Effective Electrostatic Interactions in Suspensions of Polyelectrolyte Brush-Coated Colloids

TL;DR

This paper develops a theoretical framework to describe electrostatic interactions between polyelectrolyte brush-coated colloids in electrolyte solutions, providing analytical expressions that can be tuned by core and shell dimensions.

Contribution

It introduces a linear response theory-based model for effective interactions in polyelectrolyte-coated colloids, unifying previous models for star polyelectrolytes and charged colloids.

Findings

Derived analytical expressions for pair interactions and volume energy.

Interactions can be tuned by varying core diameter and brush thickness.

Reduces to known models in limiting cases.

Abstract

Effective electrostatic interactions between colloidal particles, coated with polyelectrolyte brushes and suspended in an electrolyte solvent, are described via linear response theory. The inner cores of the macroions are modeled as hard spheres, the outer brushes as spherical shells of continuously distributed charge, the microions (counterions and salt ions) as point charges, and the solvent as a dielectric continuum. The multi-component mixture of macroions and microions is formally mapped onto an equivalent one-component suspension by integrating out from the partition function the microion degrees of freedom. Applying second-order perturbation theory and a random phase approximation, analytical expressions are derived for the effective pair interaction and a one-body volume energy, which is a natural by-product of the one-component reduction. The combination of an inner core and an outer shell, respectively impenetrable and penetrable to microions, allows the interactions between macroions to be tuned by varying the core diameter and brush thickness. In the limiting cases of vanishing core diameter and vanishing shell thickness, the interactions reduce to those derived previously for star polyelectrolytes and charged colloids, respectively.