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Salt ions play critical roles in the assembly of polyelectrolytes such as nucleic acids and colloids since ions can regulate the effective interactions between them. In this work, we investigated the effective interactions between oppositely charged particles in symmetrical ( z : z ) salt solutions by Monte Carlo simulations with salt valence  z  ranging from 1 to 4. We found that the effective interactions between oppositely charged particles are attractive for 1:1 and low multivalent salts, while they become apparently repulsive for high multivalent salts. Moreover, such effective repulsion becomes stronger as  z  increases from 2 to 3, while it becomes weaker when  z  increases from 3 to 4. Our analyses reveal that the overall effective interactions are attributed to the interplay between ion translational entropy and electrostatic energy, and the non-monotonic salt-valence dependence of the effective repulsions is caused by the rapid decrease of attractive electrostatic energy between two oppositely charged particles with their over-condensed counterions of opposite charges when  z  exceeds 3. Our further MC simulations show that the involvement of local-ranged counterion–co-ion repulsions can enhance the effective repulsions through weakening the attractive electrostatic energy, especially for higher salt valence.

Effective Repulsion Between Oppositely Charged Particles in Symmetrical Multivalent Salt Solutions: Effect of Salt Valence