Classical theory of polymer brushes

We derive from the self-consistent field equations the classical theory of polymer brushes. It results from ignoring, for each position of the polymer end-point, all but the most probable configuration. Results for the brush density profile and polymer end distribution depend sensitively on the square of the ratio of the characteristic brush height to the polymer radius of gyration, β. For finite β, the monomer density exhibits a Gaussian tail and the polymer end-points are stretched. In the limit of infinite β, this classical theory reduces to that of Milner et al. and Zhulina et al.