The Cahn-Hilliard residuum and its implications for critical-point wetting at solid solution surfaces

Area of Science:

• Materials Science
• Chemical Physics
• Surface Science

Background:

• The Cahn-Hilliard theory (1958) introduced the Laplacian of composition for excess free energy in solids.
• Integration by parts led to the gradient-square form used in phase-field models.
• The residual term from this integration has been largely overlooked.

Purpose of the Study:

• To investigate the implications of the Cahn-Hilliard integration residual in critical-point wetting.
• To compare continuum models with discrete approaches for wetting phenomena.
• To determine the influence of formulation choice on wetting layer behavior.

Main Methods:

• Atomistic Monte Carlo simulations as a benchmark.
• Classical gradient-square continuum model analysis.
• Laplacian-based continuum formulation evaluation.
• Discrete plane-by-plane model using a curvature operator.

Main Results:

• Monte Carlo simulations show continuous wetting layer thickening up to the critical temperature.
• The gradient-square model incorrectly predicts a first-order wetting transition.
• A discrete curvature-based model aligns with simulation results.
• Neglecting the residual term in discrete models also leads to incorrect first-order transitions.

Conclusions:

• The choice between gradient-square and curvature formulations fundamentally alters wetting predictions.
• Curvature-based (Laplacian) models are more accurate for describing wetting layer evolution in solids.
• The Cahn-Hilliard residual is crucial for accurate modeling of critical-point wetting phenomena.