Stability of two-dimensional soft quasicrystals in systems with two length scales

Jiang, Kezhi; Tong, Jianliang; Zhang, Pingwen; Shi, An‐Chang

doi:10.1103/physreve.92.042159

Cited by 37 publications

(51 citation statements)

References 43 publications

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“…The other discussions on the stability in relevant references concerning the two natural length scales and two wave numbers, which show the importance of the combination between thermodynamics and dynamics in the study. Some researchers [90][91][92][93] extended the Lifshitz'spioneering work and promotedhis study.…”

Section: Fig22 a Griffith Crack In A Plate Of Soft-matter Quasicrystalmentioning

confidence: 99%

Generalized Dynamics of Soft-Matter Quasicrystals

Tang¹

2017

Springer Series in Materials Science

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This article provides a detailed review on the generalized dynamics of soft-matter quasicrystals developed recent years. Comparing to solid quasicrystals consisted mainly with metallic alloys, soft-matter quasicrystals have been observed in liquid crystals, polymers, colloids, nanoparticles and surfactants, which indicates quite different formation mechanism. Based onLandau-Anderson theory and group representation theory, we have studied the symmetry, symmetry breaking and elementary excitations for the observed and possible soft-matter quasicrystals. We further proposed one more elementary excitation -fluid phonon additional to the phonon and phason for solid quasicrystals, to quantitatively describe the dynamics of soft-matter quasicrystals. The general governing equations and the solutions of the dynamics evolution on the distribution, deformation and motion of the new phase are studied, which reveal quite distinguishing dynamic behaviour with those of conventional fluids and solid quasicrystals. Someapplications are introduced, which show this is an important field of new materials and materials science. 9

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Section: Fig22 a Griffith Crack In A Plate Of Soft-matter Quasicrystalmentioning

confidence: 99%

Generalized Dynamics of Soft-Matter Quasicrystals

Tang¹

2017

Springer Series in Materials Science

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“…2 and 3 are consistent with this intuition from Faraday waves. A simplification that is made in some other models is to introduce a coefficient (the parameter c in [28,29,34,64] or γ in [32]) which effectively sends ω(k) → −∞ for all wavenumbers k = k 1 , k q , as c → ∞. This limit of perfect lengthscale selectivity makes the resulting pair interaction potentials less physically realisable.…”

Section: Figmentioning

confidence: 99%

“…Another source of important insights has been continuum theories for the density distribution. The earliest of these consist of generalised Landau-type order-parameter theories [2,3,[27][28][29][30][31][32][33][34]. More recently, classical density functional theory (DFT) [35][36][37] in conjunction with its dynamical extension DDFT [38][39][40] has been utilised.…”

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confidence: 99%

Which Wave Numbers Determine the Thermodynamic Stability of Soft Matter Quasicrystals?

et al. 2019

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For soft matter to form quasicrystals an important ingredient is to have two characteristic lengthscales in the interparticle interactions. To be more precise, for stable quasicrystals, periodic modulations of the local density distribution with two particular wavenumbers should be favored, and the ratio of these wavenumbers should be close to certain special values. So, for simple models, the answer to the title question is that only these two ingredients are needed. However, for more realistic models, where in principle all wavenumbers can be involved, other wavenumbers are also important, specifically those of the second and higher reciprocal lattice vectors. We identify features in the particle pair interaction potentials which can suppress or encourage density modes with wavenumbers associated with one of the regular crystalline orderings that compete with quasicrystals, enabling either the enhancement or suppression of quasicrystals in a generic class of systems.Matter does not normally self-organise into quasicrystals (QCs). Regular crystalline packings are much more common in nature and some specific ingredients are required for QC formation, which is why the first QCs were not identified until 1982, in certain metallic alloys [1]. Subsequently, the seminal work in Refs. [2,3] showed that normally a crucial element in QC formation, at least in soft matter, is the presence of two prominent wavenumbers in the linear response behavior to periodic modulations of the particle density distribution. This is equivalent to having two prominent peaks in the static structure factor or in the dispersion relation [4,5]. In soft matter systems, the effective interactions between molecules and aggregations of molecules (generically referred to here as particles) can be tuned to exhibit the two specific required lengthscales and thus form QCs. Such systems include block copolymers and dendrimers [6][7][8][9][10][11][12][13][14][15], certain anisotropic particles [16][17][18], nanoparticles [19,20] and mesoporous silica [21].Some of our understanding of how and why QCs can form has come from studies of particle based computer simulation models -see for example [22][23][24][25][26]. Another source of important insights has been continuum theories for the density distribution. The earliest of these consist of generalised Landau-type order-parameter theories [2,3,[27][28][29][30][31][32][33][34]. More recently, classical density functional theory (DFT) [35][36][37] in conjunction with its dynamical extension DDFT [38][39][40] has been utilised. DFT is a statistical mechanical theory for the distribution of the average particle number density that takes as input the particle pair interaction potentials, and so bridges between particle based and Landau-type continuum theory approaches. The DFT results for QC forming systems [4,5,[41][42][43] clearly demonstrate how the crucial pair of prominent wavenumbers are connected to the length and energy scales present in the pair potentials.Whilst the ratio between the two lengthscales...

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“…We will focus on searching for decagonal and dodecagonal quasicrystalline orders under the limit c→ +∞ in this subsection. Due to the geometric features of the desired patterns, we will choose q = 2cos π 5 and q = 2cos π 12 for the decagonal case and dodecagonal case, respectively, as in [35,38]. We also let t 0 =0, g 0 =0.2, g 1 =2.2 and g 2 =2.2 for the decagonal case, and t 0 = 0, g 0 = 0.8, g 1 = 2.2 and g 2 = 0.2 for the dodecagonal case.…”

Section: T−τ Phase Diagrams In the Limiting Regime C → +∞mentioning

confidence: 99%

Stability of Soft Quasicrystals in a Coupled-Mode Swift-Hohenberg Model for Three-Component Systems

Jiang

Tong

Zhang

2016

Commun. Comput. Phys.

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Abstract. In this article, we discuss the stability of soft quasicrystalline phases in a coupled-mode Swift-Hohenberg model for three-component systems, where the characteristic length scales are governed by the positive-definite gradient terms. Classic two-mode approximation method and direct numerical minimization are applied to the model. In the latter approach, we apply the projection method to deal with the potentially quasiperiodic ground states. A variable cell method of optimizing the shape and size of higher-dimensional periodic cell is developed to minimize the free energy with respect to the order parameters. Based on the developed numerical methods, we rediscover decagonal and dodecagonal quasicrystalline phases, and find diverse periodic phases and complex modulated phases. Furthermore, phase diagrams are obtained in various phase spaces by comparing the free energies of different candidate structures. It does show not only the important roles of system parameters, but also the effect of optimizing computational domain. In particular, the optimization of computational cell allows us to capture the ground states and phase behavior with higher fidelity. We also make some discussions on our results and show the potential of applying our numerical methods to a larger class of mean-field free energy functionals. PACS: 61.44.Br, 64.75.Yz, 64.70.Km,

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Stability of two-dimensional soft quasicrystals in systems with two length scales

Cited by 37 publications

References 43 publications

Generalized Dynamics of Soft-Matter Quasicrystals

Generalized Dynamics of Soft-Matter Quasicrystals

Which Wave Numbers Determine the Thermodynamic Stability of Soft Matter Quasicrystals?

Stability of Soft Quasicrystals in a Coupled-Mode Swift-Hohenberg Model for Three-Component Systems

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