Stability of quasicrystals composed of soft isotropic particles

Abstract

Quasicrystals whose building blocks are of mesoscopic rather than atomic scale have recently been discovered in several soft-matter systems. Contrary to metallurgic quasicrystals whose source of stability remains a question of great debate to this day, we argue that the stability of certain soft-matter quasicrystals can be directly explained by examining a coarse-grained free energy for a system of soft isotropic particles. We show, both theoretically and numerically, that the stability can be attributed to the existence of two natural length scales in the pair potential, combined with effective three-body interactions arising from entropy. Our newly gained understanding of the stability of soft quasicrystals allows us to point at their region of stability in the phase diagram, and thereby may help control the self-assembly of quasicrystals and a variety of other desired structures in future experimental realizations.PACS numbers: 61.44. Br, 64.75.Yz, Quasicrystals are more common than one had originally expected when their discovery was first announced. 1More than a hundred different metallic alloys are known to form stable quasicrystalline phases of icosahedral symmetry alone, 2 with a few dozen additional stable phases exhibiting decagonal (10-fold) and possibly other symmetries.3 Yet, to this date, there is no general agreement regarding the origin of their stability and the respective roles of energy and entropy in determining the observed phases.4 These growing numbers of stable solid-state quasicrystals, whose building blocks are on the atomic scale, have been joined in recent years by a host of soft-matter systems exhibiting quasiperiodic long-range order with building blocks on a much larger scale of tens to hundreds of nanometers-micelle-forming dendrimers, 5,6 star block copolymers, 7 mesoporous silica, 8 and binary systems of nanoparticles.9 These newly discovered soft quasicrystals hold the promise for applications based on self-assembled nanomaterials, 10 with unique electronic or photonic properties that take advantage of their quasiperiodicity. 11At the same time, they provide alternative experimental platforms for the basic study of quasiperiodic longrange order, and offer the opportunity to study the thermodynamic stability of quasicrystals from a fresh viewpoint. To this date, soft quasicrystals have been observed only with dodecagonal point-group symmetry, having quasiperiodic order in the 12-fold plane and periodic order normal to the plane, whereas dodecagonal solid-state quasicrystals are rare and mostly only metastable.3 Soft quasicrystals may belong, therefore, to a distinct class of quasicrystals, whose source of stability is likely to be different from their solid-state counterparts. We propose here a simple theoretical framework to address these new systems. We use it to explain the stability of the observed structures and indicate the (surprisingly simple) minimum conditions under which quasicrystals could be stabilized. Knowledge of these conditions gives us the ability to estimate ...

Controlled Self-Assembly of Periodic and Aperiodic Cluster Crystals

“…At lower temperatures, mean-field theory predicts that the quasicrystals should become unstable toward a secondary transformation into a periodic phase of lower rotational symmetry, such as a hexagonal cluster crystal [8]. We do not observe a transformation for the decagonal quasicrystal.…”

“…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 examine the analytical predictions of a particular mean-field approximation that was proposed by Barkan, Diamant, and Lifshitz (BDL) [8] to explain the stability of a certain class of soft quasicrystals in two dimensions. BDL confirmed an earlier conjecture [9] that attributed the stability of soft quasicrystals to the existence of two length scales in the pair potential, combined with effective many-body interactions arising from entropy.…”

Three-Dimensional Icosahedral Phase Field Quasicrystal

“…The latter include micellar melts [5,6] formed, e.g., from linear, dendrimer or star block copolymers. Recently, three-dimensional (3D) icosahedral QCs have been found in molecular dynamics simulations of particles interacting via a three-well pair potential [7].In recent years, model systems in two dimensions (2D) have been studied in order to understand soft matter QC formation and stability [8][9][10][11][12]. Phase field crystal models have been employed to simulate the growth of 2D QCs [13] and the adsorption properties on a quasicrystalline substrate [14].…”

“…In recent years, model systems in two dimensions (2D) have been studied in order to understand soft matter QC formation and stability [8][9][10][11][12]. Phase field crystal models have been employed to simulate the growth of 2D QCs [13] and the adsorption properties on a quasicrystalline substrate [14].…”

Electronic Properties and Complexity of Al-Based Complex Metallic Alloys

“…particles. A key conclusion of these works is that the ratio between characteristic wavelengths must be taken in the vicinity of an irrational number, which stresses how sensitive to small variations of this ratio the system is [22,23]. We are therefore inclined to look upon a similar mechanism in CMAs that will produce competing interactions whose ne-tuning will eventually dierentiate between crystals with a long period and quasicrystalline order.…”