Tensioactive properties of semidilute polymer solutions

We present a scaling description of adsorbed polymer layers in the presence of a semidilute solution. Within a very simple model where the layer is tr eated as a thermodynamic ensemble of loops with a large polydispersity in s ize, we are able to (a) describe the influence of the semidilute solution o n the structure of the layer of adsorbed chains, and (b) estimate the varia tion of the surface tension gamma of the solution as a function of the poly merization index of the chains (N) and the monomer volume fraction in the b ulk (Phi(b)). Concerning point a, this work provides a continuous picture f or the variations of the static properties of the interfacial layer from th e. dilute case (Phi(b) --> 0), to the melt case (Phi(b) --> 1). Concerning point b, we find a law gamma(Phi(b), N) of the form (good solvent condition s) gamma(VdW) - A Phi(b)(5/4) + B(Phi(b)(7/8)/N-1/2) In(N/Phi(b)(7/12)N*), where gamma(VdW) accounts for van der Waals interactions and N* is a charac teristic 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 generali zes our recent findings on the case of molten polymer liquid.