  The electrostatic double layer force is key to determining the stability and
self-assembly of charged colloids and many other soft matter systems. Fully
understanding the attractive force between two like-charged surfaces remains a
great challenge. Here we apply the modified Gaussian renormalized fluctuation
theory to study ion correlation-driven like-charge attraction in multivalent
salt solutions. The effects of spatially varying ion correlations on the
structure of overlapping double layers and their free energy are
self-consistently accounted for. In the presence of multivalent salts,
increasing surface charge or counterion valency leads to a short-range
attraction. We demonstrate that although both overcharging and like-charge
attraction are outcomes of ion correlation, there is no causal relationship
between them. Our theory also captures the non-monotonic dependence of
like-charge attraction on multivalent salt concentration. The reduction of
attraction at high salt concentrations could be a contributing factor towards
the reentrant stability of charged colloidal suspensions. Our theoretical
predictions are consistent with the observations reported in experiments and
simulations.
