Short description:
Suppose we want to characterise a cross-linked polymer. This is a very important task, since there is a link between the polymer’s physical properties (e.g. viscoelasticity) and its chemical structure (e.g. number of cross-links per mass unit). There are many ways to characterise cross-linked polymers, but solid-state NMR offers the interesting advantage of being able to analyse the intact material.
Without going into the details, with solid-state NMR we are able to distinguish two parts (or sections) of the material: (i) the cross-linked part (the less mobile part of the polymer) and (ii) the non-linked chains (or dangling ends). It happens that both parts of the material show a different relaxation decay in Hahn-echo NMR (basically, the cross-linked part decays faster than the dangling ends). And here comes the complication. It happens that the chemical shift of both parts of the polymer is identical in solid-state NMR. In other words, both contributions to the NMR signal will appear completely overlapped, i.e. exactly at the same position. However, as relaxation decays are different, both parts will have different band broadening (as a consequence of the Heissenberg principle). If we monitor the NMR signals over a short time periods, we will see also that one part of the signal decays faster than the other (although being completely overlapped).
This is a typical case that can be solved with deconvolution. We have a data matrix that shows bilinear properties, and can be explained as linear combination of n profiles in each order of measurement (in our case n=2, since we have two independent parts on the signal, i.e. the cross-linked part and the dangling ends). The complication that we had to solve was that the signals in the NMR domain were appearing exactly at the same chemical shift, showing a severe overlap. We solved the problem using multivariate curve-resolution techniques (more specifically, using alternating least squares: MCR-ALS). We had to apply the technique carefully since the initialisation could be performed by unique profiles in both directions (by finding distinctive exponential decays or distinctive NMR profiles). In fact, we found that four solutions were possible for the MCR-ALS model, depending on the order of measurement were the initial guesses were calcualted, and the order of measurment were the final constrains were imposed. The analysis was quite complicated, but we could solve it and the information about each part of the polymer could be isolated, allowing the characterization of the material. For more information, see ref. [27a].
Credits:
This project was developed at different institutions. Several people were involved. See authors of the publications for more details about authorship.
Sponsors:
Shell, University of Amsterdam, Technical University of Eindhoven.
Presentations:
Not available.
Software:
Not available.
Tags:
- Application domain: Chemicals.
- Instrument domain: NMR
- Statistics domain: Deconvolution, multivariate exploratory analysis.