Stability of the double gyroid phase to nanoparticle polydispersity in polymer-tethered nanosphere systems†

Recent simulations predict that aggregating nanospheres functionalized with polymer ‘‘tethers’’ can self-assemble to form the double gyroid (DG) phase seen in block copolymer and surfactant systems. Within the struts of the gyroid, the nanoparticles pack in icosahedral motifs, stabilizing the gyroid phase in a small region of the phase diagram. Here, we study the impact of nanoparticle size polydispersity on the stability of the double gyroid phase. We show for low amounts of polydispersity the energy of the double gyroid phase is lowered. A large amount of polydispersity raises the energy of the system, disrupts the icosahedral packing, and eventually destabilizes the gyroid. Our results show that the DG forms readily up to 10% polydispersity. Considering polydispersity as high as 30%, our results suggest no terminal polydispersity for the DG, but that higher polydispersities may kinetically inhibit the formation of phase. The inclusion of a small population of either smaller or larger nanospheres encourages low-energy icosahedral clusters and increases the gyroid stability while facilitating its formation. We also introduce a new measure for determining the volume of a component in a microphase-separated system based on the Voronoi tessellation.