The use of polymer tethered nanoparticles provides a unique method to control the self-assembly of nanoparticles into ordered mesophases that resemble the complex morphologies of block copolymers. However, due to the geometry of the nanoparticles, these tethered systems are able to adopt complex local order not normally found in block copolymer systems. For example, in the double gyroid phase nanospheres are found to form icosahedral arrangements [1] whereas nanorods are found to form liquid-crystalline, splayed-hexagonal bundle arrangements [2]. Using Brownian dynamics simulations of the self-assembly of tethered nanospheres and tethered nanorods, we characterize the local geometry of nanoparticle packings within the double gyroid phase in both systems. We find that both building blocks reduce the local packing frustration as compared to a flexible block copolymer, but in different ways owing to their different shapes. For example, we observe that partial icosahedral packings with coordination of 8 are favored for nanospheres and bundles with a splay of ~10 degrees are favored for nanorods. Based on this analysis, we find a strong connection between the stability of the double gyroid phase and the local order adopted by polymer tethered nanospheres and nanorods [3].

[1] C.R. Iacovella, A.S. Keys, M.A. Horsch, S.C. Glotzer "Icosahedral packing of polymer-tethered nanospheres and stabilization of the gyroid phase" Phys. Rev. E 75, 040801(R) (2007)

[2] M.A. Horsch, Z.L. Zhang and S.C. Glotzer, "Simulation studies of self-assembly of end-tethered nanorods in solution and role of rod aspect ratio and tether length," J. Chem. Phys., 125 (18): Art. No. 184903 NOV 14 (2006)

[3] C.R. Iacovella, M.A. Horsch,and S.C. Glotzer, preprint.