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.