We propose a heuristic explanation for the numerous non-close-packed crystal structures observed in various colloidal systems. By developing an analogy between soap froths and the soft coronas of fuzzy colloids, we provide a geometrical interpretation of the free energy of soft spheres. Within this picture, we show that the close-packing rule associated with hard-core interaction and positional entropy of particles is frustrated by a minimum-area principle associated with the soft tail and internal entropy of the soft coronas. We also discuss these ideas in terms of crystal architecture and pair distribution functions and analyze the phase diagram of a model hard-sphere-square-shoulder system within the cellular theory. We find that the A15 lattice, known to be area minimizing, is favored for a reasonable range of model parameters and so it is among the possible equilibrium states for a variety of colloidal systems. We also show that in the case of short-range convex potentials the A15 and other non-close-packed lattices coexist over a broad ranges of densities, which could make their identification difficult.

Over the past decade, quasicrystalline order has been observed in many soft-matter systems: in dendritic micelles, in star and tetrablock terpolymer melts and in diblock copolymer and surfactant micelles. The formation of quasicrystals from such a broad range of 'soft' macromolecular micelles suggests that they assemble by a generic mechanism rather than being dependent on the specific chemistry of each system. Indeed, micellar softness has been postulated and shown to lead to quasicrystalline order. Here we theoretically explore this link by studying two-dimensional hard disks decorated with step-like square-shoulder repulsion that mimics, for example, the soft alkyl shell around the aromatic core in dendritic micelles. We find a family of quasicrystals with 10-, 12-, 18- and 24-fold bond orientational order which originate from mosaics of equilateral and isosceles triangles formed by particles arranged core-to-core and shoulder-to-shoulder. The pair interaction responsible for these phases highlights the role of local packing geometry in generating quasicrystallinity in soft matter, complementing the principles that lead to quasicrystal formation in hard tetrahedra. Based on simple interparticle potentials, quasicrystalline mosaics may well find use in diverse applications ranging from improved image reproduction to advanced photonic materials.

We use both mean-field methods and numerical simulation to study the phase diagram of classical particles interacting with a hard-core and repulsive, soft shoulder. Despite the purely repulsive interaction, this system displays a remarkable array of aggregate phases arising from the competition between the hard-core and shoulder length scales. In the limit of large shoulder width to core size, we argue that this phase diagram has a number of universal features, and classify the set of repulsive shoulders that lead to aggregation at high density. Surprisingly, the phase sequence and aggregate size adjusts so as to keep almost constant inter-aggregate separation.PACS numbers: 61.30. Dk, 61.30.St,61.46.Bc Entropy is a potent force in the theory of selfassembly. It can be argued, through entropic considerations alone, that hard spheres will self-assemble into the face-centered-cubic (fcc) lattice or any of its many variants related through stacking faults. As a result, when a material exhibits an fcc phase, it is often attributed to the optimality of the close-packed lattice. When less common or less dense lattices are formed, all sundry of explanations are invoked, ranging from quantum mechanics [1], lattice effects [2], partially filled Landau levels [3], and even soft interactions [4,5]. While there has been concerted effort to tailor the pair interaction to achieve a desired periodic arrangement [6] this must be done in the context of those packing motifs that arise from generic interactions. For instance, it would be no trick to tailor a potential to make an fcc lattice.With this in mind, here we consider a seemingly simple extension of the hard sphere model, namely a hard core interaction of radius σ with a soft shoulder of radius σ s and height ǫ (HCSS):When σ s /σ 1 this potential models hard spheres with a soft pair repulsion and was used to study isostructural transitions in Cs and Ce [7]. In generic repulsive potentials, it has been shown that as the range of the soft repulsion grows (corresponding to σ s /σ ≈ 2) a rich variety of density-modulated ground states appear [8, 9, 10] which can be characterized as periodic arrangements of regular sized clusters of the original spheres. In this Letter we establish a sufficient condition on the pair potential for clustering and the subsequent ordering of the clusters which generalizes results on soft potentials without hard cores [11]. We develop a self-consistent field theory for soft repulsion and use it to study the formation of striped phases. We corroborate our analytic treatment with numerical solutions that also predict the existence of hexagonal and inverted hexagonal phases with both fluid and crystalline order in the clusters, as shown in Fig. 1. We also present results from Monte Carlo simulations of the HCSS potential which both stimulate and support the more general results. In all cases, we find that over the range of stable aggregate structures the lattice constant remains fixed while the clusters change their size and morphology so as to maint...