De Gennes self-similar carpet

The concentration in the adsorbed layer decreases away from the surface as (f) (z/b) for exponent 0.588. This power law concentration profile in an adsorbed polymer layer was proposed by de Gennes and is called the de Gennes self-similar carpet. This profile of adsorbed polymer can be described by a set of layers ot correlation blobs with their size of order of their distance to the surface z (see Fig. 5.11). The self-similar concentration profile starts at the adsorption blob ads in the first layer. The self-similar profile ends either at the correlation length of the surrounding solution if it is semidilute or at the chain size Rf bN if the surrounding solution is dilute. 

Consider multichain adsorption in a 0-solvent, of dilute chains with AT monomers of size b, and with monomer surface interaction of 6kT. Calculate the density profile of the de Gennes self-similar carpet. Calculate the thickness ads of the adsorbed layer and the coverage P. 

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