Poisson-Boltzmann Electrostatics and Ionic Partition Equilibration of Charged Nanoparticles in Aqueous Media

Most nanoparticles (NPs) dispersed in aqueous media carry a net charge. The ensuing electric field plays a fundamental role in determining the thermodynamic and chemo-dynamic features of the interactions between NPs and dissolved metal species and their lability and bioavailability in environmental and biological matrices. Although increasing attention is being paid to the analysis of metal ion speciation in dispersions of charged complexing NPs, so far the electrostatic features of NPs have only been described on the sole basis of their structural charge properties, that is, the number of (potentially) charged groups they carry. This approach intrinsically ignores the impact of counterion accumulation at/within the particle body/surface during equilibration of the system, which effectively lowers the magnitude of the net NP charge density. Herein, we present the first analysis of the potential profile of NPs after their physicochemical equilibration with the aqueous medium, and we discuss the implications thereof in terms of counterion accumulation within and/or in the vicinity of hard, soft, and core-shell NPs. The focus is on soft or core-soft shell NPs in the thick double layer limit for which bulky Donnan features are not applicable. The new conceptual framework identifies the spatial zone over which divalent counterion accumulation is significant as a function of size, charge density, and type of NP, as well as the ionic strength and electrolyte composition (1-1 and 2-1) of the aqueous medium for the most common case of negatively charged NPs.