Grafted polymers with annealed excluded volume: A model for surfactant association in brushes

The present an analytical self-consistent-held (SCF) theory for a neutral p olymer brush (a layer of long polymer chains end-grafted to a surface) with annealed excluded volume interactions between the monomer units. This mode l mimics the reversible adsorption of solute molecules or aggregates, such as small globular proteins or surfactant micelles, on the grafted chains. T he equilibrium structural properties of the brush (the brush thickness, the monomer density profile, the distribution of the end segments of the graft ed chains) as well as the overall adsorbed amount, and the adsorbate densit y profile are analyzed as a function of the grafting density, the excluded volume parameters and the chemical potential (the concentration) of the ads orbate in the solution. We demonstrate that, when the grafting density is v aried, the overall adsorbed amount always exhibits a maximum, whereas the r oot-mean-square brush thickness either increases monotonically or passes th rough a (local) minimum. At high grafting densities the chains are loaded b y adsorbed aggregates preferentially in the distal region of the brush, whe reas in the region proximal to the grafting surface depletion of aggregates occurs and the polymer brush retains an unperturbed structure. Depending o n the relative strength of the excluded volume interactions between unloade d and loaded monomers both the degree of loading of the chains and the poly mer density profile are either continuous or they exhibit, a discontinuity as a function of the distance from the grafting surface. In the latter case intrinsic phase separation occurs in the brush: the dense phase consists o f unloaded and weakly extended chains and occupies the region proximal to t he surface, whereas a more dilute phase consisting of highly loaded and str ongly extended chains forms the periphery of the brush.