The discovery of soft-matter quasicrystals and related periodic approximants in dendrimer [1-2] and block copolymer systems [3-4] hints at a unique thermodynamic mechanism that gives rise to their stability. In the past, specific interaction potentials have been contrived to stabilize quasicrystals and their approximants in computer simulations. However, such complex interactions are seemingly incompatible with the known properties of such soft-matter systems. Here, we use molecular simulation to demonstrate an alternative approach for assembling dodecagonal quasicrystals and their approximants based solely on particle functionalization and shape . These effects mimic the characteristics of the specialized potentials, thereby replacing complex energetic interactions with simpler-to-achieve bonded and excluded-volume interactions. Our model consists of spherical building blocks 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 posses shape polydispersity, where a subset of the building blocks deviate from the ideal spherical shape, which discourages the formation of close-packed crystals. We show that a model system possessing both mobile surface entities and shape polydispersity consistently assembles complex quasicrystal-like structures. We also report the spontaneous assembly of quasicrystal approximants in two micelle-forming systems of tethered nanoparticle building blocks that possess these key features. We argue that this mechanism can be widely exploited to assemble quasicrystals and approximants on the nano and microscales, and may further elucidate the recent formation of soft matter quasicrystals in experiment [1-4].
 G. Ungar, et al., Giant supramolecular liquid crystal lattice, Science 299 (2003)
 X. Zeng, et al., Supramolecular dendritic liquid quasicrystals, Nature 428, (2004)
 S. Lee, M.J. Bluemle, F.S. Bates, Discovery of a frank-kasper sigma phase in sphere-forming block copolymer melts, Science, 330 (2010)
 S. Fischer, et al. Colloidal quasicrystals with 12-fold and 18-fold diffraction symmetry, Proc. Natl. Acad. Sci., 108, (2011)
 C.R. Iacovella, A.S. Keys, S.C. Glotzer, Self assembly of soft matter quasicrystals and their approximants, preprint, http://arxiv.org/abs/1102.5589