DISCRETE HARMONIC MODEL FOR STACKED MEMBRANES - THEORY AND EXPERIMENT

A discrete harmonic (DH) model has been developed which describes the static structure factor of stacked membranes. The (DH) model was used to analyze a synchrotron small-angle X-ray scattering study in stacked membranes. We studied lyotropic lamellar L(alpha) phase samples in a quaternary mixture consisting of thin water layers coated with surfact ant sodium dodecyl sulfate (SDS) and cosurfactant (pentanol) molecules , separated by oil. The experiments on highly oriented L(alpha) phase samples covered a large interlayer spacing range from d = 49.1 to 255. 8 Angstrom produced by dodecane dilution, which considerably exceeded those of previous high resolution synchrotron scattering studies of po wder samples. Two significant differences emerge between the (DH) mode l and the continuum Caille model description of smectic-A liquid cryst als and multilayer membranes. First, whereas the continuum model is ne cessarily restricted to the vicinity of the Bragg peaks of the structu re factor, the discrete nature of the (DH) model allowed us to fit the experimentally measured X-ray structure factor over the full range of wave-vectors and dilutions. This enabled measurements of the membrane bending and multilayer compressibility elastic constants kappa and B separately, in contrast to the continuum model which gives a reliable measurement of the product kappa B. Second, the (DH) model is able to account for the universally observed anomalously large small angle sca ttering (SAS) in strongly fluctuating dilute fluid multilayer membrane s. The (SAS) is shown to contain contributions both due to concentrati on fluctuations described previously by Forte et al. and Nallet et al. , and unexpectedly from a divergent thermal-coherent diffraction effec t which dominates in single crystal multilayers.