Impact of the Distributions of Core Size and Grafting Density on the Self-Assembly of Polymer Grafted Nanoparticles

It is now well-accepted that hydrophilic nanoparticles (NPs) lightly grafted with polymer chains self-assemble into a variety of superstructures when placed in a hydrophobic homopolymer matrix or in a small molecule solvent. Currently, it is thought that a given NP sample should only assemble into one kind of superstructure depending on the relative balance between favorable NP core-core attractions and steric repulsion between grafted polymer chains. Surprisingly, we find that each sample shows the simultaneous formation of a variety of NP-assemblies, e.g., well-dispersed particles, strings, and aggregates. We show through the generalization of a simple geometric model that accounting for the distributions of the NP core size and the number of grafted chains on each NP (which is especially important at low coverages) allows us to quantitatively model the aggregate shape distribution. We conclude that, in contrast to molecular surfactants with well-defined chemistries, the self-assembly of these NP analogues is dominated by such fluctuation effects.