Fig. 4: Multiscale theory and MD simulation consistent with experimental observations, demonstrating the tunability and predictability of patch patterns and patch sizes by stencilling.
a, Schematic of the theoretical model of polymer grafting on NP surface and its dependence on [I−] and Echain. Polymers of end-to-end distance R are grafted with one end with their conformation as a function of Ω, a shape parameter that defines the spatially dependent NP surface curvature (Supplementary Note 6). b,f, Polymer grafting probability pgraft mapped onto the surfaces of an octahedron (b) and a cuboctahedron (f). c,g, MD simulations (purple, surface regions masked by iodide; cyan, grafted polymer chains) of patchy octahedron (c) and patchy cuboctahedron (g). d,h, TEM images of patchy octahedron (d) and patchy cuboctahedron (h), with patches colour-coded to their local thickness tloc (Supplementary Note 3). When two patches overlap in projection, we show the thickness map for one of them for clarity. Reaction conditions from left to right: (d) [I−] of 0, 0.17, 0.42 and 117.60 µM at a fixed [2-NAT] of 11.3 µM; (h) [I−]/[2-NAT] of 0, 0.037, 0.980 and 30.7 (Supplementary Tables 2 and 5). Scale bars, 10 nm. e, Maximum patch thickness tm (defined and labelled in d) and patch coverage fraction fcov (defined as the fraction of NP surface covered by patches) from theory (lines) and experiment (mean values as symbols, standard deviation as error bars). From low to high [I−], a total of 111, 45, 74, 98, 73 and 43 NPs are analysed for each sample, respectively. i, Phase diagram of patch patterns predicted by theory. Patchy NP configurations overlaid on the phase diagram are individual theoretical calculations. Coloured regions are approximated by examining the predicted patch patterns.
