Diffuse Interfaces and Small-Angle Scattering Intensity Behaviour

The contributions corresponding to the Porod, the oscillatory O(h^-4) and the Kirste-Porod O(h^-6) terms, present in the asymptotic expansion of the small-angle scattering (SAS) intensities, are numerically evaluated, in the presence of diffuse interfaces generated by different smoothing functions (Gaussian, spherical or Helfand-Tagami). It is shown that SAS experiments are generally unable to distinguish among different profiles, because any smoothing can be made to coincide with another type by scaling its thickness parameter. The oscillatory deviations are observable in the Porod plot of the intensities when the typical distance between parallel diffuse interfaces is greater than 50 Å and the ratio of the thickness to this distance is less than 1/4. The same conclusion applies to the infinite-slit intensities.