Self-assembly of hydrogen-bonded two-dimensional quasicrystals

Wasio, Natalie A.; Quardokus, Rebecca C.; Forrest, Ryan P.; Lent, Craig S.; Corcelli, Steven A.; Christie, John A.; Henderson, Kenneth W.; Kandel, S. Alex

doi:10.1038/nature12993

Cited by 217 publications

(181 citation statements)

References 35 publications

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“…QCs have been observed, both experimentally and computationally, not only in metallic alloys, 2 but also in molecular systems 3,4,5 and soft matter 6,7,8,9,10,11 that suggests the microscopic mechanism of QC formation is common for these systems.…”

Section: Introductionmentioning

confidence: 99%

Self-assembly of the decagonal quasicrystalline order in simple three-dimensional systems

2015

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Using molecular dynamics simulations we show that a one-component system can be driven to a three-dimensional decagonal (10-fold) quasicrystalline state just by purely repulsive, isotropic and monotonic interaction pair potential with two characteristic length scales; no attraction is needed. We found that self-assembly of a decagonal quasicrystal from a fluid can be predicted by two dimensionless effective parameters describing the fluid structure. We demonstrate stability of the results under changes of the potential by obtaining the decagonal order for three particle systems with different interaction potentials, both purely repulsive and attractive, but with the same values of the effective parameters. Our results suggest that soft matter quasicrystals with decagonal symmetry can be experimentally observed for the same systems demonstrating the dodecagonal order for an appropriate tuning of the effective parameters.

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Section: Introductionmentioning

confidence: 99%

Self-assembly of the decagonal quasicrystalline order in simple three-dimensional systems

2015

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“…First discovered in liquid crystals made of amphiphilic dendritic macromolecules [13], self-assembled soft quasicrystals have since appeared in ABC-star polymers [14], in sphere-forming block copolymers [15], in systems of nanoparticles [16], with anisotropic particles [17] and pentameric molecules [18], and in mesoporous silica [19]. These systems provide exciting platforms for the fundamental study of the physics of quasicrystals [20] and promise new applications of self-assembled nanomaterials [21].…”

mentioning

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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“…non-periodic long-range order coupled with non-crystallographic point symmetries has been observed recently [30,31], but is beyond the scope of CIP as described in this paper.…”

Section: Additional Filementioning

confidence: 77%

Removal of multiple-tip artifacts from scanning tunneling microscope images by crystallographic averaging

Straton

Moon

Bilyeu

et al. 2015

Adv Struct Chem Imag

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Crystallographic image processing (CIP) techniques may be utilized in scanning probe microscopy (SPM) to glean information that has been obscured by signals from multiple probe tips. This may be of particular importance for scanning tunneling microscopy (STM) and requires images from samples that are periodic in two dimensions (2D). The image-forming current for double-tips in STM is derived with a slight modification of the independent-orbital approximation (IOA) to allow for two or more tips. Our analysis clarifies why crystallographic averaging works well in removing the effects of a blunt STM tip (that consists of multiple mini-tips) from recorded 2D periodic images and also outlines the limitations of this image-processing technique for certain spatial separations of STM double-tips. Simulations of multiple mini-tip effects in STM images (that ignore electron interference effects) may be understood as modeling multiple mini-tip (or tip shape) effects in images that were recorded with other types of SPMs as long as the lateral sample feature sizes to be imaged are much larger than the effective scanning probe tip sizes.

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Self-assembly of hydrogen-bonded two-dimensional quasicrystals

Cited by 217 publications

References 35 publications

Self-assembly of the decagonal quasicrystalline order in simple three-dimensional systems

Self-assembly of the decagonal quasicrystalline order in simple three-dimensional systems

Controlled Self-Assembly of Periodic and Aperiodic Cluster Crystals

Removal of multiple-tip artifacts from scanning tunneling microscope images by crystallographic averaging

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