Polydispersity analysis of scattering data from self-assembled systems

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Abstract
A self-consistent method is proposed to treat the small-angle scattering data from polydispersed self-assembled systems. This method presumes a particle-size distribution to fit the scattering data, then calculates the averaged scattering contrast according to the presumed particle-size distribution. The scattering contrast should be independent of concentration, unless the presumed particle-size distribution function is not appropriate. Therefore performing this analysis as a function of concentration provides a way to self-consistently check the presumed distribution function. This method, although indirect, allows one to select a proper particle-size distribution and evaluate the system polydispersity. Seven commonly used distribution functions are discussed. In addition, the explicit forms of the intraparticle structure factor for these seven size-distribution functions were derived.