Lateral Correlation of Multivalent Counterions is the Universal Mechanism of Charge Inversion

Charge inversion is a counterintuitive phenomenon in which a strongly charged particle (a macroion) binds so many counterions that its net charge changes sign. As shown below the binding energy of a counterion with large charge Z is larger than k B T, so that this net charge is easily observable: it is the net charge that determines a particle drift in a weak field electrophoresis. Charge inversion is possible for a variety of macroions, ranging from the charged surface of mica to charged lipid membranes, colloids, DNA or actin. Multivalent metal ions, small colloidal particles, charged micelles, short or long polyelectrolytes including DNA can play the role of multivalent counterions. Recently charge inversion has attracted significant attention [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22].