1
|
Gemeinhardt A, Martinsons M, Schmiedeberg M. Stabilizing quasicrystals composed of patchy colloids by narrowing the patch width. ACTA ACUST UNITED AC 2019. [DOI: 10.1209/0295-5075/126/38001] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
|
2
|
Ajlouni R. A seed-based structural model for constructing rhombic quasilattice with 7-fold symmetry. Struct Chem 2018. [DOI: 10.1007/s11224-018-1169-2] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
|
3
|
Gemeinhardt A, Martinsons M, Schmiedeberg M. Growth of two-dimensional dodecagonal colloidal quasicrystals: Particles with isotropic pair interactions with two length scales vs. patchy colloids with preferred binding angles. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2018; 41:126. [PMID: 30338492 DOI: 10.1140/epje/i2018-11737-1] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2018] [Accepted: 09/26/2018] [Indexed: 06/08/2023]
Abstract
We explore the growth of colloidal quasicrystals with dodecagonal symmetry in two dimensions by employing Brownian dynamics simulations. On the one hand, we study the growth behavior of structures obtained in a system of particles that interact according to an isotropic pair potential with two typical length scales. On the other hand, we consider patchy colloids that possess only one typical interaction length scale but prefer given binding angles. In case of the isotropic particles, we show that an imbalance in the competition between the two distances might lead to defects with wrong nearest-neighbor distances in the resulting structure. In contrast, during the growth of quasicrystals with patchy colloids such defects do not occur due to the lack of a second interaction length scale. However, as a downside, the diffusion of patchy particles along a surface typically is slower such that domains occur where the particles possess different phononic and phasonic offsets. Our results are important to understand how soft matter quasicrystals can be grown as perfectly as possible and to obtain a deeper insight into the mechanisms of the growth of quasicrystals in general.
Collapse
Affiliation(s)
- Anja Gemeinhardt
- Institut für Theoretische Physik I, Friedrich-Alexander Universität Erlangen-Nürnberg, Staudtstraße 7, 91058, Erlangen, Germany
| | - Miriam Martinsons
- Institut für Theoretische Physik I, Friedrich-Alexander Universität Erlangen-Nürnberg, Staudtstraße 7, 91058, Erlangen, Germany.
| | - Michael Schmiedeberg
- Institut für Theoretische Physik I, Friedrich-Alexander Universität Erlangen-Nürnberg, Staudtstraße 7, 91058, Erlangen, Germany
| |
Collapse
|
4
|
Martinsons M, Schmiedeberg M. Growth of two-dimensional decagonal colloidal quasicrystals. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:255403. [PMID: 29762124 DOI: 10.1088/1361-648x/aac503] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
The growth of quasicrystals, i.e. structures with long-range positional order but no periodic translational symmetry, is more complex than the growth of periodic crystals. By employing Brownian dynamics simulations in two dimensions for colloidal particles that interact according to an isotropic pair potential with two incommensurate lengths, we study the growth of quasicrystalline structures by sequentially depositing particles at their surface. We quantify the occurrence of quasicrystalline order as a function of the temperature and the rate of added particles. In addition, we explore defects like local triangular order or gaps within the quasicrystalline structure. Furthermore, we analyze the shapes of the surfaces in grown structures which tend to build straight lines along the symmetry axes of the quasicrystal. Finally, we identify phasonic flips which are rearrangements of the particles due to additional degrees of freedom. The number of phasonic flips decreases with the distance to the surface.
Collapse
Affiliation(s)
- M Martinsons
- Institut für Theoretische Physik I, Friedrich-Alexander Universität Erlangen-Nürnberg, Staudtstraße 7, 91058 Erlangen, Germany
| | | |
Collapse
|
5
|
Schmiedeberg M, Achim CV, Hielscher J, Kapfer SC, Löwen H. Dislocation-free growth of quasicrystals from two seeds due to additional phasonic degrees of freedom. Phys Rev E 2017; 96:012602. [PMID: 29347123 DOI: 10.1103/physreve.96.012602] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2017] [Indexed: 06/07/2023]
Abstract
We explore the growth of two-dimensional quasicrystals, i.e., aperiodic structures that possess long-range order, from two seeds at various distances and with different orientations by using dynamical phase-field crystal calculations. We compare the results to the growth of periodic crystals from two seeds. There, a domain border consisting of dislocations is observed in case of large distances between the seed and large angles between their orientation. Furthermore, a domain border is found if the seeds are placed at a distance that does not fit to the periodic lattice. In the case of the growth of quasicrystals, we only observe domain borders for large distances and different orientations. Note that all distances do inherently not match to a perfect domain wall-free quasicrystalline structure. Nevertheless, we find dislocation-free growth for all seeds at a small enough distance and for all seeds that approximately have the same orientation. In periodic structures, the stress that occurs due to incommensurate distances between the seeds results in phononic strain fields or, in the case of too large stresses, in dislocations. In contrast, in quasicrystals an additional phasonic strain field can occur and suppress dislocations. Phasons are additional degrees of freedom that are unique to quasicrystals. As a consequence, the additional phasonic strain field helps to distribute the stress and facilitates the growth of dislocation-free quasicrystals from multiple seeds. In contrast, in the periodic case the growth from multiple seeds most likely leads to a structure with multiple domains. Our work lays the theoretical foundations for growing perfect quasicrystals from different seeds and is therefore relevant for many applications.
Collapse
Affiliation(s)
- M Schmiedeberg
- Institut für Theoretische Physik 1, Friedrich-Alexander-Universität Erlangen-Nürnberg, D-91058 Erlangen, Germany
| | - C V Achim
- Water Research Center for Agriculture and Mining (CRHIAM), University of Concepción, 4030000 Concepción, Chile
| | - J Hielscher
- Institut für Theoretische Physik 1, Friedrich-Alexander-Universität Erlangen-Nürnberg, D-91058 Erlangen, Germany
| | - S C Kapfer
- Institut für Theoretische Physik 1, Friedrich-Alexander-Universität Erlangen-Nürnberg, D-91058 Erlangen, Germany
| | - H Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40204 Düsseldorf, Germany
| |
Collapse
|
6
|
Reinhardt A, Schreck JS, Romano F, Doye JPK. Self-assembly of two-dimensional binary quasicrystals: a possible route to a DNA quasicrystal. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:014006. [PMID: 27830657 DOI: 10.1088/0953-8984/29/1/014006] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We use Monte Carlo simulations and free-energy techniques to show that binary solutions of penta- and hexavalent two-dimensional patchy particles can form thermodynamically stable quasicrystals even at very narrow patch widths, provided their patch interactions are chosen in an appropriate way. Such patchy particles can be thought of as a coarse-grained representation of DNA multi-arm 'star' motifs, which can be chosen to bond with one another very specifically by tuning the DNA sequences of the protruding arms. We explore several possible design strategies and conclude that DNA star tiles that are designed to interact with one another in a specific but not overly constrained way could potentially be used to construct soft quasicrystals in experiment. We verify that such star tiles can form stable dodecagonal motifs using oxDNA, a realistic coarse-grained model of DNA.
Collapse
Affiliation(s)
- Aleks Reinhardt
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge, CB2 1EW, UK
| | | | | | | |
Collapse
|
7
|
Alves GA, Vasconcelos MS, Alves TFA. Critical properties of a two-dimensional Ising magnet with quasiperiodic interactions. Phys Rev E 2016; 93:042111. [PMID: 27176258 DOI: 10.1103/physreve.93.042111] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2015] [Indexed: 11/07/2022]
Abstract
We address the study of quasiperiodic interactions on a square lattice by using an Ising model with ferromagnetic and antiferromagnetic exchange interactions following a quasiperiodic Fibonacci sequence in both directions of a square lattice. We applied the Monte Carlo method, together with the Metropolis algorithm, to calculate the thermodynamic quantities of the system. We obtained the Edwards-Anderson order parameter q_{EA}, the magnetic susceptibility χ, and the specific heat c in order to characterize the universality class of the phase transition. We also use the finite size scaling method to obtain the critical temperature of the system and the critical exponents β,γ, and ν. In the low-temperature limit we obtained a spin-glass phase with critical temperature around T_{c}≈2.274, and the critical exponents β,γ, and ν, indicating that the quasiperiodic order induces a change in the universality class of the system. Also, we discovered a spin-glass ordering in a two-dimensional system which is rare and, as far as we know, the unique example is an under-frustrated Ising model.
Collapse
Affiliation(s)
- G A Alves
- Departamento de Física, Universidade Estadual do Piauí, 59078-900, Teresina - PI, Brazil
| | - M S Vasconcelos
- Escola de Ciências e Tecnologia, Universidade Federal do Rio Grande do Norte, 59078-900, Natal - RN, Brazil
| | - T F A Alves
- Departamento de Física, Universidade Federal do Piauí, 57072-970, Teresina - PI, Brazil
| |
Collapse
|
8
|
Achim CV, Schmiedeberg M, Löwen H. Growth modes of quasicrystals. PHYSICAL REVIEW LETTERS 2014; 112:255501. [PMID: 25014822 DOI: 10.1103/physrevlett.112.255501] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/13/2014] [Indexed: 06/03/2023]
Abstract
The growth of quasicrystals, i.e., aperiodic structures with long-range order, seeded from the melt is investigated using a dynamical phase field crystal model. Depending on the thermodynamic conditions, two different growth modes are detected, namely defect-free growth of the stable quasicrystal and a mode dominated by phasonic flips which are incorporated as local defects into the grown structure such that random tilinglike ordering emerges. The latter growth mode is unique to quasicrystals and can be verified in experiments on one-component mesoscopic systems.
Collapse
Affiliation(s)
- C V Achim
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40204 Düsseldorf, Germany
| | - M Schmiedeberg
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40204 Düsseldorf, Germany
| | - H Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40204 Düsseldorf, Germany
| |
Collapse
|
9
|
Reinhardt A, Romano F, Doye JPK. Computing phase diagrams for a quasicrystal-forming patchy-particle system. PHYSICAL REVIEW LETTERS 2013; 110:255503. [PMID: 23829745 DOI: 10.1103/physrevlett.110.255503] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2013] [Indexed: 06/02/2023]
Abstract
We introduce an approach to computing the free energy of quasicrystals, which we use to calculate phase diagrams for systems of two-dimensional patchy particles with five regularly arranged patches that have previously been shown to form dodecagonal quasicrystals. We find that the quasicrystal is a thermodynamically stable phase for a wide range of conditions and remains a robust feature of the system as the potential's parameters are varied. We also demonstrate that the quasicrystal is entropically stabilized over its crystalline approximants.
Collapse
Affiliation(s)
- Aleks Reinhardt
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, Oxford OX1 3QZ, United Kingdom
| | | | | |
Collapse
|
10
|
Ichikawa T, Fujimura K, Yoshio M, Kato T, Ohno H. Designer lyotropic liquid-crystalline systems containing amino acid ionic liquids as self-organisation media of amphiphiles. Chem Commun (Camb) 2013; 49:11746-8. [DOI: 10.1039/c3cc45429k] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
|
11
|
Cartwright JHE, Mackay AL. Beyond crystals: the dialectic of materials and information. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2012; 370:2807-2822. [PMID: 22615461 PMCID: PMC3367679 DOI: 10.1098/rsta.2012.0106] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
We argue for a convergence of crystallography, materials science and biology, that will come about through asking materials questions about biology and biological questions about materials, illuminated by considerations of information. The complex structures now being studied in biology and produced in nanotechnology have outstripped the framework of classical crystallography, and a variety of organizing concepts are now taking shape into a more modern and dynamic science of structure, form and function. Absolute stability and equilibrium are replaced by metastable structures existing in a flux of energy-carrying information and moving within an energy landscape of complex topology. Structures give place to processes and processes to systems. The fundamental level is that of atoms. As smaller and smaller groups of atoms are used for their physical properties, quantum effects become important; already we see quantum computation taking shape. Concepts move towards those in life with the emergence of specifically informational structures. We now see the possibility of the artificial construction of a synthetic living system, different from biological life, but having many or all of the same properties. Interactions are essentially nonlinear and collective. Structures begin to have an evolutionary history with episodes of symbiosis. Underlying all the structures are constraints of time and space. Through hierarchization, a more general principle than the periodicity of crystals, structures may be found within structures on different scales. We must integrate unifying concepts from dynamical systems and information theory to form a coherent language and science of shape and structure beyond crystals. To this end, we discuss the idea of categorizing structures based on information according to the algorithmic complexity of their assembly.
Collapse
Affiliation(s)
- Julyan H. E. Cartwright
- Instituto Andaluz de Ciencias de la Tierra, CSIC–Universidad de Granada, Campus Fuentenueva, E-18071 Granada, Spain
| | - Alan L. Mackay
- Birkbeck College, University of London, Malet Street, London WC1E 7HX, UK
| |
Collapse
|
12
|
van der Linden MN, Doye JPK, Louis AA. Formation of dodecagonal quasicrystals in two-dimensional systems of patchy particles. J Chem Phys 2012; 136:054904. [DOI: 10.1063/1.3679653] [Citation(s) in RCA: 45] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
|
13
|
Ichikawa T, Yoshio M, Hamasaki A, Taguchi S, Liu F, Zeng XB, Ungar G, Ohno H, Kato T. Induction of Thermotropic Bicontinuous Cubic Phases in Liquid-Crystalline Ammonium and Phosphonium Salts. J Am Chem Soc 2012; 134:2634-43. [DOI: 10.1021/ja209010m] [Citation(s) in RCA: 133] [Impact Index Per Article: 11.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Takahiro Ichikawa
- Department of Chemistry and
Biotechnology, School of Engineering, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
- Department of Biotechnology, Tokyo University of Agriculture and Technology, Nakacho,
Koganei, Tokyo 184-8588, Japan
| | - Masafumi Yoshio
- Department of Chemistry and
Biotechnology, School of Engineering, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
| | - Atsushi Hamasaki
- Department of Biotechnology, Tokyo University of Agriculture and Technology, Nakacho,
Koganei, Tokyo 184-8588, Japan
| | - Satomi Taguchi
- Department of Biotechnology, Tokyo University of Agriculture and Technology, Nakacho,
Koganei, Tokyo 184-8588, Japan
| | - Feng Liu
- Department of Materials Science
and Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, United Kingdom
| | - Xiang-bing Zeng
- Department of Materials Science
and Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, United Kingdom
| | - Goran Ungar
- Department of Materials Science
and Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, United Kingdom
- WCU Program C2E2, School
of Chemical and Biological Engineering, Seoul National University, Seoul, South Korea
| | - Hiroyuki Ohno
- Department of Biotechnology, Tokyo University of Agriculture and Technology, Nakacho,
Koganei, Tokyo 184-8588, Japan
| | - Takashi Kato
- Department of Chemistry and
Biotechnology, School of Engineering, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
| |
Collapse
|
14
|
|
15
|
Rosen BM, Wilson CJ, Wilson DA, Peterca M, Imam MR, Percec V. Dendron-Mediated Self-Assembly, Disassembly, and Self-Organization of Complex Systems. Chem Rev 2009; 109:6275-540. [DOI: 10.1021/cr900157q] [Citation(s) in RCA: 1066] [Impact Index Per Article: 71.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
Affiliation(s)
- Brad M. Rosen
- Roy & Diana Vagelos Laboratories, Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323
| | - Christopher J. Wilson
- Roy & Diana Vagelos Laboratories, Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323
| | - Daniela A. Wilson
- Roy & Diana Vagelos Laboratories, Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323
| | - Mihai Peterca
- Roy & Diana Vagelos Laboratories, Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323
| | - Mohammad R. Imam
- Roy & Diana Vagelos Laboratories, Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323
| | - Virgil Percec
- Roy & Diana Vagelos Laboratories, Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323
| |
Collapse
|
16
|
|
17
|
Doye JPK, Louis AA, Lin IC, Allen LR, Noya EG, Wilber AW, Kok HC, Lyus R. Controlling crystallization and its absence: proteins, colloids and patchy models. Phys Chem Chem Phys 2007; 9:2197-205. [PMID: 17487316 DOI: 10.1039/b614955c] [Citation(s) in RCA: 140] [Impact Index Per Article: 8.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The ability to control the crystallization behaviour (including its absence) of particles, be they biomolecules such as globular proteins, inorganic colloids, nanoparticles, or metal atoms in an alloy, is of both fundamental and technological importance. Much can be learnt from the exquisite control that biological systems exert over the behaviour of proteins, where protein crystallization and aggregation are generally suppressed, but where in particular instances complex crystalline assemblies can be formed that have a functional purpose. We also explore the insights that can be obtained from computational modelling, focussing on the subtle interplay between the interparticle interactions, the preferred local order and the resulting crystallization kinetics. In particular, we highlight the role played by "frustration", where there is an incompatibility between the preferred local order and the global crystalline order, using examples from atomic glass formers and model anisotropic particles.
Collapse
Affiliation(s)
- Jonathan P K Doye
- Physical and Theoretical Chemistry Laboratory, Oxford University, South Parks Road, Oxford, UK OX1 3QZ.
| | | | | | | | | | | | | | | |
Collapse
|