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(q)z(-q)) is greatly modified: no longer consistent with a q(-1) law at large wavelengths but rather with a q(-3.3+/-0.2) law, revealing a very different physical mechanism whose origin is discussed.