Chemo-elasto-electro free energy of non-uniform system in the diffuse interface context

Area of Science:

• Condensed Matter Physics
• Thermodynamics
• Materials Science

Background:

• Accurate free energy formulations are crucial for understanding non-uniform systems.
• Existing models, like Cahn-Hilliard, provide a foundation but may lack comprehensive physical interpretation.
• Modeling interfaces, especially solid-fluid interfaces, presents unique challenges due to scale differences.

Purpose of the Study:

• To develop an alternative, more comprehensive approach for deriving free energy formulations in non-uniform systems.
• To provide a deeper physical interpretation of individual energy contributions (entropy, interaction, internal energy).
• To address limitations in modeling multi-scale systems, particularly solid-fluid interfaces.

Main Methods:

• Reformulation of local composition within interface regions using fundamental calculus.
• Application of classic thermodynamic principles to derive energy density formulations.
• Integration of energy densities to obtain a comprehensive free energy expression.
• Reformulation of wall free energy as a function of average composition for multi-scale systems.

Main Results:

• A comprehensive free energy expression consistent with Cahn-Hilliard but with enhanced physical interpretation.
• Formal expressions for entropy, interaction energy, and internal energy as functions of composition and gradients.
• Derivations of elastic energy and electric potential energy formulations for non-uniform systems.
• A novel approach to wall free energy formulation suitable for multi-scale solid-fluid interfaces.

Conclusions:

• The proposed approach offers a more thorough understanding of free energy construction in non-uniform condensed matter systems.
• The method provides a clearer physical basis for energy contributions compared to previous models.
• The reformulated wall free energy successfully addresses challenges in multi-scale interface modeling.