Statics and correlations of ions near charged surfaces

Many macromolecules in soft matter and biological systems attain a net electric charge when immersed in an aqueous environment, due to the dissociation of counterions from the macromolecular surface. Therefore, the interaction of charged surfaces with their counterions and the additional salt ions in solution, as well as the electrostatic interactions between macromolecules mediated by such micro-ions, is of fundamental importance in these systems. In this Thesis, we investigate a variety of problems involving the equilibrium behaviour of ions near charged surfaces. We begin by reviewing the mean-field Poisson-Boltzmann (PB) theory for ions near charged surfaces. For homogeneously charged surfaces, delocalized "condensation" of oppositely charged counterions effectively renormalizes the surface charge. However, the discrete nature of realistic macromolecular surface charge distributions can qualitatively alter the distribution of counterions near the surface. To encapsulate the effects of surface charge discretization, we develop a simple two-state model that allows ions to bind locally to discrete surface charges. The behavior of counterions around charged surfaces can also lead to novel macromolecular interactions. In particular, the presence of multivalent counterions can actually induce a net attractive interaction between identical highly charged surfaces. This attractive interaction can cause highly charged polylelectrolytes (e.g. DNA, actin, microtubules) to form well-ordered bundles of a finite size. After reviewing the different mechanisms that can account for this attractive interaction, we investigate several thermodynamic and kinetic barriers that may limit bundle growth.