Apparent repulsion between equally and oppositely charged spherical polyelectrolytes in symmetrical salt solutions

Ion-mediated interactions are very important for the properties of colloids and biomacromolecules such as nucleic acids and proteins. In this work, the ion-mediated interactions between equally and oppositely charged spherical polyelectrolytes (SPEs) in symmetrical divalent electrolytes have been investigated by Monte Carlo simulations, and an unexpected apparent repulsion was observed at high divalent salt concentration. Our investigations also show that the effective repulsion becomes more pronounced for SPEs with higher charge densities and for counterions with larger sizes and was found to be tightly accompanied with the over-neutralization to SPEs by condensed counterions and their release upon the approach of SPEs. Such attractive interaction can be reproduced by our proposed modified Poisson-Boltzmann model and is mainly attributed to the increase in the electrostatic repulsion between on charged SPE and the over-neutralized counterions around the other oppositely SPE with the approach of the two SPEs.