When, why, and how does like like like?: Electrostatic attraction between similarly charged species

Area of Science:

• Colloid and Surface Science
• Physical Chemistry
• Statistical Mechanics

Background:

• The established Derjaguin-Landau-Verwey-Overbeek (DLVO) framework posits purely repulsive colloidal interactions between similarly charged particles.
• DLVO theory assumes electrostatic Helmholtz free energy equals electrostatic Gibbs free energy (ΔG(el) = ΔF(el)).

Purpose of the Study:

• To re-evaluate the assumptions within the DLVO framework regarding colloidal interactions.
• To investigate the implications of statistical-thermodynamic differences between ΔF(el) and ΔG(el) for charged macroions.
• To address and correct criticisms of Sogami's theory on colloidal attraction.

Main Methods:

• Statistical-thermodynamic analysis of electrostatic free energies (ΔF(el) vs. ΔG(el)).
• Mean-field theoretical approach.
• Critical review of existing theoretical critiques (e.g., Overbeek's critique of Sogami theory).

Main Results:

• Electrostatic free energies ΔF(el) and ΔG(el) are generally not equal for ionic solutions.
• The difference (ΔG(el) - ΔF(el)) increases with ion charge number, becoming significant for highly charged macroions.
• Sogami's theory, which predicts attraction at the ΔG(el) level, is validated; Overbeek's critique is refuted.
• Colloidal attraction is confirmed to exist for both multi-valent and mono-valent counterions.

Conclusions:

• The DLVO framework's assumption of ΔG(el) = ΔF(el) is incorrect, leading to an incomplete understanding of colloidal forces.
• A more nuanced view of colloidal interactions, including attraction, is necessary, extending beyond the traditional DLVO model.
• The findings necessitate a revision of theories relying on the equality of these free energy terms, including Debye-Hückel theory.