Data analysis

In the past, it has been customary to use a method of “peeling off” information from the scattering patterns, as opposed to an attempt at fitting an entire scattering pattern at once [1,2]. This was customary, partly perhaps because of its methodic clarity, but perhaps also due to the lack of computing power. The latter issue has been lifted off our shoulders by the ever increasing availability of power.

Whilst the complete model fit method is indeed less robust when compared to the sequential analysis method, the complete model fit eliminates potential weighting of the fitting parameters. In other words, if dependent parameters are determined sequentially, the chosen sequence will influence the fitting results (do note that the method is perfectly acceptable for independent parameters).

Therefore, a complete model fit to the entire scattering pattern would be the preferred method as opposed to a sequential determination. Complex samples, however, require either a very good initial guess, or initial fitting parameters from a sequential determination.

As it is, we are dealing with many parameters in these ordered systems, all of which influence the scattering pattern significantly. Personally, I have found Matlab a little lacking in its solving skills in this respect, so the hunt is on for me to find a suitable fitting method.

Additionally, the results that I have seen published so far, are quite light on the statistical details. I myself am quite unfamiliar with the topic myself, but it would be nice to see some statistical information on the model fits with these results. Therefore I hereby personally pledge to include these in any relevant publications.

I am working with dr. K.D. Joensen on SAXS analysis software, well documented and written in Matlab, chosen for its comprehensibility. This will be available shortly, and allows a complete model fit. Statistical data extraction on the fit is mine still to implement.

[1] N. Stribeck. Analysis of saxs fiber patterns by means of projections. In B. S. Hsiao, editor, ACS symposium series, volume 739 of ACS symposium series, pages 41–56. American Chemical Society, 2000.
[2] H. F. Zhang, B. Q. Yang, and Z. S. Mo. Small angle x-ray scattering study of structural parameters of the aggregated state in polyamide 110 + bmi. European Polymer Journal, 32:57–59, 1996.

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