Kyle J. M. Bishop, Chemical & Biological Engineering, Northwestern University, 2145 Sheridan Rd/TECH E136, Evanston, IL 60208 and Bartosz A. Grzybowski, Chemical Engineering, Northwestern University, 2145 Sheridan Rd/TECH E136, Evanston, IL 60208.
What happens when solutions containing objects bearing charges of opposite polarities are mixed? It depends on the scale and is thought to be fundamentally different in the molecular and the colloidal regimes. Whereas oppositely charged microparticles precipitate continuously over a wide range of relative particle concentrations, mixtures of oppositely-charged nanoparticles (NPs) precipitate sharply only at the point of NP electroneutrality. This behavior – reminiscent of threshold precipitation of inorganic ions – is specific to the nanoscale and is due to the formation of like-charged, “core-and-shell” clusters stabilized in solution by mutual electrostatic repulsions. The formation of these charged clusters is rationalized by deriving the electrostatic interaction potentials between NPs accounting for the adsorption/desorption of counterions from the NPs' surface. Interestingly, this model predicts that the attractive energy between oppositely charged NPs at contact is nearly twice the repulsive energy of like-charged NPs at the same distance. Monte Carlo simulations employing these potentials confirm the formation of “core-and-shell” aggregates and sharp precipitation at electroneutrality. Finally, I show how nanoparticle titrations based on these phenomena provide a uniquely accurate tool for determining charges tethered onto nanoscopic objects and for studying the thermodynamics of surface reactions at the nanoscale.