The whole discussion of polymer adsorption so far makes the fundamental assumption that the layer is at thermodynamic equilibrium. The relaxation times measured experimentally for polymer adsorption are very long and this equilibrium hypothesis is in many cases not satisfied [29]. The most striking example is the study of desorption: if an adsorbed polymer layer is placed in contact with pure solvent, even after very long times (days) only a small fraction of the chains desorb (roughly 10%); polymer adsorption is thus mostly irreversible. A kinetic theory of polymer adsorption would thus be necessary. A few attempts have been made in this direction but the existing models remain rather rough [30,31].
A simpler approach is to assume that polymer adsorption is an equilibrium process under constraint. In most experiments, the chains cannot diffuse outside the adsorbed
layer and the total adsorbed polymer amount Г is fixed, but the conformation of the chains can equilibrate (at full thermal equilibrium the chemical potential of the chains is fixed by the bulk solution). Even if the adsorbed layer is starved and has a low value of Г, the structure of the layer at constant adsorbed amount is very similar to that at thermal equilibrium; the monomer concentration decays with the same power law. The thickness H of the layer increases with Г.
In certain cases a higher degree of irreversibility is observed. This is the case for the so-called pseudo-brushes where the monomer adsorption on the surface is supposed to be irreversible and where the loop size distribution remains fixed under swelling. A pseudobrush is obtained by placing the adsorbing surface in contact with a molten polymer (or a concentrated semidilute solution). All the chains within one Gaussian radius of gyration R ~ N / a adsorb on the surface and the adsorbance is Г ~ N/ a~ . The adsorption is irreversible and after washing with pure solvent, only the adsorbed chains remain attached to the surface; the adsorbed layer swells in the solvent forming the pseudo-brush. The pseudo-brush is thus equivalent to a polydisperse brush where the irreversibly adsorbed monomers play the role of the anchoring points; the equivalent graft density is a = Г/ N ~ N~1/2a~2. Using the result given earlier for the thickness of a grafted layer (Eq. (1)) the thickness of the brush is H ~ aN5/6. It is again a structure where the chains are highly stretched. A more detailed analysis of the pseudo-brush structure in terms of loop size distribution has been performed by Guiselin [32]. Pseudo-brushes have sometimes been used to coat surfaces in adhesion or friction experiments; they present the great advantage of being easy to make even though their properties are less understood theoretically than those of true brushes [33].