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

We discuss polymer brushes containing a small fraction of minority chains t hat differ from the majority brush-forming chains both in length and in che mical structure. We consider the situation that the solvent is good for bot h types of chain. Furthermore, we assume that the minority chains are longe r than the brush chains and consist of adsorption-active monomers, which th erefore are able to adsorb onto grafting surface. We examine this case by n umerical self-consistent-field calculations fora lattice model and by an an alytical continuum theory. The contour length and the adsorption interactio n parameter of the minority chains are the variables. With the numerical mo del, 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 turn s out to be bimodal. The analytical theory, using a two-state approximation , describes the conformational adsorbed chain-to-flower transition as a fir st-order phase transition (in the appropriate thermodynamic limit). The dep endence of the transition point on the chain length ratio, the grafting den sity 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 graf ting surface in a brush on the transition point is discussed.