title: Self-assembly of soft-matter quasicrystals and their approximants.
abstract: The surprising recent discoveries of quasicrystals and their approximants in soft-matter systems poses the intriguing possibility that these structures can be realized in a broad range of nanoscale and microscale assemblies. It has been theorized that soft-matter quasicrystals and approximants are largely entropically stabilized, but the thermodynamic mechanism underlying their formation remains elusive. Here, we use computer simulation and free-energy calculations to demonstrate a simple design heuristic for assembling quasicrystals and approximants in soft-matter systems. Our study builds on previous simulation studies of the self-assembly of dodecagonal quasicrystals and approximants in minimal systems of spherical particles with complex, highly specific interaction potentials. We demonstrate an alternative entropy-based approach for assembling dodecagonal quasicrystals and approximants based solely on particle functionalization and shape, thereby recasting the interaction-potential-based assembly strategy in terms of simpler-to-achieve bonded and excluded-volume interactions. Here, spherical building blocks are functionalized with mobile surface entities to encourage the formation of structures with low surface contact area, including non-close-packed and polytetrahedral structures. The building blocks also possess shape polydispersity, where a subset of the building blocks deviate from the ideal spherical shape, discouraging the formation of close-packed crystals. We show that three different model systems with both of these features-mobile surface entities and shape polydispersity-consistently assemble quasicrystals and/or approximants. We argue that this design strategy can be widely exploited to assemble quasicrystals and approximants on the nanoscale and microscale. In addition, our results further elucidate the formation of soft-matter quasicrystals in experiment.
authors.affiliation: Department of Chemical Engineering and Department of Materials Science and Engineering, University of Michigan, Ann Arbor, Michigan 48109-2136, USA.
authors.forename: Christopher R
authors.initials: CR
authors.lastname: Iacovella
authors.forename: Aaron S
authors.initials: AS
authors.lastname: Keys
authors.forename: Sharon C
authors.initials: SC
authors.lastname: Glotzer
mesh_terms: D003102:Colloids / Q000737:chemistry*; D003198:Computer Simulation; D003460:Crystallization / Q000379:methods*; D008823:Micelles; D008958:Models, Molecular; D049329:Nanostructures / Q000737:chemistry*; D013816:Thermodynamics
chemical_list: D003102:Colloids; D008823:Micelles