Universal reduction of pressure between charged surfaces by long - wavelength surface charge modulation

– We predict theoretically that long-wavelength surface charge modulations universally reduce the pressure between the charged surfaces with counterions compared with the case of uniformly charged surfaces with the same average surface charge density. The physical origin of this effect is the fact that surface charge modulations always lead to enhanced counte-rion localization near the surfaces, and hence, fewer charges at the midplane. We confirm the last prediction with Monte Carlo simulations. Introduction-The interaction of charged interfaces is a basic problem in surface science, and is relevant to e.g., colloid stabilization, membrane adhesion, microemulsion formation [1]. While many theories have focused on the simple case of homogeneously charged surfaces, real interfaces are characterized by discrete surface charge distributions. Theoretical analysis of the problem predicts two important properties of these systems: the spatial dependence of the counterion/salt density and the pressure between The main question is whether one can provide universal predictions of the effect of surface charge discreteness (modulations) on the counterion spatial distribution and on the interaction law between the interfaces, independently of the details of the surface distribution of discrete charges (modulations). Our work shows that indeed, there are quite general effects induced by surface charge discreteness. The principal conclusion of previous studies based on the solution of linear or quasi-linear Debye-Huckel equation with non-uniform surface charge distributions with either excess salt [2,3,15], or with counterions only [15], is the following: The discreteness (or modulations) of surface charge always leads to an enhanced repulsive interaction between the surfaces compared with the case of uniformly charged surfaces with the same average surface charge density, provided the charges (or charge modulations) on the two surfaces are in-phase. If the charges (charge modulations) on the two surfaces are out-of-phase, the repulsion can be either enhanced or reduced compared with the uniformly charged surface case. These studies [2, 3, 15] calculated the effects of charge modulations on the counterion spatial distribution and on the electrostatic potential to first order in the amplitude of modulations. The only relevant terms in the pressure are therefore due to the square of the non-zero components of the electric field, E, at the midplane ∼ E