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Colloidal cluster phases, gelation and nuclear matter

The combination of short-range attractions and long-range repulsions can lead to interesting clustering phenomena. In particular there are strong indications that the colloidal cluster phase is in fact a manifestation of such a competition. Here we compute the stability boundary of the cluster phase by invoking counter-ion condensation. It is found that a condensation catastrophe leading to an infinite cluster sets in if the level of charge on the colloid is too low. The same ingredients leading to the cluster phase are found in nuclear physics: strong short-range attractions due to nuclear force and weak long-range Coulomb repulsions. We will show explicitly here the equivalence of a semi-empirical mass formula for the binding energy of the nucleus and the free energy of a cluster in a colloidal cluster phase. This identification enables an exploitation of theoretical results from nuclear physics to the colloidal domain and, perhaps, the construction of a colloidal system mimicking various aspects of nuclear matter.