Experiments and Simulations of Nanoplate String Assembly in Lamellar Diblock Copolymer

Within poly(styrene-b-methyl methacrylate) (PS-b-PMMA) block copolymer (BCP) lamellae, oriented nanoplates grafted with polyethylene glycol assemble into aligned strings at small interparticle separations. These assemblies are studied using X-ray scattering, electron microscopy, and hybrid particle/self-consistent field theory (hSCFT) simulations. The insertion of a nanoplate in a BCP microdomain is expected to produce a local domain bulge as the PS/PMMA interface distorts to optimize conformational chain entropy. 2D simulations of the equilibrium BCP structure show bulge formation around the nanoplates. As a function of particle separation, the potential of mean force (PMF) reveals a global minimum corresponding to an interparticle spacing of 7.0 nm, in good agreement with experimentals, 6.42 nm. The PMF calculation exhibits an activation barrier due to the high curvature penalty between two nanoplates at a separation of 21.7 nm. Ultimately, nanoplate strings form to optimize free energy contributions from interfacial area and chain stretching. The effect of BCP molecular weight on the PMF will also be presented.