Long minority chains in a polymer brush: A first-order adsorption transition

We discuss polymer brushes containing a small fraction of minority chains that differ from the majority brush-forming chains both in length and in chemical structure. We consider the situation that the solvent is good for both types of chain. Furthermore, we assume that the minority chains are longer than the brush chains and consist of adsorption-active monomers, which therefore are able to adsorb onto grafting surface. We examine this case by numerical self-consistent-field calculations fora lattice model and by an analytical continuum theory. The contour length and the adsorption interaction parameter of the minority chains are the variables. With the numerical model, we show that the minority chains undergo a cooperative transition from an adsorbed state to a flower conformation consisting of a stretched seem and a coiled crown. The end-point distribution for the minority chains turns out to be bimodal. The analytical theory, using a two-state approximation, describes the conformational adsorbed chain-to-flower transition as a first-order phase transition (in the appropriate thermodynamic limit). The dependence of the transition point on the chain length ratio, the grafting density of the brush chains, and the adsorption energy of the minority chains is analyzed in some detail. The influence of a depletion zone near the grafting surface in a brush on the transition point is discussed.