We perform atomistic simulations of nanometer-separated charged surfaces in the presence of monovalent counterions at fixed water chemical potential. The counterion density profiles are well described by a modified Poisson-Boltzmann (MPB) approach that accounts for non-electrostatic ion-surface interactions, while the effects of smearedout surface-charge distributions and dielectric profiles are relatively unimportant. The simulated surface interactions are for weakly charged surfaces well described by the additive contributions of hydration and MPB repulsions, but already for a moderate surface density of σ = −0.77 e/nm 2 this additivity breaks down, which we rationalize by a modification of the hydration repulsion due to interfacial water reorientation. 1 Keywords Charged surfaces, hydration repulsion, modified Poisson-Boltzmann theory, ion distributions, surface interactions, water orientation. Many biologically and industrially relevant surfaces are charged in water, classical examples are lipid membranes 1-3 , ionic surfactant layers 4 and solid surfaces such as glass, silica or mica 5-8 . The experimental and theoretical descriptions of the interaction between charged surfaces across aqueous electrolytes forms the foundation of colloidal science. The celebrated Poisson-Boltzmann (PB) theory 9 treats water as a dielectric continuum and becomes valid when surface charge density and ion valencies are low and thus ion correlations are negligible.According to PB theory the interaction pressure between similarly charged surfaces is always repulsive and decays exponentially for large surface separation, two predictions that are confirmed by numerous experiments 5-8 .
Surface separations in the nanometer range have been investigated in experiments andsimulations for systems such as silica 10-13 , clay 14,15 or membrane stacks [16][17][18][19][20] . At such low surface separations an additional, exponentially decaying repulsive pressure contribution is present, which is similar to the hydration pressure found for soft polar surfaces with a zero net charge [16][17][18][19] . Experimental pressures between charged surfaces have been successfully fitted by assuming additivity of hydration and PB contributions 21-24 . However, such fits are of only limited persuasive power since the surface charge density and its location are mere fitting parameters.Indeed, additional effects for nanometer surface separations suggest an essential modification of the traditional PB theory: i) Water confined in nanometer slabs exhibits dielectric properties distinctly different from bulk 25-28 . This is also suggested by a modified interfacial water structure inferred from non-linear spectroscopy 29-31 . ii) Surface charge distributions are neither laterally homogeneous nor sharply peaked normal to the surface, as typically assumed in PB modeling, but rather are discrete 32 and broadly distributed 25 . iii) Ions interact with charged as well as uncharged surface groups via ion-surface interactions which involve