Two-dimensional clusters of identical bubbles

We discuss in detail the assembly of two-dimensional identical bubbles in stable clusters. The clusters are classified into perfect and defective clusters, depending on the number of sides of their inner cells (defective clusters have inner cells with a number of neighbours different from 6). We evaluate the surface energy of clusters by a broken-bond method and compare with exact energy calculations for simple clusters. Special attention is given to perfect clusters which are classified by their symmetry. For particular values of the number of cells, N, called magic numbers, perfect clusters have special properties. We identify the clusters of smallest energy, for fixed number of cells N (minimal clusters). For large N the minimal dusters are perfect, but for small N a minimal cluster may be a defective cluster. We produced two-dimensional clusters with N up to 15 by the 'monolayer foam' method and studied their relative incidence for N = 6.