Softness- and Size-Dependent Packing Symmetries of Polymer-Grafted Nanoparticles.

Achieving ordered arrays of nanoparticles (NPs) with controlled packing symmetry and interparticle spacing is of great importance to design complex metamaterials. Herein, we report softness- and size-dependent self-assembly behavior of polystyrene-grafted Au NPs (Au@PS NPs). We varied the core size of Au NPs from 1.9 to 9.6 nm and the number-average molecular weight (Mn) of thiol-terminated polystyrene from 1.8 to 7.9 kg mol-1. The optimal packing model based on an "effective softness" parameter λeff that accounts for close-packed and semidilute brush regimes could predict the effective radius of Au@PS NPs (within ±9%) for a wide range of PS Mn, grafting density, and Au core size. With increasing λeff, the self-assembled Au@PS NP superlattices undergo a symmetry transition from hexagonal close packed (hcp) to body-centered tetragonal (bct) to body-centered cubic (bcc). This work demonstrates the effective softness model as a simple but robust tool for the design of NP superlattices with precisely controlled interparticle distance and packing symmetry, both of which are critical for the development of sophisticated materials through control of nanoscale structure.