Immersion Depth of Positively versus Negatively Charged Nanoparticles at the Air–Water Interface: A Poisson–Boltzmann Model

Abstract

Electrostatic interactions affect the immersion depth of charged nanoparticles that are trapped at an air-water interface. Recent experiments indicate that upon adding salt negatively charged nanoparticles penetrate deeper into the aqueous phase, whereas positively charged nanoparticles exhibit opposite behavior. It has been proposed that this unexpected lack of invariance with respect to the nanoparticle's charge reversal is caused by a negative surface potential of the air-water interface. To support this hypothesis, we have performed detailed calculations based on nonlinear Poisson-Boltzmann theory of individual spherical particles that are either negatively or positively charged and reside at the interface between air and water. The nanoparticles possess dissociable surface groups that become charged when exposed to the aqueous environment. We calculate the optimal immersion depth from a numerical minimization of the total free energy, which we express as the sum of a surface tension term and an electrostatic contribution. In all calculations we fix the surface potential at the air-water surface at -50 mV. In qualitative agreement with recent experiments, our model predicts opposite behaviors of negatively versus positively charged nanoparticles: adding salt increases/decreases the water immersion depth of negatively/positively charged nanoparticles.