Attraction between like-charged surfaces: effect of counterion dimerization.

A force between two equally charged surfaces depends on the composition of intervening solution. While the force is always repulsive for monovalent counterions, multivalent counterions turn the interaction into the attractive one. An example of the attraction between like charged surfaces is the aggregation of colloidal particles mediated by multivalent counterions with spatially separated charges. A model system represents the colloids by equally charged planar surfaces. In our consideration the intervening salt-free solution is composed of rod-like dimmers. Some of dimmers can be disconnected to monovalent ions. This model system was solved using the Monte Carlo (MC) simulations and the Poisson-Boltzmann (PB) theory, which was extended to deal with rigid complex ions. The study was made by varying a range of parameters including the surface charge density and the ratio of the number of monovalent counterions to the number of all counterions. The calculated pressure shows that with increasing surface charge density the lower fraction of dimeric counterions is needed to induce attractive force between surfaces. A good agreement between the MC simulations and the theoretical results was obtained.