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Open structures can display a number of unusual properties, including anegative Poisson's ratio, negative thermal expansion, and holographicelasticity, and have many interesting applications in engineering. However, itis a grand challenge to self-assemble open structures at the colloidal scale,where short-range interactions and low coordination number can leave themmechanically unstable. In this paper we discuss the self-assembly of openstructures using triblock Janus particles, which have two large attractivepatches that can form multiple bonds, separated by a band with purelyhard-sphere repulsion. Such surface patterning leads to open structures thatare stabilized by orientational entropy (in an order-by-disorder effect) andselected over close-packed structures by vibrational entropy. For differentpatch sizes the particles can form into either tetrahedral or octahedralstructural motifs which then compose open lattices, including the pyrochlore,the hexagonal tetrastack and the perovskite lattices. Using an analytic theory,we examine the phase diagrams of these possible open and close-packedstructures for triblock Janus particles and characterize the mechanicalproperties of these structures. Our theory leads to rational designs ofparticles for the self-assembly of three-dimensional colloidal structures thatare possible using current experimental techniques.

Self-assembly of three-dimensional open structures using patchy colloidal particles