Mean force between like-charged macroions at high electrostatic coupling

Interactions between two like-charged macroions in the presence of their counterions confined in a cylindrical cell have been investigated by Monte Carlo simulations. The mean force and the potential of mean force (pmf) as a function of the macroion separation have been determined at conditions at which short-range attractions become significant. As the electrostatic coupling is increased, the nature of the mean force changes from being purely repulsive to being attractive at short separations and finally attractive at all separations. At a sufficiently large electrostatic coupling, the attractive mean force is promoted by an increase of the macroion charge to counterion charge ratio and by an increase of the macroion volume fraction (assuming a not too concentrated solution). At the onset of an attractive force, nearly all counterions are localized at the macroion surfaces, but the counterions still display a two-dimensional fluid structure. The pmfs determined from the cylindrical cell model agreed qualitatively very well with those obtained from simulations of corresponding fluids, suggesting that higher-order macroion correlations are of less importance. Finally, it is argued that the attractive component of the mean force originates from spatial correlations between counterions residing near different macroions.