Block copolymers and surfactants have long been known to self-assemble into a wide variety of complex microstructures where the assembly is driven by immiscibility between chemically distinct blocks in the polymers and between the head and tail groups in surfactants. These ordered microstructures are highly sought for applications at the nanoscale, ranging from photonic-bandgap materials to templates for nanoparticle assembly. Hybrid building blocks have recently been created that resemble block copolymers where the individual blocks consist of nanoparticles and polymers; these hybrid building blocks, or tethered nanoparticles, constitute a class of "shape amphiphiles" where microphase separation occurs due to the immiscibility between the nanoparticle and polymeric tether resulting in mesostructured equilibrium phases that resemble the morphologies of block copolymers and surfactants.

Specifically, we have simulated the phase behavior of nanospheres each functionalized with a single polymer tether -- analogous to a diblock copolymer or surfactant -- finding hexagonally packed cylinders, the double gyroid, perforated lamella, and lamella [1,2], as expected [3]. However, due to the geometry of the nanoparticles, these tethered systems are able to adopt complex local order not normally found in block copolymer and surfactant systems. For example, in our simulation studies of monotethered nanospheres, we find distinct icosahedral and HCP ordering between nanospheres [2]. This local ordering has additional consequences. For example, when considering the bicontinuous, double gyroid structure, we find that the icosahedral ordering between nanospheres reduces the packing frustration at the nodes, potentially leading to a greater range of stability as compared to a flexible block copolymer system [2,4]. Similarily, in our simulations of nanorods functionalized by a single tether, we find that these tethered nanorods also order into the double gyroid structure where packing frustration is also reduced at the nodes, here as a result of the nanorods adopting liquid-crystalline, splayed-hexagonal bundles [4].

The similarities between tethered nanospheres and block copolymers also extends into the area of triblock copolymer systems. Linear and star triblock copolymers are known to self assemble into an even wider array of complex morphologies than typical diblocks. We have investigated the nanoparticle analog of a triblock copolymer by replacing the middle block of an ABC triblock with a nanosphere. We investigated the phase behavior under melt conditions as a function of both nanoparticle diameter and dihedral angle, the angle separating the two tethers.   We found a variety of phases that resemble those of linear and star triblock copolymers, including the alternating diamond, alternating gyroid, and alternating orthorhombic tricontinuous lattices, tetragonal and [8,8,4] columnar phases, and a unique phase of NaCl ordered spherical micelles not seen for triblocks [5].  The ability to adjust the geometry of the tethers allows for additional control over the ordering and placement of the nanospheres within the system. Additionally, we have explored the phase behavior (i) as a function of block fraction under melt conditions and show evidence of a transition from tricontinuous to lamellar structures, and (ii) as a function of volume fraction under selective solvent conditions for which we find the double gyroid, hexagonally packed cylinder, and BCC ordered micelle phases [5]. Overall, we find we have a wide array of control over the placement and organization of nanoparticles in both mono- and ditethered systems.

Building from our research results, we created The Soft Matter Wiki, an community driven online encyclopedia of soft matter and simulation terminology, with the help of the Materials Digital Library Pathway (MATDL) [6]. This has been used as an educational resource within numerous classes within the University of Michigan. In related work, we have created interactive simulation modules based on our research codes for use in both the undergraduate and graduate curriculum and distributed these through the Soft Matter Wiki.

[1] C.R. Iacovella, M.A. Horsch, Z-L Zhang, S.C. Glotzer. "Phase diagrams of self-assembled mono-tethered nanospheres from molecular simulation and comparison to surfactants" Langmuir, 21 (21), 9488-9494, (2005)

[2] 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)

[3] M.A. Horsch, Z-L. Zhang, C.R. Iacovella, S.C. Glotzer. "Hydrodynamics and microphase ordering in blockcopolymers: Are hydrodynamics required for ordered phases with periodicity in more than one dimension?", Journal of Chemical Physics, 121(22): 11455-11462, (2004)

[4] C.R. Iacovella, M.A. Horsch, S.C. Glotzer, "Local Ordering Of Tethered Nanospheres And Nanorods And The Stabilization Of The Gyroid Phase", preprint.

[5] C.R. Iacovella, and S.C. Glotzer, preprint.

[6] L.M. Bartolo, C.S. Lowe, S.C. Glotzer, C.R. Iacovella 
"Development of a wiki-based, expert community-driven nanosystem vocabulary."
Proceedings of the International Conference on Dublin Core and Metadata Applications 211-214, (2006)