Statistical thermodynamics of polymer layers

According to scaling theory, adsorbed homopolymer layers split up into a proximal, a central and a distal region. This picture is recovered in numerical self-consistent-field (SCF) calculations. Analytical treatments of the loop and tail contributions in various regimes, from dilute to concentrated, are now available. For polymer brushes, full convergence between SCF, scaling, and simulations exists. Brush theory, however, is far ahead of experiments. A recent unified scaling analysis of polymer layers, based upon the loop distribution, captures both adsorbed layers in various conditions as well as polymer brushes with and without adsorption energy and irreversibly bound polymer. This promising approach awaits further examination.