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

Abstract

The larrellar 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 it) its intensity scales linearly with the bilayer volume fraction iii) it is sensitive to the scattering length density profile of the arrphiphilic 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 smecticA symmetry of our systems.The model has two important consequences : I) the form factor of the arrphiphilic bilayer may be extracted from the large wave vector diffuse scattering ; it) 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.Introduction.An interesting variety of structures and behaviours are