Measurement by x-ray diffraction methods of the layer compressional elastic constantBin the lyotropic smectic-A(Lα) phase of the lecithin-water system

A high-resolution synchrotron x-ray study of oriented, supported, hydrated dilauryl phosphatidylcholine in the lyotropic $L_{\alpha }$ (smectic-A or ‘‘fluid’’) phase shows that thermal fluctuations give rise to algebraic decay of positional order in stacking of the bimolecular lamellae, the so-called ‘‘Landau-Peierls’’ state. For planar monocrystalline samples of thickness 10–20 μm, the exponents derived from intensity profiles are in accord with harmonic theory. When combined with previous measurements of the splay elastic constant K in this lyotropic system, the exponents indicate a bulk compressional elastic constant B=(1.9±1.0)×${10}^8$ erg/${\mathrm{cm}}^3$, consistent in magnitude with values measured in thermotropic liquid crystals. Samples of thickness ∼1–2 μm show anomalous behavior in the wings of the longitudinal intensity profiles, but are not in accord with harmonic theory, suggesting that surface effects partially quench the thermal fluctuations. Grandjean terraces on sample surfaces produce striking refractive effects at low Bragg angles.