Decoration of microparticles by highly charged nanoparticles

A negatively charged microparticle is immersed into an aqueous solution containing highly negatively charged nanoparticles and an electrolyte. Using a modified Poisson-Boltzmann equation which takes into account the van der Waals interactions between microparticle and nanoparticles and in which the latter are treated as macro-ions, it was found that there are conditions under which the concentration of nanoparticles close to the microparticle becomes larger (even much larger) than the bulk one and halos are formed around the latter particles. Halos are formed when the van der Waals attractive interactions between the microparticle and nanoparticles are stronger than the repulsive interactions between the same particles plus the repulsive interactions between the nanoparticles.