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Analytic density-functional self-consistent-field theory of diblock copolymers near patterned surfaces
Chaok Seok1, Karl F Freed, Igal Szleifer
1Department of Pharmaceutical Chemistry, University of California in San Francisco, San Francisco, California 94143-2240, USA.
The Journal of Chemical Physics
|July 23, 2004
Summary
Analytical solutions reveal diblock copolymer behavior near surfaces. This method efficiently explores parameters, predicting lamellar ordering perpendicular or parallel to patterned surfaces.
Area of Science:
- Polymer Physics
- Materials Science
- Statistical Mechanics
Background:
- Diblock copolymers exhibit complex phase behavior.
- Surface patterning influences copolymer organization.
- Understanding these interactions is crucial for materials design.
Purpose of the Study:
- Develop analytical solutions for copolymer density profiles and free energies near patterned surfaces.
- Provide an efficient method to explore parameter space in copolymer systems.
- Investigate the influence of surface patterns on copolymer ordering.
Main Methods:
- Density-functional self-consistent-field theory with a Gaussian chain model.
- Expansion of chain distribution function around an inhomogeneous reference state.
- Solving a sixth-degree polynomial via a generalized eigenvalue problem.
Main Results:
- Analytical solutions for density profiles and free energies derived.
- Density profiles determined by real and complex roots of a sixth-degree polynomial.
- Lamellar ordering observed near surfaces above the order-disorder transition.
Conclusions:
- The analytical formulation efficiently explores copolymer behavior near surfaces.
- Lamellar orientation (perpendicular/parallel) depends on surface pattern commensurability.
- This approach serves as a valuable approximation for more complex models.