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.

• Received 22 August 1991

DOI:https://doi.org/10.1103/PhysRevA.45.2428