Erratum: Formation of Polymorphic Cluster Phases for a Class of Models of Purely Repulsive Soft Spheres [Phys. Rev. Lett.96, 045701 (2006)]

Abstract

We present results from density functional theory and computer simulations that unambiguously predict the occurrence of first-order freezing transitions for a large class of ultrasoft model systems into cluster crystals. The clusters consist of fully overlapping particles and arise without the existence of attractive forces. The number of particles participating in a cluster scales linearly with density, therefore the crystals feature density-independent lattice constants. Clustering is accompanied by polymorphic bcc-fcc transitions, with fcc being the stable phase at high densities.PACS numbers: 64.70. Dv, 82.30.Nr, 61.20.Ja, 82.70.Dd The distinguishing feature of soft matter systems is the vast separation of length and time scales characterizing the extent and motion of their constituent entities. Whereas soft matter mixtures are typically solutions in a microscopic solvent, the solute particles are complex macromolecular aggregates of mesoscopic spatial dimensions [1]. The ability to control the architecture and chemical nature of these macromolecules, combined with the flexibility in influencing the solvent properties and the composition of the system, gives rise to an unprecedented freedom in tuning the effective interactions between the particles and opens up the possibility to steer the macroscopic properties of the system [1, 2]. The richness of spontaneously forming complexes in soft matter encompasses length scales that exceed the dimensions of the individual macromolecules. Indeed, the latter can self-organize in a variety of ways, giving rise to so-called hypermolecular structures [3] that encompass a large number of mesoscopically-sized entities. Characteristic examples are the complex phases encountered in ternary mixtures of oil, water, and amphiphilic surfactants or in block copolymer blends, as well as the emergence of cluster formation between colloidal particles, which has attracted a great deal of attention recently [4,5,6,7,8,9,10,11,12]. The underlying physical mechanism that drives the emergence of hypermolecular structures is widely believed to rest on the existence of competing interactions among the mesoscopic solute constituents. For example, the dominant mechanism that guarantees the stability of finite clusters in colloidal [5,7,8] or biological [6] systems stems from the presence of short-range attractions and long-range repulsions in their effective interaction potential. Whereas the former provide the driving force for unlimited cluster growth, the latter act as a barrier against it. The efficiency of the barrier grows fast with increasing cluster population, therefore further accumulation of colloids into the clusters is brought to an end when a specific, optimal cluster occupancy is reached [3,7]. Cluster formation is a highly topical issue in current soft matter research, due to the large variety of cluster morphologies that form [5,9,11] and to the relevance of these structures in influencing vitrification and gelation [5,9,12].In this Letter, we report on a different mecha...

Phase diagram of Hertzian spheres

“…Density functional theory and molecular simulations have confirmed the occurrence of cluster crystals for the generalized exponential model. 11 It is expected that certain dendrimers could form such crystals, 12 but thus far experiments are lacking (see, however, ref. 13).…”

Packing of Soft Asymmetric Dumbbells

“…The study of the physical properties of systems adopting these exotic intercations, some of which allowing for even complete overlap among the components, has been the subject of several publications [14][15][16][17][18][19][20][21][22]. These studies unveiled the existance of an unprecedented richness in phenomenological behavior including the possibility for some classes of interactions to form polymorphic cluster phases [23] or reentrant melting transitions followed by multiple transitions between ordered crystalline phases [24][25][26], and set the stage for the work presented in this paper. For a recent review on the subject we refer the reader to reference [27].…”

An unconstrained DFT approach to microphase formation and application to binary Gaussian mixtures

“…1 Another instance of this rather general scenario which has gained considerable attention in recent times is cluster formation in particles interacting via isotropic, bounded repulsive potentials of ultrasoft type such that not only are the overlaps between particles allowed but also the resulting energy penalty is very low. [11][12][13] At high enough density, these systems form crystal phases, whose lattice sites are occupied by clusters of many particles, at variance with the single-particle occupancy of atomic crystals. The theoretical investigation of these phases has brought forth many remarkable properties, the most prominent of which is that a change in the density of the crystal is achieved by changing the average number of particles in a cluster, while leaving the lattice constant almost unchanged.…”