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, K2 CO3 ). 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.