Note: Part one of this three- or four-part series can be found here. Additionally, my topical review paper on SAXS data collection and correction which also lightly discusses data fitting is available open access here. After the initial “scoping out” of a collected scattering pattern, it is time to try to see what can be done in terms of fitting in step 2. Here, we are trying to see if parts of the scattering pattern might be described by some basic scattering functions.
This news has also been covered by Birmingham University, Martin Hollamby and The Schnepp Group, and may appear in other news outlets soon. [update: like at azonano.com, nanowerk.com, the Mumbai mirror, FuelCellsWorks, supergen fuel cells, green car congress and phys.org. update2: Some more selected outlets: Ars Technica, the Conversation, World of Chemicals, Renewables Europe, Hydrogen and Fuel Cell letter (paywalled), and The Himalayan Mirror ] Imagine you could turn pigs into catalysts. You’d think that that would take quite some work, but it turns out to be surprisingly easy as long as you have a good oven and some salts lying around. This has been demonstrated by Zoe Schnepp (of the newly formed Schnepp Group at the U. of Birmingham) in collaboration with Yuanjian Zhang, Martin Hollamby and others during her time here at NIMS, and has just been published here. So what did we do?…
By the way, my topical review paper on SAXS data collection and correction has been published and is available open access here! Recently, some good colleagues (who are not familiar with scattering) have started asking questions on how to go about fitting a scattering pattern. This was a very good opportunity to think about the process from a layman perspective. How do we get from scattering pattern to morphological information in a straightforward way?
This series is part of a set to determine which corrections matter when. We all heard -or read- about corrections Small-angle Scatterers do not need to do, because they are supposedly negligible. Let’s look at some of them and determine if this is really true or not. The first looks at the sample direction-dependent absorption. This is the effect of scattered radiation travelling a slightly different distance through the sample (and therefore experiencing different levels of absorption) depending on the direction of scattering. Take, for example, the simplest case of a sample like a plate or sheet (c.f. Figure 1). From this figure, it can easily be seen that the radiation scattering to an angle has to travel longer through the sample than radiation passing straight through. Therefore, the scattered radiation suffers from more absorption. But how much more? In this document: plate_transmission, with the help of Samuel Tardif, we calculated the exact angle-dependent absorption of a plate-like sample. The short answer, for those who do not want to read the document: The sample absorption indeed accounts for less than a percent of deviation to a scattering angle of 10 degrees (degrees, as this effect is independent of the wavelength), if the sample absorption is lower than 75 % (which is already much more absorption than the max. 30% rule-of-thumb you were told by your senior scatterers). The full diagram is shown in Figure 2 (click to enlarge). So, on the grand scale of things, this correction is indeed negligible for most samples (watch out for the highly absorbing ones though!). However, given its simplicity, it should not be much trouble to implement for sheet-like samples at least. The correction is very straightforward to implement (see document) as you only need to know the transmission factor (which you knew anyway, because you measured it for the background subtraction, right?). This only applies to sheet-like or plate-like samples, the calculation for a capillary is a little bit more complicated. The capillaries also suffer from this, but this plate-like absorption is the maximum correction to apply for capillary geometry (in the direction parallel to the capillary axis). So also for capillaries, implementation is unnecessary unless you are hunting for the final fractions of a percent accuracy. Next time we discuss another one: the polarization correction!
…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…
Do not fret, for I have more software (with documentation!) lined up for presentation on this website soon, but I am still working on the documentation. Please bear with me as I shamelessly promote another publication of mine that came out just days ago. The paper is available here: http://dx.doi.org/10.1016/j.polymer.2010.07.045 It concerns curious observations of oscillations in the scattering pattern from looped single filaments of aramid filaments. As an aside, loading the 12-micron filaments into the microchannel devices is for young eyes only, and even then may be accompanied by expletives. Nevertheless, I am very happy that this is published.