Abstract
Numerical self-consistent field (SCF) theory is used to study the equilibrium segregation of A/B gradient copolymers to the interface between immiscible A and B homopolymers. A generalized SCF theory is developed that allows arbitrary composition gradients to be investigated. The focus of this paper is on symmetric copolymers consisting of equal amounts of A and B repeat units, with a linear or hyperbolic tangent composition gradient. A gradient parameter, λ, is introduced that describes the length of the composition gradient relative to the length of the entire copolymer molecule. Critical values of the copolymer chemical potential corresponding to the formation of copolymer micelles, or to a vanishing interfacial free energy between A and B homopolymer phases, decrease with λ, and are about 1.6kBT lower for λ = 1 than for λ = 0. The width of the concentration profile of A or B repeat units within a lamellar copolymer phase, or across an emulsified interface, increases with λ, and is equal to about twice the copolymer radius of gyration for λ = 1.
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