Quantitative analogy between polymer-grafted nanoparticles and patchy particles.

We establish a quantitative analogy between polymer grafted nanoparticles (PGNPs) and patchy nanoparticles (NPs). Over much of the experimentally relevant parameter space, we show that PGNPs behave quantitatively like Janus NPs, with the patch size having a universal dependence on the number of grafts and the ratio of the size of the NPs to the grafted chain size. The widely observed anisotropic self-assembly of PGNP into superstructures can thus be understood through simple geometric considerations of single patch models, in the same spirit as the geometry-based surfactant models of Israelachvili.