Ionic equilibria and swelling of soft permeable particles in electrolyte solutions

Abstract

We discuss osmotic equilibria between soft permeable particles, of radius $R$ and volume charge density $\rho$, and bulk electrolyte solutions of the inverse Debye length $\kappa$. Existing models are based on a simplifying assumption of weakly charged particles. Here we derive analytical approximations for a distribution of a potential, ions and pressure in the system, suitable even when $\rho$ is quite large. Our theory is valid not only for ``large'' particles ($\kappa R \gg 1$), where a central part is fully screened, but also for weakly screened ``small'' particles ($\kappa R \leq 1$) with overlapping inner diffuse layers. Besides, we present novel coarse-grained simulations to validate the analysis and illustrate the variation of potential/ions profiles in response to changes in $\kappa R$ and $\rho$. 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.