title: Analytic density-functional self-consistent-field theory of diblock copolymers near patterned surfaces.
abstract: Analytical solutions are derived for the density profiles and the free energies of compressible diblock copolymer melts (or incompressible copolymer solutions) near patterned surfaces. The density-functional self-consistent-field theory is employed along with a Gaussian chain model for bonding constraints and a random mixing approximation for nonbonded interactions. An analytical solution is rendered possible by expanding the chain distribution function around an inhomogeneous reference state with a nontrivial analytical solution, by retaining the linear terms, and by requiring consistency with the homopolymer limit. The density profiles are determined by both real and complex roots of a sixth-degree polynomial that may easily be obtained by solving a generalized eigenvalue problem. This analytical formulation enables one to efficiently explore the large nine-dimensional parameter space and can serve as a first approximation to computationally intensive studies with more detailed models. Illustrative computations are provided for uniform and patterned surfaces above the order-disorder transition. The results are consistent with the previous self-consistent-field calculations in that lamellar ordering appears near the surface above the order-disorder transition and the lamella order perpendicular or parallel to the surface depending on the commensurability between the periods of the surface pattern and the density oscillations.
authors.affiliation: Department of Pharmaceutical Chemistry, University of California in San Francisco, San Francisco, California 94143-2240, USA.
authors.forename: Chaok
authors.initials: C
authors.lastname: Seok
authors.forename: Karl F
authors.initials: KF
authors.lastname: Freed
authors.forename: Igal
authors.initials: I
authors.lastname: Szleifer