Quantitative analysis of lyotropic lamellar phases SANS patterns in powder oriented samples.

We have developed a detailed numerical method based on the Caillé model to fit Small Angle Neutron Scattering profiles of powder-oriented lyotropic lamellar phases. We thus obtain quantitative values for the Caillé parameter and the smectic penetration length from which we can derive the smectic compression modulus and the membrane mean bending modulus. Our method, applied to a surfactant lamellar phase system decorated by amphiphilic copolymers, provides excellent fits for any intermembrane spacing or membrane concentration over the entire q-range of the SANS experiments. We compare our fits with those obtained from the model of Nallet et al. (J. Phys. II 3, 487 (1993)), which is reviewed. Good fits are obtained with both methods for samples exhibiting "hard" smectic order (sharp Bragg peak, moderate small angle scattering). Only our procedure, however, gives good fits in the case of "soft" smectic order (smooth Bragg peak, strong small angle scattering). A quantitative criterion to discriminate between these "soft" and "hard" samples is also proposed, based on a simple analogy with smectic-A liquid crystal in contact with an undulating solid surface. This allows us to anticipate the type of thermodynamic information that can be derived from the fits.