Modelling X-ray or neutron scattering spectra of lyotropic lamellar phases : interplay between form and structure factors

(Received 4 August 1992, revised 18 December 1992, accepted 6 January 1993)

Abstract
The lamellar phase of two binary systems, AOT/water and DDAB/water, is studied by X-ray or neutron scattering techniques, along dilution lines. We observe on both systems a large wave vector diffuse scattering with the following features : i) its shape is independent of dilution ; ii) its intensity scales linearly with the bilayer volume fraction ; iii) it is sensitive to the scattering length density profile of the amphiphilic bilayer. With the help of a model combining geometry of the bilayers and layer displacement fluctuations, we quantitatively describe our data. This allows us to ascribe the diffuse scattering to the strongly enhanced thermal diffuse scattering which originates in the Landau-Peierls instability characteristic of the smectic A symmetry of our systems. The model has two important consequences : i) the form factor of the amphiphilic bilayer may be extracted from the large wave vector diffuse scattering ; ii) the Bragg peak intensities, modulated by the bilayer form factor, also depend on the amplitude of the thermally-excited elastic waves, i.e. on the magnitude of the elastic constants.