Comments on Deschamps, 2011 and A clarification on Guinier for Polydisperse systems

After browsing through a recent Journal of Applied Crystallography, I came across a paper by Deschamps. It indicates to me that there is a slight lack of information communication in some aspects of SAXS.

Firstly, it mentions in the introduction that the advanced (Fourier-transform-based) SAXS analysis methods cannot “extract simultaneously the precipitate form factor and the precipitate size distribution”. Indeed they cannot, but neither can the classical methods (see for example page 147 of [1]). It is only when we assume a shape of the scatterer in the classical methods, that the number of possible size distributions reduces to a single solution. Inversely, if we assume a size distribution, there is only one general form factor which will match. This leads to the erroneous conclusion that the classical methods can result in a simultaneous determination of size and polydispersity.

 

My main point, however, is the research on the behaviour of the Guinier method in polydisperse systems. I, too, have been looking at this and found out that others have tread this path before me. My results here are in agreement with the results of others that the radius of gyration of the Guinier method in polydisperse systems follows the volume-squared weighted radius of gyration [2]. The limits of applicability shift accordingly.

 

The work by Deschamps on the Porod behaviour in polydisperse systems is to my knowledge unique, but I have not looked in detail into this.

 

[1] O. Glatter and O. Kratky, Small angle X-Ray Scattering, (Academic Press, 1982), available online

[2] G. Beaucage, H. Kammler, and S. Pratsinis, Journal of Applied Crystallography 37, 523 (Jan 2004).

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Notes on Guinier

…well, his famous SAXS analysis method.
This documentGuinier_short, copyright Brian Pauw
gives a short description and review of the applicability of the Guinier method to polydisperse systems.

It also shows, through analysis of simulated data, what q-range should be measured for the Guinier method to be valid. In short, the rule of qmax=1.3/Rg still holds, but Rg in polydisperse systems is the volume-squared weighted Rg of the distribution.

This then implies that the Guinier method for polydisperse systems quickly becomes unusable as the required qmax cannot be reached with anything but USAXS systems for polydisperse samples.

This text (the linked PDF) is released under copyright (copyright by Brian R. Pauw, 2011) as I may want to include some of this in a later publication. I hope you understand…

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