Attraction between Like Charged Surfaces Mediated by Uniformly Charged Spherical Colloids in a Salt Solution

Like-charged macromolecules repel in electrolyte solutions that contain small (i.e. point-like) monovalent coand counterions. Yet, if the mobile ions of one species are spatially extended instead of being point-like, the interaction may turn attractive. This effect can be captured within the mean-field Poisson-Boltzmann framework if the charge distribution within the spatially extended ions is accounted for. This has been demonstrated recently for rod-like ions. In the present work, we consider an electrolyte solution that is composed of monovalent point-like salt ions and uniformly charged spherical colloids, sandwiched between two planar like-charged surfaces. Minimization of the mean-field free energy yields an integral-differential equation for the electrostatic potential that we solve numerically within the linear Debye-Hückel limit. The free energy, which we calculate from the potential, indeed predicts attractive interactions for sufficiently large spherical colloids. We derive an approximate analytical expression for the critical colloid size, above which attraction between like-charged surfaces starts to emerge. (doi: 10.5562/cca1824)