Calculation of small-angle scattering from models for surfactant systems

A finite-element method for calculating small-angle X-ray or neutron scattering curves on an absolute scale from arbitrary structural models for surfactant systems is presented. The scattering-length density function is sampled on a cubic lattice, the discrete Fourier transform is applied to the resulting array, aliasing is eliminated by convolution, and the one-dimensional scattering curve I(q) is obtained by averaging over angles. The curves for a single sphere and for dense systems of hard spheres are in good agreement with those obtained by analytic methods. The scattering from a low-water sample from the L₂ phase in the system didodecyldimethylammonium bromide/cyclohexane/water is shown to be incompatible with models of spheres and cubic random cells, but to be consistent with a disordered network of connected spheres and cylinders.