Assembling and ordering polymer-grafted nanoparticles in three dimensions

Taking advantage of the aqueous biphasic behavior of polyethylene glycol (PEG)/salts, recent experiments have demonstrated self-assembly and crystallization of PEG-grafted gold nanoparticles (PEG-AuNPs) into tunable two-dimensional (2D) supercrystals by adjusting salt concentration (for instance, K₂CO₃). In those studies, combined experimental evidence and theoretical analysis have pointed out the possibility that similar strategies can lead to three-dimensional (3D) formation of ordered nanoparticle precipitates. Indeed, a detailed small-angle X-ray scattering (SAXS) study reported herein reveals the spontaneous formation of PEG-AuNPs assemblies in high-concentration salt solutions that exhibit short-range 3D order compatible with fcc symmetry. We argue that the assembly into fcc crystals is driven by partnering nearest-neighbors to minimize an effective surface-tension gradient at the boundary between the polymer shell and the high-salt media. We report SAXS and other results on PEG-AuNPs of various Au core diameters in the range of 10 to 50 nm and analyze them in the framework of brush-polymer theory revealing a systematic prediction of the nearest-neighbor distance in the 3D assemblies.