Adsorption of long polymers dissolved in a semi-dilute solution of shorter chains

The adsorption of dilute long polymers of length N dissolved in a semi-dilute solution of shorter chains of length P is considered using a scaling approach. The short chains themselves are considered as non-adsorbableTwo qualitatively different phase diagrams in the concentration adsorption-strength diagram are predicted depending on the value of N/P~. An overall concentration and chain length controlled adsorption cross-over may be found. An ideal adsorption regime is possible for N < P~. The scaling of the radius of gyration of the adsorbed chains as well as the concentration profile are derived in the various adsorption regimes. The surface concentration effects of the adsorbed long chains are calculated from the condition of chemical equilibrium between the surface and the bulk. The plateau adsorption density~ which may be considered as the maximum amount of adsorbed polymers, may be controlled by the overall bulk concentration of the bimodal system. This provides an easy way to control the polymer surface concentration.