From Lumps to Lattices: Crystallized Clusters Made Simple

Abstract

Using a minimal model based on the continuum theory of a 2D hard-core/square-shoulder ensemble, we reinterpret the main features of cluster mesophases formed by colloids with soft shoulder-like repulsive interactions. We rederive the lattice spacing, the binding energy and the phase diagram. We also extend the clustering criterion [Likos, C. N., et al. Phys. Rev. E, 2001, 63, 031206; Glaser, M. A., et al. EPL 2007, 78, 46004] to include the effect of the hard cores, which precludes the formation of clusters at small densities.

Effective interactions between inclusions in an active bath

“…It is worth mentioning here that each inclusion with its two active-particle rings can be thought of as a single colloidal unit with a hard core and a soft repulsive shoulder. Qualitatively similar scenarios, incorporating hard-core/softshoulder pair potentials, have been considered in the equilibrium context of non-active colloids and shown to result in a diverse phase diagram [109,110]. Those findings may, however, be inapplicable to the present case, in which the circular soft-ring zones due to active-particle 2).…”

“…Using Brownian Dynamics simulations, and by considering both chiral and non-chiral active baths, we show how the salient, and previously unexplored, aspects of the spatial distribution of active particles, including formation of circular layers (or 'rings') of active particles around the inclusions, determine the qualitative nature (e.g., repulsive versus attractive) as well as quantitative features (e.g., non-monotonic behavior with distance) of the two-body interaction force profiles. The sequential overlaps of active-particle rings, which in a way create soft, repulsive, 'shoulders' [109,110] around the inclusions, generate the distinct features of the force profiles as the inclusions are brought to small surface separations. Active-particle chirality leads to suppression of particle rings and partial depletion of active particles from the intervening region and the farther proximity of the inclusions.…”

Emergent colloidal dynamics in electromagnetic fields

“…13 This is counterintuitive because the interactions between the colloids are purely repulsive; 14 however, due to geometrical constraints they experience a so-core repulsion that favours clustering despite the lack of attractions. [15][16][17] Interestingly, a similar sequence of structures can be observed in hard-sphere colloids subjected to so harmonic connement. 18 A collective assembly of paramagnetic colloidal particles driven above the periodic stripes of the domain walls by an alternating magnetic eld in a uniaxial ferrimagnetic yttrium iron garnet lm 19 also revealed a similar sequence of selfassembled structures, shown in panel A of Fig.…”

Self-assembly of anisotropic soft particles in two dimensions

“…3b, top). The fact that the particle's cores within a given stripe do not locate in a triangular sublattice indicate that clustering is not close-packed in this case, in sharp contrast with the case of isotropic potentials where clusters of close-packed particles are predicted [30]. The spacing between consecutive lanes is dictated by the condition that the coronas of adjacent lanes do not overlap, as shown in the respective inset.…”