DOCSLIB.ORG

Acoustically Trapped Colloidal Crystals That Are Reconfigurable in Real Time

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Acoustically Trapped Colloidal Crystals That Are Reconfigurable in Real Time Acoustically trapped colloidal crystals that are reconfigurable in real time Mihai Caleap1 and Bruce W. Drinkwater Faculty of Engineering, University of Bristol, Bristol BS8 1TR, United Kingdom Edited* by John B. Pendry, Imperial College London, London, United Kingdom, and approved March 5, 2014 (received for review December 13, 2013) Photonic and phononic crystals are metamaterials with repeating tuned, they do not facilitate real-time reconfigurability and so unit cells that result in internal resonances leading to a range of cannot be used in an active mode. wave guiding and filtering properties and are opening up new In this article we report for the first time, to our knowledge, applications such as hyperlenses and superabsorbers. Here we the experimental realization of a 3D colloidal metamaterial that show the first, to our knowledge, 3D colloidal phononic crystal is reconfigurable in real time and demonstrate its ability to that is reconfigurable in real time and demonstrate its ability to rapidly alter its acoustic filtering characteristics. The reconfig- rapidly alter its frequency filtering characteristics. Our reconfig- urable metamaterial is assembled from a low-density aqueous urable material is assembled from microspheres in aqueous solu- suspension of microspheres. Our metadevice generates a high- tion, trapped with acoustic radiation forces. The acoustic radiation amplitude megahertz-frequency (MHz) acoustic standing wave force is governed by an energy landscape, determined by an which results in acoustic radiation forces that lead to particles applied high-amplitude acoustic standing wave field, in which moving to, and becoming trapped in, a simple orthorhombic particles move swiftly to energy minima. This creates a colloidal lattice (although here we explore only simple tetragonal forms). crystal of several milliliters in volume with spheres arranged in an By varying the frequency of the acoustic standing wave in the orthorhombic lattice in which the acoustic wavelength is used to metadevice we are able to control the lattice geometry. We use control the lattice spacing. Transmission acoustic spectroscopy transmission acoustic spectroscopy to explore the reconfigur- shows that the new colloidal crystal behaves as a phononic meta- ability of the resulting metamaterial. These measurements reveal material and exhibits clear band-pass and band-stop frequencies a complex and tunable distribution of band-gap and band-stop ENGINEERING which are adjusted in real time. phenomena over a wide range of frequencies. reconfigurable acoustic assembly | acoustic metamaterials | Results aqueous suspension of microspheres The metadevice used to form the 3D reconfigurable meta- material is summarized in Fig. 1. To generate the desired lattice rtificially engineered metamaterials have attracted signifi- pattern, the metadevice creates a high-amplitude acoustic Acant research interest due to their useful wave guiding and standing wave field using five planar piezoceramic transducers transmission properties. The interest in these materials stems from arranged as shown in Fig. 1A. The metadevice consists of three the possibility of gaining previously unheralded control over wave orthogonally arranged systems: the levitation system, arranged phenomena, for example, controlling the path of waves leads to vertically, which lifts the particles and holds them in horizontal incredibly efficient lenses (1) or invisibility cloaking (2, 3) and planes, and two orthogonal manipulation stages, which use the controlling their transmission and reflection leads to highly ef- counterpropagating wave method to produce a grid of acoustic ficient filters (4), diodes (5–7), or superabsorbers (8). traps in the horizontal plane. The lattice spacing can be con- Photonic and phononic crystals are periodic metamaterials trolled by the frequencies of the standing waves and the form typically created from multiple elementary repeating cells. They and location of the lattice by the phase differences (16). The exhibit a well-known series of band-pass and band-stop fre- quencies that have attracted significant attention for use as filters Significance and absorbers. Here we demonstrate a phononic crystal recon- figurable in real time, although the same principles could be used We have been working on metamaterials that are reconfig- to fabricate other metamaterials including photonic crystals, as urable in real time with a view to creating genuinely active well as the more elaborate configurations required for applica- metamaterials. Such materials will allow researchers to gain tions such as cloaking. unprecedented control over a range of optical and acoustic The frequencies of the band gaps in phononic crystals can be wave phenomena. To date, although numerous examples of tuned by changing the lattice geometry (9), and the width of the metamaterials exist, none is reconfigurable in three dimensions. gaps depends on the contrast between the densities and sound We have developed a method for creating three-dimensional velocities of the component materials. Most of the work to date colloidal crystals that are reconfigurable in real time. Our method has not involved any reconfigurability, for example, 2D phononic uses acoustic assembly to trap a suspension of microspheres in crystals with a periodicity millimeter order and above have been patterns resembling crystal lattices. We show that it is possible to assembled manually and used to explore their basic properties dynamically alter the geometry of the colloidal crystal and use (10, 11). A reconfigurable phononic crystal has been created in our metamaterial as an ultrasonic filter that can be tuned in 2D using optical tweezers but this is limited to a relatively small real time. scale (’ 1 × 108-m2 area) and to transparent or dielectric particles (12). Three-dimensional experimental realizations of phononic Author contributions: M.C. and B.W.D. designed research; M.C. performed research; M.C. crystals have either been manufactured with millimeter period- and B.W.D. analyzed data; and M.C. and B.W.D. wrote the paper. icity or as colloids (13, 14). Colloids represent a particularly at- The authors declare no conflict of interest. tractive option as they are known to self-assemble into simple 3D *This Direct Submission article had a prearranged editor. crystalline structures. Recent work on 3D hypersonic (GHz) col- Freely available online through the PNAS open access option. loidal crystals has led to experimental observation of the hyper- 1To whom correspondence should be addressed. E-mail: [email protected]. sonic Bragg gaps (15). However, whereas the choice of particle This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. shape, size, volume fraction, etc. allows the colloidal crystal to be 1073/pnas.1323048111/-/DCSupplemental. www.pnas.org/cgi/doi/10.1073/pnas.1323048111 PNAS Early Edition | 1of5 Downloaded by guest on September 27, 2021 Fig. 1. Acoustic metadevice capable of manipulat- ing the acoustic space and controlling the propa- gation of waves. (A) Schematic view of the fabri- cated metadevice with piezoceramic transducers for generating standing acoustic waves and a pair of broadband transducers for acoustic transmission spectroscopy. Note a photograph of the device can be seen in SI Text, Fig. S4.(B) Acoustic manipulator with four transducers, positioned as two orthogonal pairs. Exciting weakly resonant waves in the piezo- ceramic plates, polystyrene microspheres suspended in a fluid are driven to the pressure nodes of the standing wave field. (C) Acoustic levitator with one transducer at the base of the device holds particles against gravity in horizontal planes inside a thin- wall transparent polyester tube; the free surface of the aqueous suspension above the levitator acts as a reflector to form standing waves. (D) Experimental apparatus for acoustic transmission spectroscopy. The ultrasonic pulse generated by a monolithic transducer is incident upon the colloidal crystal in the center of the device and the transmitted signal is collected by a 2D matrix array transducer whose center elements are collinear with the incident wave. The image in the background shows a typical acoustic scattering be- havior of a colloidal crystal lattice at an instant time. Arrows indicate direction of propagation of the waves. resultant 3D standing wave exerts an acoustic radiation force on cited in-phase, the particles were further formed into ap gridffiffiffi in the particles (17). This force stems from a combination of the the horizontalpffiffiffi X À Y plane with lattice spacing ax = λx= 2 and time-averaged acoustic pressure and inertial interaction between ay = λy= 2. Here the wavelengths in the X- and Y directions, λx the particles and the acoustic field (18). Under Rayleigh scat- and λy, were used to reconfigure the metamaterial (see the sec- tering conditions, the wavelength is larger than the particle size ond section of SI Text). Typical acoustic landscape is depicted ðλ >> aÞ and acoustic radiation force due to a standing wave is in Fig. S2, while the particle positions are shown in Fig. S3. governed by the spatial gradient of the energy landscape, U, i.e., The acoustic standing wave patterns were first characterized F = −∇U (17). Particles with densities greater than the fluid ex- by a Schlieren optical system which maps the time-averaged perience forces toward pressure nodes. However, whereas this intensity field distribution. Fig. 2 shows the intensity distri-
Load more

Recommended publications
  • 2 a Primer on Polymer Colloids: Structure, Synthesis and Colloidal Stability
    A. Al Shboul, F. Pierre, and J. P. Claverie 2 A primer on polymer colloids: structure, synthesis and colloidal stability 2.1 Introduction A colloid is a dispersion of very fine objects in a fluid [1]. These objects can be solids, liquids or gas, and the corresponding colloidal dispersion is then referred to as sus- pension, emulsion or foam. Colloids possess unique characteristics. For example, as their size is smaller than the wavelength of light, they scatter light. They also offer a large interfacial surface area, meaning that interfacial phenomena are of paramount importance in these dispersions. The weight of each dispersed particle being small, gravity and buoyancy forces are not sufficient to counteract the thermal random mo- tion of the particle, named Brownian motion (in tribute to the 19th century botanist Robert Brown who first characterized it). The particles do not remain in a dispersed state indefinitely: they will sooner or later aggregate (phase separation). Thus, thecol- loidal state is in general metastable and colloidal stability is one of the key features to take into account when working with colloids. Among all colloids, the polymer colloid family is one of the most widely inves- tigated [2]. Polymer colloids are used for a large number of applications, ranging from coatings, adhesives, inks, impact modifiers, drug-delivery vehicles, etc. The particles range in size from about 10 nm to 1 000 nm (1 μm) in diameter. They are usually spherical, but numerous other shapes have been observed. Polymer colloids are not uncommon in nature. For example, natural rubber latex, the secretion of the Hevea brasiliensis tree, is in fact a dispersion of polyisoprene nanoparticles in wa- ter.
    [Show full text]
  • 4. Fabrication of Polymer-Immobilized Colloidal Crystal Films (851Kb)
    R&D Review of Toyota CRDL, Vol.45 No.1 (2014) 17- 22 17 Special Feature: Applied Nanoscale Morphology Research Report Fabrication of Polymer-immobilized Colloidal Crystal Films Masahiko Ishii Report received on Feb. 28, 2014 A fabrication method for polymer-immobilized colloidal crystal fi lms using conventional spray coating has been developed for application of the fi lms as practical colored materials. By controlling both the viscosity of the silica sphere-acrylic monomer dispersions and the wettability of the substrates, colloidal crystalline fi lms with brilliant iridescent colors were successfully obtained by spray coating and UV curing. The color could be controlled by adjusting both the sphere concentration and diameter. Scanning electron microscopy was applied to study the crystal structure of the coated fi lms, and revealed that the fi lms are composed of highly oriented face-centered-cubic grains with (111) planes parallel to the substrate surface. A method for utilizing the colloidal crystal fi lms as pigments was also proposed. Flakes obtained by crushing the colloidal crystal coated fi lms were added to a commercial clear paint and coated on a substrate. The coated fi lms exhibited iridescent colors that varies with viewing angle. Colloidal Crystal, Self-assembly, Silica, Polymeric Material, Spray Coating 1. Introduction arrays of monodispersed sub-micrometer sized spheres. They exhibit iridescent colors due to Bragg diffraction Jewels such as diamonds and rubies are beautiful, of visible light when they have a periodicity on the attracting the attention of people worldwide. Most of scale of the wavelength of the light. The most common these are natural minerals with crystalline structures.
    [Show full text]
  • Colloidal Crystals with a 3D Photonic Bandgap
    Part I General Introduction I.1 Photonic Crystals A photonic crystal (PC) is a regularly structured material, with feature sizes on the order of a wavelength (or smaller), that exhibits strong interaction with light.1-3 The main concept behind photonic crystals is the formation of a 'photonic band gap'. For a certain range of frequencies, electromagnetic waves are diffracted by the periodic modulations in the dielectric constant of the PC forming (directional) stop bands. If the stop bands are wide enough to overlap for both polarization states along all crystal directions, the material is said to possess a complete photonic band gap (CPBG). In such a crystal, propagation of electromagnetic waves with frequencies lying within the gap is forbidden irrespective of their direction of propagation and polarization.1,2 This leads to the possibility to control the spontaneous emission of light. For example, an excited atom embedded in a PC will not be able to make a transition to a lower energy state as readily if the frequency of the emitted photon lies within the band gap, hence increasing the lifetime of the excited state.1,2 Photonic crystals with a (directional) stop gap can also have a significant effect on the spontaneous-emission rate.4 If a defect or mistake in the periodicity is introduced in the otherwise perfect crystal, localized photonic states in the gap will be created. A point defect could act like a microcavity, a line defect like a wave-guide, and a planar defect like a planar wave-guide. By introducing defects, light can be localized or guided along the defects modes.1,2 1 2 a b Figure I.1–1 Scanning electron micrograph (SEM) of a face-centered-cubic (fcc) colloidal crystal of closed-packed silica spheres (R = 110 nm).
    [Show full text]
  • Colloidal Crystal: Emergence of Long Range Order from Colloidal Fluid
    Colloidal Crystal: emergence of long range order from colloidal fluid Lanfang Li December 19, 2008 Abstract Although emergence, or spontaneous symmetry breaking, has been a topic of discussion in physics for decades, they have not entered the set of terminologies for materials scientists, although many phenomena in materials science are of the nature of emergence, especially soft materials. In a typical soft material, colloidal suspension system, a long range order can emerge due to the interaction of a large number of particles. This essay will first introduce interparticle interactions in colloidal systems, and then proceed to discuss the emergence of order, colloidal crystals, and finally provide an example of applications of colloidal crystals in light of conventional molecular crystals. 1 1 Background and Introduction Although emergence, or spontaneous symmetry breaking, and the resultant collective behav- ior of the systems constituents, have manifested in many systems, such as superconductivity, superfluidity, ferromagnetism, etc, and are well accepted, maybe even trivial crystallinity. All of these phenonema, though they may look very different, share the same fundamental signature: that the property of the system can not be predicted from the microscopic rules but are, \in a real sense, independent of them. [1] Besides these emergent phenonema in hard condensed matter physics, in which the interaction is at atomic level, interactions at mesoscale, soft will also lead to emergent phenemena. Colloidal systems is such a mesoscale and soft system. This size scale is especially interesting: it is close to biogical system so it is extremely informative for understanding life related phenomena, where emergence is origin of life itself; it is within visible light wavelength, so that it provides a model system for atomic system with similar physics but probable by optical microscope.
    [Show full text]
  • In Situ X-Ray Crystallographic Study of the Structural Evolution of Colloidal Crystals Upon Heating
    X-ray diffraction and imaging Journal of Applied In situ X-ray crystallographic study of the structural Crystallography evolution of colloidal crystals upon heating ISSN 0021-8898 A. V. Zozulya,a* J.-M. Meijer,b A. Shabalin,a A. Ricci,a F. Westermeier,a R. P. Received 2 November 2012 Kurta,a U. Lorenz,a A. Singer,a O. Yefanov,c A. V. Petukhov,b M. Sprunga and Accepted 6 February 2013 I. A. Vartanyantsa,d aDeutsches Electronen-Synchrotron (DESY), Notkestrasse 85, D-22607 Hamburg, Germany, bVan ’t Hoff Laboratory for Physical and Colloid Chemistry, Debye Institute, University of Utrecht, Padualaan 8, 3508 TB Utrecht, The Netherlands, cCenter for Free-Electron Laser Science, DESY, Notkestrasse 85, D-22607 Hamburg, Germany, and dNational Research Nuclear University ‘MEPhI’, 115409 Moscow, Russian Federation. Correspondence e-mail: [email protected] The structural evolution of colloidal crystals made of polystyrene hard spheres has been studied in situ upon incremental heating of a crystal in a temperature range below and above the glass transition temperature of polystyrene. Thin films of colloidal crystals having different particle sizes were studied in transmission geometry using a high-resolution small-angle X-ray scattering setup at the P10 Coherence Beamline of the PETRA III synchrotron facility. The transformation of colloidal crystals to a melted state has been observed in a narrow temperature interval of less than 10 K. 1. Introduction not well studied, although it has important technological Colloidal crystals are close-packed self-assembled arrange- aspects regarding the tolerable temperature range of a ments of monodisperse colloidal particles of sub-micrometre photonic device.
    [Show full text]
  • Colloidal Matter: Packing, Geometry, and Entropy Vinothan N
    Colloidal matter: packing, geometry, and entropy Vinothan N. Manoharan Harvard John A. Paulson School of Engineering and Applied Sciences and Department of Physics, Harvard University, Cambridge MA 02138 USA This is the author's version of the work. It is posted here by permission of the AAAS for personal use, not for redistribution. The definitive version was published in Science volume 349 on August 8, 2015. doi: 10.1126/science.1253751 The many dimensions of colloidal matter. The self-assembly of colloids can be controlled by changing the shape, topology, or patchiness of the particles, by introducing attractions between particles, or by constraining them to a curved surface. All of the assembly phenomena illustrated here can be understood from the interplay between entropy and geometrical constraints. Summary of this review article Background: Colloids consist of solid or liquid particles, each about a few hundred nanometers in size, dispersed in a fluid and kept suspended by thermal fluctuations. While natural colloids are the stuff of paint, milk, and glue, synthetic colloids with well-controlled size distributions and interactions are a model system for understanding phase transitions. These colloids can form crystals and other phases of matter seen in atomic and molecular systems, but because the particles are large enough to be seen under an optical microscope, the microscopic mechanisms of phase transitions can be directly observed. Furthermore, their ability to spontaneously form phases that are ordered on the scale of visible wavelengths makes colloids useful building blocks for optical materials such as photonic crystals. Because the interactions between particles can be altered and the effects on structure directly observed, experiments on colloids offer a controlled approach toward understanding and harnessing self-assembly, a fundamental topic in materials science, condensed matter physics, and biophysics.
    [Show full text]
  • Evolution of Size and Shape in the Colloidal Crystallization of Gold Nanoparticles Owen C
    Published on Web 06/06/2007 Evolution of Size and Shape in the Colloidal Crystallization of Gold Nanoparticles Owen C. Compton and Frank E. Osterloh* Contribution from the Department of Chemistry, UniVersity of California, DaVis, One Shields AVenue, DaVis, California 95161 Received December 17, 2006; E-mail: [email protected] Abstract: The addition of dodecanethiol to a solution of oleylamine-stabilized gold nanoparticles in chloroform leads to aggregation of nanoparticles and formation of colloidal crystals. Based on results from dynamic light scattering and scanning electron microscopy we identify three different growth mechanisms: direct nanoparticle aggregation, cluster aggregation, and heterogeneous aggregation. These mechanisms produce amorphous, single-crystalline, polycrystalline, and core-shell type clusters. In the latter, gold nanoparticles encapsulate an impurity nucleus. All crystalline structures exhibit fcc or icosahedral packing and are terminated by (100) and (111) planes, which leads to truncated tetrahedral, octahedral, and icosahedral shapes. Importantly, most clusters in this system grow by aggregation of 60-80 nm structurally nonrigid clusters that form in the first 60 s of the experiment. The aggregation mechanism is discussed in terms of classical and other nucleation theories. Introduction and of its interfacial energy. Growth can only continue when Periodic arrangement of inorganic particles, or colloidal crystals have reached a critical nucleation size, beyond which crystals, continues to be of great academic
    [Show full text]
  • Photonic Band Structure of Fcc Colloidal Crystals
    VOLUME 76, NUMBER 2 PHYSICAL REVIEW LETTERS 8JANUARY 1996 Photonic Band Structure of fcc Colloidal Crystals I.˙ Inan¸˙ c Tarhan and George H. Watson Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716 (Received 22 March 1995) Polystyrene colloidal crystals form three dimensional periodic dielectric structures which can be used for photonic band structure measurements in the visible regime. From transmission measurements the photonic band structure of an fcc crystal has been obtained along the directions between the L point and the W point. Kossel line patterns were used for locating the symmetry points of the lattice for exact positioning and orientation of the crystals. In addition, these patterns reveal the underlying photonic band structure of the crystals in a qualitative way. PACS numbers: 78.20.Ci, 42.50.–p, 81.10.Aj, 82.70.Dd For the last eight years, the analogy between the propa- not expected to exhibit large gaps because of the relatively gation of electromagnetic waves in periodic dielectric low index contrast, it does permit study of photonic band structures, dubbed photonic band gap (PBG) or photonic structure, as reported here. The lattice parameter of these crystals, and electron waves in atomic crystals has moti- self-organizing structures can be easily tailored, providing vated scientists to explore new possibilities in this field flexibility in designing photonic crystals for use in specific [1–5]. On account of the periodic modulations in dielec- spectral regions. tric constant in PBG crystals, with spatial periods designed Illumination of a single colloidal crystal by a monochro- to be on the order of a desired wavelength, electromag- matic laser beam can exhibit an interesting phenomenon: netic waves incident along a particular direction are dif- various dark rings and arcs (conic cross sections) superim- fracted for a certain range of frequencies, forming stop posed on a diffusely lit background form in both transmis- bands.
    [Show full text]
  • Elastomeric Nematic Colloids, Colloidal Crystals and Microstructures with Complex Topology† Cite This: DOI: 10.1039/D0sm02135k Ye Yuan, a Patrick Kellerb and Ivan I
    Soft Matter View Article Online PAPER View Journal Elastomeric nematic colloids, colloidal crystals and microstructures with complex topology† Cite this: DOI: 10.1039/d0sm02135k Ye Yuan, a Patrick Kellerb and Ivan I. Smalyukh *acd Control of physical behaviors of nematic colloids and colloidal crystals has been demonstrated by tuning particle shape, topology, chirality and surface charging. However, the capability of altering physical behaviors of such soft matter systems by changing particle shape and the ensuing responses to external stimuli has remained elusive. We fabricated genus-one nematic elastomeric colloidal ring-shaped particles and various microstructures using two-photon photopolymerization. Nematic ordering within both the nano-printed particle and the surrounding medium leads to anisotropic responses and actuation when heated. With the thermal control, elastomeric microstructures are capable of changing from genus-one to genus-zero surface topology. Using these particles as building blocks, we Received 1st December 2020, investigated elastomeric colloidal crystals immersed within a liquid crystal fluid, which exhibit Accepted 15th January 2021 crystallographic symmetry transformations. Our findings may lead to colloidal crystals responsive to a DOI: 10.1039/d0sm02135k large variety of external stimuli, including electric fields and light. Pre-designed response of elastomeric nematic colloids, including changes of colloidal surface topology and lattice symmetry, are of interest rsc.li/soft-matter-journal for both fundamental
    [Show full text]
  • Colloidal Crystals Structure and Dynamics
    Colloidal Crystals Structure and Dynamics Ivan Vartaniants DESY, Hamburg, Germany National Research University, ‘MEPhI’, Moscow, Russia Ivan Vartaniants | APS, Argonne, February 3, 2016 | Page 1 DESY Coherent X-ray Scattering and Imaging Group at DESY Present members: Former members: • S. Lazarev • I. Zaluzhnyy • A. Zozulya (now@PETRA III) • I. Besedin • M. Rose • A. Mancuso (now@XFEL) • P. Skopintsev • O. Gorobtsov • O. Yefanov (now@CFEL) • D. Dzhigaev • N. Mukharamova • R. Dronyak • J. Gulden (now@FH-Stralsund) • U. Lorenz (now@University of Potsdam) • A. Singer (now@UCSD) • R. Kurta (now@XFEL) • A. Shabalin (now@CFEL) Ivan Vartaniants | APS, Argonne, February 3, 2016 | Page 3 High resolution microscopy Ivan Vartaniants | APS, Argonne, February 3, 2016 | Page 4 High resolution electron microscopy Atomic structure of the Au68 gold Atomic resolution imaging of nanoparticle determined by electron graphene microscopy. M. Azubel, et al., Science 345, 909 (2014) A. Robertson and J. Warner, Nanoscale, (2013),5, 4079-4093 Simulated HREM images for GaN[0001] From: Wikipedia From: Web Images From: Web Images Can we develop x-ray microscope with atomic resolution? It does not work with conventional approach due to the lack of atomic resolution X-ray optics Can coherent x-ray diffraction imaging be the way to go? What is Coherence? Coherence is an ideal property of waves that enables stationary interference Soap bubble wikipedia.org Whether X-rays are coherent waves? Max von Laue Nobel Prize in Physics, 1914 W. Friedrich, P. Knipping, M. von Laue, Ann. Phys. (1913) 100 years later LCLS FLASH H. Chapman et al., A. Mancuso et al., Nature (2011) New J.
    [Show full text]
  • Microscopic Theory of Entropic Bonding for Colloidal Crystal Prediction
    Microscopic Theory of Entropic Bonding for Colloidal Crystal Prediction Thi Vo1 and Sharon C. Glotzer,1,2∗ 1Department of Chemical Engineering, University of Michigan – Ann Arbor 2 Biointerfaces Institute, University of Michigan – Ann Arbor ∗To whom correspondence should be addressed; E-mail: [email protected]. Entropy alone can self-assemble hard particles into colloidal crystals of remarkable complexity whose structures are the same as atomic and molecular crystals, but with larger lattice spacings. Although particle-based molecular simulation is a powerful tool for predicting self-assembly by exploring phase space, it is not yet possible to predict colloidal crystal structures a priori from particle shape as we can for atomic crystals based on electronic valency. Here we present such a first principles theory. By directly calculating and minimizing excluded volume within the framework of statistical mechanics, we describe the directional forces that emerge between hard shapes in familiar terms used to describe chemical bonds. Our theory predicts thermodynamically preferred structures for four families of hard polyhedra that match, in every instance, previous simulation results. The success of this first principles approach to entropic colloidal crystal structure prediction furthers fundamental understanding of both entropically driven crystallization and conceptual pictures of bonding in matter. 1 Introduction In his 1704 treatise, Opticks, Sir Isaac Newton wrote of an “attractive” force that holds particles of matter together. By observing that matter stays together in a host of different everyday situations, he inferred the presence of what we now refer to as chemical bonds, one of the most fundamental concepts in science. Chemical bonds originate in electronic interactions.
    [Show full text]
  • Soft Condensed Matter Daan Frenkel
    Physica A 313 (2002) 1–31 www.elsevier.com/locate/physa Soft condensed matter Daan Frenkel FOM Institute for Atomic and Molecular Physics, Kruislaan 407, 1098 SJAmsterdam, The Netherlands Abstract These lectures illustrate some of the concepts of soft-condensed matter physics, taking exam- ples from colloid physics. Many of the theoretical concepts will be illustrated with the results of computer simulations. After a brief introduction describing interactions between colloids, the paper focuses on colloidal phase behavior (in particular, entropic phase transitions), colloidal hydrodynamics and colloidal nucleation. c 2002 Elsevier Science B.V. All rights reserved. PACS: 82.70.Dd; 02.70.Ns; 64.70.Md; 64.60.Qb Keywords: Soft matter; Colloids; Computer simulation 1. Introduction The topic of these lectures is soft condensed matter physics—but not all of it. My aim is to discuss a few examples that illustrate the analogies and di6erences between “soft” and “hard” matter. The choice of the examples is biased by my own experience. Most of the examples that I discuss apply to colloids. In many ways, colloids behave like giant atoms, and quite a bit of the colloid physics can be understood in this way. However, much of the interesting behavior of colloids is related to the fact that they are, in many respects, not like atoms. In this lecture, I shall start from the picture of colloids as oversized atoms or molecules, and then I shall selectively discuss some features of colloids that are di6erent. My presentation of the subject will be a bit strange, because I am a computer simulator, rather than a colloid scientist.
    [Show full text]