Gibbs adsorption equation for planar fluid-fluid interfaces: Invariant formalism

Area of Science:

• Physical Chemistry
• Surface Science
• Thermodynamics

Background:

• The Gibbs adsorption equation (GAE) is a cornerstone in understanding interfacial phenomena.
• Various interpretations exist regarding the location of the dividing surface and adsorbed amounts.
• Clarifying these ambiguities is crucial for accurate thermodynamic analysis of interfaces.

Purpose of the Study:

• To elucidate the fundamental underpinnings of the Gibbs adsorption equation.
• To reconcile zero-volume (Gibbs) and finite-volume (Guggenheim) thermodynamic treatments of surface phases.
• To demonstrate the thermodynamic generality and rigor of the GAE.

Main Methods:

• Comparison of GAE with finite-volume thermodynamic analyses (Guggenheim and Hansen).
• Application of invariant surface properties within the GAE framework.
• Review of GAE applications to electrolytes, electrified interfaces, and surface complexation.

Main Results:

• The GAE yields identical results for both zero-volume and finite-volume surface treatments when invariant surface properties are used.
• The Gibbs phase rule is essential for identifying invariant surface properties.
• The GAE is broadly applicable, including to molecular simulations and interfacial-tension equations of state.

Conclusions:

• The GAE is thermodynamically general and rigorous, irrespective of the chosen surface model.
• Precise definition of invariant adsorbed amounts resolves interpretational ambiguities.
• The GAE provides a unified framework for interfacial thermodynamics.