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Simple inversion formula for the small-angle X-ray scattering intensity from polydisperse systems of spheres

2012; Wiley; Volume: 45; Issue: 3 Linguagem: Inglês

10.1107/s0021889812012812

1600-5767

Robert Botet, Bernard Cabane,

Iron oxide chemistry and applications

A practical inversion method to calculate the size distribution of colloidal homogeneous particles from small-angle scattering experiments is presented. It is based on the analysis of the deviations of the scattering signal from the Porod law. The resulting inversion formula provides a reliable way to assess complex size distributions such as power-law, multimodal or very broad distributions. It is particularly suitable for colloidal dispersions that have a substantial fraction of very small particles. These cases correspond to large deviations from the Porod law over a broad range of scattering vector values, q . Shannon's theorem gives a way to obtain the maximum amount of information concerning the size distribution, without requiring an arbitrary extrapolation of the data beyond the available q range. It is demonstrated that this protocol yields a calculated distribution of particle sizes that is stable.