“…Counterions can bind to charged particles and consequently modulate effective interactions between charged particles. Beyond the mean-field descriptions, for oppositely charged particles, multivalent ions of a high concentration can modulate intrinsically Coulombic attractions into effective repulsions. − In parallel, for like-charged particles, multivalent ions can modulate intrinsically Coulombic repulsions into effective attractions, which could drive the condensation or aggregation of charged particles such as nucleic acids, − proteins, , and colloids. − The mechanisms for multivalent ion-mediated like-charge attractions are diverse and are attributed to counterion bridging, ,,− depletion force, , and charge fluctuations of condensed counterions. ,− Alternatively, condensed counterions could be modeled as one component plasma around oppositely charged particles (voids), and the effective like-charge attraction could be attributed to a competition among the ion–ion and void–void repulsions and the ion–void attraction . Recently, specific counterion configuration and depletion were reported to be able to cause the like-charge attractions at high monovalent salt concentrations.…”