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 ͗z͑q͒z͑2q͒͘ is greatly modified: no longer consistent with a q 24 law at large wavelengths but rather with a q 23.360.2 law, revealing a very different physical mechanism whose origin is discussed. [S0031-9007(97)02940-2]

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