How and Why Nanoparticle's Curvature Regulates the Apparent pKa of the Coating Ligands

Dissociation of ionizable ligands immobilized on nanopaticles (NPs) depends on and can be regulated by the curvature of these particles as well as the size and the concentration of counterions. The apparent acid dissociation constant (pK(a)) of the NP-immobilized ligands lies between that of free ligands and ligands self-assembled on a flat surface. This phenomenon is explicitly rationalized by a theoretical model that accounts fully for the molecular details (size, shape, conformation, and charge distribution) of both the NPs and the counterions.