Static and dynamic screening effects in the electrostatic self-assembly of nano-particles

In the description of charge screening in the electrostatic self-assembly of nanoparticles (molecules) embedded into a polar solvent, the static screening effects (a contribution associated with the rapid spatial redistribution of small and highly mobile ions of a solvent) are traditionally treated phenomenologically, using the Yukawa short-range potential for describing the interaction between these particles. However, this model has a limited range of applicability being valid only for infinitely diluted systems and high salt concentrations. During a slow self-assembling process with nanoparticle formation, very dense structural elements (aggregates) are formed, in which the distances between the nanoparticles could become comparable to the Debye radius in the Yukawa potential. For such structural elements dynamic screening effects (the contribution of nanoparticles themselves to the screening potential) become important. In this paper, using a novel integrated approach (nonlinear integro-differential kinetic equations for the correlation functions of particles), we have obtained the self-consistent solution in the 3d case and compared roles of both static (equilibrium) and dynamic (nonequilibrium) charge screening effects in different situations. This paper is a continuation of our recent study [Phys. Chem. Chem. Phys., 2014, 16, 13974], where the polar solvent effects were now taken into account.