Modeling small-angle scattering data of porous and/or bicontinuous structures in n dimensions

Fractal structures are often observed in small-angle scattering experiments where a simple power law q-α describes the scattering intensity over many orders of magnitude. Most theories, however, level off towards lower q in a Guinier scattering that describes a simple maximum size with no specific structure. There is a demand for a scattering model for porous structures with repeated domains of a certain size. This is then observed experimentally as a scattering peak that decays in a power law towards higher q. The starting point for the model presented here is the well known Teubner–Strey theory for bicontinuous microemulsions, which is modified to different dimensionalities to match the desired power law. A combination of several such model functions can describe scattering profiles along multiple length scales, similarly to the well known Beaucage model.