Understanding long-range opposite charge repulsion in multivalent salt solutions.

The article focuses on the phenomenon of repulsion between two oppositely charged planar surfaces immersed in multivalent salt solutions and its relationship with overcharging, using a modified Gaussian renormalized fluctuation theory. This theory accurately incorporates spatially varying ion–ion correlations and quantitatively reproduces simulation results for divalent, trivalent, and tetravalent ions, revealing that opposite-charge repulsion is a long-range effect increasing monotonically with multivalent salt concentration. The study clarifies that opposite-charge repulsion arises from enhanced ion accumulation in the double layer, which raises osmotic pressure and screens electrostatic attraction, and demonstrates that this repulsion can occur independently of overcharging, which is the excess accumulation of counterions near a charged surface. Additionally, the addition of monovalent salt reduces opposite-charge repulsion by diminishing ion correlations and osmotic pressure.