Entropic networks in colloidal self-assembly

A critical phase separation in self-assembling colloidal dispersions is predicted. The coexisting phases are a dilute gas of ends that coexists with a high-density liquid of branching points. Our model provides a unified explanation for the branched structures, the unusually low critical temperature and density, and the consequent two-phase coexistence 'islands' in both cylindrical microemulsions and dilute dispersions of dipolar particles (e.g. ferrofluids).