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We study theoretically a binary system in which an attraction of unlike particles is combined with a type-independent soft-core repulsion. The possible experimental implementation of the system is a mixture of DNA-covered colloids, in which both the repulsion and the attraction may be induced by DNA solution. The system is shown to exhibit surprisingly diverse and unusual morphologies. Among them are the diamond lattice and the membrane phase with in-plane square order, a striking example of spontaneous compactification.
Alexei V. Tkachenko (Mon,) studied this question.