Critical adsorption of crosslinked polymer blends

The purpose of this paper is a quantitative investigation of the critical adsorption of crosslinked polymer blends in the molten state or in solution. These mixtures are assumed to be in contact with a wall that strongly attracts one connected polymer, at the spinodal temperature, where a microphase separation takes place. This is the so-called critical adsorption. The latter is studied through the composition fluctuation profile. Using an extended de Gennes theory, we find that, at criticality, the equilibrium profile obeys a universal scaling law, which depends only on two kinds of lengths, namely the perpendicular distance from the wall and the mesh size (microdomains size). For critical crosslinked binary polymer mixtures, we show that the composition fluctuation profile is given by: ϕ(z)=(σN/ξ*)f(z/ξ*), where σ is the monomer size, N the common polymerization degree of connected chains, z the perpendicular distance, ξ*∼σn the mesh size (n being the number of monomers of the section of a chain between two neighboring crosslinks), and f(x) a known universal scaling function. For critical crosslinked polymer blends in solution, using the blob model, we show that the composition fluctuation profile, δx(z), is governed by the scaling law: δx(z)=(σNΦ-1/8/ξ^*)f^(z/ξ^*), with the new mesh size ξ^*∼σnΦ-1/8 and the known universal scaling function f^(x). Here, Φ accounts for the overall monomer fraction. Extension of these results, away from the spinodal temperature, is also discussed. Finally, the present work must be considered as a generalized study of the critical adsorption of uncrosslinked polymer blends.