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Here, real spectra illustrate how to be your own critic when evaluating band-fitted spectra.
It is common for overlapping spectral lines to occur in Raman spectra. To the extent that analytical bands can provide physical or chemical meaning relevant to the material being studied, it becomes necessary to follow these spectral lines separately as sample parameters change. Anyone who has band-fitted spectra knows that the results are fraught with pitfalls. The most common one is to add a spectral component in order to improve the overall fit. The problem with this approach is that there may not be physical or chemical meaning to this extra component. Another problem is that the fits typically are not unique. That is, the final fit may depend on the starting parameters and how well the algorithm converges. In this installment, we will use real spectra to illustrate how one can be his or her own critic in performing this valuable operation.
Analytical Raman spectra provide bonding information for chemical species. As such it can be sensitive to anything that changes the chemical bonding — for example, solvation, pH, temperature, applied stress, and crystallinity. Because the spectra are sensitive to such chemical or physical changes, the spectra can be used to infer how the sample of interest is affected by these environmental parameters. However, when the spectra are complex, there are overlapping bands that make the identification of cause and effect difficult. In principle, band-fitting enables separation of the multiple components, which aids in this task.
The complexity of a vibrational spectrum is determined by the number of degrees of freedom, which, in turn, is directly related to the number of moving atoms. Larger molecules have more degrees of freedom, and therefore more vibrational bands. In a certain sense, polymers offer one of the most challenging systems for band-fitting. The molecules are "infinitely" long, they can orient in particular directions, there can be many conformations — especially around single bonds — and the polymer can be (partially) crystalline. In fact, all of this variability is used to engineer-in particular physical and chemical properties. So vibrational spectra, especially Raman spectra, can be an asset in engineering a material or determining failure mode (especially mechanical failure).
For a model system I will use the spectra of spin-oriented fibers of polyethylene terephthalate that I worked on many years ago as a collaboration with Herman Noether (1), who had retired from Hoechst Celanese. He had a set of fibers that had been spin-oriented from the melt at 1500, 2500, 3500, 4500, and 5500 m/min. In addition, we had samples from this same set of fibers that we had drawn at room temperature (RT, which is below the glass transition temperature, Tg). From birefringence measurements it was known that the orientation in the fibers increased with take-up speed; the birefringence also increased after the RT-draw, with the slowest spun fiber responding the most to the drawing operation. From X-ray diffraction (XRD) it was known that there was crystallinity in only the two most rapidly spun materials. Our goal at the time was to follow the orientation of the molecules in the fibers by recording polarized Raman spectra as a function of take-up speed. In addition to intensity changes, what we found was that changes in band positions of vibrations of the glycol atoms correlated with the increasing orientation which was consistent with the early band assignments (2–5). We also confirmed that the width of the carbonyl band correlated with the degree of crystallinity, which was also consistent with previous studies (6). What we want to show here is how some of the bands' positions or intensities correlate with orientation and therefore enable prediction of the conformation distribution. But because of the complexity of the spectrum, this can only be done by band-fitting the spectra and following the separated bands. Ultimately, this detailed information can be combined with the assignments of Stokr and colleagues (7), thereby aiding in the description of the conformation of the polymer at the molecular level. The goal of this column installment is not to make these detailed assignments; the reader is directed to the more recent literature (8–10).
Spectra of single fibers (<10 µm in diameter) were measured on a Raman microscope. The fibers were taped to a slide with minimum tension. Spectra were measured with the laser and Raman polarization either parallel to the fiber axis or perpendicular to it. The spectra were baseline corrected (using a third order polynomial) and then the bands were manually selected based on knowledge of the spectroscopic behavior of these materials. After the bands were selected, the algorithm in LabSpec Raman spectroscopy software (Horiba) optimized the fit, reporting χ2 and standard error, peak position, peak amplitude, peak width, percent Gaussian in the fit, and integrated area of the bands. These parameters can be exported into an Excel (Microsoft) spreadsheet for further manipulation.
Figure 1 shows the ZZ spectra (laser and Raman polarization parallel to the fiber) between 750 and 1220 cm-1 of these fibers, which is the region of the spectrum that has been shown, for the most part, to be sensitive to the conformation of the bonds of the glycol region. The spectra have been band-fit and stacked to evaluate the changes due to the increasing orientation and possible crystallization. The left part of the figure shows spectra of the as-spun fibers, and the right part of the figure shows spectra of the same fibers after drawing at room temperature. Systematic spectral changes are seen; exporting the band-fit parameters enables correlation of these changes to the polymer behavior in terms of molecular orientation and crystallization. Referring to the literature assignments one can then understand the morphological state of a sample in light of the history of that sample (2–4,7–10).
Figure 1: ZZ band-fitted spectra of PET fibers spin-oriented (from top to bottom) at 5500, 4500, 3500, 2500, and 1500 m/min. The figure on the left shows spectra recorded from as-spun fibers, and the figure on the right shows spectra from fibers that had been subsequently drawn to the break point at room temperature. Each set of spectra was scaled so that the intensity of the band close to 1120 cm-1 was set to the same value. Table I summarizes the observed changes.
What we want to focus on now is the region between 750 and 950 cm-1 . Figure 2 shows the spectra of the fiber spin-oriented at 4500 m/min before and after the room-temperature draw. The reason for focus on this region is that the residual in the fit exhibits systematic evidence for a less than perfect fit. The residuals, shown in red in the bottom two traces of the top of Figure 2, have wiggles that are seen in the other fibers as well (not shown). When additional bands were added to the fits, the residuals, seen in the top of the figure, went flat. The top two traces show the same spectra fit with the additional peaks. The strong peak near 860 cm-1 is now fit by a sharp and a broader band. And near 890 cm-1 a second small, but sharp peak has been added. The overall fit in this region is much improved. As an alternative to this fit, we also tried replacing the two broad peaks near 825 and 886 cm-1 by one very broad band that would span the entire range, but found the fit to be poor, and in fact, the algorithm did not converge to anything reasonable. The bottom figure in Figure 2 shows the second fits expanded to emphasize what is happening to the residual and the small bands. The residual is quite flat (except for the noise) and the "extra" band at 886 cm-1 is diminished in the spectrum of the drawn fiber, which brings us to the next point.
Table I: Changes of the glycol vibrations as a function of sample orientation
Unlike Fourier transform infrared (FT-IR) spectroscopy, which is an absorption technique where the intensity axis has real physical meaning, Raman is a scattering phenomenon, and there can be many, many variables affecting the measured intensities. To evaluate the spectra in Figure 2, we set the intensity at 860 cm-1 the same in the two spectra. But we see that there are two components at 860 cm-1 plus a significant baseline (actually the overlap of the two broad bands), so this operation cannot be rigorously accurate. However, others have observed that the intensity of the band at 796 cm-1 is relatively constant and independent of polarization (5). The ratio of the intensity of the small band at 886 cm-1 to that of the 796 cm-1 band shows that the sharper band at 886 cm-1 is diminished in the drawn sample. This is consistent with the assignment to the gauche conformer, which would tend to convert to trans in the drawing operation. The results of the band-fitting are shown in Table II. The top of the table shows the band-fit parameters using four bands, the bottom using six bands. The differences include extra bands near 860 and 886 cm-1, as seen in Figure 2.
Table II: Band-fitted parameters of spectra of fiber spun at 4500 m/min before and after drawing at room temperature
So why would one go to all this trouble? In this case, the underlying presumption is that the history of the polymer determines its morphology that is, the conformer of the chains in these fibers. By relying on the band assignments, one can say what the melt-spinning and drawing has done to the chains, from which one can account for the physical and chemical properties of the fibers. It is interesting that the best fits seem to require two bands in the region of 860 cm-1 . This band is assigned to a ring stretch. Usually one assumes that because of the rigidity of the aromatic ring, its vibration is not significantly affected by morphology. But these results show that this is not necessarily true. What would be the origin of this is beyond the scope of this column installment. Our purpose is to show the information that potentially can be extracted from these measurements.
Figure 2: Band-fitted spectra of fiber spun at 4500 m/min before and after drawing at room temperature. In the top figure, the spectra from bottom to top represent the as-spun fiber fit to four bands, the drawn fiber fit to four bands, the as-spun fiber fit to six bands, and the drawn fiber fit to six bands. The bottom figure shows the spectra fit to six bands expanded to emphasize the quality of the fits.
Until now we have not directly addressed the issue of how to decide when to introduce additional bands into the band-fitting operation. My colleague, Dr. Sergey Mamedov, has worked extensively with glasses. In these systems, the Raman bands are broad, and the fit of a spectrum could be done with numerous combinations of bands. I have heard him say recently that rational fitting of this type of spectra requires the spectra of a series of related materials to be recorded. One can then follow analogous bands and show that sample variations correlate with band behavior systematically.
Raman spectra of spin-oriented and drawn fibers were band-fitted to illustrate how this spectral treatment can unravel correlations between molecular conformers and sample history. Care must be taken to avoid over-fitting spectra; there should be chemical or physical reasons for introducing bands to improve the overall fit.
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Fran Adar is the Worldwide Raman Applications Manager for Horiba Jobin Yvon (Edison, New Jersey). She can be reached by e-mail at firstname.lastname@example.org.