The theta-point and critical point of polymeric fractals : a step beyond Flory approximation

(Received 16 October 1992, accepted in final form 22 December 1992)

Abstract
We propose a new form of free energy for polymeric fractals (chain-like, branched or membranes) based on self-similarity arguments and on the existence of a maximum gyration radius. Results are obtained concerning the size exponents at the theta-point and critical point. These two exponents depend on a single parameter only, for which a simple phenomenological expression is provided. A very good fit is obtained with numerical or experimental results concerning linear and branched polymers. A comparison with the Flory-de Gennes free-energy emphasizes the non mean-field features of the new free-energy.