Relevance of packing to colloidal self-assembly

Abstract

Since the 1920s, packing arguments have been used to rationalize crystal structures in systems ranging from atomic mixtures to colloidal crystals. Packing arguments have recently been applied to complex nanoparticle structures, where they often, but not always, work. We examine when, if ever, packing is a causal mechanism in hard particle approximations of colloidal crystals. We investigate three crystal structures composed of their ideal packing shapes. We show that, contrary to expectations, the ordering mechanism cannot be packing, even when the thermodynamically self-assembled structure is the same as that of the densest packing. We also show that the best particle shapes for hard particle colloidal crystals at any finite pressure are imperfect versions of the ideal packing shape.

The entropic bond in colloidal crystals

“…Motivated by a growing body of work (8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26) showing entropydriven self-assembly of hard, anisotropic particles into crystals comprised of local geometric motifs with temporal stability, we investigated whether these stable motifs act as "bonds" in a similar sense to familiar chemical bonds. Surprisingly, our results show that even minimal, classical, single-component systems of hard hexagons exhibit behavior that resembles conventional bonding.…”

“…Entropic ordering (6)(7)(8)(9) is another unconventional mechanism that involves local (free) energy gradients (10) and temporal stability. Counterintuitively, hard particles in the range of nanometers to a few microns and with no interactions other than excluded volume can rearrange from a disordered fluid into an ordered crystal, or from one crystal structure to another, upon crowding (8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26). These colloidal crystals can be surprisingly complex and remarkably structurally diverse, and arise solely from particle shape anisotropy and the statistical thermodynamic principle of entropy maximization.…”

Densest versus jammed packings of bent-core trimers

“…Special techniques are necessary to avoid jamming or glass-formation. However, a multitude of such techniques are now available [9,10], and understanding particles' densest possible packings remains highly useful for understanding and ultimately controlling those they form under realistically achievable preparation protocols [11,12]. Thus studies that characterize both the densest packings that a given class of fused-sphere particles can form and those that they do form under a variety of preparation protocols, and identify key reasons for any differences between these, are of particular interest.…”

Densest versus jammed packings of two-dimensional bent-core trimers

“…The first is that understanding how anistropy affects jamming is critical because most real granular materials are composed of anisotropic grains. The second is that constituentparticle anistropy affects systems' jamming phenomenology and their thermal-solidification phenomenology in similar ways, and hence studying the jamming of grains of a given shape can provide insight into the thermal solidification of similarly shaped molecules and/or colloids [6][7][8][9]. Such studies are maximally effective when they are complemented by identifying the particles' densest possible packings since the differences between densest and jammed packings are often analogous to the differences between crystals and glasses formed via thermal solidification [9][10][11].…”