Scaling description of a colloidal particle clothed with polymers

We present a scaling approach to describe an arbitrary polymer layer coating a colloidal particle. Our analysis is based on a description of the layer in terms of loops and tails. Within a simple scaling model for the behavior of the loops and tails, we are able to relate the features of the interface to the "loop density profile" (S) over tilde(n), defined as the number of loops and tail having more than n monomers on the particle. Our theory predicts (as functions of (S) over tilde) the variations of the monomer density inside the layer, the extension, the adsorbance, and the effective free-energy of the polymer coating, for various solvent conditions ("good" solvent, Theta solvent or melt). In all cases, the key parameter which controls the influence of the curvative on the structure of the interface appears to be R/L, where R is the radius of the bare particle and L is the extension that the same layer would have on a flat surface (by same layer, we mean a layer characterized by the same "loop distribution profile" S). As an illustration of our approach, we consider the situation where polymer chains adsorb reversibly on colloidal particles. Both quantitative and qualitative new results are obtained for this problem.