre 5: L’émergence spontanée de la chiralité par Mohan Sinivasarao
Collective book on liquid crystals
Françoise Brochard - Wyart
Two years ago, Mme Françoise Brochard-Wyart, director of the field "Physics of Soft Matter" at ISTE Editions, proposed us to write a book on recent advances in Liquid Crystals. The team of contributing authors and the content of the book were set thanks to Tigran Galstian who invited six of the authors to the 18th Conference on Optics of liquid Crystals in Quebec City.
We are glad to announce today that the book is available.
Contents :
Chapter 1: Singular optics of liquid crystals defects by Etienne Brasselet
Chapter 2: Control of microparticles with liquid crystals by Chenhui Peng and Oleg Lavrentovich
Chapter 3: Thermomechanical effects in liquid crystals by Patrick Oswald, Alain Dequidt and Guilhem Poy
Chapter 4: Physics of the dowser texture by Pawel Pieranski and Maria Helena Godinho
Chapter 5: Spontaneous emergence of chirality by Mohan Sinivasarao
E. Brasselet
C. Peng
O. Lavrentovich
P. Oswald
A. Dequidt
G. Poy
M.H. Godinho
P. Pieranski
M. Srinivasarao
Article published in AJP
In November 2019 three students from Ecole Normale Supérieure Paris-Cachan - Juliette Plo, Dihya Sadi and Elio Thellier - came to our lab for a two months internship untitled "From liquid crystals to displays". During the internship they worked simultaneously on two projects: 1°- detection of the isotropic - nematic phase transition and the measure of the quadropolar order parameter by means of RMN. 2° - detection of the magnetic and dielectric anisotropies of nematics by means of a new setup, built during the internship, inspired by the method invented by Mieczyslaw Jezewski and Wilhelm Kast about 100 years ago. Results of the internship were reported in an article untitled "Fréedericksz transition on air" published in American Journal Physics - well known bulletin of the American Association of Physics Teachers.
Abstract: The operational principle of twisted nematic displays involves the dielectric anisotropy of nematics. This crucial property was discovered about a hundred years ago by Jezewski and Kast who used a so-called resonance method in which the frequency of an LC tank circuit was set by the capacitance of a capacitor filled with a nematic liquid crystal. Jezewski and Kast observed that the resonance frequency changed upon application of a magnetic field to the capacitor. They interpreted the corresponding change in the dielectric permittivity as being due to reorientation of molecules by the magnetic field. Here, we describe a modern, simple, and low-cost version of this experiment. Instead of the LC oscillator working with vacuum lamps, we use an op-amp RC oscillator in which a twisted nematic display plays the role of the capacitor. For the purpose of classroom demonstrations, the oscillator frequency f is detected by a software-defined radio operating in the double-side band mode (DSB). Upon an appropriate tuning of the reception frequency f, even small changes of f become audible. This setup is very convenient for demonstration and measurements of all characteristics of the Freedericksz transition driven by magnetic or electric fields.
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