DOI: 10.1051/jp2:1995174
J. Phys. II France 5 (1995) 1155-1163

Discrete Harmonic Model for Stacked Membranes: Theory and Experiment

Ning Lei^{1, 2, 3}, C.R. Safinya^{1, 4} and R.F. Bruinsma<sup>4, 5

1</sup>  Materials and Physics Departments and the Interdepartmental Program on Biochemistry and Molecular Biology, University of Califronia, Santa Barbara, CA 93106, USA
²  Physics Department, Rutgers, The State University of New University of New Jersey, New Brunswick, NJ 08903, USA
³  Exxon Research and Engineering Company, Annandale, NJ 08801, USA
⁴  Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106, USA
⁵  Physics Department, University of California, Los Angeles, CA 90024, USA

(Received 16 January 1995, accepted 21 April 1995)

Abstract
The 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 phase samples in a quaternary mixture consisting of thin water layers coated with surfactant sodium dodecyl sulfate (SDS) and cosurfactant (pentanol) molecules, separated by oil. The experiments on highly oriented L phase samples covered a large interlayer spacing range from d=49.1 to 255.8 Å produced by dodecane dilution, which considerably exceeded those of previous high resolution synchrotron scattering studies of powder samples. Two significant differences emerge between the (DH) model and the continuum Caillé model description of smectic-A liquid crystals and multilayer membranes. First, whereas the continuum model is necessarily restricted to the vicinity of the Bragg peaks of the structure 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 compressiblity elastic constants and B separately, in contrast to the continuum model which gives reliable measurement of the product B. Second, the (DH) model is able to account for the universally observed anomalously large small angle scattering (SAS) in strongly fluctuating dilute fluid multilayer membranes. The (SAS) is shown to contain contributions both due to concentration fluctuations described previously by Porte et al. and Nallet et al. and unexpectedly from a divergent thermal-coherent diffraction effect which dominates in single crystal multilayers.

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