Theory of the Grafted Polymer Brush

We calculate the free energy of surfaces coated with grafted polymers in a solvent. We use a self-consistent field (SCF) method appropriate for weak excluded-volume interactions and at moderately high surface coverage. We give the exact solution for the “classical limit” of our SCF equations which shows that, at high molecular weight, the concentration profile approaches a parabolic form rather than the step-function suggested by Alexander and de Gennes. Accordingly, the energy required to slightly compress the brush varies as the cube of the compression distance. An extension of the method to the good-solvent, semidilute regime is described.