The range of validity of scaling and mean field models for polymers at interfaces is discussed. According to a recent analysis by Schaefer, mean field theories describe the properties of polymers in solution correctly over a wider range of concentration and solvency than does scaling. Only for flexible polymers in very good solvents at concentrations below a few percent are scaling methods preferred. In polymer adsorption, high segment densities occur and therefore mean field theories are more appropriate than scaling. The most detailed mean field theory for polymers at interfaces has been proposed by Scheutjens and Fleer. The distribution of segments as a function of ranking number and, consequently, end effects (tails) are taken fully into account. Several results are given for adsorbing and nonadsorbing polymers at a surface and for the effect of polymers on colloidal stability (bridging, steric stabilization and depletion flocculation). In some cases, a comparison with the outcome of other theories is made. Experimental results, available so far, corroborate the main predictions.
Fleer, G. J., Scheutjens, J. M. H. M., & Cohen Stuart, M. A. (1988). Theoretical progress in polymer adsorption, steric stabilization and flocculation. Colloids and Surfaces, 31, 1-29. https://doi.org/10.1016/0166-6622(88)80178-1