DOCSLIB.ORG

Modeling Single-Layer Dual-Phase Nematic Elastomer Ribbons

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Modeling Single-Layer Dual-Phase Nematic Elastomer Ribbons RSC Advances View Article Online PAPER View Journal | View Issue Patterning order and disorder with an angle: modeling single-layer dual-phase nematic Cite this: RSC Adv.,2019,9, 8994 elastomer ribbons† Vianney Gimenez-Pinto ‡*ab and Fangfu Yeacd Liquid crystal polymer networks have demonstrated a rich variety of actuation behavior and stimulus- responsive properties. Actuation in these single-phase materials is given by spatial variations in their liquid crystal director microstructure in balanced coexistence with rubber elasticity. However, experimental studies have shown that complex actuation in elastomeric materials can also be engineered by combining well-defined isotropic regions along with liquid crystalline ordered regions. Via finite element elastodynamics simulations, we investigate the actuation behavior of these dual-phase nematic elastomer ribbons based on several key design factors: director orientation, pattern orientation, Received 13th November 2018 as well as domain and sample size. We demonstrate the variety of shapes that these materials can Accepted 12th February 2019 Creative Commons Attribution 3.0 Unported Licence. exhibit, including twisting, bending, accordion folding, and hybrid flat-helix states. Overall, our DOI: 10.1039/c8ra09375j simulations show an exceptional agreement with experimental observations, providing light for the rsc.li/rsc-advances further development of soft stimulus-responsive materials with complex microstructures. Liquid crystal polymer networks are hybrid materials that deformation. A non-uniform director microstructure produces encode complex shape transformation and stimulus-responsive a non-uniform distribution of strains under external stimulus, capabilities given the coexistence of liquid crystalline order and driving then complex actuation. a crosslinked polymer network with characteristic rubber-like Nonetheless, additional design approaches can be imple- This article is licensed under a elasticity. By engineering complex microstructures in the mented towards engineering complex spatial distribution of nematic director eld, complex shape actuation under external inner strains in the material and, as a result, complex actuation stimulus can be custom-designed in these materials. A wide under external-stimuli. Recently, Liu et al.16 synthetized single- Open Access Article. Published on 18 March 2019. Downloaded 9/26/2021 9:08:47 PM. variety of nematic director patterns in delicate combination layer dual-phase thin- lm elastomer actuators, which inge- with the elastic response, have demonstrated an exquisite niously combine well-dened isotropic regions and twist- repertoire of shapes, including the formation of cones,1 pyra- nematic liquid crystalline regions. Yang and Zhao17 also ach- mids where Gaussian curvature is suppressed by in-plane vari- ieved synthetizing single-layer hybrid elastomer samples within ations of the director,2 chiral helicoids and elastic springs,3–8 their studies implementing non-uniform optical inscription of foldable actuators,6,9–13 and other complex bio-inspired isotropic–liquid crystalline patterns. Furthermore, Katsonis and morphologies.14,15 The vast majority of these single-phase coworkers18 recently developed elastomer lms with stripes of designs are based on spatial variations of the nematic director isotropic and liquid crystal domains and implemented them for eld within the sample. When external stimuli such as light, the study of high-power light-driven actuation in paired chiral temperature change, variation in chemical environment, etc. ribbons. Similarly to single-phase liquid crystal elastomers, change the liquid crystalline order parameter, inner strains these dual-phase materials can display a variety of out of plane arise in the material and produce a macroscopic shape actuation behavior covering chiral twisting and bending, as well as the formation of accordion folds. Here, actuation is encoded aBeijing National Laboratory for Condensed Matter Physics, CAS Key Laboratory of within the nematic director microstructure coexisting in So Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing combination with the over-imposed in-plane isotropic pattern. 100190, China. E-mail: [email protected] Combining order and disorder in the microstructure of bDepartment of Chemical Engineering, Columbia University, USA liquid crystal elastomers has also been implemented in bi-layer c School of Physical Sciences, University of Chinese Academy of Sciences, Beijing dual-phase materials within the past 15 years. Ikeda and 100049, China coworkers19 rst introduced photo-responsive dual-phase dSongshan-Lake Materials Laboratory, Dongguan 523808, China † Electronic supplementary information (ESI) available. See DOI: bilayer elastomers with one isotropic layer and an anisotropic 20 10.1039/c8ra09375j smectic layer. Also, Dai et al. synthetized humidity-responsive ‡ Current addresses: Department of Physics and Astronomy, University of dual-layer elastomers with an isotropic layer in coexistence with Pennsylvania and Department of Physics, Temple University. 8994 | RSC Adv.,2019,9, 8994–9000 This journal is © The Royal Society of Chemistry 2019 View Article Online Paper RSC Advances a nematic layer with splay conguration. In both cases, the materials. Our study shows that dual phase elastomer ribbons stacked arrangement of one isotropic and one liquid crystalline can exhibit similar actuation to their single-phase counterparts, layer added mechanical strength to the sample, avoiding frac- or a modied deformation by the inuence of inactive isotropic ture and cracking. We note that these mechanically reinforced domains, depending on their size relative to sample size. bi-layer dual-phase strips arrange order and disorder along In materials with a striped isotropic–nematic pattern, sample thickness. Conversely, single-layer dual-phase materials narrow inactive isotropic stripes do not distort overall implement in-plane order–disorder patterns, allowing further morphology aer actuation, and only changes in the magnitude options for design parameters towards engineering complex of the actuation and stimulus response are observed. Wider actuation, such as signicant variations in the size of isotropic isotropic stripes can distort and/or isolate the effect of their regions as well as the use of in-plane angles in the material adjacent active nematic regions affecting overall out-of-plane microstructure. actuation. In these later cases, we observe at inactive regions In this work, we perform nite-element elastodynamics in coexistence with active morphing regions. Wide-stripe simulations for investigating the actuation of these novel single- samples exhibit distorted-bending, distorted-twisting, accor- layer dual-phase materials given their order–disorder patterned dion folds and hybrid twist-at morphologies depending on microstructure as well as director conguration in the nematic stripe width and angular offset. Our simulation study sheds regions. This numerical method had successfully demonstrated light on the different morphologies reported by experimental a wide variety of in-plane and out-of-plane actuation behavior in groups that previously synthetized these materials, and give single-phase nematic elastomers including chiral bending,8 insights on the key design factors for engineering actuation in twisting,8,22 cone and anti-cone (saddle) formation,21 accordion smart materials by patterning order and disorder with an angle. folds,9 origami boxes,11 and bas-relief designs,21 given by Methods: We implement nite element elastodynamics different complex director microstructures. Also, nite element simulations as developed by Selinger and coworkers.23 For this, elastodynamics has been implemented for studying the actua- each three-dimensional sample is discretized to an unstruc- 22 24 Creative Commons Attribution 3.0 Unported Licence. tion of smectic elastomers. However, until now there is no tured tetrahedral mesh with an open source CAD so ware. record of this approach being implemented for the study of The system is described via the Hamiltonian dual-phase patterned elastic solids. More importantly, given the 1 X 1 X H ¼ m n 2 þ V tC t3 t3 t freshness of single-layer experimental realizations, the current 2 n n 2 ijkl ij kl n t literature still lacks theoretical and numerical studies for these novel dual-phase rubbery materials. X Àa0 V t3 t Q t À Q t Here, we focus on single-layer dual-phase elastomers with ij ij ij;flat t a 90 degree twist-nematic conguration in the nematic region, analyze the effect of a varying offset angle in director macro- where implementing the Green-Lagrange non-linear strain This article is licensed under a 3 ¼ v v v v structure as well as a varying offset angle in the orientation of tensor ij iuj + jui + iuk juk allows large deformations. Cijkl the isotropic pattern. Overall, we demonstrate the different corresponds with the elastic stiffness tensor of an isotropic ¼ cases and geometries where curling, folding, bending and elastic solid (rubber). Coupling between nematic order, Qij Shn n À d/3i and strain 3 is given by the term a(Q À Qref) Open Access Article. Published on 18 March 2019. Downloaded 9/26/2021 9:08:47 PM. accordion-like folds appear under external stimulus in these i j ij ij ij Fig. 1 Schematics of dual-phase nematic actuators: white regions have nematic order with 90 degree twist between top and bottom substrates. Grey regions correspond with isotropic states. In the fabrication of these
Load more

Recommended publications
  • Order and Disorder: Poetics of Exception
    Order and disorder Página 1 de 19 Daniel Innerarity Order and disorder: Poetics of exception “While working, the mind proceeds from disorder to order. It is important that it maintain resources of disorder until the end, and that the order it has begun to impose on itself does not bind it so completely, does not become such a rigid master, that it cannot change it and make use of its initial liberty” (Paul Valéry 1960, 714). We live at a time when nothing is conquered with absolute security, neither knowledge nor skills. Newness, the ephemeral, the rapid turn-over of information, of products, of behavioral models, the need for frequent adaptations, the demand for flexibility, all give the impression that we live only in the present in a way that hinders stabilization. Imprinting something onto the long term seems less important that valuing the instant and the event. That being said, thought has always been connected to the task of organizing and classifying, with the goal of conferring stability on the disorganized multiplicity of the manifestations of reality. In order to continue making sense, this articulation of the disparate must understand the paradoxes of order and organization. That is what has been going on recently: there has been a greater awareness of disorder and irregularity at the level of concepts and models for action and in everything from science to the theory of organizations. This difficulty is as theoretical as it is practical; it demands that we reconsider disorder in all its manifestations, as disorganization, turbulence, chaos, complexity, or entropy.
    [Show full text]
  • Arxiv:1212.0736V1 [Cond-Mat.Str-El] 4 Dec 2012 Non-Degenerate Polarized Phase
    Disorder by disorder and flat bands in the kagome transverse field Ising model M. Powalski,1 K. Coester,1 R. Moessner,2 and K. P. Schmidt1, ∗ 1Lehrstuhl f¨urTheoretische Physik 1, TU Dortmund, Germany 2Max Planck Institut f¨urkomplexe Systeme, D-01187 Dresden, Germany (Dated: August 10, 2018) We study the transverse field Ising model on a kagome and a triangular lattice using high-order series expansions about the high-field limit. For the triangular lattice our results confirm a second- order quantum phase transition in the 3d XY universality class. Our findings for the kagome lattice indicate a notable instance of a disorder by disorder scenario in two dimensions. The latter follows from a combined analysis of the elementary gap in the high- and low-field limit which is shown to stay finite for all fields h. Furthermore, the lowest one-particle dispersion for the kagome lattice is extremely flat acquiring a dispersion only from order eight in the 1=h limit. This behaviour can be traced back to the existence of local modes and their breakdown which is understood intuitively via the linked cluster expansion. PACS numbers: 75.10.Jm, 05.30.Rt, 05.50.+q,75.10.-b I. INTRODUCTION for arbitrary transverse fields providing a novel instance of disorder by disorder in which quantum fluctuations The interplay of geometric frustration and quantum select a quantum disordered state out of the classically fluctuations in magnetic systems provides a fascinating disordered ground-state manifold. There is no conclu- field of research. It gives rise to a multitude of quan- sive evidence excluding a possible ordering of the kagome tum phases manifesting novel phenomena of quantum transverse field Ising model (TFIM) and its global phase order and disorder, featuring prominent examples such diagram remains unsettled.
    [Show full text]
  • Order and Disorder in Liquid-Crystalline Elastomers
    Adv Polym Sci (2012) 250: 187–234 DOI: 10.1007/12_2010_105 # Springer-Verlag Berlin Heidelberg 2011 Published online: 3 December 2010 Order and Disorder in Liquid-Crystalline Elastomers Wim H. de Jeu and Boris I. Ostrovskii Abstract Order and frustration play an important role in liquid-crystalline polymer networks (elastomers). The first part of this review is concerned with elastomers in the nematic state and starts with a discussion of nematic polymers, the properties of which are strongly determined by the anisotropy of the polymer backbone. Neutron scattering and X-ray measurements provide the basis for a description of their conformation and chain anisotropy. In nematic elastomers, the macroscopic shape is determined by the anisotropy of the polymer backbone in combination with the elastic response of elastomer network. The second part of the review concentrates on smectic liquid-crystalline systems that show quasi-long-range order of the smectic layers (positional correlations that decay algebraically). In smectic elasto- mers, the smectic layers cannot move easily across the crosslinking points where the polymer backbone is attached. Consequently, layer displacement fluctuations are suppressed, which effectively stabilizes the one-dimensional periodic layer structure and under certain circumstances can reinstate true long-range order. On the other hand, the crosslinks provide a random network of defects that could destroy the smectic order. Thus, in smectic elastomers there exist two opposing tendencies: the suppression of layer displacement fluctuations that enhances trans- lational order, and the effect of random disorder that leads to a highly frustrated equilibrium state. These effects can be investigated with high-resolution X-ray diffraction and are discussed in some detail for smectic elastomers of different topology.
    [Show full text]
  • Calculating the Configurational Entropy of a Landscape Mosaic
    Landscape Ecol (2016) 31:481–489 DOI 10.1007/s10980-015-0305-2 PERSPECTIVE Calculating the configurational entropy of a landscape mosaic Samuel A. Cushman Received: 15 August 2014 / Accepted: 29 October 2015 / Published online: 7 November 2015 Ó Springer Science+Business Media Dordrecht (outside the USA) 2015 Abstract of classes and proportionality can be arranged (mi- Background Applications of entropy and the second crostates) that produce the observed amount of total law of thermodynamics in landscape ecology are rare edge (macrostate). and poorly developed. This is a fundamental limitation given the centrally important role the second law plays Keywords Entropy Á Landscape Á Configuration Á in all physical and biological processes. A critical first Composition Á Thermodynamics step to exploring the utility of thermodynamics in landscape ecology is to define the configurational entropy of a landscape mosaic. In this paper I attempt to link landscape ecology to the second law of Introduction thermodynamics and the entropy concept by showing how the configurational entropy of a landscape mosaic Entropy and the second law of thermodynamics are may be calculated. central organizing principles of nature, but are poorly Result I begin by drawing parallels between the developed and integrated in the landscape ecology configuration of a categorical landscape mosaic and literature (but see Li 2000, 2002; Vranken et al. 2014). the mixing of ideal gases. I propose that the idea of the Descriptions of landscape patterns, processes of thermodynamic microstate can be expressed as unique landscape change, and propagation of pattern-process configurations of a landscape mosaic, and posit that relationships across scale and through time are all the landscape metric Total Edge length is an effective governed and constrained by the second law of measure of configuration for purposes of calculating thermodynamics (Cushman 2015).
    [Show full text]
  • Order and Disorder in Nature- G
    DEVELOPMENT OF PHYSICS-Order And Disorder In Nature- G. Takeda ORDER AND DISORDER IN NATURE G. Takeda The University of Tokyo and Tohoku University, Sendai, Japan Keywords:order,disorder,entropy,fluctuation,phasetransition,latent heat, phase diagram, critical point, free energy, spontaneous symmetry breaking, open system, convection current, Bernard cell, crystalline solid, lattice structure, lattice vibration, phonon, magnetization, Curie point, ferro-paramagnetic transition, magnon, correlation function, correlation length, order parameter, critical exponent, renormalization group method, non-equilibrium process, Navier-Stokes equation, Reynold number, Rayleigh number, Prandtl number, turbulent flow, Lorentz model, laser. Contents 1. Introduction 2. Structure of Solids and Liquids 2.1.Crystalline Structure of Solids 2.2.Liquids 3. Phase Transitions and Spontaneous Broken Symmetry 3.1.Spontaneous Symmetry Breaking 3.2.Order Parameter 4. Non-equilibrium Processes Acknowledgements Glossary Bibliography Biographical Skectch Summary Order-disorder problems are a rapidly developing subject not only in physics but also in all branches of science. Entropy is related to the degree of order in the structure of a system, and the second law of thermodynamics states that the system should change from a more ordered state to a less ordered one as long as the system is isolated from its surroundings.UNESCO – EOLSS Phase transitions of matter are the most well studied order-disorder transitions and occur at certain fixed values of dynamical variables such as temperature and pressure. In general, the degreeSAMPLE of order of the atomic orCHAPTERS molecular arrangement in matter will change by a phase transition and the phase at lower temperature than the transition temperature is more ordered than that at higher temperature.
    [Show full text]
  • Equilibrium Phases of Dipolar Lattice Bosons in the Presence of Random Diagonal Disorder
    Equilibrium phases of dipolar lattice bosons in the presence of random diagonal disorder C. Zhang,1 A. Safavi-Naini,2 and B. Capogrosso-Sansone3 1Homer L. Dodge Department of Physics and Astronomy, The University of Oklahoma, Norman, Oklahoma ,73019, USA 2JILA , NIST and Department of Physics, University of Colorado, 440 UCB, Boulder, CO 80309, USA 3Department of Physics, Clark University, Worcester, Massachusetts, 01610, USA Ultracold gases offer an unprecedented opportunity to engineer disorder and interactions in a controlled manner. In an effort to understand the interplay between disorder, dipolar interaction and quantum degeneracy, we study two-dimensional hard-core dipolar lattice bosons in the presence of on-site bound disorder. Our results are based on large-scale path-integral quantum Monte Carlo simulations by the Worm algorithm. We study the ground state phase diagram at fixed half-integer filling factor for which the clean system is either a superfluid at lower dipolar interaction strength or a checkerboard solid at larger dipolar interaction strength. We find that, even for weak dipolar interaction, superfluidity is destroyed in favor of a Bose glass at relatively low disorder strength. Interestingly, in the presence of disorder, superfluidity persists for values of dipolar interaction strength for which the clean system is a checkerboard solid. At fixed disorder strength, as the dipolar interaction is increased, superfluidity is destroyed in favor of a Bose glass. As the interaction is further increased, the system eventually develops extended checkerboard patterns in the density distribution. Due to the presence of disorder, though, grain boundaries and defects, responsible for a finite residual compressibility, are present in the density distribution.
    [Show full text]
  • Entropy (Order and Disorder)
    Entropy (order and disorder) Locally, the entropy can be lowered by external action. This applies to machines, such as a refrigerator, where the entropy in the cold chamber is being reduced, and to living organisms. This local decrease in entropy is, how- ever, only possible at the expense of an entropy increase in the surroundings. 1 History This “molecular ordering” entropy perspective traces its origins to molecular movement interpretations developed by Rudolf Clausius in the 1850s, particularly with his 1862 visual conception of molecular disgregation. Sim- ilarly, in 1859, after reading a paper on the diffusion of molecules by Clausius, Scottish physicist James Clerk Boltzmann’s molecules (1896) shown at a “rest position” in a solid Maxwell formulated the Maxwell distribution of molec- ular velocities, which gave the proportion of molecules having a certain velocity in a specific range. This was the In thermodynamics, entropy is commonly associated first-ever statistical law in physics.[3] with the amount of order, disorder, or chaos in a thermodynamic system. This stems from Rudolf Clau- In 1864, Ludwig Boltzmann, a young student in Vienna, sius' 1862 assertion that any thermodynamic process al- came across Maxwell’s paper and was so inspired by it ways “admits to being reduced to the alteration in some that he spent much of his long and distinguished life de- way or another of the arrangement of the constituent parts veloping the subject further. Later, Boltzmann, in efforts of the working body" and that internal work associated to develop a kinetic theory for the behavior of a gas, ap- with these alterations is quantified energetically by a mea- plied the laws of probability to Maxwell’s and Clausius’ sure of “entropy” change, according to the following dif- molecular interpretation of entropy so to begin to inter- ferential expression:[1] pret entropy in terms of order and disorder.
    [Show full text]
  • REVIEW Theory of Displacive Phase Transitions in Minerals
    American Mineralogist, Volume 82, pages 213±244, 1997 REVIEW Theory of displacive phase transitions in minerals MARTIN T. DOVE Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ, U.K. ABSTRACT A lattice-dynamical treatment of displacive phase transitions leads naturally to the soft- mode model, in which the phase-transition mechanism involves a phonon frequency that falls to zero at the transition temperature. The basic ideas of this approach are reviewed in relation to displacive phase transitions in silicates. A simple free-energy model is used to demonstrate that Landau theory gives a good approximation to the free energy of the transition, provided that the entropy is primarily produced by the phonons rather than any con®gurational disorder. The ``rigid unit mode'' model provides a physical link between the theory and the chemical bonds in silicates and this allows us to understand the origin of the transition temperature and also validates the application of the soft-mode model. The model is also used to reappraise the nature of the structures of high-temperature phases. Several issues that remain open, such as the origin of ®rst-order phase transitions and the thermodynamics of pressure-induced phase transitions, are discussed. INTRODUCTION represented in Figure 1. In each case, the phase transitions involve small translations and rotations of the (Si,Al)O The study of phase transitions extends back a century 4 tetrahedra. One of the most popular of the new devel- to the early work on quartz, ferromagnets, and liquid-gas opments in the theory of displacive phase transitions in phase equilibrium.
    [Show full text]
  • Biochemical Thermodynamics
    © Jones & Bartlett Learning, LLC. NOT FOR SALE OR DISTRIBUTION CHAPTER 1 Biochemical Thermodynamics Learning Objectives 1. Defi ne and use correctly the terms system, closed, open, surroundings, state, energy, temperature, thermal energy, irreversible process, entropy, free energy, electromotive force (emf), Faraday constant, equilibrium constant, acid dissociation constant, standard state, and biochemical standard state. 2. State and appropriately use equations relating the free energy change of reactions, the standard-state free energy change, the equilibrium constant, and the concentrations of reactants and products. 3. Explain qualitatively and quantitatively how unfavorable reactions may occur at the expense of a favorable reaction. 4. Apply the concept of coupled reactions and the thermodynamic additivity of free energy changes to calculate overall free energy changes and shifts in the concentrations of reactants and products. 5. Construct balanced reduction–oxidation reactions, using half-reactions, and calculate the resulting changes in free energy and emf. 6. Explain differences between the standard-state convention used by chemists and that used by biochemists, and give reasons for the differences. 7. Recognize and apply correctly common biochemical conventions in writing biochemical reactions. Basic Quantities and Concepts Thermodynamics is a system of thinking about interconnections of heat, work, and matter in natural processes like heating and cooling materials, mixing and separation of materials, and— of particular interest here—chemical reactions. Thermodynamic concepts are freely used throughout biochemistry to explain or rationalize chains of chemical transformations, as well as their connections to physical and biological processes such as locomotion or reproduction, the generation of fever, the effects of starvation or malnutrition, and more.
    [Show full text]
  • PHASE DIAGRAM of the ORDER-DISORDER TRANSITION in Ni3fe J
    PHASE DIAGRAM OF THE ORDER-DISORDER TRANSITION IN Ni3Fe J. van Deen, F. van der Woude To cite this version: J. van Deen, F. van der Woude. PHASE DIAGRAM OF THE ORDER-DISORDER TRANSITION IN Ni3Fe. Journal de Physique Colloques, 1980, 41 (C1), pp.C1-367-C1-368. 10.1051/jphyscol:19801138. jpa-00219622 HAL Id: jpa-00219622 https://hal.archives-ouvertes.fr/jpa-00219622 Submitted on 1 Jan 1980 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. JOURNAL DE PHYSIQUE Colloque Cl ,suppl&ment au n O 1, Tome 41,janvier 1980,page Cl-367 PHASE DIAGRAM OF ME ORDER-DISORDER TRANSITION IN Ni3Fe J.K. Van Deen and F. Van Der Woude Solid state Physics Laboratory, Materials Science Center, University of Groningen, GRONINGEN, The Netherlands. 1. Introduction. - The phase diagram of the Ni-Fe binary alloy system in the region around the 3: 1 composition has been investigated by means of MES. .The NigFe system is a well known example of an al- loy, ordering in the LIZ structure, a superstructure of the fcc-lattice. The transition temperature rea- ches a maximum at 789 K and 27 at.% Fe, slightly away from the stoichiometric 3:l composition.
    [Show full text]
  • Entropy and Art: Essay on Disorder and Order
    ENTROPY AND ART AN ESSAY ON DISORDER AND ORDER RUDOLF ARNHEIM ABSTRACT. Order is a necessary condition for anything the hu- man mind is to understand. Arrangements such as the layout of a city or building, a set of tools, a display of merchandise, the ver- bal exposition of facts or ideas, or a painting or piece of music are called orderly when an observer or listener can grasp their overall structure and the ramification of the structure in some detail. Or- der makes it possible to focus on what is alike and what is differ- ent, what belongs together and what is segregated. When noth- ing superfluous is included and nothing indispensable left out, one can understand the interrelation of the whole and its parts, as well as the hierarchic scale of importance and power by which some structural features are dominant, others subordinate. 2 RUDOLF ARNHEIM CONTENTS Part 1. 3 1. USEFUL ORDER 3 2. REFLECTIONS OF PHYSICAL ORDER 4 3. DISORDER AND DEGRADATION 7 4. WHAT THE PHYSICIST HAS IN MIND 11 5. INFORMATION AND ORDER 13 6. PROBABILITY AND STRUCTURE 17 7. EQUILIBRIUM 21 8. TENSION REDUCTION AND WEAR AND TEAR 22 9. THE VIRTUE OF CONSTRAINTS 25 10. THE STRUCTURAL THEME 27 Part 2. 32 11. ORDER IN THE SECOND PLACE 32 12. THE PLEASURES OF TENSION REDUCTION 35 13. HOMEOSTASIS IS NOT ENOUGH 39 14. A NEED FOR COMPLEXITY 40 15. ART MADE SIMPLE 43 16. CALL FOR STRUCTURE 46 References 48 ENTROPY AND ART AN ESSAY ON DISORDER AND ORDER 3 Part 1.
    [Show full text]
  • 'Order to Disorder' for Entropy Change
    24 Chem. Educator 2005, 10, 24–25 “Order-to-Disorder” for Entropy Change? Consider the Numbers! Evguenii I. Kozliak*,† and Frank L. Lambert‡ †Department of Chemistry, University of North Dakota, Grand Forks, ND 58202-9024, [email protected] and ‡Professor Emeritus, Occidental College, Department of Chemistry, Los Angeles, CA 90041, [email protected] Received June 8, 2004. Accepted November 16, 2004. Abstract: Defining entropy increase as a change from order to disorder is misleading at best and incorrect at worst. Although Boltzmann described it this way in 1898, he did so innocently in the sense that he had never calculated the numerical values of W using ∆S = kBln (W/W0) (because this equation was not stated, kB was not known, and W0 was indeterminable before 1900–1912). Prior publications have demonstrated that the word “disorder” is misleading in describing entropy change. In this paper, convincing evidence is provided that no starting system above ca. 1 K can be said to be orderly so far as the distribution of its energy (the fundamental determinant of entropy) is concerned. This is supported by a simple calculation showing that any system with “a practical state of zero entropy” has an incomprehensibly large number of microstates. Recently, Lambert showed examples of how beginning explanation via change in the number of accessible microstates students can be seriously misled by the long-accepted for the energy of the system [1a, 2b, 3]. In this paper, we shall definition of entropy as disorder [1a] and urged that entropy show that the first part of this old definition of entropy change change be measured by the change in dispersal of motional is also misleading.
    [Show full text]