Interplay between Depletion and Electrostatic Interactions in Polyelectrolyte–Nanoparticle Systems

Abstract

We use a numerical implementation of polymer self-consistent field theory to study the effective interactions between two spherical particles in polyelectrolyte solutions. We consider a model in which the particles possess fixed charge density and the polymers contain a prespecified amount of dissociated charges. We quantify the polymer-mediated interactions between the particles as a function of the particle charge, polymer concentrations and particle sizes. We study the interplay between depletion interactions, which arise as a consequence of polymer exclusion from the particle interiors, and the electrostatic forces which result from the presence of charges on the polymers and particles. Our results indicate that for weakly charged and uncharged particles, the polymer-mediated interactions predominantly consist of a short-range attraction and a long-range repulsion. When the particle charge is increased, the interactions become purely repulsive. A longer range, albeit weaker, bridging attraction was also evident for some parametric regimes. We demonstrate that the short-range attraction and the longer-range repulsion can be modeled as a sum of a depletion-like attraction and an electrostatic Debye–Huckel like repulsion. However, the amplitude and range underlying the depletion and electrostatic interactions are shown to possess a complex relationship to the parameters of our system. We present scaling arguments and analytical theory to rationalize some of the dependencies underlying the parameters governing the interaction potentials.