Density profiles around nanoparticles and distant perturbations

Abstract

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 0<r-R<<R close to the sphere 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.