Bending Energy of Amphiphilic Films at the Nanometer Scale

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 $〈z\left(q\right)z(-q)〉$ is greatly modified: no longer consistent with a $q^{-4\mathrm{}}$ law at large wavelengths but rather with a $q^{-3.3\mathrm{}\pm 0.2}$ law, revealing a very different physical mechanism whose origin is discussed.