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Iii) Finally, in the central region (and with the assumption that b is the largest length scale in the problem), D
x b , the proÿle is universal and from Eq. 14) A sketch of the di erent scaling regions in the adsorption proÿle is given in Fig. 18a. Included in this ÿgure are corrections in the proximal region, which is discussed further below. R. Netz, D. Andelman / Physics Reports 380 (2003) 1 – 95 49 with a polymer reservoir of vanishing concentration. It should be emphasized that this limit is not consistent with the assumption of a semi-dilute polymer solution in the bulk.

In a ÿeld-theoretic formalism, the problem of accounting for di erent polymer conformations is converted into a functional integral over di erent monomer-concentration proÿles [15]. Within transfer-matrix techniques, the Markov-chain property of ideal polymers is exploited to re-express the conformational polymer uctuations as a product of matrices [119]. However, there are cases where uctuations in the local monomer concentration become unimportant. Then, the adsorption behavior of a single polymer chain is obtained using simple mean-ÿeld theory arguments.

E ects due to bad solvent [158] and more complex interactions are neglected. One example for the latter are interactions due to the dielectric discontinuity at the substrate surface and to the impenetrability of the substrate for salt ions. 3) and on the surface (as obtained within the Gouy–Chapman theory). Although these e ects are important for highly charged system [159], most of the important features of single PE adsorption already appear on the linearized Debye–Huckel level. Because of the conÿnement in the adsorbed layer, the polymer feels an entropic repulsion.

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