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Periodic chain clusters of two-dimensional bubbles

We study periodic chain clusters comprising equal numbers of two-dimensional bubbles of two different areas, with at most four bubbles per period. The cluster energies are calculated as a function of the ratio λ of bubble areas and of the imposed strain ϵ. We identify the clusters of lowest energy for each (λ,ϵ), and obtain the Young's moduli of all clusters in their unstrained state. An approximately linear correlation has been found between the Young's moduli and the cluster binding energy per unit area, similar to that which holds for crystalline solids (e.g. metals).