Effective Repulsion Between Oppositely Charged Particles in Symmetrical Multivalent Salt Solutions: Effect of Salt Valence - Li, Yao; Dong, Hai-Long; Zhang, Jin-Si; Lin, Cheng; Tan, Zhi-Jie (Frontiers in Physics, 2021)
Salts play critical roles in 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 become apparent repulsions for high multivalent salts. Moreover, such repulsion becomes stronger as z increases from 2 to 3, while becomes weaker when z exceeds 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 nonmonotonic salt-valence dependence of the effective repulsion is caused by the rapid decrease of attractive electrostatic energy between two oppositely charged particles with their apparently over-condensed counterions of opposite charges when z exceeds 3. Our further MC simulations show that the involvement of local-ranged counterion-coion repulsions can enhance the effective repulsions through weakening the attractive electrostatic energy especially for higher salt valence.