The Gibbs-Duhem type relation for ionic/nonionic mixed micelles--an alternative approach to Hall's method

Area of Science:

• Physical Chemistry
• Colloid Science
• Surfactant Science

Background:

• Understanding the thermodynamics of mixed micelles is crucial for various applications.
• Existing models, like D.G. Hall's Donnan equilibrium approach, provide a basis for analysis.
• A simpler, unambiguous method is needed for practical applications.

Purpose of the Study:

• To develop a simplified micellar Gibbs-Duhem relation for two-component ionic/nonionic mixed micelles.
• To express the relation in terms of the apparent bound amount to micelles.
• To compare the new approach with existing theories.

Main Methods:

• Formulation of the micellar Gibbs-Duhem relation.
• Consideration of uni-univalent electrolytes with a common counterion.
• Comparison with D.G. Hall's Donnan equilibrium theory.

Main Results:

• A simplified and unambiguous micellar Gibbs-Duhem relation was derived.
• The relation is expressed using the apparent bound amount to micelles.
• The new approach yields results nearly identical to Hall's theory.

Conclusions:

• The presented micellar Gibbs-Duhem relation offers a simpler and unambiguous method for analyzing mixed micellar systems.
• The model is applicable to systems with ionic surfactants, nonionic surfactants, and salts.
• The findings support the validity and utility of the new thermodynamic approach.