Formation of a dodecagonal quasicrystalline phase in a simple monatomic liquid

Dzugutov, Mikhail

doi:10.1103/physrevlett.70.2924

Cited by 173 publications

(179 citation statements)

References 20 publications

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“…2B), we expect similar overall sphericities (see below). Formation of the DDQC structure as a metastable intermediate state before the formation of the equilibrium Frank-Kasper σ phase appears quite similar to the simulated phase behavior of collections of uniformly sized spherical particles governed by the Dzugotov potential, a modified Lennard-Jones interparticle potential that contains a repulsive feature that suppresses the formation of closepacked (BCC, HCP, and FCC) crystal structures (20,30,31). There are important differences between this computational model and the experimental polymer system, most significantly the consequences of mass exchange during the formation of the σ phase, which leads to five discrete particle shapes and volumes in the tetrahedral unit cell, features that are not represented in the hard sphere simulations.…”

Section: Discussionmentioning

confidence: 77%

Dodecagonal quasicrystalline order in a diblock copolymer melt

Gillard

Lee

Bates

2016

Proc. Natl. Acad. Sci. U.S.A.

188

264

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We report the discovery of a dodecagonal quasicrystalline state (DDQC) in a sphere (micelle) forming poly(isoprene-b-lactide) (IL) diblock copolymer melt, investigated as a function of time following rapid cooling from above the order-disorder transition temperature (T ODT = 66°C) using small-angle X-ray scattering (SAXS) measurements. Between T ODT and the order-order transition temperature T OOT = 42°C, an equilibrium body-centered cubic (BCC) structure forms, whereas below T OOT the Frank-Kasper σ phase is the stable morphology. At T < 40°C the supercooled disordered state evolves into a metastable DDQC that transforms with time to the σ phase. The times required to form the DDQC and σ phases are strongly temperature dependent, requiring several hours and about 2 d at 35°C and more than 10 and 200 d at 25°C, respectively. Remarkably, the DDQC forms only from the supercooled disordered state, whereas the σ phase grows directly when the BCC phase is cooled below T OOT and vice versa upon heating. A transition in the rapidly supercooled disordered material, from an ergodic liquid-like arrangement of particles to a nonergodic soft glassy-like solid, occurs below ∼40°C, coincident with the temperature associated with the formation of the DDQC. We speculate that this stiffening reflects the development of particle clusters with local tetrahedral or icosahedral symmetry that seed growth of the temporally transient DDQC state. This work highlights extraordinary opportunities to uncover the origins and stability of aperiodic order in condensed matter using model block polymers.quasicrystals | Frank-Kasper phases | block polymers T he discovery of aperiodic order, today referred to as quasicrystalline order, in rapidly cooled Al-Mn alloys by Shechtman and coworkers in 1984 heralded a paradigm shift in the understanding of what constitutes long-range order in matter (1, 2). More recently, quasicrystalline order has been found in an expanding variety of soft materials including self-assembling wedge-shaped dendrimers, mixtures of ligand coated nanoparticles, concentrated solutions of surfactant and block polymer micelles, multicomponent polymer blends containing ABC-type miktoarm star polymers, and an ABA′C-type linear multiblock polymer (3-8). The underlying principles that govern the formation of quasicrystals in soft materials remain largely unresolved.Block polymers are uniquely tunable self-assembling soft materials in which the nanoscale morphology, characteristic length scale, chemical and physical properties, and dynamics can be precisely controlled through the judicious choice of block repeat unit chemistries, block molecular weights, and molecular architecture (9, 10). Such exquisite control over structure, and the associated dynamics, makes block polymers ideal model materials for fundamental inquiries into the formation and stability of soft quasicrystals. In this article, we report the discovery of a long-lived metastable dodecagonal quasicrystalline phase (DDQC) in a (nominally) single-component poly(1,4-is...

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Section: Discussionmentioning

confidence: 77%

Dodecagonal quasicrystalline order in a diblock copolymer melt

Gillard

Lee

Bates

2016

Proc. Natl. Acad. Sci. U.S.A.

188

264

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“…One may also consider pair interactions between particles that involve an oscillatory potential and therefore a finite barrier between a 'bonded and a 'non bonded' state between neighboring particles. Interestingly, such a potential has been used for a long time to describe the formation of a single component quasicrystal 29 , which is also a good glass former. It will be of interest to study the statistical properties of simple flows in such models in order to obtain a mapping onto our more coarse grained description.…”

Section: Discussionmentioning

confidence: 99%

Spontaneous formation of permanent shear bands in a mesoscopic model of flowing disordered matter

2012

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This study proposes a coherent scenario of the formation of permanent shear bands in the flow of yield stress materials. It is a well accepted point of view that flow in disordered media is occurring via local plastic events, corresponding to small size rearrangements, that yield a long range stress redistribution over the system. Within a minimalistic mesoscopic model that incorporates these local dynamics, we study the spatial organisation of the local plastic events. The most important parameter in this study is the typical restructuring time needed to regain the original structure after a local rearrangement. In agreement with a recent mean field study [Coussot et al., Eur. Phys. J. E, 2010, 33, 183] we observe a spontaneous formation of permanent shear bands, when this restructuring time is large compared to the typical stress release time in a rearrangement. The bands consist of a large number of plastic events within a solid region that remains elastic. This heterogeneous flow behaviour is different in nature from the transient dynamical heterogeneities that one observes in the small shear rate limit in flow without shear-banding [Martens et al., Phys. Rev. Lett., 2011, 106, 156001]. We analyse in detail the dependence of the shear bands on system size, shear rate and restructuring time. Further we rationalise the scenario within a mean field version of the spatial model, that produces a non monotonous flow curve for large restructuring times. This explains the instability of the homogeneous flow below a critical shear rate, that corresponds to the minimum of the curve. Our study therefore strongly supports the idea that the characteristic time scales involved in the local dynamics are at the physical origin of permanent shear bands.

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“…That stable quasicrystals may need two length scales in their effective interaction potentials is not new [10]. Many two-length-scale potentials were investigated over the years and found to exhibit stable quasiperiodic phases [11]. The novelty of BDL was in their quantitative understanding of the stabilization mechanism, allowing them to pinpoint regions of stability in the parameter spaces of different potentials, instead of performing an exhaustive search.…”

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confidence: 99%

Controlled Self-Assembly of Periodic and Aperiodic Cluster Crystals

2014

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Soft particles are known to overlap and form stable clusters that self-assemble into periodic crystalline phases with density-independent lattice constants. We use molecular dynamics simulations in two dimensions to demonstrate that, through a judicious design of an isotropic pair potential, one can control the ordering of the clusters and generate a variety of phases, including decagonal and dodecagonal quasicrystals. Our results confirm analytical predictions based on a mean-field approximation, providing insight into the stabilization of quasicrystals in soft macromolecular systems, and suggesting a practical approach for their controlled self-assembly in laboratory realizations using synthesized soft-matter particles. DOI: 10.1103/PhysRevLett.113.098304 PACS numbers: 82.70.Dd, 61.44.Br, 64.70.D-, 64.75.Yz Particles interacting via pair potentials with repulsive cores, which are either bounded or only slowly diverginglike those found naturally in soft matter systems [1]-can be made to overlap under pressure to form clusters [2], which then self-assemble to form crystalline phases [3]. The existence of such cluster crystals was recently confirmed in amphiphilic dendritic macromolecules using monomer-resolved simulations [4], and in certain bosonic systems [5]. They occur even when the particles are purely repulsive, and typically exhibit periodic fcc or bcc structures. Here we employ molecular dynamics (MD) simulations in two dimensions, guided by analytical insight, to show how isotropic pair potentials can be designed to control the self-assembly of the clusters, suggesting a practical approach that could be applied in the laboratory. We obtain novel phases, including a striped (lamellar) phase and a hexagonal superstructure, as well as decagonal (tenfold) and dodecagonal (twelvefold) quasicrystals.Given a system of N particles in a box of volume V, interacting via an isotropic pair potential UðrÞ with a repulsive core, a sufficient condition for the formation of a cluster crystal is a negative global minimumŨ min ¼Ũðk min Þ < 0 in the Fourier transform of the potential [6]. This condition implicitly requires the potential not to diverge too strongly, so that the Fourier transform exists. The wave number k min determines the length scale for the order in the system by setting the typical distance between neighboring clusters. Above a sufficiently high mean particle densityc ¼ N=V, a further increase ofc increases the number of overlapping particles within each cluster, but does not change the distance between their centers. It also determines the spinodal temperature k B T sp ¼ −Ũ minc [3,6], below which the liquid becomes unstable against crystallization, where k B is the Boltzmann constant.As the particles form increasingly larger clusters, the system becomes well characterized by a continuous coarse-grained density function cðrÞ. The thermodynamic behavior can then be described in a mean-field approximation, which becomes exact in the high-density hightemperature limit [7]. Using MD simulations, we ex...

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Formation of a dodecagonal quasicrystalline phase in a simple monatomic liquid

Cited by 173 publications

References 20 publications

Dodecagonal quasicrystalline order in a diblock copolymer melt

Dodecagonal quasicrystalline order in a diblock copolymer melt

Spontaneous formation of permanent shear bands in a mesoscopic model of flowing disordered matter

Controlled Self-Assembly of Periodic and Aperiodic Cluster Crystals

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