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            <title xml:lang="en">Tensioactive properties of semidilute polymer solutions</title>
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              <p>We present a scaling description of adsorbed polymer layers in presence of a semi-dilute solution. Within a very simple model where the layer is treated as a thermodynamic ensemble of loops with a large polydispersity in size, we are able to a) describe the influence of the semidilute solution on the structure of the layer of adsorbed chains, and b) estimate the variation of the surface tension $\gamma $ of the solution as a function of the polymerization index of the chains (N) and the monomer volume fraction in the bulk ($\Phi_b$). Concerning point a), this work provides a continuous picture for the variations of the static properties of the interfacial layer from the dilute case ($\Phi_b\rightarrow 0$), to the melt case ($\Phi_b\rightarrow 1$). Concerning point b), we find a law $\gamma (\Phi_b,N)$ of the form (good solvent conditions) $\gamma_{VdW}-A\Phi_b^{5/4}+B\Phi_b^{7/8}/N^{1/2}\ln( N/\Phi_b^{7/12}N*)$, where $\gamma _{VdW}$ accounts for Van der Waals interactions and N* is a characteristic index of polymerization of the polymer under consideration (A and B are calculated within numerical coefficients of order unity). This law is in good quantitative agreement with experimental measurements and generalizes our recent findings on the case of molten polymer liquid. (Aubouy, Manghi, Raphaël, to be published in Physical Review Letters).</p>
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