Three Facets of Modern Liquid Crystal Science
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The Elastic Constants of a Nematic Liquid Crystal
The Elastic Constants of a Nematic Liquid Crystal Hans Gruler Gordon McKay Laboratory, Harvard University, Cambridge, Mass. 02138, U.S.A. (Z. Naturforsch. 30 a, 230-234 [1975] ; received November 4, 1974) The elastic constants of a nematic liquid and of a solid crystal were derived by comparing the Gibbs free energy with the elastic energy. The expressions for the elastic constants of the nematic and the solid crystal are isomorphic: k oc | D | /1. In the nematic phase | D | and I are the mean field energy and the molecular length. In the solid crystal, | D | and I correspond to the curvature of the potential and to the lattice constant, respectively. The measured nematic elastic constants show the predicted I dependence. 1. Introduction The mean field of the nematic phase was first derived by Maier and Saupe 3: The symmetry of a crystal determines the number D(0,P2) = -(A/Vn2)P2-P2±... (2) of non-vanishing elastic constants. In a nematic liquid crystal which is a uniaxial crystal, we find five 0 is the angle between the length axis of one mole- elastic constants but only three describe bulk pro- cule and the direction of the preferred axis (optical perties 2. Here we calculate the magnitude of these axis). P2 is the second Legendre polynomial and three elastic constants by determining the elastic P2 is one order parameter given by the distribution function f{0): energy density in two different ways. On the one hand the elastic energy density can be expressed by the elastic constants and the curvature of the optical p2 = Tf (@) Po sin e d e/tf (&) sin e d 0 . -
Liquid Crystal Nanoparticles for Commercial Drug Delivery
This is a repository copy of Liquid crystal nanoparticles for commercial drug delivery. White Rose Research Online URL for this paper: http://eprints.whiterose.ac.uk/119939/ Version: Accepted Version Article: Mo, J, Milleret, G and Nagaraj, M orcid.org/0000-0001-9713-1362 (2017) Liquid crystal nanoparticles for commercial drug delivery. Liquid Crystals Reviews, 5 (2). pp. 69-85. ISSN 2168-0396 https://doi.org/10.1080/21680396.2017.1361874 © 2017 Taylor & Francis. This is an Accepted Manuscript of an article published by Taylor & Francis in Liquid Crystals Reviews on 17 August 2017, available online: http://www.tandfonline.com/10.1080/21680396.2017.1361874. Uploaded in accordance with the publisher's self-archiving policy. Reuse Items deposited in White Rose Research Online are protected by copyright, with all rights reserved unless indicated otherwise. They may be downloaded and/or printed for private study, or other acts as permitted by national copyright laws. The publisher or other rights holders may allow further reproduction and re-use of the full text version. This is indicated by the licence information on the White Rose Research Online record for the item. Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing [email protected] including the URL of the record and the reason for the withdrawal request. [email protected] https://eprints.whiterose.ac.uk/ Liquid crystal nanoparticles for commercial drug delivery J. Moa G. Millereta and M. Nagaraja* a School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, UK [email protected] 1 Liquid crystal nanoparticles for commercial drug delivery Liquid crystals are an intermediate state of matter that exists between conventional solids and liquids. -
Liquid Crystals
www.scifun.org LIQUID CRYSTALS To those who know that substances can exist in three states, solid, liquid, and gas, the term “liquid crystal” may be puzzling. How can a liquid be crystalline? However, “liquid crystal” is an accurate description of both the observed state transitions of many substances and the arrangement of molecules in some states of these substances. Many substances can exist in more than one state. For example, water can exist as a solid (ice), liquid, or gas (water vapor). The state of water depends on its temperature. Below 0̊C, water is a solid. As the temperature rises above 0̊C, ice melts to liquid water. When the temperature rises above 100̊C, liquid water vaporizes completely. Some substances can exist in states other than solid, liquid, and vapor. For example, cholesterol myristate (a derivative of cholesterol) is a crystalline solid below 71̊C. When the solid is warmed to 71̊C, it turns into a cloudy liquid. When the cloudy liquid is heated to 86̊C, it becomes a clear liquid. Cholesterol myristate changes from the solid state to an intermediate state (cloudy liquid) at 71̊C, and from the intermediate state to the liquid state at 86̊C. Because the intermediate state exits between the crystalline solid state and the liquid state, it has been called the liquid crystal state. Figure 1. Arrangement of Figure 2. Arrangement of Figure 3. Arrangement of molecules in a solid crystal. molecules in a liquid. molecules in a liquid crystal. “Liquid crystal” also accurately describes the arrangement of molecules in this state. In the crystalline solid state, as represented in Figure 1, the arrangement of molecules is regular, with a regularly repeating pattern in all directions. -
Liquid Crystals - the 'Fourth' Phase of Matter
GENERAL I ARTICLE Liquid Crystals - The 'Fourth' Phase of Matter Shruti Mohanty The remarkable physical properties of liquid crystals have been exploited for many uses in the electronics industry_ This article summarizes the physics of these beautiful and I • complex states of matter and explains the working of a liquid crystal display. Shruti Mohanty has worked What are Liquid Crystals? on 'thin film physics of free standing banana liquid The term 'liquid crystal' is both intriguing and confusing; while crystal films' as a summer it appears self-contradictory, the designation really is an attempt student at RRI, Bangalore. to describe a particular state of matter of great importance She is currently pursuing her PhD in Applied Physics today, both scientifically and technologically. TJ!e[:w:odynamic at Yale University, USA. phases of condensed matter with a degree of order intermediate Her work is on supercon between that of the crystalline solid and the simple liquid are ductivity, particularly on called liquid crystals or mesophases. They occutliS Stable phases superconducting tunnel 'junctions and their for many compounds; in fact one out of approximately two applications. hundred synthesized organic compounds is a liquid crystalline material. The typical liquid crystal is highly ani'sotropic - in some cases simply an anisotropic liquid, in other cases solid-like in some directions. Liquid-crystal physics, although a field in itself, is often in cluded in the larger area called 'soft matter', including polymers, colloids, and surfactant solutions, all of which are highly de formable materials. This property leads to many unique and exciting phenomena not seen in ordinary condensed phases, and possibilities of novel technological applications. -
Strange Elasticity of Liquid Crystal Rubber: Critical Phase
Strange elasticity of liquid-crystal rubber University of Colorado Boulder $ NSF-MRSEC, Materials Theory, Packard Foundation UMass, April 2011 Outline • Diversity of phases in nature! • Liquid-crystals! • Rubber! • Liquid-crystal elastomers! • Phenomenology! • Theory (with Xing, Lubensky, Mukhopadhyay)! • Challenges and future directions! “White lies” about phases of condensed matter T P States of condensed matter in nature • magnets, superconductors, superfluids, liquid crystals, rubber, ! colloids, glasses, conductors, insulators,… ! Reinitzer 1886 (nematic, Blue phase) Liquid Crystals … T crystal … smectic-C smectic-A nematic isotropic cholesteric smectic layer vortex lines pitch fluctuations Reinitzer 1886 (nematic, Blue phase) Liquid Crystals … T crystal … smectic-C smectic-A nematic isotropic cholesteric smectic layer vortex lines pitch fluctuations • Rich basic physics – critical phenomena, hydrodynamics, coarsening, topological defects, `toy` cosmology,… • Important applications – displays, switches, actuators, electronic ink, artificial muscle,… N. Clark Liquid-crystal beauty “Liquid crystals are beautiful and mysterious; I am fond of them for both reasons.” – P.-G. De Gennes! Chiral liquid crystals: cholesterics cholesteric pitch • color selective Bragg reflection from cholesteric planes • temperature tunable pitch à wavelength Bio-polymer liquid crystals: DNA M. Nakata, N. Clark, et al Nonconventional liquid crystals • electron liquid in semiconductors under strong B field! 4 5 4 5 4 5 4 half-filled high Landau levels! ν=4+½ • -
Introduction to Liquid Crystals
Introduction to liquid crystals Denis Andrienko International Max Planck Research School Modelling of soft matter 11-15 September 2006, Bad Marienberg September 14, 2006 Contents 1 What is a liquid crystal 2 1.1 Nematics . 3 1.2 Cholesterics . 4 1.3 Smectics.............................................. 5 1.4 Columnar phases . 6 1.5 Lyotropic liquid crystals . 7 2 Long- and short-range ordering 7 2.1 Order tensor . 7 2.2 Director . 9 3 Phenomenological descriptions 10 3.1 Landau-de Gennes free energy . 10 3.2 Frank-Oseen free energy . 11 4 Nematic-isotropic phase transition 14 4.1 Landau theory . 14 4.2 Maier-Saupe theory . 15 4.3 Onsager theory . 17 5 Response to external fields 18 5.1 Frederiks transition in nematics . 18 6 Optical properties 20 6.1 Nematics . 20 6.2 Cholesterics . 22 7 Defects 23 8 Computer simulation of liquid crystals 24 9 Applications 27 1 Literature Many excellent books/reviews have been published covering various aspects of liquid crystals. Among them: 1. The bible on liqud crystals: P. G. de Gennes and J. Prost “The Physics of Liquid Crystals”, Ref. [1]. 2. Excellent review of basic properties (many topics below are taken from this review): M. J. Stephen, J. P. Straley “Physics of liquid crystals”, Ref. [2]. 3. Symmetries, hydrodynamics, theory: P. M. Chaikin and T. C. Lubensky “Principles of Condensed Matter Physics”, Ref. [3]. 4. Defects: O. D. Lavrentovich and M. Kleman, “Defects and Topology of Cholesteric Liquid Crys- tals”, Ref. [4]; Oleg Lavrentovich “Defects in Liquid Crystals: Computer Simulations, Theory and Experiments”, Ref. -
States of Matter Part I
States of Matter Part I. The Three Common States: Solid, Liquid and Gas David Tin Win Faculty of Science and Technology, Assumption University Bangkok, Thailand Abstract There are three basic states of matter that can be identified: solid, liquid, and gas. Solids, being compact with very restricted movement, have definite shapes and volumes; liquids, with less compact makeup have definite volumes, take the shape of the containers; and gases, composed of loose particles, have volumes and shapes that depend on the container. This paper is in two parts. A short description of the common states (solid, liquid and gas) is described in Part I. This is followed by a general observation of three additional states (plasma, Bose-Einstein Condensate, and Fermionic Condensate) in Part II. Keywords: Ionic solids, liquid crystals, London forces, metallic solids, molecular solids, network solids, quasicrystals. Introduction out everywhere within the container. Gases can be compressed easily and they have undefined shapes. This paper is in two parts. The common It is well known that heating will cause or usual states of matter: solid, liquid and gas substances to change state - state conversion, in or vapor1, are mentioned in Part I; and the three accordance with their enthalpies of fusion ∆H additional states: plasma, Bose-Einstein f condensate (BEC), and Fermionic condensate or vaporization ∆Hv, or latent heats of fusion are described in Part II. and vaporization. For example, ice will be Solid formation occurs when the converted to water (fusion) and thence to vapor attraction between individual particles (atoms (vaporization). What happens if a gas is super- or molecules) is greater than the particle energy heated to very high temperatures? What happens (mainly kinetic energy or heat) causing them to if it is cooled to near absolute zero temperatures? move apart. -
Interactions and Confinement of Particles in Liquid Crystals: Novel Particles and Defects
Interactions and Confinement of Particles in Liquid Crystals: Novel Particles and Defects Anne Helen Macaskill Submitted in accordance with the requirements for the degree of Doctor of Philosophy The University of Leeds School of Physics and Astronomy July 2019 Declaration The candidate confirms that the work submitted is her own and that appropriate credit has been given where reference has been made to the work of others. This copy has been supplied on the understanding that it is copyright material and that no quotation from the thesis may be published without proper acknowledgement. ©2019 The University of Leeds and Anne Helen Macaskill i Acknowledgements UOM: University of Manchester UOL: University of Leeds SMP: Soft Matter Physics LC: Liquid Crystals The original research proposal and funding for this project were secured by J. Cliff Jones (then UOM, currently UOL) and Ingo Dierking (UOM). At this time both were members of the Soft Matter Research Group, University of Manchester. Both Jones and Dierking oversaw, supervised and oversaw many details of this project, especially early on, during chapter 3. Later chapters of the project, from chapter 4 onwards, were primarily supervised by Helen F. Gleeson (originally UOM, now UOL), with exceptions given below. In Chapter 3, the synthetic particles were produced by Sean Butterworth of the Organic Materials Innovation Centre, School of Chemistry, UOM. Other members of the research group also gave advice on, for example, choosing a solvent for the particles (notably Steve Yeates and Joshua Moore). The group also allowed the use of their labs and equipment. From chapter 4 onwards, the focus of the project began to move to the interaction of particles with defects and particle tracking (a suggestion originally made by Gleeson). -
Exotic States of Matter in an Oscillatory Driven Liquid Crystal Cell
Exotic states of matter in an oscillatory driven liquid crystal cell Marcel G. Clerc,1 Michal Kowalczyk,2 and Valeska Zambra1 1Departamento de Física and Millennium Institute for Research in Optics, FCFM, Universidad de Chile, Casilla 487-3, Santiago, Chile. 2Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático (UMI 2807 CNRS), Universidad de Chile, Casilla 170 Correo 3, Santiago, Chile Abstract. Matter under different equilibrium conditions of pressure and temperature exhibits different states such as solid, liquid, gas, and plasma. Exotic states of matter, such as Bose- Einstein condensates, superfluidity, chiral magnets, superconductivity, and liquid crystalline blue phases are observed in thermodynamic equilibrium. Rather than being a result of an aggregation of matter, their emergence is due to a change of a topological state of the system. Here we investigate topological states of matter in a system with injection and dissipation of energy. In an experiment involving a liquid crystal cell under the influence of a low-frequency oscillatory electric field, we observe a transition from non-vortex state to a state in which vortices persist. Depending on the period and the type of the forcing, the vortices self-organise forming square lattices, glassy states, and disordered vortex structures. Based on a stochastic amplitude equation, we recognise the origin of the transition as the balance between stochastic creation and deterministic annihilation of vortices. Our results show that the matter maintained out of equilibrium by means of the temporal modulation of parameters can exhibit exotic states. arXiv:2009.06528v1 [cond-mat.soft] 14 Sep 2020 2 a) b) t [s] 550 μm CMOS 550 μm 1000 P2 400 NLC Vω(t) 300 P1 200 y 0 x Figure 1. -
The Scientific Life and Influence of Clifford Ambrose Truesdell
Arch. Rational Mech. Anal. 161 (2002) 1–26 Digital Object Identifier (DOI) 10.1007/s002050100178 The Scientific Life and Influence of Clifford Ambrose Truesdell III J. M. Ball & R. D. James Editors 1. Introduction Clifford Truesdell was an extraordinary figure of 20th century science. Through his own contributions and an unparalleled ability to absorb and organize the work of previous generations, he became pre-eminent in the development of continuum mechanics in the decades following the Second World War. A prolific and scholarly writer, whose lucid and pungent style attracted many talented young people to the field, he forcefully articulated a view of the importance and philosophy of ‘rational mechanics’ that became identified with his name. He was born on 18 February 1919 in Los Angeles, graduating from Polytechnic High School in 1936. Before going to university he spent two years at Oxford and traveling elsewhere in Europe. There he improved his knowledge of Latin and Ancient Greek and became proficient in German, French and Italian.These language skills would later prove valuable in his mathematical and historical research. Truesdell was an undergraduate at the California Institute of Technology, where he obtained B.S. degrees in Physics and Mathematics in 1941 and an M.S. in Math- ematics in 1942. He obtained a Certificate in Mechanics from Brown University in 1942, and a Ph.D. in Mathematics from Princeton in 1943. From 1944–1946 he was a Staff Member of the Radiation Laboratory at MIT, moving to become Chief of the Theoretical Mechanics Subdivision of the U.S. Naval Ordnance Labo- ratory in White Oak, Maryland, from 1946–1948, and then Head of the Theoretical Mechanics Section of the U.S. -
Phase Behaviour of Lyotropic Liquid Crystals in External Fields And
Eur. Phys. J. Special Topics 222, 3053–3069 (2013) c EDP Sciences, Springer-Verlag 2013 THE EUROPEAN DOI: 10.1140/epjst/e2013-02075-x PHYSICAL JOURNAL SPECIAL TOPICS Review Phase behaviour of lyotropic liquid crystals in external fields and confinement A.B.G.M. Leferink op Reininka, E. van den Pol, A.V. Petukhov, G.J. Vroege, and H.N.W. Lekkerkerker Van ’t Hoff Laboratory for Physical and Colloid Chemistry, Debye Institute for Nanomaterials Science, Utrecht University, Padualaan 8, 3584 Utrecht, The Netherlands Received 6 September 2013 / Received in final form 17 September 2013 Published online 25 November 2013 Abstract. This mini-review discusses the influence of external fields on the phase behaviour of lyotropic colloidal liquid crystals. The liquid crystal phases reviewed, formed in suspensions of highly anisotropic particles ranging from rod- to board- to plate-like particles, include ne- matic, smectic and columnar phases. The external fields considered are the earth gravitational field and electric and magnetic fields. For elec- tric and magnetic fields single particle alignment, collective reorienta- tion behaviour of ordered phases and field-induced liquid crystal phase transitions are discussed. Additionally, liquid crystal phase behaviour in various confining geometries, e.g. slit-pore, circular and spherical confinement will be reviewed. 1 Introduction The vast majority of studies of colloidal suspensions deal with spherical particles [1–3]. Their behaviour in external fields was studied in detail and one can find ex- tended examples in other mini-reviews in this issue [4–8]. In contrast, here we shall only discuss the phase behaviour of suspensions of highly non-spherical particles with high aspect ratio. -
Flexoelectricity of Model and Living Membranes
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Biochimica et Biophysica Acta 1561 (2001) 1^25 www.bba-direct.com Review Flexoelectricity of model and living membranes Alexander G. Petrov * Institute of Solid State Physics, Bulgarian Academy of Sciences, 72 Tzarigradsko chaussee, 1784 So¢a, Bulgaria Received 25 April 2001; received in revised form 14 June 2001; accepted 20 June 2001 Abstract The theory and experiments on model and biomembrane flexoelectricity are reviewed. Biological implications of flexoelectricity are underlined. Molecular machinery and molecular electronics applications are pointed out. ß 2001 Else- vier Science B.V. All rights reserved. Keywords: Bilayer lipid membrane; Biomembrane; Curvature; Flexoelectricity; Mechanosensitivity; Electromotility; Membrane machine; Molecular electronics 1. Introduction Furthermore, the recognition of some speci¢c, me- chanical pathways for energy transformation in bio- In 1943 Erwin Schro«dinger postulated that a living membranes is needed. cell should function like a mechanism [1]. He was Biomembranes constitute the basic building units then concerned about ‘solid’ parts of the cells, i.e. of the majority of cells and cellular organelles. It DNA molecules. appears that most membranes are built up according The present review aims at an extension of Schro«- to the general principles of lyotropic liquid crystal dinger’s postulate to the liquid crystal parts of the structures [2]. The widely accepted ‘£uid lipid^glob- cell, the biomembranes. In the ¢rst place this implies ular protein mosaic model’ [3^5] claims that lipids the recognition of the existence of an appropriate are organized in a bilayer in which the proteins are mechanical degree of freedom in a biomembrane.