Microphase separation patterns in diblock copolymers on curved surfaces using a nonlocal Cahn-Hilliard equation.

Area of Science:

• Materials Science
• Computational Physics
• Polymer Science

Background:

• Understanding microphase separation in polymers is crucial for designing advanced materials.
• Simulating these phenomena on curved surfaces presents significant computational challenges.
• Diblock copolymers exhibit complex self-assembly behaviors influenced by surface geometry.

Purpose of the Study:

• To develop and validate an efficient numerical method for simulating microphase separation.
• To investigate the influence of surface curvature on diblock copolymer morphology.
• To provide a computational tool for predicting self-assembly patterns on complex geometries.

Main Methods:

• Numerical solution of a nonlocal Cahn-Hilliard equation for diblock copolymers.
• Implicit representation of curved surfaces using a signed distance function and a discrete narrow band grid.
• Application of the closest point method with a pseudo-Neumann boundary condition to simplify the operators.
• Utilizing an unconditionally stable scheme (Eyre's scheme) and Jacobi iteration for efficient computation.

Main Results:

• Successfully implemented a computationally efficient and stable algorithm for simulating microphase separation on curved surfaces.
• Demonstrated the ability to accurately capture microphase separation patterns influenced by surface geometry.
• The method allows for the use of standard finite difference schemes on a minimal grid, enhancing speed and simplicity.

Conclusions:

• The developed numerical approach is effective for studying polymer self-assembly on curved substrates.
• This method offers a fast and simple way to explore microphase separation patterns in diblock copolymers.
• The findings contribute to the predictive modeling of nanostructured materials with tailored morphologies.