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Joseph M, Read DJ, Rucklidge AM. Design of Linear Block Copolymers and ABC Star Terpolymers That Produce Two Length Scales at Phase Separation. Macromolecules 2023; 56:7847-7859. [PMID: 37841536 PMCID: PMC10569105 DOI: 10.1021/acs.macromol.3c00800] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2023] [Revised: 09/04/2023] [Indexed: 10/17/2023]
Abstract
Quasicrystals (materials with long-range order but without the usual spatial periodicity of crystals) were discovered in several soft matter systems in the last 20 years. The stability of quasicrystals has been attributed to the presence of two prominent length scales in a specific ratio, which is 1.93 for the 12-fold quasicrystals most commonly found in soft matter. We propose design criteria for block copolymers such that quasicrystal-friendly length scales emerge at the point of phase separation from a melt, basing our calculations on the Random Phase Approximation. We consider two block copolymer families: linear chains containing two different monomer types in blocks of different lengths, and ABC star terpolymers. In all examples, we are able to identify parameter windows with the two length scales having a ratio of 1.93. The models that we consider that are simplest for polymer synthesis are, first, a monodisperse ALBASB melt and, second, a model based on random reactions from a mixture of AL, AS, and B chains: both feature the length scale ratio of 1.93 and should be relatively easy to synthesize.
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Affiliation(s)
- Merin Joseph
- School of Mathematics, University of Leeds, Leeds LS2 9JT, U.K.
| | - Daniel J. Read
- School of Mathematics, University of Leeds, Leeds LS2 9JT, U.K.
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2
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Archer AJ, Dotera T, Rucklidge AM. Rectangle-triangle soft-matter quasicrystals with hexagonal symmetry. Phys Rev E 2022; 106:044602. [PMID: 36397536 DOI: 10.1103/physreve.106.044602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2021] [Accepted: 08/03/2022] [Indexed: 06/16/2023]
Abstract
Aperiodic (quasicrystalline) tilings, such as Penrose's tiling, can be built up from, e.g., kites and darts, squares and equilateral triangles, rhombi- or shield-shaped tiles, and can have a variety of different symmetries. However, almost all quasicrystals occurring in soft matter are of the dodecagonal type. Here we investigate a class of aperiodic tilings with hexagonal symmetry that are based on rectangles and two types of equilateral triangles. We show how to design soft-matter systems of particles interacting via pair potentials containing two length scales that form aperiodic stable states with two different examples of rectangle-triangle tilings. One of these is the bronze-mean tiling, while the other is a generalization. Our work points to how more general (beyond dodecagonal) quasicrystals can be designed in soft matter.
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Affiliation(s)
- Andrew J Archer
- Department of Mathematical Sciences and Interdisciplinary Centre for Mathematical Modelling, Loughborough University, Loughborough, Leicestershire LE11 3TU, United Kingdom
| | - Tomonari Dotera
- Department of Physics, Kindai University, 3-4-1 Kowakae Higashi, Osaka 577-8502, Japan
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Ganguly S, Shrivastav GP, Lin SC, Häring J, Haussmann R, Kahl G, Oettel M, Fuchs M. Elasticity in crystals with a high density of local defects: Insights from ultra-soft colloids. J Chem Phys 2022; 156:064501. [DOI: 10.1063/5.0073624] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Saswati Ganguly
- Soft Condensed Matter Theory, Fachbereich Physik, Universität Konstanz, D-78457 Konstanz, Germany
| | | | - Shang-Chun Lin
- Institut für Angewandte Physik, Eberhard Karls Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany
| | - Johannes Häring
- Soft Condensed Matter Theory, Fachbereich Physik, Universität Konstanz, D-78457 Konstanz, Germany
| | - Rudolf Haussmann
- Soft Condensed Matter Theory, Fachbereich Physik, Universität Konstanz, D-78457 Konstanz, Germany
| | - Gerhard Kahl
- Institut für Theoretische Physik, TU Wien, Wiedner Hauptstrasse 8-10, A-1040 Wien, Austria
| | - Martin Oettel
- Institut für Angewandte Physik, Eberhard Karls Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany
| | - Matthias Fuchs
- Soft Condensed Matter Theory, Fachbereich Physik, Universität Konstanz, D-78457 Konstanz, Germany
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Tracey DF, Noya EG, Doye JPK. Programming patchy particles to form three-dimensional dodecagonal quasicrystals. J Chem Phys 2021; 154:194505. [PMID: 34240894 DOI: 10.1063/5.0049805] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022] Open
Abstract
Model patchy particles have been shown to be able to form a wide variety of structures, including symmetric clusters, complex crystals, and even two-dimensional quasicrystals. Here, we investigate whether we can design patchy particles that form three-dimensional quasicrystals, in particular targeting a quasicrystal with dodecagonal symmetry that is made up of stacks of two-dimensional quasicrystalline layers. We obtain two designs that are able to form such a dodecagonal quasicrystal in annealing simulations. The first is a one-component system of seven-patch particles but with wide patches that allow them to adopt both seven- and eight-coordinated environments. The second is a ternary system that contains a mixture of seven- and eight-patch particles and is likely to be more realizable in experiments, for example, using DNA origami. One interesting feature of the first system is that the resulting quasicrystals very often contain a screw dislocation.
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Affiliation(s)
- Daniel F Tracey
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, Oxford OX1 3QZ, United Kingdom
| | - Eva G Noya
- Instituto de Química Física Rocasolano, Consejo Superior de Investigaciones Científicas, CSIC, Calle Serrano 119, 28006 Madrid, Spain
| | - Jonathan P K Doye
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, Oxford OX1 3QZ, United Kingdom
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Scacchi A, Sammalkorpi M, Ala-Nissila T. Self-assembly of binary solutions to complex structures. J Chem Phys 2021; 155:014904. [PMID: 34241377 DOI: 10.1063/5.0053365] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Self-assembly in natural and synthetic molecular systems can create complex aggregates or materials whose properties and functionalities rise from their internal structure and molecular arrangement. The key microscopic features that control such assemblies remain poorly understood, nevertheless. Using classical density functional theory, we demonstrate how the intrinsic length scales and their interplay in terms of interspecies molecular interactions can be used to tune soft matter self-assembly. We apply our strategy to two different soft binary mixtures to create guidelines for tuning intermolecular interactions that lead to transitions from a fully miscible, liquid-like uniform state to formation of simple and core-shell aggregates and mixed aggregate structures. Furthermore, we demonstrate how the interspecies interactions and system composition can be used to control concentration gradients of component species within these assemblies. The insight generated by this work contributes toward understanding and controlling soft multi-component self-assembly systems. Additionally, our results aid in understanding complex biological assemblies and their function and provide tools to engineer molecular interactions in order to control polymeric and protein-based materials, pharmaceutical formulations, and nanoparticle assemblies.
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Affiliation(s)
- Alberto Scacchi
- Department of Chemistry and Materials Science, Aalto University, P.O. Box 16100, FI-00076 Aalto, Finland
| | - Maria Sammalkorpi
- Department of Chemistry and Materials Science, Aalto University, P.O. Box 16100, FI-00076 Aalto, Finland
| | - Tapio Ala-Nissila
- Quantum Technology Finland Center of Excellence and Department of Applied Physics, Aalto University, P.O. Box 11000, FI-00076 Aalto, Finland
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Subramanian P, Ratliff DJ, Rucklidge AM, Archer AJ. Density Distribution in Soft Matter Crystals and Quasicrystals. PHYSICAL REVIEW LETTERS 2021; 126:218003. [PMID: 34114856 DOI: 10.1103/physrevlett.126.218003] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2020] [Revised: 04/15/2021] [Accepted: 04/20/2021] [Indexed: 06/12/2023]
Abstract
The density distribution in solids is often represented as a sum of Gaussian peaks (or similar functions) centered on lattice sites or via a Fourier sum. Here, we argue that representing instead the logarithm of the density distribution via a Fourier sum is better. We show that truncating such a representation after only a few terms can be highly accurate for soft matter crystals. For quasicrystals, this sum does not truncate so easily, nonetheless, representing the density profile in this way is still of great use, enabling us to calculate the phase diagram for a three-dimensional quasicrystal-forming system using an accurate nonlocal density functional theory.
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Affiliation(s)
- P Subramanian
- Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom
| | - D J Ratliff
- Department of Mathematical Sciences and Interdisciplinary Centre for Mathematical Modelling, Loughborough University, Loughborough LE11 3TU, United Kingdom
- Department of Mathematics, Physics and Electrical Engineering, Northumbria University, Newcastle upon Tyne NE1 8ST, United Kingdom
| | - A M Rucklidge
- School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom
| | - A J Archer
- Department of Mathematical Sciences and Interdisciplinary Centre for Mathematical Modelling, Loughborough University, Loughborough LE11 3TU, United Kingdom
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