Abstract
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.
Highlights
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
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
We found that the effective interactions between oppositely charged particles are attractive at 1:1 salt and at low multivalent salts, while the interactions become apparent repulsions at high multivalent salts
Summary
Salt ions can regulate the effective interactions among polyelectrolytes such as colloids [1,2,3,4,5,6,7], nucleic acids [8,9,10,11,12,13,14,15,16,17,18,19,20,21,22], and proteins [23,24,25,26,27,28,29], and impact diverse physical phenomena including the structural assembly of polyelectrolytes [30], the stability of colloids [31, 32], and the collapse of nucleic acids [33,34,35]. Such effect becomes more pronounced for lower 1:1 salt due to more release of ion translational entropy and more loss of electrostatic attraction between condensed counterions and charged particles with lower ion neutralization, causing more attractive ΔGS(x) and more repulsive ΔGE(x) (see Figures 5, 6F,G).
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