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.

中文翻译：

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对称多价盐溶液中带相反电荷的粒子之间的有效排斥：盐价的影响

盐在聚合电解质（如核酸和胶体）的组装中起着关键作用，因为离子可以调节它们之间的有效相互作用。在这项工作中，我们通过蒙特卡罗模拟研究了对称 (z:z) 盐溶液中带相反电荷的粒子之间的有效相互作用，盐价 z 的范围从 1 到 4。我们发现带相反电荷的粒子之间的有效相互作用对 1 :1 和低多价盐，而对高多价盐则明显排斥。此外，当 z 从 2 增加到 3 时，这种排斥会变得更强，而当 z 超过 3 到 4 时，这种排斥会变弱。我们的分析表明，整体有效相互作用归因于离子平移熵和静电能之间的相互作用，