Scaling Law for Entropic Effects at Interfaces between Grafted Layers and Polymer Melts

We consider surfaces protected by polymer chains of N monomers grafted at a density σ, that are immersed in a melt of chemically similar chains of polymerization index P . We have used the self-consistent field approximation to analyze the practically useful (but analytically untractable) case of moderately long melt chains and moderately stretched grafted chains. We have confirmed previous analyses of concentration profiles, but we have also arrived at new features by looking in a systematic way at the interaction energy between two grafted surfaces: (i) we have found a general scaling criterion that an entropic attraction between two such surfaces exists if > ( N / P ) 2, which differs from predictions obtained for very stretched brushes; (ii) this work also demonstrates the existence of an attraction for sparsely grafted layers ( < 1) provided that P is large enough. These subtle entropic effects should be of direct consequence for “macroscopic” phenomena such as wetting of protected surfaces and colloidal stabilization.