Like likes like: counterion-mediated attraction in macroionic and colloidal interaction.

Area of Science:

• Colloid and Interface Science
• Physical Chemistry
• Statistical Mechanics

Background:

• The Derjaguin-Landau-Verwey-Overbeek (DLVO) theory is the standard model for describing interactions between charged colloidal particles.
• DLVO theory typically predicts only repulsive forces between like-charged particles in electrolyte solutions.
• Existing models often assume the equality of Gibbs free energy and Helmholtz free energy for electrostatic interactions.

Purpose of the Study:

• To investigate colloidal and macroionic interactions within a mean-field approach, particularly for highly charged systems.
• To explain the origin of attractive forces observed in certain charged colloidal and macroionic systems.
• To re-evaluate the applicability and limitations of the DLVO theory for different charge regimes.

Main Methods:

• Experimental observation of bound pairs of latex particles using photography at low particle volume fractions.
• Theoretical analysis using a mean-field approach, incorporating the Fowler-Guggenheim-McQaurrie analysis of Debye-Hückel theory.
• Comparison of electrostatic Helmholtz free energy (F(el)) and Gibbs free energy (G(el)) to understand interparticle potentials.

Main Results:

• Effective pair-potentials show an attractive tail for highly charged colloidal samples, but no attraction for low-charge samples.
• Reversible aggregation of polystyrene sulfonate and DNA strands by multivalent counterions demonstrates this attraction.
• The DLVO theory's prediction of only repulsion is challenged; attraction emerges when G(el) is considered instead of F(el).

Conclusions:

• The assumption G(el) = F(el) in the DLVO theory limits its accuracy to low-charge systems.
• For highly charged macroions and colloidal particles, the electrostatic osmotic pressure (G(el)-F(el))/V is significant and leads to attraction.
• The mean-field approach, when correctly accounting for free energy differences, predicts both short-range repulsion and long-range attraction for like-charged particles.