Sphere Packing in Cylinders

Packing of hard and soft spheres in cylinders

That nature creates forms and structures of great diversity according to the requirements of simple physical laws is a subject of endless fascination. The possible ways in which atoms, spheres or cells fit together into alternative structures depends on both symmetry and the nature of the physical forces involved. While these physical interactions maybe simple, nevertheless the high pressures encountered in strongly confined systems can compel molecules to adopt complex yet ordered arrangements. In such systems there exists an intimate connection between molecular morphology and the precise shape of the container.

An example of this is the dense packing of equal-sized hard (or soft) spheres inside a cylinder. Through numerical simulations we showed that the dense packing of monodisperse (equal-sized) hard spheres inside a cylinder produces a remarkable series of helical structures as the ratio of the cylinder diameter to the sphere diameter is varied. We were able to provide a complete taxonomy of the competing phases and also elucidate the geometric relationships between them. This was done by showing that the packings were of two types: maximal contact packings (where each sphere has six contacts) or line-slip arrangements (whereby spiral chains slide over each other so that some of the spheres only have five contacts).

We subsequently extended these findings to include packing of soft spheres in cylinders.