Dense Packing and Symmetry in Small Clusters of Microspheres

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Original entry: Lidiya Mishchenko, APPHY 226, Spring 2009


V.N. Manoharan et al. Science 301, 483 (2003);


Colloidal packing, colloidal stability, interfaces, emulsions, capillarity


"When small numbers of colloidal microspheres are attached to the surfaces of liquid emulsion droplets, removing fluid from the droplets leads to packings of spheres that minimize the second moment of the mass distribution. The structures of the packings range from sphere doublets, triangles, and tetrahedra to exotic polyhedra not found in infinite lattice packings, molecules, or minimum–potential energy clusters. The emulsion system presents a route to produce new colloidal structures and a means to study how different physical constraints affect symmetry in small parcels of matter."

Soft Matter Example

The way these sphere clusters are created applies many soft matter concepts, such as emulsions, capillarity, and surface charge.

The sphere packing is produced as follows: Polymer (PS) colloidal spheres are dispersed in toluene, and then water is added to create an oil-in-water emulsion consisting of small droplets of toluene with colloidal spheres at the interface. The colloids are strongly bound to the interface because of surface tension. As the toluene is preferentially evaporated, the spheres form spherical packing at the surface, followed by deformation of the interface as the oil is removed further. At the final stages of evaporation, strong capillary forces rapidly rearrange the spheres to form clusters of various numbers of colloids (See Figure 1).

Figure 1: Emulsion process and in-situ micrographs of the packing process

The interesting part of the packing is the surface interaction of the sphere interfaces. Sulfate terminated polystyrene spheres have a negative surface charge in water, but are almost neutral in toluene. Also, van der Waals forces are much stronger between particles in water than toluene. Thus, in toluene, the particles act as hard spheres, and interact mostly through short-range steric repulsion. Since the particles interact like hard spheres when they pack, they only stick together through van der Waals forces as all the toluene is evaporated. Also, as the toluene is evaporated, more and more of the particle surface area is exposed to water, leading to surface charges, preventing aggregation with other clusters and allowing them to be stable in the suspension.

The forces constraining this system are complicated. Capillary forces provide a spherically symmetric compressive strain on the system until packing constraints break the symmetry (again, this all happens as the toluene is evaporated). In the end, it was found that up to a certain number of particles, the configuration that minimizes the moment of inertia of the cluster is the one that forms (See Figure 2).

Figure 2: SEM images of cluster configurations for clusters that match minimum moment of inertia (computer rendering). Symmetry groups are also shown for the structures.

Though the paper does not propose a unifying minimization criterion that predicts packing for smaller and larger clusters alike, these structures are reproducible and can be easily separated by centrifuging. Thus, suspensions of any one of these clusters can be used for assembly of entirely new crystal/glass structures.

The difference between finite and bulk packing is mentioned here as well. Some finite packing arrangements cannot be repeated for bulk, crytalline phases or are inconsistent with the normal fcc packing for particles subject to Lennard-Jones potential (as many molecules and colloidal suspensions are). These packing arrangements are however observed in glasses and liquids. This issue of packing and order of matter at different length scales is very important in soft matter.

In general this paper is important in a fundamental way because it allows for the study of packing phenomena under different constraints (not necessarily interparticle attraction) and leads to entirely new sphere-packing motifs.

Relevant Article

Interestingly, ellipsoids pack more closely than spheres during random orienting. See Packing in the Spheres for more information.