Electrostatic free energy of interacting ionizable double layers

Area of Science:

• Physical Chemistry
• Colloid Science
• Surface Science

Background:

• Understanding electrostatic interactions is crucial for charge-regulating materials.
• The interaction free energy determines adhesion forces between surfaces or particles.
• Previous models often simplified the complex contributions to electrostatic energy.

Purpose of the Study:

• To present a unified method for calculating the electrostatic contribution to interaction free energy for charge-regulating materials.
• To analyze the components of electrostatic work (electric and chemical) in the diffuse double layer.
• To provide examples for various surface charge types and models.

Main Methods:

• Integration of the diffuse double layer contributions to free energy.
• Summation of surface contributions to free energy over two surfaces.
• Application to diffuse double layer and Stern-Gouy-Chapman models.
• Consideration of ion adsorption effects.

Main Results:

• The electrostatic contribution includes both electric and chemical work.
• Surface contributions were exemplified for acidic, basic, zwitterionic, and amphoteric (1-pK, 2-pK) materials.
• Calculations were performed for diffuse double layer and Stern-Gouy-Chapman models, with and without ion adsorption.
• The interaction free energy at contact is consistently finite for charge-regulating materials.

Conclusions:

• A straightforward calculation method exists for the electrostatic interaction free energy of charge-regulating materials.
• The finite interaction energy at contact has implications for adhesion phenomena.
• The presented approach offers a comprehensive framework for diverse material types and surface models.