Charge Regulation Effect on Nanoparticle Interaction Mediated by a Polyelectrolyte

The ability to precisely control surface charge using charged polymers is fundamental to many nanotechnology applications, enabling the design and fabrication of materials with tailored properties and functionalities. Here, we study the effect of charge regulation (CR) on the interaction between two nanoparticles (NPs) mediated by an oppositely charged polyelectrolyte (PE) in an electrolyte solution. To this end, we employ a hybrid CR Monte Carlo/molecular dynamics simulation framework to systematically explore the effects of pH, salt concentration, and polymer chain length on NP surface charge behavior. For comparison, we also conduct molecular simulations under constant charge (CC) conditions. Our results reveal that CR enhances PE adsorption onto NP surfaces compared to the CC case, where polymer bridging dominates across a wide range of NP intersurface separations. This enhanced adsorption under CR leads to a weak net repulsion driven by osmotic forces. In contrast, the CC model yields a stronger net attraction due to the bridging force. Furthermore, we find that the CR effects are more pronounced under deionized conditions, whereas at a higher salt concentration, counterion screening dominates in both CR and CC cases, diminishing the CR effect. These findings highlight the importance of incorporating charge regulation in characterizing nanoparticle interactions within a complex biochemical environment, particularly in low salt concentrations.