Like-charge attraction and association in polyelectrolyte solutions

The phenomenon of like-charge attraction has been reported in various physical and biological systems, such as charged colloids, DNA, proteins, and plasma. Previous theoretical and simulation studies have observed this phenomenon in polyelectrolyte solutions mediated by counter-ion solvation, supported by some experimental findings. In this study, we use coarse-grained molecular dynamics simulations to further investigate the underlying mechanisms driving like-charge attraction in polyelectrolyte solutions. We study the effect of charge fluctuations of counter-ions in regions around the polyelectrolytes as a function of varying counterion-solvent interaction strength and polyelectrolyte concentration. To quantify the effective attraction better, we also compute the free energy profile as a function of the distance between two polyelectrolyte molecules using umbrella sampling. We observe that for higher counterion-solvent interaction strengths, the counterions tend to cluster with correlated charge fluctuations in regions between the polyelectrolytes, resulting in effective attraction. In the absence of preferential interaction between counterions and solvent, the counterions do not mediate significant inter-polyelectrolyte attraction. Our results provide quantitative insights into the mechanisms driving like-charge attraction in polyelectrolyte solutions and have implications for explaining various similar phenomena in physical and biological systems.