J. Phys. II France
Volume 1, Numéro 9, September 1991
Page(s) 1101 - 1120
DOI: 10.1051/jp2:1991207
J. Phys. II France 1 (1991) 1101-1120

Scaling laws for some physical properties of the L 3 (sponge) phase

G. Porte1, M. Delsanti2, I. Billard2, M. Skouri1, J. Appell1, J. Marignan1 and F. Debeauvais2

1  Groupe de Dynamique des Phases Condensées, USTL - Case 26, 34095 Montpellier Cedex 5, France
2  Laboratoire de Spectrométrie et Imagerie Ultrasonore, Université Louis Pasteur, 4 rue Blaise Pascal, 67070 Strasbourg Cedex, France

(Received 18 March 1991, accepted 10 June 1991)

The swollen lamellar phase L $_{\alpha}$ and the anomalous isotropic phase L 3 (sponge) are presently the only two dilute phases of fluid membranes in amphiphilic systems that have been clearly characterized. We here deal with the L 3 phase. We first recall the scale invariance argument leading to the $\phi^3$ scaling law for the free energy density of phases of fluid membranes. We extend it further in order to derive scaling laws for several static and dynamic physical properties of L 3. The effects of renormalizations of the membrane area and of its elastic constants with scale length scattering, electric birefringence and flow birefringence. The results obtained are puzzling since static quantities exhibit logarithmic corrections due to renormalizations while dynamic ones do not.

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