Diffusiophoresis of charge-regulated nanoparticles comprising finite ion size and electrostatic correlation effects

Abstract

Diffusiophoresis of nanoparticles is studied based on a modified electrokinetic model accounting the electrostatic correlation of finite sized ions and their non-electrostatic steric interactions. Hydrated ions are modeled as charged hard spheres suspended in the medium, which creates a volume exclusion due to ion–ion steric interactions and the medium viscosity to vary with the ionic volume fraction. The surface charge of the particle is considered to depend on the pH and concentration of electrolyte. We have adopted the Carnahan–Starling equation of state to model the ion steric interactions. The electrostatic correlation is incorporated by minimizing the free energy, which leads to a fourth-order modified Poisson equation for the electric field with the correlation length depending on the bulk ionic concentration, surface charge, and valence of the counterions. Due to the consideration of the ion–ion correlation, the effective screening length of the surface charge expands as the ionic concentration as well as valence of counterions is increased. The counterion saturation created by the ion steric interaction attenuates the screening of the surface charge. In addition, the ion steric interaction augments the diffusion field. Thus, the modified electrokinetic model shows a significant deviation from the standard Poisson–Nernst–Planck model. Governing equations in their full form are solved numerically through a control volume approach. A simplified model based on a linear perturbation analysis is also developed. We have considered multivalent electrolytes and demonstrated the overscreening of the surface charge and an oscillation in the charge density distribution. Through this study, we have elucidated the impact of several non-linear electrostatic phenomenon such as charge regulation, ion steric interactions, and ion–ion correlations, which has not been addressed in the context of diffusiophoresis.