Density profiles around nanoparticles and distant perturbations.

We investigate how density profiles around a spherical nanoparticle in a critical solvent are affected by distant perturbations such as a wall or other particles. Using a new type of “fusion expansion,” we evaluate the isotropic and anisotropic changes in the densities at distances r from the sphere center which are of the order of the sphere radius R, with both R and r much smaller than the correlation length and the distance between the sphere and the perturbations. Our results bridge the gap between the changes in the region 0sphere surface that determine the local pressure and force on the spherical particle and in the more distant region R⪡r where the “small sphere expansion” applies. Applications to particles in critical binary liquid mixtures and in solutions of long, flexible nonadsorbing polymers are considered.