A description of the physical properties of polymer solutions in terms of irreducible diagrams. (I)

Abstract

Polymer solutions can be conveniently studied in a grand canonical formalism; in this case, the osmotic pressure, the correlations functions and the concentrations of polymers with different lengths, can be expanded in terms of chemical potentials and polymer interactions. It is shown that these expansions can be simplified by expressing the preceding quantities by means of diagrams which are irreducible with respect to the interaction lines. The process applies to monodisperse and to polydisperse polymers. The elimination of short range divergences leads to simple scaling laws