Phase Change Enthalpies and Entropies of Liquid Crystals

Total Page:16

File Type:pdf, Size:1020Kb

Phase Change Enthalpies and Entropies of Liquid Crystals Phase Change Enthalpies and Entropies of Liquid Crystals William E. Acree, Jr.a… Department of Chemistry, University of North Texas, Denton, Texas 76203 James S. Chickosb… Department of Chemistry and Biochemistry, University of Missouri-St. Louis, St. Louis, Missouri 63121 ͑Received 11 February 2004; revised manuscript received 1 August 2004; accepted 7 September 2004; published online 17 July 2006͒ The thermochemical behavior of more than 3000 organic compounds known to form liquid crystals is reported along with references to the original literature. A group addi- tivity approach used to estimate total phase change entropies of organic molecules ap- plied to 627 of these liquid crystals is found to significantly overestimate their total phase change entropies. Comparison of experimental and estimated values also show significant scatter relative to database compounds. The origins of these discrepancies are discussed in terms of a model used to explain liquid crystal formation. © 2006 American Institute of Physics. ͓DOI: 10.1063/1.1901689͔ Key words: fusion enthalpy; fusion entropy; liquid crystals; liquid crystal compendium; phase transitions; total phase change entropy. Contents List of Tables 1. ⌬Tiso Contributions to 0 Stpce by the hydrocarbon portion of acyclic and aromatic molecules....... 1053 1. Introduction................................ 1052 2. Contributions of acyclic functional groups used 1.1. Phase Change Enthalpies................. 1052 T in estimating ⌬ isoS of liquid crystals; 2. Phase Change Entropies...................... 1053 0 tpce functional groups dependent on the substitution 2.1. Estimation of Total Phase Change Entropy... 1053 patterns. .................... 1053 2.2. ⌬Tiso Some Estimations of 0 Stpce of Liquid 3. Contributions of the remaining acyclic functional Crystals............................... 1055 ⌬Tiso groups used in estimating 0 Stpce of liquid 2.2.1. 1,2,13,14-Tetrahydroxytetradecane.... 1055 crystals................................... 1054 2.2.2. 4-Butylcyclohexyl 4. Contributions of the cyclic hydrocarbon portions 4-methoxycinnamate................ 1055 of the molecule............................. 1054 2.2.3. Diphenyl 4,4Ј-biphenyldicarboxylate.. 1055 5. Contributions of the cyclic functional groups 2.2.4. bis͑4-Heptyloxyphenyl͒ ⌬Tiso used in estimating 0 Stpce of liquid crystals. 1055 2,5-thiophenedicarboxylate.......... 1056 6. Application of group additivity toward the 2.2.5. Benzene hexa-nonanoate............ 1056 ⌬Tiso estimation of 0 Stpce of liquid crystals........ 1056 2.3. Statistics of the Correlations of Total Phase 7. A series of compounds including liquid crystals Change Entropy......................... 1056 whose heat capacity and phase transitions of the 2.3.1. Database Compounds............... 1056 crystalline phase have been studied over most 2.3.2. ⌬Tiso of the experimentally accessible region. ........ 1059 Calculations of 0 Stpce for Liquid Crystals.......................... 1057 8. Some examples of compounds forming liquid ⌬Tiso crystals upon supercooling the melt............ 1062 3. A Discussion of Stpce for Liquid Crystals. 1058 0 9. Group values for estimating heat capacities of 4. A Discussion of T , T and T for Liquid fus cld iso solids at Tϭ298K.......................... 1063 Crystals................................... 1060 10. Abbreviations and notations used in Table 11. 1064 5. Why Do Liquid Crystals Form?............... 1062 11. The solid-liquid phase change properties of 6. A Compendium of the Thermochemical liquid crystals.............................. 1065 Behavior of Liquid Crystals................... 1064 12. References for Table 11...................... 1323 7. Acknowledgment........................... 1330 8. References................................. 1330 List of Figures ͒ 1. A comparison of the experimental and calculated a Electronic mail: [email protected] b͒Electronic mail: [email protected]; corresponding author. total phase change entropies of 2637 compounds.. 1056 © 2006 American Institute of Physics. 2. A comparison of calculated and experimental Õ Õ Õ Õ Õ 0047-2689 2006 35„3… 1051 280 $40.001051 J. Phys. Chem. Ref. Data, Vol. 35, No. 3, 2006 1052 W. E. ACREE, JR. AND J. S. CHICKOS ⌬Tiso tween anisotropic solids that are rigidly and uniquely ar- 0 Stpce for 627 liquid crystals............... 1057 3. A histogram of the distribution of errors in ranged in a lattice with very little mobility, plastic crystals ⌬TisoS (exp)Ϫ⌬TisoS (calc) for 2637 that flow under stress and usually characterized by rotational 0 tpce 0 tpce motion within a lattice, and isotropic liquids characterized by compounds used in deriving and validating group parameters for estimating total phase free rotational and translational motion. If the forces of in- change entropies............................ 1057 teraction are sufficiently strong, a more limited form of self- 4. A histogram of the distribution of errors in association can also be detected in the gas phase, as exem- T T plified by the dimerization observed with some carboxylic ⌬ isoS (exp)Ϫ⌬ isoS (calc) for liquid crystals.. 1058 0 tpce 0 tpce acids. 5. A plot of the difference between experimental Of all the techniques used to study liquid crystals, thermal and calculated ⌬TisoS as a function of the 0 tpce analysis, while perhaps not the most sensitive, provides a number of carbon atoms..................... 1058 quantitative measure of the magnitude of the interactions re- 6. A plot of the entropy of the benzene sponsible for self-assembly. A study of the thermal behavior hexa-n-alkanoates as a function of the number exhibited by liquid crystals may also provide insight into the of carbon atoms............................ 1059 associative behavior of other molecules that behave noniso- 7. A comparison of the melting and clearing tropically but do not form liquid crystals. This study reports temperatures of the odd thiocholesteryl the thermal behavior of some 3000ϩ liquid crystals and n-alkanoates............................... 1060 compares the total molar phase change entropy (⌬TisoS ) 8. A comparison of the melting and clearing 0 tpce temperatures of the even thiocholesteryl of a representative number of them to the total molar phase n-alkanoates............................... 1060 change entropy of substances that are believed to melt to 9. A comparison of the melting and clearing isotropic liquids. In view of the large number of compounds temperatures of the alkyl in the database, the calculated and experimental total molar 4Ј-methoxybiphenyl-4-carboxylates.. ......... 1061 phase change entropy of some 667 entries on approximately 600 different compounds were compared. Compounds were selected to include a variety of functional groups and struc- 1. Introduction tures. In order to simplify the calculations, members of ho- mologous series were frequently chosen. If the compounds Since their first discovery back in 1888, interest in the selected included multiple independent determinations of properties and practical applications of liquid crystals has their thermal properties, all entries for the compound were 1,2 increased dramatically. General acceptance of liquid crys- included in the analysis. tals as a distinct phase of matter was slow, occurring some 30 Throughout this article, Tfus , Tcld , and Tiso are used to years since they were first reported. Liquid crystalline behav- distinguish between slightly different events and conditions. ior is found among numerous classes of compounds that in- The temperature, Tfus, refers to the temperature at which a clude biphenyls, cholesterol esters, soaps, lipids, polymers, solid is converted to either an isotropic liquid or to a liquid and elastomers. More than 76 000 compounds have been 3͑a͒–͑c͒ crystal. Tcld is used to refer to the clearing temperature if the identified as exhibiting liquid crystalline behavior. This isotropic liquid is converted to the liquid crystal by super- paper will review the total phase change enthalpies and en- cooling the isotropic liquid below Tfus ; Tcld may be observed tropies of the more than 3000 compounds whose condensed experimentally at the temperature the supercooled liquid be- phase thermochemical properties have been studied. comes cloudy. The term T has been used to refer to tem- Unlike most small molecules that behave isotropically iso peratures at which the liquid becomes isotropic above T . upon liquefaction, many molecules that are highly non- fus The relationship between these terms is defined as follows: spherical in shape, exhibit marked self-assembly in the liquid T ϽT рT . phase that persists even upon continued heating. Cylindrical cld fus iso rod, disk, and banana shaped molecular structures are among 1.1. Phase Change Enthalpies those most frequently encountered exhibiting this behavior. Loss of self-assembly can occur in stages and can be moni- An examination of the phase change enthalpies of liquid tored by changes in a variety of physical properties. In some crystals reveals that these substances exhibit several thermal cases, liquid crystalline behavior is observed, only upon su- transitions that can be detected. For most substances, the percooling of the melt. In these instances, the melting of the largest enthalpic change occurs upon conversion of the solid solid first produces an isotropic liquid; self-association is ob- to a nematic or smectic phase. In a few cases, some highly ͑ served upon supercooling below the melting temperature. Al- substituted anthraquinones for example, see C124H216O18 , ͒ though
Recommended publications
  • Phase-Transition Phenomena in Colloidal Systems with Attractive and Repulsive Particle Interactions Agienus Vrij," Marcel H
    Faraday Discuss. Chem. SOC.,1990,90, 31-40 Phase-transition Phenomena in Colloidal Systems with Attractive and Repulsive Particle Interactions Agienus Vrij," Marcel H. G. M. Penders, Piet W. ROUW,Cornelis G. de Kruif, Jan K. G. Dhont, Carla Smits and Henk N. W. Lekkerkerker Van't Hof laboratory, University of Utrecht, Padualaan 8, 3584 CH Utrecht, The Netherlands We discuss certain aspects of phase transitions in colloidal systems with attractive or repulsive particle interactions. The colloidal systems studied are dispersions of spherical particles consisting of an amorphous silica core, coated with a variety of stabilizing layers, in organic solvents. The interaction may be varied from (steeply) repulsive to (deeply) attractive, by an appropri- ate choice of the stabilizing coating, the temperature and the solvent. In systems with an attractive interaction potential, a separation into two liquid- like phases which differ in concentration is observed. The location of the spinodal associated with this demining process is measured with pulse- induced critical light scattering. If the interaction potential is repulsive, crystallization is observed. The rate of formation of crystallites as a function of the concentration of the colloidal particles is studied by means of time- resolved light scattering. Colloidal systems exhibit phase transitions which are also known for molecular/ atomic systems. In systems consisting of spherical Brownian particles, liquid-liquid phase separation and crystallization may occur. Also gel and glass transitions are found. Moreover, in systems containing rod-like Brownian particles, nematic, smectic and crystalline phases are observed. A major advantage for the experimental study of phase equilibria and phase-separation kinetics in colloidal systems over molecular systems is the length- and time-scales that are involved.
    [Show full text]
  • Phase Transitions in Quantum Condensed Matter
    Diss. ETH No. 15104 Phase Transitions in Quantum Condensed Matter A dissertation submitted to the SWISS FEDERAL INSTITUTE OF TECHNOLOGY ZURICH¨ (ETH Zuric¨ h) for the degree of Doctor of Natural Science presented by HANS PETER BUCHLER¨ Dipl. Phys. ETH born December 5, 1973 Swiss citizien accepted on the recommendation of Prof. Dr. J. W. Blatter, examiner Prof. Dr. W. Zwerger, co-examiner PD. Dr. V. B. Geshkenbein, co-examiner 2003 Abstract In this thesis, phase transitions in superconducting metals and ultra-cold atomic gases (Bose-Einstein condensates) are studied. Both systems are examples of quantum condensed matter, where quantum effects operate on a macroscopic level. Their main characteristics are the condensation of a macroscopic number of particles into the same quantum state and their ability to sustain a particle current at a constant velocity without any driving force. Pushing these materials to extreme conditions, such as reducing their dimensionality or enhancing the interactions between the particles, thermal and quantum fluctuations start to play a crucial role and entail a rich phase diagram. It is the subject of this thesis to study some of the most intriguing phase transitions in these systems. Reducing the dimensionality of a superconductor one finds that fluctuations and disorder strongly influence the superconducting transition temperature and eventually drive a superconductor to insulator quantum phase transition. In one-dimensional wires, the fluctuations of Cooper pairs appearing below the mean-field critical temperature Tc0 define a finite resistance via the nucleation of thermally activated phase slips, removing the finite temperature phase tran- sition. Superconductivity possibly survives only at zero temperature.
    [Show full text]
  • The Superconductor-Metal Quantum Phase Transition in Ultra-Narrow Wires
    The superconductor-metal quantum phase transition in ultra-narrow wires Adissertationpresented by Adrian Giuseppe Del Maestro to The Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the subject of Physics Harvard University Cambridge, Massachusetts May 2008 c 2008 - Adrian Giuseppe Del Maestro ! All rights reserved. Thesis advisor Author Subir Sachdev Adrian Giuseppe Del Maestro The superconductor-metal quantum phase transition in ultra- narrow wires Abstract We present a complete description of a zero temperature phasetransitionbetween superconducting and diffusive metallic states in very thin wires due to a Cooper pair breaking mechanism originating from a number of possible sources. These include impurities localized to the surface of the wire, a magnetic field orientated parallel to the wire or, disorder in an unconventional superconductor. The order parameter describing pairing is strongly overdamped by its coupling toaneffectivelyinfinite bath of unpaired electrons imagined to reside in the transverse conduction channels of the wire. The dissipative critical theory thus contains current reducing fluctuations in the guise of both quantum and thermally activated phase slips. A full cross-over phase diagram is computed via an expansion in the inverse number of complex com- ponents of the superconducting order parameter (equal to oneinthephysicalcase). The fluctuation corrections to the electrical and thermal conductivities are deter- mined, and we find that the zero frequency electrical transport has a non-monotonic temperature dependence when moving from the quantum critical to low tempera- ture metallic phase, which may be consistent with recent experimental results on ultra-narrow MoGe wires. Near criticality, the ratio of the thermal to electrical con- ductivity displays a linear temperature dependence and thustheWiedemann-Franz law is obeyed.
    [Show full text]
  • Density Fluctuations Across the Superfluid-Supersolid Phase Transition in a Dipolar Quantum Gas
    PHYSICAL REVIEW X 11, 011037 (2021) Density Fluctuations across the Superfluid-Supersolid Phase Transition in a Dipolar Quantum Gas J. Hertkorn ,1,* J.-N. Schmidt,1,* F. Böttcher ,1 M. Guo,1 M. Schmidt,1 K. S. H. Ng,1 S. D. Graham,1 † H. P. Büchler,2 T. Langen ,1 M. Zwierlein,3 and T. Pfau1, 15. Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany 2Institute for Theoretical Physics III and Center for Integrated Quantum Science and Technology, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany 3MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA (Received 15 October 2020; accepted 8 January 2021; published 23 February 2021) Phase transitions share the universal feature of enhanced fluctuations near the transition point. Here, we show that density fluctuations reveal how a Bose-Einstein condensate of dipolar atoms spontaneously breaks its translation symmetry and enters the supersolid state of matter—a phase that combines superfluidity with crystalline order. We report on the first direct in situ measurement of density fluctuations across the superfluid-supersolid phase transition. This measurement allows us to introduce a general and straightforward way to extract the static structure factor, estimate the spectrum of elementary excitations, and image the dominant fluctuation patterns. We observe a strong response in the static structure factor and infer a distinct roton minimum in the dispersion relation. Furthermore, we show that the characteristic fluctuations correspond to elementary excitations such as the roton modes, which are theoretically predicted to be dominant at the quantum critical point, and that the supersolid state supports both superfluid as well as crystal phonons.
    [Show full text]
  • Feas: Heat Capacity, Enthalpy Increments, Other Thermodynamic Properties from 5 to 1350 K, and Magnetic Transition A
    M-2341 J. Chem. Thermodynumics 1989,21, 363-373 FeAs: Heat capacity, enthalpy increments, other thermodynamic properties from 5 to 1350 K, and magnetic transition a DOMINGO GONZALEZ-ALVAREZ, Fact&ad de Ciencias de la Universidad de Zaragoza, Departamento de Fisica Fundamental, 5009 Zaragoza, Spain FREDRIK GR0NVOLD, Chemical Institute, University of Oslo, Blindern, Oslo 3, Norway BENGT FALK,b EDGAR F. WESTRUM, JR., Department of Chemistry, University of Michigan, Ann Arbor, MI 48109, U.S.A. R. BLACHNIK,’ and G. KUDERMANNd Technical University, Siegen, Federal Republic of Germany (Received 2 January 1989) The heat capacity of iron monoarsenide has been determined by adiabatic calorimetry from 5 to 1030 K and bv drou calorimetrv relative to 298.15 K over the range 875 to 1350 K. A small h-type transition is observed at ?;, = (70.95 kO.02) K. It is related & the disappearance of a doubly helically ordered magnetic-spin structure on heating. The obviously cooperative entropy increment of transition is only A&JR = 0.021. The higher-temperature heat capacity rises considerably above lattice expectations. Part of the rise is ascribed to low-spin electron redistribution in iron, while the further excess above 800 K presumably arises from a beginning low- to high-spin transition, possibly connected with interstitial defect formation in the MnP- type structure. FeAs melts at about 1325 K with A,,,Hk=6180R.K. Thermodynamic functions have been evaluated and the values of C,,,(T), S:(T), H:(T), and @i(T), are 6.057R, 7.513R,1177R.K, and 3.567Rat 298.15 K, and 8.75R,16.03R, 6287R.K, and 9.74512at 1000 K.
    [Show full text]
  • High Temperature Enthalpies of the Lead Halides
    HIGH TEMPERATURE ENTHALPIES OF THE LEAD HALIDES: ENTHALPIES AND ENTROPIES OF FUSION APPROVED: Graduate Committee: Major Professor Committee Member Min fessor Committee Member X Committee Member UJ. Committee Member Committee Member Chairman of the Department of Chemistry Dean or the Graduate School HIGH TEMPERATURE ENTHALPIES OF THE LEAD HALIDES: ENTHALPIES AND ENTROPIES OF FUSION DISSERTATION Presented to the Graduate Council of the North Texas State University in Partial Fulfillment of the Requirements For the Degree of DOCTOR OF PHILOSOPHY By Clarence W, Linsey, B. S., M. S, Denton, Texas June, 1970 ACKNOWLEDGEMENT This dissertation is based on research conducted at the Oak Ridge National Laboratory, Oak Ridge, Tennessee, which is operated by the Uniofl Carbide Corporation for the U. S. Atomic Energy Commission. The author is also indebted to the Oak Ridge Associated Universities for the Oak Ridge Graduate Fellowship which he held during the laboratory phase. 11 TABLE OF CONTENTS Page LIST OF TABLES iv LIST OF ILLUSTRATIONS v Chapter I. INTRODUCTION . 1 Lead Fluoride Lead Chloride Lead Bromide Lead Iodide II. EXPERIMENTAL 11 Reagents Fusion-Filtration Method Encapsulation of Samples Equipment and Procedure Bunsen Ice Calorimeter Computer Programs Shomate Method Treatment of Data Near the Melting Point Solution Calorimeter Heat of Solution Calculations III. RESULTS AND DISCUSSION 41 Lead Fluoride Variation in Heat Contents of the Nichrome V Capsules Lead Chloride Lead Bromide Lead Iodide Summary BIBLIOGRAPHY ...... 98 in LIST OF TABLES Table Pa8e I. High-Temperature Enthalpy Data for Cubic PbE2 Encapsulated in Gold 42 II. High-Temperature Enthalpy Data for Cubic PbF2 Encapsulated in Molybdenum 48 III.
    [Show full text]
  • Equation of State and Phase Transitions in the Nuclear
    National Academy of Sciences of Ukraine Bogolyubov Institute for Theoretical Physics Has the rights of a manuscript Bugaev Kyrill Alekseevich UDC: 532.51; 533.77; 539.125/126; 544.586.6 Equation of State and Phase Transitions in the Nuclear and Hadronic Systems Speciality 01.04.02 - theoretical physics DISSERTATION to receive a scientific degree of the Doctor of Science in physics and mathematics arXiv:1012.3400v1 [nucl-th] 15 Dec 2010 Kiev - 2009 2 Abstract An investigation of strongly interacting matter equation of state remains one of the major tasks of modern high energy nuclear physics for almost a quarter of century. The present work is my doctor of science thesis which contains my contribution (42 works) to this field made between 1993 and 2008. Inhere I mainly discuss the common physical and mathematical features of several exactly solvable statistical models which describe the nuclear liquid-gas phase transition and the deconfinement phase transition. Luckily, in some cases it was possible to rigorously extend the solutions found in thermodynamic limit to finite volumes and to formulate the finite volume analogs of phases directly from the grand canonical partition. It turns out that finite volume (surface) of a system generates also the temporal constraints, i.e. the finite formation/decay time of possible states in this finite system. Among other results I would like to mention the calculation of upper and lower bounds for the surface entropy of physical clusters within the Hills and Dales model; evaluation of the second virial coefficient which accounts for the Lorentz contraction of the hard core repulsing potential between hadrons; inclusion of large width of heavy quark-gluon bags into statistical description.
    [Show full text]
  • THERMODYNAMIC EVALUATION of the Cu-Ti SYSTEM in VIEW of SOLID STATE AMORPHIZATION REACTIONS L
    THERMODYNAMIC EVALUATION OF THE Cu-Ti SYSTEM IN VIEW OF SOLID STATE AMORPHIZATION REACTIONS L. Battezzati, M. Baricco, G. Riontino, I. Soletta To cite this version: L. Battezzati, M. Baricco, G. Riontino, I. Soletta. THERMODYNAMIC EVALUATION OF THE Cu- Ti SYSTEM IN VIEW OF SOLID STATE AMORPHIZATION REACTIONS. Journal de Physique Colloques, 1990, 51 (C4), pp.C4-79-C4-85. 10.1051/jphyscol:1990409. jpa-00230769 HAL Id: jpa-00230769 https://hal.archives-ouvertes.fr/jpa-00230769 Submitted on 1 Jan 1990 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. ~OLLOQUEDE PHYSIQUE Colloque C4, suppl6ment au 11'14, Tome 51, 15 juillet 1990 THERMODYNAMIC EVALUATION OF THE Cu-Ti SYSTEM IN VIEW OF SOLID STATE AMORPHIZATION REACTIONS L. BATTEZZATI* , M. BARICCO*~ *""" , G. RIONTINO" *"* and I. SOLETTA** * '~ipartimento di Chimica Inorganics, Chimica Fisica e Chimica dei Materiali, Universitd di Torino, Italy ""~stitutoElettrotecnico Nazionale Galileo Perraris, Torino, Italy *.* Dipartimento di Chimica, Universitd di Sassari, Italy *et* INPM, Unita' di Ricerca di Torino, Italy Resumk -La description thermodynamique du sist6me Cu-Ti est reconsideree, car les calculs he la littgrature, bien que donnant une bonne representation du diagramme de phase, ne prevoient pas la possibilit6 de l'amorphisation.
    [Show full text]
  • 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 .
    [Show full text]
  • Efficient Approach to Compute Melting Properties Fully from Ab Initio With
    PHYSICAL REVIEW B 96, 224202 (2017) Efficient approach to compute melting properties fully from ab initio with application to Cu Li-Fang Zhu,* Blazej Grabowski, and Jörg Neugebauer Max-Planck-Institut für Eisenforschung GmbH, D-40237 Düsseldorf, Germany (Received 3 August 2017; revised manuscript received 16 October 2017; published 13 December 2017) Applying thermodynamic integration within an ab initio-based free-energy approach is a state-of-the-art method to calculate melting points of materials. However, the high computational cost and the reliance on a good reference system for calculating the liquid free energy have so far hindered a general application. To overcome these challenges, we propose the two-optimized references thermodynamic integration using Langevin dynamics (TOR-TILD) method in this work by extending the two-stage upsampled thermodynamic integration using Langevin dynamics (TU-TILD) method, which has been originally developed to obtain anharmonic free energies of solids, to the calculation of liquid free energies. The core idea of TOR-TILD is to fit two empirical potentials to the energies from density functional theory based molecular dynamics runs for the solid and the liquid phase and to use these potentials as reference systems for thermodynamic integration. Because the empirical potentials closely reproduce the ab initio system in the relevant part of the phase space the convergence of the thermodynamic integration is very rapid. Therefore, the proposed approach improves significantly the computational efficiency while preserving the required accuracy. As a test case, we apply TOR-TILD to fcc Cu computing not only the melting point but various other melting properties, such as the entropy and enthalpy of fusion and the volume change upon melting.
    [Show full text]
  • 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.
    [Show full text]
  • Superconducting Phase Transition in Inhomogeneous Chains of Superconducting Islands
    Air Force Institute of Technology AFIT Scholar Faculty Publications 2020 Superconducting Phase Transition in Inhomogeneous Chains of Superconducting Islands Eduard Ilin Irina Burkova Xiangyu Song Michael Pak Air Force Institute of Technology Dmitri S. Golubev See next page for additional authors Follow this and additional works at: https://scholar.afit.edu/facpub Part of the Condensed Matter Physics Commons, and the Electromagnetics and Photonics Commons Recommended Citation Ilin, E., Burkova, I., Song, X., Pak, M., Golubev, D. S., & Bezryadin, A. (2020). Superconducting phase transition in inhomogeneous chains of superconducting islands. Physical Review B, 102(13), 134502. https://doi.org/10.1103/PhysRevB.102.134502 This Article is brought to you for free and open access by AFIT Scholar. It has been accepted for inclusion in Faculty Publications by an authorized administrator of AFIT Scholar. For more information, please contact [email protected]. Authors Eduard Ilin, Irina Burkova, Xiangyu Song, Michael Pak, Dmitri S. Golubev, and Alexey Bezryadin This article is available at AFIT Scholar: https://scholar.afit.edu/facpub/671 PHYSICAL REVIEW B 102, 134502 (2020) Superconducting phase transition in inhomogeneous chains of superconducting islands Eduard Ilin ,1 Irina Burkova ,1 Xiangyu Song ,1 Michael Pak ,2 Dmitri S. Golubev ,3 and Alexey Bezryadin 1 1Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA 2Department of Physics, Air Force Institute of Technology, Wright-Patterson AFB, Dayton, Ohio 45433, USA 3Pico group, QTF Centre of Excellence, Department of Applied Physics, Aalto University, FI-00076 Aalto, Finland (Received 7 August 2020; revised 11 September 2020; accepted 11 September 2020; published 2 October 2020) We study one-dimensional chains of superconducting islands with a particular emphasis on the regime in which every second island is switched into its normal state, thus forming a superconductor-insulator-normal metal (S-I-N) repetition pattern.
    [Show full text]