Interaction between like-charged surfaces mediated by uniformly charged counter-nanoparticles

An electric interfacial layer appears when the mobile ions or nanoparticles of an electrolyte solution interact with an extended, charged surface. The distribution of ions or nanoparticles is driven by electrostatic interactions and entropy. We consider continuously charged spherical nanoparticles of finite size. At thermodynamic equilibrium, the spatial profile of the concentration is obtained by deriving the appropriate Euler-Lagrange equations. We discuss how various model parameters of the nanoparticles influence structural properties of the electric interfacial layer. We calculate the pressure between two like-charged surfaces embedded in a water solution of continuously charged spherical nanoparticles.