Critical Casimir forces between planar and crenellated surfaces

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Surface Science

Background:

• Critical Casimir forces arise from critical fluctuations in confined systems.
• These forces are significant in nanoscopic and colloidal systems.
• Structured substrates introduce geometric complexities to force calculations.

Purpose of the Study:

• To investigate critical Casimir forces between planar walls and crenellated substrates.
• To evaluate the accuracy of the proximity force approximation for structured surfaces.
• To develop a corrected model for more precise force predictions.

Main Methods:

• Utilizing mean-field theory to study critical Casimir forces.
• Considering crenellated surfaces with periodic rectangular crenels and merlons.
• Developing a first-order correction to the proximity force approximation.

Main Results:

• The proximity force approximation overestimates forces due to its pairwise addition formalism.
• Numerically determined forces deviate significantly from the proximity force approximation predictions.
• A step contribution correction accurately models forces from right-angled steps on merlons.

Conclusions:

• The proximity force approximation is insufficient for complex geometries like crenellated surfaces.
• The proposed step contribution correction enhances the accuracy of critical Casimir force calculations.
• This work provides a more refined understanding of Casimir forces in structured environments.