Compression and interpenetration of adsorption-active brushes

Compression and interpenetration of two opposing polymer brushes formed by end-grafted adsorption-active chains are studied by numerical self-consistent field approach and by analytical theory. For sufficiently strong polymer-surface attraction, a fraction of chains in the adsorption-active brush condenses into a near-surface layer, while the remaining ones form the outer brush with reduced effective grafting density. Analysis shows that the normal pressure in {adsorption-active} brushes can be understood in terms of the effective grafting density concept although the pressure at small separations is affected by presence of the dense adsorbed phase. We propose a simple theory modification that accounts for this effect. We also formulate a procedure for extracting the value of the effective grafting density directly from the pressure vs. separation curves {by inverting the equation of state} . In contrast to the normal pressure, the interpenetration of the two opposing {adsorption-active} brushes demonstrates a much more intricate behavior. At weak to moderate compressions, the effective grafting density concept works well but fails spectacularly at small interbrush separations. We identify two interpenetration regimes for {adsorption-active} brushes: i) at separations larger than the ideal Gaussian coil size N1/2, the overlap of the two brushes is concentrated in the mid-plane region, in the same way as in {brushes grafted onto non-attractive surface}; ii) at separations less than N1/2, the brush overlap is strongly enhanced in the wall regions where the attractive interaction plays an important role both in generating the dense layer for the "proper" brush and in attracting the "foreign" chains.