Model-independent X-ray scattering study of a silica sol surface

The structure of the adsorbed layer of alkali ions on the surface of colloidal silica solutions with a particle size of $27$ nm has been studied by reflectometry and diffuse scattering of synchrotron radiation with a photon energy of about $71$ keV. Electron density profiles in the direction perpendicular to the surface have been reconstructed from experimental data and spectra of the correlation function of heights in the surface plane have been obtained. The revealed deviation of the integral and frequency characteristics of the roughness spectra of the silica sol surface from predictions of the capillary-wave theory is of a fundamental character. This deviation is due to the contribution from roughnesses with low spatial frequencies $\nu < 10^{-4}$ nm$^{-1}$ and to the interference of diffuse scattering from different layer interfaces of the surface structure.