The interaction between charged macroions induced by rod-like ions

We study a model for the interaction between two planar, like-charged macroions, separated by an aqueous solution containing rod-like counterions. Each counterion consists of two positive charges that are separated by a fixed distance. This is a specific case of ions that possess a spatially extended electric charge distribution. Such systems are not well described by mean-field theory. We thus suggest a density functional approach that accounts for charge-charge correlations within each rod-like ion but still neglects correlations between different ions. Our approach results in an integral-differential equation that can be solved numerically. The solution shows that orientational ordering of rod-like ions in the electric field between the two macroions gives rise to an attractive macroions-macroions interaction. We demonstrate that the attraction arises for sufficiently long rod-like ions and high surface charge densities of the two macroions.