An electric interfacial layer is created when the mobile ions or charged nanoparticles of an electrolyte interact with a surface of an extended charged object. The competition between electrostatic attraction and translational entropy loss of the mobile nanoparticles results in a diffuse interfacial layer of nanoparticles close to the charged surface. Due to its simplicity and transparency first wide spread theoretical description of the electric interfacial layer was the Poisson-Boltzmann theory. Numerous improvements were applied that account for charge-charge correlations, steric effects and solvent properties. The present article focuses on spherical mobile nanoparticles which have charge distributed over the surface and have finite size. The nanoparticles are sandwiched between two parallel like-charged walls. We perform the minimization of an appropriate free energy functional, which leads to a non-linear integro-differential equation for the electrostatic potential that is solved numerically. Our model predicts condensation of nanoparticles to oppositely charged surface. For highly charged surfaces and nanoparticles of finite size we observed big differences in the volume charge density profiles between soft and hard spheres. The theoretical predictions are in a good agreement with Monte Carlo simulations.
