End-Adsorbed Polymer Brushes in High- and Low-Molecular-Weight Matrices

Numerical self-consistent-field theory (Scheutjens−Fleer theory) is used to describe the crossover from “dry” brush behavior, where the matrix from which the polymers adsorb is itself a high-molecular-weight polymer, to “wet” brush behavior, where the matrix is a small-molecule solvent. The free energy, f*, required to add an additional chain to an existing brush is calculated for different values of N_a, N_b, χ, and z*, where N_b and N_a are the respective degrees of polymerization of the adsorbing and nonadsorbing molecules, χ is the Flory interaction parameter between different segment types, and z* is the integrated volume fraction of adsorbing chains. In situations where the adsorbing and nonadsorbing molecules have the same statistical segment length, f* is completely specified by N_b/N_a, χN_a, and z*/R_g, where R_g is the unperturbed radius of gyration of the adsorbing molecules. For a large range of these parameters, results for f*, and the closely related adsorption isotherms, are in good agreement with analytic predictions from a simple scaling argument.