Packing in the Spheres

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Original entry: William Bonificio, AP 224, Fall 2009


Packing in the Spheres David A. Weitz, Science , vol 303 968 (2004)


close, packing, spheres


The paper discusses how nonspeherical objects pack compared to spherical ones. Surprisingly, ellipsoidal and oblate objects take less energy to reach a close packed structure. Some reasons for this unintuitive result are discussed.

Excluded volume (shown in yellow) between particles of different geometries. Purple particles are micelles (not to scale)

Soft Matter Example

Colloidal physics often deals with the problem of packing. For the most part, scientists will approximate all object that are being packed as spheres and then calculate the packing efficiency with that basis. One such type of packing that can occur is when the spheres still have a completely random orientation, but are packed as tightly as they can be, this is called random close packing, or RCP. For spheres, the volume fraction for RCP is 0.64. If we allow the spheres to be ordered, and pack them as tightly as possible they take a configuration called hexagonal close packed, or HCP. In this configuration the spheres form hexagonal layers, and each layer above will fall into the crevices formed by the layer below. The volume fraction for spheres in HCP is 0.74.