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We systematically study the design of simple patchy sphere models thatreversibly self-assemble into monodisperse icosahedral clusters. We find thatthe optimal patch width is a compromise between structural specificity (thepatches must be narrow enough to energetically select the desired clusters) andkinetic accessibility (they must be sufficiently wide to avoid kinetic traps).Similarly, for good yields the temperature must be low enough for the clustersto be thermodynamically stable, but the clusters must also have enough thermalenergy to allow incorrectly formed bonds to be broken. Ordered clusters canform through a number of different dynamic pathways, including directnucleation and indirect pathways involving large disordered intermediates. Thelatter pathway is related to a reentrant liquid-to-gas transition that occursfor intermediate patch widths upon lowering the temperature. We also find thatthe assembly process is robust to inaccurate patch placement up to a certainthreshold, and that it is possible to replace the five discrete patches with asingle ring patch with no significant loss in yield.Comment: 12 pages, 12 figure

Reversible self-assembly of patchy particles into monodisperse icosahedral clusters