Ionic equilibria and swelling of soft permeable particles in electrolyte solutions

We discuss osmotic equilibria between soft permeable particles, of radius R and volume charge density ρ , and bulk electrolyte solutions of inverse Debye length κ . Existing models are based on a simplified assumption of weakly charged particles. Here we derive analytical approximations for the distribution of potentials, ions and pressure in a system, suitable even when ρ is quite large. Our theory is valid not only for "large" particles ( κR > 1), where the central part is fully screened, but also for weakly screened "small" particles ( κR ≤ 1) with overlapping inner diffuse layers. Besides, we present novel coarse-grained simulations to validate the analysis and illustrate the variation of potential/ion profiles in response to changes in κR and ρ . Our simulations also allow us to argue that swelling of both "large" and "small" particles is uniform, although their inner non-uniform local pressure profiles are essentially and qualitatively different. These results are directly relevant for a variety of permeable charged objects, from polymer micro- and nanogels to more rigid porous colloids. We report an analytical theory and coarse-grained simulations of electro-osmotic equilibria of uniformly charged soft permeable particles immersed in electrolyte solutions.