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| Despite their elegance, nature seldom adopts an empty shell - or sphere - as an energetically favorable state. Exceptions to this rule do exist at the nanoscale, with the self-assembly processes of viral capsids and the more recently discovered spontaneous assembly of polyoxometalate (POM) macroions into supramolecular spherical structures called ``blackberries" as examples. The underlying physical mechanisms that govern these assemblies remain largely unknown, and models for these processes have grown increasingly complex and problem-dependent. We exploit recent mathematical advances to present a simpler approach.
Specifically, using only pairwise and isotropic interactions we derive the basic principles on the interaction that predict when hollow shells will form. We then use these principles to find, for the first time, a purely isotropic physical model that will produce such assemblies. Time permitting we will also consider the effects on spherical self assembly associated to non-isotropic forces. |
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