A Geometric Measure Theory Approach to Identify Complex Structural Features on Soft Matter Surfaces

Area of Science:

• Soft Matter Physics
• Materials Science
• Chemical Engineering
• Computational Chemistry

Background:

• Structural features at soft matter interfaces influence chemical reactivity and transport.
• Identifying these structures is challenging due to varied morphologies and interfacial roughness.
• Existing methods lack robustness in detecting complex surface features.

Purpose of the Study:

• To develop a robust algorithm for identifying organized surface structures at soft matter interfaces.
• To rank the likelihood of identified structures being complex features using a probabilistic approach.
• To apply and validate the algorithm on a surfactant-laden water/oil interface.

Main Methods:

• Developed a novel algorithm integrating geometric measure theory, algebraic topology, and optimization.
• Employed a probabilistic framework to assess the significance of candidate surface structures.
• Tested the algorithm on a surfactant-laden water/oil interface, comparing results with visual inspection.

Main Results:

• The algorithm successfully identified candidate structures at the soft matter surface.
• It robustly detected protrusions responsible for water transport at the water/oil interface.
• Results showed strong agreement with structures identified through manual visual inspection.

Conclusions:

• The developed algorithm provides a robust method for identifying complex structural features at soft matter interfaces.
• This represents the first application of geometric measure theory to analyze properties within chemical/materials science systems.
• The findings have implications for understanding and predicting interfacial phenomena, including transport processes.