Fran Adar

In our previous column we discussed the application of two-dimensional correlation spectroscopy (2D COS) to the temperature-dependent, polarized Raman spectra of polyethylene terephthalate (PET) fibers to get some insight into the conformational changes that occur as the material’s morphology is changing. As indicated at the time, we are now going to show spectra that include the very low frequency region (the so called “terahertz” range) where it is believed that the real indicators for crystallinity appear. By applying the interpretation rules of 2D COS, we can determine the sequence of changes that occur as the polymer is crystallizing.

	After a discussion with Professor Noda, and under his recommendation, we decided this time to examine the temperature dependent behavior of amorphous, nonoriented polyethylene terephthalate (PET), because when looking at fibers it becomes difficult to disentangle the effects of orientation from crystallization. We prepared a fully amorphous bit of PET by melting a pellet in a nonstick frying pan and quenching it in ice water. The rapid solidification of the material prevents crystallization that can only occur on a longer timescale.

	Figure 1 shows the spectra of the amorphous material after the rapid quench, and "crystalline" material after a slow cool. Note that polymers are almost never 100% crystalline, and PET is never seen to be much more than 50% crystalline. A comparison of these spectra reminds us which bands are robust indicators of changes that have been associated with crystallinity. In these spectra, however, we also see the low-frequency contributions. In the low-frequency region, shown in Figure 2, there are several spectral features. There is the strict Rayleigh scattering caused by "particles" much smaller than the laser wavelength; the spectral width does not change, but the scattering is so intense as to overwhelm the detector under the conditions that we used. Then there is "quasi-elastic" scattering that is centered around the laser wavelength but broadened by interactions with the material sample. In amorphous material there can also be scattering by acoustic phonons, but in crystalline solids that scattering is forbidden by the selection rule based on conservation of momentum in an ordered material. In amorphous materials, where order is lacking, scattering by acoustic modes is possible. This band, called the 

, is broad because the intensity at each wavenumber shift corresponds to the density of vibrational states at that energy; in fact, if one needs to determine the "true" boson peak, the spectrum has to be divided by the Bose factor (n(ω) + 1). There is also the possibility of a longitudinal acoustic mode (LAM), which is also an acoustic mode but is described as an accordion-like motion in crystalline lamellae of polymers. Actually, I have not seen any reports of LAM modes in PET, and enquiries of Neil Everall and John Chalmers confirmed this. Other possibilities for low-frequency scattering include both rotational and translational motion of the chains (1), but in the case of PET, there cannot be translational phonons because there is only one chain per unit cell (2).

Raman Spectra of Amorphous and Crystalline PET

	The spectra shown in Figures 1–5 are displayed several ways. Initially the full spectra (-300 to 1800 cm

) are displayed; note that the bands in the low-frequency region and the bands between 950 and 1200 cm

 have been band fit because these bands have been shown to reflect the molecular configurations that are consistent with the crystalline state. The second display shows the low-frequency region, and the remaining displays show the fingerprint region with varying enlargements to enhance the understanding of the changes. I have displayed the spectra this way because the low-frequency region is so intense that not much else can be seen easily in the full display.


	Figure 1: Raman spectra of amorphous, nonoriented sample of PET (top) versus crystalline nonoriented material (bottom). 

	The focus of this column is to determine if, and how well, two-dimensional correlation (2D COS) Raman spectroscopy can provide these details without going to the effort of band-fitting, whose results are known to be non-unique in many cases.


	Figure 2: Low-frequency, Stokes–anti-Stokes Raman spectra of nonoriented amorphous (top) and nonoriented crystalline (bottom) PET. 

	The rigorous definition of crystallinity is uniform packing with translational symmetry. For polymers this requires uniform conformation of the chains. Relying on the discussion in the textbook by Bower and Maddams (3), who cite Zerbi, Ciampelli, and Zamboni's definitions for regularity peaks, we can begin to differentiate different morphological states. Zerbi and colleagues define three types of regularity peaks: peaks assigned to conformational regularity (that is, trans versus gauche rotational isomerism) that can occur in both the solid and melt or solution but with varying relative intensities; the misnamed "crystallinity" peaks arising from long stereoregular chains; and then true crystallinity peaks that directly reflect interchain interactions. Although specific peaks in the spectra of polymers have been well correlated with crystallinity (such as by correlating with density), if one does not understand the true nature of the vibration represented by a particular spectral band, the correlation may yield misleading results under some circumstances. Specifically in the case of PET, the carbonyl (>C=O) peak has been correlated with crystallinity following the 1972 article by Melveger (4). However, even Melveger stated that "the assumption of constant amorphous density in oriented samples may not be valid," which he knew would invalidate his method; in fact, the oriented, amorphous (mesomorphic) polymer would have different density than a randomly oriented amorphous sample.


	Figure 3: Fingerprint and aromatic–carbonyl regions of the Raman spectra of nonoriented amorphous (top) and crystalline (bottom) PET. The regions where bands have been associated with morphological changes have been band-fit and the following two figures will show the results of band-fitting more clearly. 

	I will be citing band assignments from the literature that have been helpful in characterizing PET morphology. However, to extract the maximum of information, one needs to fit the bands in the spectra (which itself is an operation that does not always yield unique results). The hope is that similar information can be extracted using 2D COS with much less work, and in addition, that the possibility for introducing artifacts from band-fitting will be avoided. Another important advantage is that bands that do not separate spectrally may separate in the 2D COS plots.


	Figure 4: Fingerprint region of the Raman spectra of nonoriented amorphous (top) and crystalline (bottom) PET. The regions where bands have been associated with morphological changes have been band-fit.

Spectral Interpretations and What to Look for in 2D COS

	I know of only two publications showing spectra of the low-frequency behavior of PET in the literature (1,5). Bulkin and colleagues (1) note that the normal mode analysis by Boerio and colleagues (6), predicts B

 that are derived from a twisting motion between the carbonyl carbon and the aromatic ring, and twisting about the same carbonyl carbon and the ester oxygen atom. In fact, the Boerio publication also predicts a third mode at 35 cm

 composed of a third combination of the same twisting motions. The spectra in Figure 2 clearly show that bands close to these values only occur in the crystalline state, presumably because the variety of conformations in the amorphous state would wash out any defined peak. (The lowest frequency band is less obvious in the original spectra, but I added it to the fit to improve the result-before I noticed the third low-frequency band in Boerio and colleagues original Table VIII [6]!)

	Now we want to examine more carefully the assignments of the "crystalline" sensitive bands in the fingerprint and carbonyl region to determine if 2D COS can tell us the order in which the conformations change, relative to the low-frequency bands, and how that impacts crystallization. However, we need to remember that the low-frequency bands do not directly reflect packing order (which is impossible in PET because there is only one chain in the unit cell), but still may be informative. Because the low-frequency "crystalline" bands that we are seeing presumably reflect the twisting motions determined by Boerio and colleagues (6), we may be able to argue that it is only when the chain is highly ordered that these bands will emerge from the quasi-elastic scattering.

	Inspection of the bands in the fingerprint/carbonyl region indicates that the biggest "crystallization"-sensitive change is the growth and sharpening of the central carbonyl band near 1725 cm

 (Figure 5). There is actually much in the literature describing these changes. The carbonyl band can be fit by three components (7) (1716 and 1735 cm

, which sharpens in the crystalline phase).


	Figure 5: Raman spectrum in the region of the aromatic and carbonyl bands of nonoriented amorphous (top) and crystalline (bottom) PET, enlarged to provide better detail of the fitted bands, in particular the ones that have been associated with changes in morphology. 

	Possibly of more interest are the bands that reflect gauche to trans conformational changes because the crystalline regions require the trans conformation. Until recently, I believed that this was based on "reasonableness," but in fact I found a publication in which 2D nuclear magnetic resonance (NMR) data were able to quantify the amounts of trans and gauche conformers and confirm that the crystalline form requires the trans conformation (8).

	The bulk of the publications on Raman spectra of oriented PET (fibers and films) document the ability to measure orientation (by controlling polarization conditions) and gauche-trans transconformers by relying on normal mode analysis and changes that parallel the development of orientation, which require the trans conformation (7,9–13). The bands that have been recognized as gauche conformers (which will put kinks into the polymer chain in amorphous regions) are at 886 and 1030 cm

 (9). Bands indicating the trans conformer are at 998 and 1096 cm

 and C-C stretching of the glycol unit, and the 1096 cm

 band has been assigned to a combination of the C-O stretch, the C-O-C bend, the C-C-O bend, and the C-C stretch (all motions also in the glycol unit). Both the 998 and 1096 cm

 bands are markers for the crystalline conformation. The amorphous material has a broad band centered near 1120 cm

 from which the "crystal" contributions grow. I put "crystal" in quotes because we are trying to separate crystal effects from conformational effects, and the normal mode calculations were presumably done for the crystalline conformation known from X-ray diffraction (XRD).

	The band-fit in the fingerprint region in Figure 4 allows one to follow the behavior of the bands identified as reflecting the trans versus gauche conformations. We confirm that the band at 886 cm

 drops in intensity in the crystalline form, while the band at 995 cm

 we see the growth of the trans band at 1096 cm

 as well as other smaller features (such as a shoulder at 1080 cm

), some of which have been noticed by other workers (10). It would take a lot of work to sort out all of these small features using calculations, but by inspecting the 2D COS plots, we hope to see what is systematic, and even separate features that do not resolve spectrally because they are too close together. The plots that we will show were produced by 2D Shige (14) software available on the internet.

	2D COS software produces two two-dimensional plots of a set of spectra generated systematically by changing a variable that affects the spectrum. The two axes correspond to the wavelength (or wavenumber shift for Raman) that is spanned by the data. The synchronous plots, Φ(

) indicate which bands change simultaneously; note that simultaneous may mean in the same direction or in opposite directions. To be more explicit, if one species is converting to a second, the bands of the first species will decrease as the bands of the second increase. This change will be shown as two different colors in the 2D COS Φ(

), are a bit more difficult to understand, but can provide more information because they correlate sequential changes and responses from different origins. The asynchronous plot, 

). If the two have the same sign, then the change occurs at 

. If they have different signs, then the change occurs at 

. In our case, we want to see if we can determine the order in which the changes occur in the glycol region, the carbonyl group, and the very low frequency region.

	Figure 6 shows both the synchronous and the asynchronous plots for the full spectra of the melt-quenched sample which were measured as a function of temperature between room temperature and just above the melt, and then again at room temperature after a slow cool that presumably yields a crystalline material. The intensities in red versus blue indicate that the output of the 2D COS calculation produces opposite signs at these points. To see more clearly what is in these plots, they will be enlarged in the regions of interest.


	Figure 6: 2D COS of an amorphous sample that was followed as the temperature was raised from room temperature beyond T

 (~90 °C), to the melt at ~230 °C and then again at room temperature after a slow cool which enables the material to crystallize. Because of detector saturation in the Rayleigh line at 0 cm

	Figure 7 shows the 2D COS plots between 700 and 1200 cm

 on the other axis because these spectra indicate how changes in the conformation of the glycol are related to the changes in the carbonyl region. Then Figure 10 shows slices of the 2D COS plots with almost the full spectrum along 

). Having normalized all spectra to the peak intensity of the aromatic band at 1614 cm

 (the most constant feature in the spectrum) we can look at the spectra and say, for example, that the 1120 cm

 band does not change very much but the 1096 cm

 band grows as the material is converted to the trans conformation as the temperature is raised above 

. In fact, the asynchronous plot does show these bands changing sequentially.


	Figure 7: (a) Synchronous (left) versus asynchronous (right) in the region of the glycol bands where changes associated with "crystallization" are known to occur. (b) Synchronous (left) versus asynchronous (right) in the region of the glycol bands at 1000 cm

 where changes associated with "crystallization" are known to occur. 

	To see this change more clearly, first look at Figure 7, which shows the 2D COS plots in the region of the glycol bands. On the synchronous plot on the left we can see clearly the gain in intensity (red color) of the band at 1096 cm

 but the increase in intensity of the band at 1000 cm

 is less clear. That only really shows up in Figure 7b where the region around 1000 cm

is expanded. Now, when examining the horizontal axis close to 1000 cm

 we can see a faint blue area centered at 

, which is the band that is replaced by the 1000 cm

 band in the oriented or crystalline form. In the asynchronous plot we confirm that the band near 1000 cm

	In Figure 8, we can examine the carbonyl region in the same way. In the synchronous plot we can see the strong increase in the band at 1725 cm

 that is known to increase in the crystal form. In addition, we see that the band near 1720 cm

 is much less affected than the band at 1725 cm

 is curiously increasing with the 1725 cm

 band. We can start to suggest assignments to the components in the carbonyl region. Note that there are two carbonyl groups on each aromatic group that presumably can interact. In the crystalline form, where there is a center of symmetry, when they move in sync the mode will be Raman active, but when they move out of phase, the motion will be infrared (IR) active only. But in the amorphous material, there is no center of symmetry so the selection rule is no longer valid. Presumably both modes of motion will be active in the Raman spectrum-accounting for the two broad bands near 1720 and 1735 cm

, and my guess is that the band at 1720 cm

 would be the asymmetric (more IR active) mode, which is consistent to the assignment of the overtone of the carbonyl band in the IR spectrum at 3433 cm


	Figure 8: Synchronous (left) versus asynchronous (right) in the region of the aromatic ring and carbonyl bands where sharpening of the carbonyl is known to be associated with "crystallization."

	Now we want to look at the relationships between the bands of the glycol group and the carbonyl. Figure 9 shows the 2D COS map for 700 to 1200 cm

 (aromatic and carbonyl bands). Let's look at the 

. There are positive bands just under 1000 cm

. However, there are negative bands centered at about 875, 1030, and 1120 cm

. These are bands that we know have decreased intensity in the "crystalline" form when the 1725 cm

 carbonyl band grows. There are also two lobes between 1175 and 1200 cm

 that represent a band shift in the crystalline form, something that we haven't focused on in this discussion. But clearly one is going up as the other is going down-an observation consistent with some of the amorphous material being consumed by the crystalline transformation. Note that the vertical axis just above 1600 cm

 also confirms the presence of a second band in the aromatic region that we had to consistently use in the band fitting; the two components clearly separate even though the lower energy part only appeared as an asymmetry in the spectral traces.


	Figure 9: Synchronous (left) versus asynchronous (right) 2D COS in the heteroregion, crossing the glycol behavior with the carbonyl behavior. 

	Finally, we look at the relationship between the low-frequency spectrum and the fingerprint or aromatic-carbonyl region that is shown in Figure 10. Actually, looking for the relationship between a low-frequency crystalline band (such as the rotation at 78 cm

) and the higher-frequency vibrations is not so straightforward. Perhaps one can examine the bands representing combinations of C-C and C-O stretches (700–1150 cm

) in comparison to the low-frequency twists, but in discussing these results with Professor Noda, we realized that there was a problem with the experimental design for the low-frequency data. Because the spectral intensity is modulated by the Bose factor (which is a function of the spectral shift and the temperature), and that factor will be quite important in the low-frequency region, any comparison of low-frequency spectra recorded at different temperatures will have significant systematic errors. So, to achieve our goal of determining the relationship between atomic motions and crystallinity, we now realize that we have to make a different set of measurements. The next set of measurements will be an isothermal crystallization because under these conditions the Bose factor will not change from spectrum to spectrum. Stay tuned for a future installment on this topic.


	Figure 10: Synchronous (left) versus asynchronous (right) 2D COS in the heteroregion, crossing the full spectrum with the low-frequency behavior.

	The novice studying polymer behavior can be overwhelmed by the concepts and nomenclature that are presented. A polymer can be "crystalline," but the nature of the crystallinity will be different than for other solids based on smaller molecular species. The point to be recognized is that because the length dimension of the chain is so much larger than its lateral dimensions there is the certainty that there will be chain "entanglements." Presumably, these chain entanglements are what affects the limitations preventing 100% crystallization. Once the chains are entangled, it is highly unlikely that they will magically untangle and align. Models of partially crystalline polymers describe regions where the chains do line up, but there may be limited lengths of a given chain that will reside in crystalline regions, while the rest of the same chain will be in amorphous regions. Then if the material is "drawn," which means stretched out, parts of chains can likewise be lined up, and the entangled parts will remain in amorphous disordered regions. What we found many years ago (16) in our PET fibers that had been drawn at room temperature was that they aligned, without crystallizing because the treatment was done well below 

 (~90 °C). And we also found that the fiber that originally had the least amount of orientation and crystallinity from manufacture was the one that could be drawn and oriented the most.

	Because of the structural use of polymers, it is important to understand the origin of their strength, elongation to break, elasticity, flexibility, and so on. Clearly, only knowing the amount of crystalline versus amorphous material will not tell the entire story. And that is where spectroscopy can help. Unlike XRD which can only characterize the crystalline phase, spectroscopy has the capability to analyze the amorphous phase as well, including its degree of orientation and the conformation of some important functional groups. Note that it will not be possible to orient entangled material, but the entangled material may increase strength against breakage. By drawing the molecular chains, the material is predisposed to crystallization. Thus, it becomes clear why spectroscopy, in combination with other physical measurements, can be critical in predicting a material's behavior, based on its history.

	So, I haven't yet gotten the result that I am after-that is, to determine details of the crystallization process in polyethylene terephthalate. Stay tuned. This determination will require another set of measurements. My apologies to the purists of my readers who feel that an unfinished project is not worthy of publication. Remember that my goal here is to indicate what this technology can offer, so showing the entire process in painful detail may be helpful to some.

	My sincerest thanks to Professor Isao Noda for encouraging me in this work and making extremely useful critical comments. I should also indicate how sad I am that Herman Noether, with whom I originally worked on these polymers, is no longer with us to see how useful this technology can be to his polymer physics.

	(1) F.J. Deblase, M.L. McKelvy, M. Lewin, and B.J. Bulkin,

	(2) R. deDaubeny, C.W. Bunn, and C.J. Brown, 

	(3) D.I. Bower and W.F. Maddams, in the 

, E.A. Davis and I.M. Ward, Eds. (Cambridge U. Press, UK, 1992).

	(5) T. Achibat, A. Boukenter, E. Duval, G. Lorentz, and S. Etienne,

	(6) F.J. Boerio, S.K. Bahl, and G.E. McGraw, 

	(7) F. Adar, D. Armellino, and H. Noether, "Raman Microprobe Spectroscopy of Polyethylene Terephthalate Fibers: Separation by Band-Fitting of Amorphous-Oriented and Crystalline Components," 

SPIE 1336 Raman and Luminescence Spectroscopies in Technology II,

	(8) K. Schmidt-Rohr, W. Hu, and Z. Zumbulyadis, 

	(9) F. Adar and H. Noether, "Use of Band-Fitted Raman Spectra for the Characterization of Polymers and Measurement of the Oriented Amorphous Phase," 

SPIE 1636 Applied Spectroscopy in Materials Science

	(10) J.C. Rodriguez-Cabello, L. Quintanilla, and J.M. Pastor, 

	(11) C.C.C. Lesko, J.F. Rabolt, R.M. Ikeda, B. Chase, and A. Kennedy, 

	(13) M. Richard-Lacroix and C. Pellerin, 

	(14) 2DShige, developed by Prof. Shigeaki Morita (Osaka Electro-Communication University, Japan). Available at: 

https://sites.google.com/site/shigemorita/home/2dshige

	(15) G. Dandiliooti, G.K. Govaris, and V.G. Gregoriou, 

	(16) F. Adar and H. Noether, "Use of Band-Fitted Raman Spectra for the Physical Characterization of Polymers and Measurement of the Oriented Amorphous Phase," 

SPIE 1636 Applied Spectroscopy in Materials Science II,

 is the Principal Raman Applications Scientist for Horiba Scientific in Edison, New Jersey. Direct correspondence to: 

Articles

Because of the structural use of polymers, it is important to understand the origin of their strength, elongation to break, elasticity, flexibility, and so on. It is in the very low frequency region (the so called “terahertz” range) where it is believed that the real indicators for crystallinity appear.

2D COS of Temperature-Dependent Raman Spectra of Amorphous, Nonoriented Polyethylene Terephthalate to Separate Molecular Conformational Changes from True Crystallization

Two-dimensional correlation spectroscopy (2D COS) is a well-developed technique for treating vibrational spectra, but it has not been extensively applied until now. The temperature-dependent spectra of polyester fibers that I showed recently have been subjected to 2D COS analysis. The results show that features that are not spectroscopically resolvable can be separated in the 2D COS analysis, and they also show the sequence of changes in the spectra. Ultimately, this characteristic enables teasing out of the structural changes occurring in the polyester molecules in the fibers as they are annealed under tension.

	I am yet again going to use the spectra of fibers of polyethylene terephthalate (PET) to illustrate a new method to tease out the chemical or structural information from Raman spectra. As I said in my previous column on PET fibers (1), this material is used as an example to illustrate what information can be extracted from the spectra because we already understand a lot about what is happening. In this case, I am going to consider again the spectra of a fiber under tension that was exposed to temperatures approaching 

, the glass transition temperature. In a previous installment (1), we showed that we could see spectral changes associated with conformational changes such as the gauche to trans conformational change in the glycol units, and the sharpening of the carbonyl band, which has often been associated with crystallization. What we will see here is a better separation of these phenomena, and more importantly the sequence at which they occurred. All of this is based on the methodology developed by Professor Isao Noda when he was characterizing polymers at Procter & Gamble, with continued developments since he has joined the Department of Materials Science and Engineering at the University of Delaware (2,3). Whereas initially the goal was to follow a given chemical species undergoing a perturbation, it became clear that when the species itself was evolving, even more information was accessible. Although this second formalism was developed to describe a system of chemical reactions (4), it is clear that the algorithms can be applied to describe polymers undergoing morphological changes. In the past it was assumed that the amorphous to crystalline transformation might be a fairly straightforward process; in fact, there can be multiple conformational changes in a polymer like PET that do not necessarily occur simultaneously, but all of which are changes that occur obligatorily before crystallization. This column offers a mini introduction to two-dimensional correlation spectroscopy (2D COS) to illustrate this behavior.

	It is certainly beyond the scope of this column to provide a complete introduction to these methods, but I am going to attempt to offer an intuitive description of what Professor Noda has developed-enough for you to understand what we are saying, and to access the formal literature if you are interested (4).

	The idea of these methods is that one can perturb a sample systematically while recording its spectrum. Then by calculating the 2D correlation spectra you can plot the synchronous (coordinated) and asynchronous (sequential) variations of the spectral intensities. With some knowledge of band assignments, you can know something about how the molecule is changing. Before doing the calculations, the data are usually "mean centered", 

), the average spectrum (of all the perturbations) is subtracted from each spectrum where 

 represents the kth iteration of the perturbation. The synchronous and asynchronous 2D correlation spectra are defined as

	In the synchronous 2D spectrum Φ, at any υ

 combination, for each perturbation value 

, the spectral values at those wavelengths are multiplied and summed over all the 

's. In the asynchronous 2D spectrum, Ψ, the spectral value at υ

 values (first multiplying each off-diagonal term by 

). The result is that in the synchronous spectrum the intensities at υ

 are coordinated, with a positive value if the changes at the two wavelengths are in the same direction. If one is increasing while the other is decreasing, Φ(υ

) will be negative. In contrast, the out-of-phase or sequential changes in the asynchronous spectra will be used to determine the order in which the changes occur. So, if Φ(υ

) have the same sign, then the variation at υ

) = 0, then the intensities are synchronized, and if Φ(υ

) = 0, the sequential order cannot be determined.

	Now we are going to show the results of these calculations on the 

 spectra of a PET fiber whose temperature was controlled while fixed under tension in the Linkam tensile stage (Linkam Scientific).

	As we discussed in a recent column (1), multiple changes are happening in PET as it is annealed. The sharpening of the carbonyl band accompanies crystallization, as do some changes in the region of the single bonds of the glycol linkage. But as we discussed earlier, these are really correlative changes rather than obligatory changes for crystallization. In conceptualizing the changes that occur I think of the polymer orienting, which we see in the polarization behavior of the Raman spectrum, and changes in bands in the single bond region of the glycol group as the disorder in the chain is converted to alignment of the molecular chains with conversion of gauche conformations to trans. We also have shown that sharpening of the carbonyl band is actually a result of the emergence of a new profile of bands as the material crystallizes. But does the sharpening of the carbonyl really reflect crystallization? Maybe it is necessary, but not sufficient. 

 means that the molecules align and pack into a lattice. Maybe the sharpening of the carbonyl reflects interactions with the aromatic ring or with neighboring carbonyl groups. 2D COS can begin to provide us insight. Ultimately to pin down the crystallization, we will need low frequency data as well as the fingerprint data that we show here. The low frequency data will come in a later installment.


	Figure 1: ZZ polarized Raman spectra of a fiber of PET held in the Linkam tensile stage as the temperature was raised from 40 &3176;C (bottom) to 100 &3176;C (top), just above the glass transition temperature where the flexibility of some of the polymer's bonds increases. Spectra are displayed (a) with z displacement to evaluate which bands are changing and (b) overlapped to clarify the systematic changes.

	Figure 2 shows the entire 2D COS plot of the spectra shown in Figure 1. The synchronous plot shows that there are correlations between almost all of the bands in the spectra. But the asynchronous plot shows more-selective interactions. To understand more fully what is going on we need to look at limited regions of these plots.


	Figure 2: Synchronous (left) and asynchronous (right) plots of the 2D COS spectra of the ZZ spectra of the PET fiber perturbed as a function of temperature.

	Figure 3a shows the 2D spectra between 1580 and 1780 cm

, a region that covers the bands identified with the aromatic group and the carbonyl. In the synchronous plot all bands are increasing together because the 

 intensities increase with orientation that is known to occur. However, the asynchronous plots show more complicated behavior that requires some discussion. The asynchronous plots in the aromatic and carbonyl regions are expanded in Figure 3b. The clear difference in shading demonstrates the difference in evolution of different components in each band. In the aromatic band it was not even clear that there is a second component unless you try to fit to a single Lorentzian Gaussian band. But looking at the asynchronous 2D correlation you can see two lobes, one positive and one negative, indicating that the component at 1613 cm

. In the carbonyl region there are bands at 1720 and 1739 cm

 that behave differently from the band at 1728 cm

 is approached. And because it is sharp, the entire envelope in the carbonyl region appears to sharpen.


	Figure 3: (a) Synchronous (left) and asynchronous (right) plots of the 2D COS ZZ spectra between 1580 and 1780 cm

 of the PET fiber perturbed as a function of temperature. (b) Asynchronous plots of the 2D COS ZZ spectra expanded from the right side of Figure 3b for the aromatic region (left) and the carbonyl region (right).

	We can now look at the bands in the region of the C-C and C-O single bonds of the glycol unit. Figure 4 shows the spectra only in this region of the single bonds. We can list again the changes that are occurring in this region. The (unpolarized) band at 1030 cm

 is replaced by a polarized band at 1000 cm

 band is growing out of a shoulder on the 1118 cm

 band, there is a hint of a band at 1084 cm

 that grows and then diminishes, and the band at 1178 cm

 broadens, probably because this band shifts frequency in the crystalline phase. We have chosen to focus on the bands between 1050 and 1150 cm

 in the 2D COS spectra that are shown in Figure 5.


	Figure 4: ZZ polarized Raman spectra of a fiber of PET held in the Linkam tensile stage as the temperature was raised from 40 &3176;C (bottom) to 100 &3176;C (top), just above the glass transition temperature where the flexibility of some of the polymer's bonds increase. Spectra are overlapped to emphasize the subtle changes that are occurring.

	What may be even more enlightening is to compare the behavior in the carbonyl versus glycol regions of the spectra, the so-called 

. The expansion of the asynchronous spectra in the 1615 versus 1100 cm

 blocks from Figure 2 is shown in Figure 6. Note that both regions have positive and negative lobes. Can this behavior be attributed to changes in conformation at bonds, to orientational-induced changes in intensity, or to symmetry changes because of a change in state? At the present time we are unable to differentiate these possibilities, but what we want to say here is that the information provided has the capability to provide the correct choice of mechanism.


	Figure 5: The synchronous (left) and asynchronous (right) bands in the region of the C-C and C-O single bonds. The synchronous spectrum show an increase in intensity of all bands, while the asynchronous spectrum shows that the component at 1094 cm-1 increases after the component at 1118 cm-1-that is, its intensity increases as the temperature is raised.

	We have taken an available set of spectra and subjected them to analysis by 2D COS. We confirm the ability to determine bands that change together in the synchronous spectra (either growing or diminishing in parallel, or one band growing while the other diminishes), and the ability to determine which changes occur before others in the asynchronous spectra. We also see that spectral features that are difficult to differentiate (because of limitations in spectral resolution) are clearly visible in 2D COS. In combination with band assignments, one can now describe, in detail, the changes in the physical state of this polymer at the molecular level, which then can be used to understand changes in the physical characteristics of the polymer.


	Figure 6: Asynchronous hetero-correlation spectra expanded from Figure 2. Single bonds versus aromatic band on left, single bonds versus carbonyl on the right. 

	(3) I. Noda, A.E. Dowrey, and C. Marcott, 

This introduction to two-dimensional correlation spectroscopy (2D COS) illustrates how to understand the structural changes occurring in polyester molecules in the fibers as they are annealed under tension.



Use of 2D COS to Tease Out Structural Information on Polymers

Polarized Raman spectra of polymeric fibers are known to provide information on molecular orientation. We have long felt that it would be of interest to study spin-oriented fibers of polyethylene terephthalate (PET) in situ, under tensile stress. In this column installment, we show Raman spectra acquired as a function of increasing stress and temperature. With knowledge of Raman band assignments (such as which molecular vibrating units, in which conformations, are responsible for particular Raman bands), it becomes possible to understand, in detail, the molecular changes that are responsible for polymer orientation and crystallization. Ultimately, the goal would be to confirm (or not) certain models for polymer morphology.

	Polarized Raman spectra of polymeric fibers are known to provide information about molecular orientation (1). In collaboration with Dr. Herman Noether, a retired polymer physicist from Hoechst Celanese (now deceased), we showed that the polarized spectra of a series of spin-oriented fibers of polyethylene terephthalate (PET) clearly showed the development of molecular orientation in the fibers as a function of take-up speed (2). We also showed that if the fibers had been drawn above the glass transition temperature (

) they exhibited crystallinity, as reflected in the width of the carbonyl band (2). In addition, we determined that fibers that are drawn at room temperature show increased orientation, but without an increase in crystallinity. We have long felt that it would be of interest to study such fibers, in situ, under tensile stress. In this installment of "Molecular Spectroscopy Workbench," we show spectra acquired as a function of increasing stress and temperature. With knowledge of Raman band assignments (such as which molecular vibrating units, in which conformations, are responsible for particular Raman bands [3]), it becomes possible to understand, in detail, the molecular changes that are responsible for orientation and crystallization. Ultimately the goal would be to confirm (or not) certain models for polymer morphology.

	Before starting the measurements that will be shown, I went through my "collection" of fibers and thought it might be interesting to study the behavior of spider silk fibers under stress. Spider silk is interesting because the animal spins multiple types of fibers for different purposes. But this idea had to be tabled because the sample labeled spider silk in my drawer could not be spider silk since it had no amide I band. In addition, I contacted Professor Michel Pezolet to see if he had any material that he could spare, and he told me that some years ago he had built a tension device to study 

 silk fibers under stress (4). In the interest of time, I decided to use fibers of amorphous polyethylene terephthalate (PET) as my sample of study; PET has the advantage of being fairly well-studied and understood. Based on my previous work, I had certain expectations of what I might see. So for those of you who follow my work, I apologize that I am working yet again on PET. On the other hand, because we know so much about this material, interpretation of the results has the potential to contain less conjecture.

Description of the Sample and Measurement Conditions

	The fibers that I used were totally noncrystalline. PET is known to crystallize at a temperature near 90 °C, a value that is somewhat dependent on the history of the sample. We also know that we can increase the orientation by drawing the fibers, even at room temperature. A 1–2 in. segment of a 19-fiber bundle of amorphous PET fibers was teased apart and mounted in the tensile chuck of a Linkam TST350 stage (Linkam Scientific Instruments), which can take a sample to a temperature as high as 350 °C. I mounted the fibers in the chuck and then either varied the distance between the plates of the chuck or the temperature (while maintaining tension on the fibers). Initially, I measured the full polarization spectra (ZZ, RR, RZ, and ZR) for a fiber that had been oriented to confirm that the Raman system was doing what was expected. The fiber was fixed on the stage, and the laser polarization and Raman analyzer were controlled to select conditions. The measurements were made on an Evolution Raman microscope (Horiba Scientific), using a 1800-g/mm grating in an 800-mm focal length spectrograph, so that I would have the capability of monitoring small frequency shifts, if they occurred. Because this grating produces significant dichroism, a scrambler was mounted behind the analyzer. For a full explanation of the requirements to make this type of measurement, refer to one of my previous columns (5).

	Figure 1 shows the ZZ, RR, ZR, and RZ spectra of a fiber in the tensile stage under conditions where the sample exhibited "necking," and the spectra were measured in the necking region. 

 is a phenomenon that occurs when these fibers are subjected to stress, and the material yields. In fact, we recorded the load measured by the stage and found that for the most part the load did not change as the chuck was separated, because of yielding, as exhibited by necking. For these measurements, unfortunately, we do not know how to calculate the actual load on the fibers examined because we do not know how many of the fibers in the bundle were actually captured in the chuck. (In the future, a small number of fibers needs to be mounted and confirmed to have been captured). So we are currently showing these measurements for proof of principle, not to be quantitative.


	Figure 1: Polarized spectra of a partially oriented PET fiber mounted in a tensile stage. The laser polarization was either vertical (Z in this configuration) or horizontal (radially oriented to the fiber). An analyzer behind the microscope selected either the Z or R polarization, and a scrambler behind the analyzer compensated for differences in the instrument responses for the two polarizations. (The bands marked with an asterisk (*) are Hg plasma lines from the fluorescent lamps in the lab.)

	The top spectrum in the figure was recorded with both the laser and the Raman analyzer parallel to the 

-axis. The next spectrum from the top has both the laser and the Raman analyzer perpendicular to the 

-axis. (I have consistently referred to this direction as 

, even though it is not a nomenclature that has been adopted. I use 

 because the fibers are clearly uniaxial and are best described in cylindrical coordinates, whereas 

 imply something about crystallographic axes.) The two bottom spectra, RZ and ZR, should be equivalent except under some very unusual conditions that are not relevant for this sample. The spectra are clearly equivalent, which means that these conditions compensate for the possible instrumental artifacts of my conditions. In addition, you can see that bands at about 630 and 780 cm

 have higher intensities in the off-diagonal spectra (ZR and RZ) than either of the diagonal spectra (ZZ and RR), which is consistent with the group theoretical predictions for this material (2).

Temperature-Dependent Series of Measurements

	In this section, we discuss spectra of a fiber fixed in the tensile stage and measured as a function of temperature. Figure 2 shows the ZZ and RR spectra of a fiber fixed in the stage and measured at 40 °C and 90 °C. Even though I did not adjust the tension, you can see the development of orientation by examining the change in the ZZ:RR spectral ratios.


	Figure 2: ZZ and RR spectra of a fiber fixed in the tensile chuck and recorded at 40 °C (bottom) and 90 °C (top).

	I believe that the ratio increased with temperature because there has been yielding of the fiber. I did notice that the diameter of the fiber decreased, but unfortunately I did not measure it. However, I did record the measured tension, which decreased from 0.67 N to 0.42 N during the measurements. Clearly, a more thorough set of measurements should be done on a small set of fibers known to be fixed in the chuck so that there would be better control of the tension, measuring both in the narrowed region and the region that has not yielded. In addition to the development of molecular orientation as seen in the ZZ:RR ratio, especially in the aromatic band at 1615 cm

, you can see clear changes in the region of the C-C and C-O bands between approximately 900 and 1200 cm

. The significant changes for which we have some interpretation are highlighted with arrows in Figure 2. As the fiber develops orientation, the band at approximately 1030 cm

, which is unpolarized, is replaced by a polarized band just under 1000 cm

 is seen only as a shoulder in nonoriented material. Even the earliest articles discussing the vibrational spectra of amorphous versus crystalline PET considered the role of gauche and trans configurations in the glycol linkages; normal modes composed of C-C and C-O bonds would clearly arise from the glycol linkage (6). Examination of the carbonyl band at approximately 1725 cm

 indicates that it has narrowed in the spectrum recorded at 90 °C, which is consistent with the understanding that the width of the carbonyl is a marker for crystallinity (7).


	Figure 3: ZZ spectra of fiber recorded as a function of temperature.

	The following figures follow these changes in more detail. Figure 3 shows the entire fingerprint spectrum for this fiber held at 40, 50, 60, 65, 70, 75, 80, 85, and 90 °C. The changes near 1000 and 1100 cm

 occur continuously even though the glass transition temperature (

) is close to 90 °C at the end of the range measured; this result means that whatever is responsible for these changes is not crystallization. In addition, the width of the carbonyl band near 1730 cm


	Figure 4: (a) ZZ spectrum as a function of temperature and band-fitted. (b) Peak ratio of bands at 1098 to 1117 cm

. Both peak height values and peak areas are plotted.

	Figure 4 shows the important region between 950 and 1200 cm

 of the ZZ spectrum as a function of temperature, after band-fitting the various components. The peak positions are not labeled in the figure because the figure becomes too busy with those labels. As an alternative, the band-fitted peaks are tabulated in Table I.

	The arrows are placed to draw attention to the band just below 1100 cm

 whose intensity is increasing with temperature (relative to the common band at about 1120 cm

). Because the results of the fitting procedure can be imported into Excel, the behavior of the fitting parameters can be plotted as a function of temperature. Figure 4b shows the ratios of peak areas and peak heights (1098 cm

) as derived from the band-fitting. Clearly, the peak height values better reflect what one "sees" in the data, although more sophisticated mathematical algorithms such as principal component analysis or two-dimensional spectroscopy may reveal other behavior that may be of relevance to understand the morphological changes in these fibers.

	Figure 5 shows both the ZZ and RR spectra between 1550 and 1800 cm

 as a function of temperature. The ZZ spectra show clear evidence of sharpening of the carbonyl band at 1725 cm

We show Raman spectra of polymeric fibers acquired as a function of increasing stress and temperature. With  knowledge of Raman band assignments, it becomes possible to understand, in detail, the molecular changes that are responsible for polymer orientation and crystallization.

Fran Adar

Articles

2D COS of Temperature-Dependent Raman Spectra of Amorphous, Nonoriented Polyethylene Terephthalate to Separate Molecular Conformational Changes from True Crystallization

Use of 2D COS to Tease Out Structural Information on Polymers

Raman Microscopy Combined with Tensile Deformation for Understanding Changes in Polymer Morphology