J. Phys. II France
Volume 3, Numéro 4, April 1993
Page(s) 547 - 555
DOI: 10.1051/jp2:1993150
J. Phys. II France 3 (1993) 547-555

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

Daniel Lhuillier

Université P. et M. Curie, Laboratoire de Modélisation en Mécanique associé au CNRS, Case 162, 4 Place Jussieu, 75252 Paris Cedex 05, France

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

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.

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