  In a previous article [E.M. Blokhuis, K.I. Skau, and J.B. Avalos, J. Chem.
Phys. 119, 3483 (2003)], a self-consistent field formalism was derived for
weakly adsorbing polymers, valid for any chain length. It was shown that the
presence of a solid wall induces an ordering of the polymers on the scale of
the radius of gyration far away from the surface (the distal region). These
oscillations in the polymer concentration profile were first noted in work by
Semenov et al., and later observed in numerical solutions of the Scheutjens and
Fleer self-consistent field model. In the present paper, we compare the weak
adsorption model in more detail with the numerical results from the Scheutjens
and Fleer model. Quantitative agreement is obtained for the polymer segment
density profile in a good (athermal) solvent. For theta solvent and poor
solvent conditions, it is necessary to extend the weak adsorption model to take
the non-local character of the polymer-solvent interaction into account. Again,
quantitative agreement is obtained for the polymer segment density profile, in
particular for the transition from an oscillatory decaying profile to a
monotonically decaying profile when the bulk polymer density is below a certain
threshold value.
