Theory of end-adsorbed polymer brushes in polymeric matrices

A detailed self-consistent field theory is used to calculate the properties of end-adsorbed polymer chains, or polymer "brushes," in equilibrium with a blend of adsorbing B polymer and nonadsorbing A polymer. The brush properties depend on χ_ab, N_a/N_b and β, where χ_ab is the Flory interaction parameter characterizing the thermodynamic interaction between the A and B polymers, N_a and N _b, are the respective degrees of polymerization of the A and B polymers and k_BTβ is the net attractive interaction between the adsorbing chain end and the surface. For χ_ab=0,β≫1 and N_a/N_b ≫ 1 an asymptotic limit is reached where the brush properties are completely specified by z*/R_g^b, where z* is the integrated surface excess of the adsorbing polymer and R_g^b is its unperturbed radius of gyration. In this strong adsorption, dry brush regime the volume fraction of adsorbing polymer at the surface increases rapidly from 0.0 to 0.96 as z*/R_g^b increases from 0.0 to 1.6. For z*/R_g^b > 1.6 the surface volume fraction of the adsorbing polymer is close to one and the brush profiles are accurately described by a hyperbolic tangent form where the only adjustable parameter is a width parameter describing the interpenetration of the brush and the matrix polymer. This width decreases from 2R_g ^b at z*/R_g^b = 1.6 to 1.6R _g^b at z*/R_g^b=3.3. For high values of N_a/N_b there is an attractive interaction between opposing polymer brushes, or between a single polymer brush and a nonadsorbing surface, which can be attributed to the free energy associated with the distortion of the matrix chains adjacent to the brush. Results are also extended to cases of weak adsorption characterized by low values of β.