Electrostatic disorder-induced interactions in inhomoge- neous dielectrics

– We investigate the effect of quenched surface charge disorder on electrostatic interactions between two charged surfaces in the presence of dielectric inhomogeneities and added salt. We show that in the linear weak-coupling regime (i.e., by including mean-field and Gaussian-fluctuations contributions), the image-charge effects lead to a non-zero disorderinduced interaction free energy between two surfaces of equal mean charge that can be repulsive or attractive depending on the dielectric mismatch across the bounding surfaces and the exact location of the disordered charge distribution. Electrostatic interactions are one of the two fundamental components of the DLVO theory of colloidal stability [1, 2]. They are standardly described by the Poisson-Boltzmann (PB) theory [1, 3] embodying the mean-field approach to classical charged systems. Mean-field interactions between like-charged macroions are repulsive in nature and thereby tend to stabilize solutions of charged macroions. In strongly coupled systems (e.g., when multivalent counterions are present), electrostatic interactions however induce strong attractive forces between like-charged macroions [4,5], and thus act more like Lifshitz-van der Waals interactions that tend to destabilize charged solutions. This attraction can not be captured by the meanfield approach and a new paradigm dubbed the strong-coupling limit [6, 7] was introduced to describe the equilibrium properties of Coulomb fluids when the mobile counterion charges become large. The crossover from the mean-field Poisson-Boltzmann description to the strongcoupling limit is governed by a single dimensionless electrostatic coupling parameter, which is given by the ratio of the Bjerrum length (identifying Coulombic interaction between ions themselves) and the Gouy-Chapman length (describing electrostatic interaction between ions and the charged macroion surface) [4]. Electrostatic interactions between charged macroions in the mean-field and the strong-coupling limit thus unfold into a much richer structure than conveyed for many years by the DLVO paradigm. The collapse of a highly charged polyelectrolyte, such as DNA, in the presence of multivalent counterions is the most dramatic example of unexpected and counter-intuitive features of the strong-coupling electrostatics [7, 8]. Recently we added a new twist to the theory of electrostatic interactions in charged systems [9]: not only can electrostatic interactions between like-charged macroions turn from repulsive to attractive due to strong-coupling counterion-induced correlations, but we showed