Effective Electrostatic Interactions in Suspensions of Polyelectrolyte   Brush-Coated Colloids
  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. 
Hao Wang and Alan R. Denton