Oscillatory Interactions between Colloidal Particles in Polyelectrolyte Solutions: Linear Response Theory

An analytical theory for the interaction potential between surfaces (e.g., colloids) in polyelectrolyte solutions is derived. A superposition of a Debye–Hückel interaction potential and a damped oscillatory interaction potential, commonly employed to fit measured colloidal interactions, follows naturally from our theory. Using appropriate expressions for the structure factor of the bulk polyelectrolyte solution in the dilute, semidilute and concentrated regimes explicit expressions for the wavelength and decay length of the oscillatory part of the interaction potential were derived. Quantitative agreement between experimental measurements and our theory is found in the dilute and semidilute concentration regimes. In the concentrated regime, the theory predicts very weak oscillations and a large attractive region due to the electrostatically induced depletion interactions, in agreement with simulations.