Abstract
ABSTRACTClusters and shells based on icosahedral symmetry are characterised, constructed from component particles that retain memory of their neighbours in a specific reference structure. This memory provides the particles with ‘addressable’ characteristics, with a ground state corresponding to the structure where all the components are correctly addressed in terms of the local environment. The interparticle potentials have separate attractive and repulsive components, defined by the reference structure. For a single target structure, the relaxation efficiency is mostly determined by the variation of the attractive component for correctly and incorrectly addressed particles. The effects of varying the addressability can be visualised directly in terms of the underlying energy landscape, and follow quantitative predictions from catastrophe theory. A doubly-addressable landscape can be designed within the same framework. In well-defined regions of parameter space, the predicted global minima for aggregates of the target cluster (target monomer) form ‘superclusters’, which can be described in terms of multiple interacting copies of local minima for the monomer. The predicted lowest energy superclusters formed from aggregates of addressable icosahedral clusters and shells are themselves based on icosahedral packing. These hierarchical icosahedral structures could be realised experimentally if particles can be synthesised to match the interactions encoded in the addressable potentials.
Highlights
As for familiar macroscopic length scales, creating a molecular machine requires assembly of components into specific relative positions
For suitable parameter choices we find that aggregates of the two types of icosahedral targets are composed of well-defined target monomers, having each addressable particle correctly sited within each monomer
The disconnectivity graphs for LJI1h3 and PYI1h2 indicate that the efficiency of relaxation to the target addressable cluster will increase systematically as ǫaNtNt N decreases from one to zero (Figures 1 and 2), as the next-nearest neighbour attractions are progressively turned off
Summary
As for familiar macroscopic length scales, creating a molecular machine requires assembly of components into specific relative positions. Such components are termed ‘addressable’, since the target design is encoded in their interactions via a reference structure, and in the underlying potential energy landscape. One promising route for addressable self-assembly employs DNA-coated nanoparticles, in which the choice of DNA sequences determines the aggregation [1], and complex phase behaviour can be designed with such particles [2]. Self-assembly of thousands of distinct ‘DNA bricks’ into a target structure has been achieved experimentally [3], initiating an active new field of research. Colloids may offer an alternative route to realisation of new addressable materials, and here again, experimental advances [6, 7] have stimulated a variety of theoretical and computational studies [8,9,10,11,12]
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