The influence of discrete surface charges on the force between charged surfaces

The force between two parallel charged flat surfaces, with discrete surface charges, has been calculated with Monte Carlo simulations for different values of the electrostatic coupling. For low electrostatic coupling (small counterion valence, small surface charge, high dielectric constant, and high temperature) the total force is dominated by the entropic contribution and can be described by mean field theory, independent of the character of the surface charges. For moderate electrostatic coupling, counterion correlation effects lead to a smaller repulsion than predicted by mean field theory. This correlation effect is strengthened by discrete surface charges and the repulsive force is further reduced. For large electrostatic coupling the total force for smeared out surface charges is known to be attractive due to counterion correlations. If discrete surface charges are considered the attractive force is weakened and can even be turned into a repulsive force. This is due to the counterions being strongly correlated to the discrete surface charges forming effective, oppositely directed, dipoles on the two walls.