Bending Energy of Amphiphilic Films at the Nanometer Scale

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The diffuse scattering of x rays by the thermally excited out-of-plane fluctuations of different amphiphilic films was measured for in-plane wavelengths down to the nanometer range, giving access to nontrivial bending effects. The Helfrich Hamiltonian applies on pure water and in the solid phase of an arachidic acid monolayer a large bending rigidity constant was measured. When formed on a subphase containing divalent cadmium ions, the height-height fluctuation spectrum $〈z(q)z(\ensuremath{-}q)〉$ is greatly modified: no longer consistent with a ${q}^{\ensuremath{-}4}$ law at large wavelengths but rather with a ${q}^{\ensuremath{-}3.3\ifmmode\pm\else\textpm\fi{}0.2}$ law, revealing a very different physical mechanism whose origin is discussed.