a) Scheme of a polymer-coated NP interacting with a planer surface. b) Contour maps of the polymer volume fractions for the NP functionalized with short (left panel) and long (right panel) neutral polymers at a position close to the surface. Top panels (A–B) correspond to chains with no lateral mobility, while the figures in the bottom (C–D) correspond the mobile tethered chains. R=5nm, σ= 0.25 long chains/nm2, σ= 0.5 short chains/nm2, Nshort= 20 segments, Nlong= 20 segments. c) Free energy as a function of the distance between the NP and the surface. Adapted from Nap et al., Soft Matter, 2012, 8, 1688–1700 with permission of The Royal Society of Chemistry.107