Theory of end-adsorbed polymer brushes in polymeric matrices

Abstract

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 χab, Na/Nb and β, where χab is the Flory interaction parameter characterizing the thermodynamic interaction between the A and B polymers, Na and Nb are the respective degrees of polymerization of the A and B polymers and kBTβ is the net attractive interaction between the adsorbing chain end and the surface. For χab=0, β≫1 and Na/Nb≫1 an asymptotic limit is reached where the brush properties are completely specified by z*/Rbg, where z* is the integrated surface excess of the adsorbing polymer and Rbg 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*/Rbg increases from 0.0 to 1.6. For z*/Rbg>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 2Rbg at z*/Rbg=1.6 to 1.6Rbg at z*/Rbg=3.3. For high values of Na/Nb 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.