Particle size distribution: review of “Small-Angle X-ray and Neutron Scattering of Polydisperse Systems: Determination of the Scattering-Particle-Size Distribution”

The determination of the particle size distribution from small-angle scattering curves is usually achieved by assuming a certain statistical size distribution model (f.ex. a Schultz distribution, a Gaussian distribution or a log-normal distribution), and fitting this to the data using a non-linear least-squares optimisation method.

Fitting multimodal distributions then implies the addition of multiple contributions, each with their own set of parameters. This increase in the number of parameters may make the fitting function unstable and the results unreliable.

Retrieval of distribution model-independent size information therefore would be of great benefit to the experimentalist. One problem with this is that the scattering intensity of particles scales with the volume of the particle squared (i.e. for spherical particles with the radius to the sixth power). This then causes information on the small particle sizes to be drowned out by the signal of the larger particles.

A method to retrieve this information is presented in the 1996 paper entitled “Small-Angle X-ray and Neutron Scattering of Polydisperse Systems: Determination of the Scattering-Particle-Size Distribution” (M. Mulato and I. Chambouleyron, J. Appl. Cryst. 1996, 29, 29-36). This paper presents an iterative method for retrieval of this information, and compares it to existing methods such as implemented in the GNOM package. A particularly challenging bimodal size distribution with one mode at 0.5 nm and another at 5 nm reveals that the newly presented model is capable of retrieving this distribution to good agreement.

This then is a very interesting approach to the problem of the determination of polydispersity information from systems of hard spheres. Personally, I will certainly implement this approach. In addition, the paper provides good insight in the challenges associated with scattering problems of a polydisperse nature. Lastly, its clear writing makes it recommended reading material.

All in all, an interesting paper worth reading. I will let you know how it works for me if I can get it implemented.


  1. Were you able to implement this method for your polydispersed system? I am working with micellar assemblies and am interested in using SAXS for size and polydispersity measurements.

  2. Hi Ali,

    If the polydispersity is relatively narrow and you can dilute your sample, it is no problem to use. You do need very good quality data, though.



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