J. Phys. II France
Volume 2, Numéro 3, March 1992
Page(s) 425 - 451
References of J. Phys. II France 2 425-451
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  16. For a review : Statistical Mechanics of Membranes and Surfaces (Jerusalem Winter School), D. N. Nelson, T. Piran and S. Weinberg Eds. (World Scientific, Singapore, 1989).
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  21. We are doing the calculation for a fixed number of surfactant molecules in the bilayer, in which case there is no surface tension contribution (by the Schulman criterion). See : de Gennes P. G. and Taupin C., J. Phys. Chem. 86 (1982) 2294 [CrossRef]. The result remains true in the presence of thermal fluctuations, as shown by David F. and Leibler S., J. Phys. Ii 1 (1991) 959 [CrossRef]. If the P surface is in chemical equilibrium with surfactant molecules in solution or with micelles, then in principle a chemical potential should be added which would be of the form of a surface tension term. Measurements of the static form factor by X-ray diffraction of the L$_{\alpha}$ phase (ref. [17]) can however only be interpreted if one does not include such a surface tension term. A possible reason is that the equilibration time between micelles and the surfactant layer is so long that for the time scales of scattering probes we are effectively in a constant area ensemble. Since light or X-ray scattering are the main tools for measuring the excitation spectrum, we will restrict ourselves to the constant area ensemble.
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