Tutorial on Solution NMR of Polymers - American Chemical Society

Chapter 3

Tutorial on Solution NMR of Polymers

Downloaded by DUKE UNIV on December 11, 2012 | http://pubs.acs.org Publication Date (Web): October 14, 2011 | doi: 10.1021/bk-2011-1077.ch003

Peter L. Rinaldi* Department of Chemistry, The University of Akron, Akron, Ohio 44325-3601 *E-mail: [email protected]

This paper is derived from a tutorial on the use of solution NMR methods to characterize polymers. The presentation has a dual purpose: 1) to orient new scientists who are just starting to use NMR methods in polymer science; and 2) to introduce new developments in NMR to experienced practitioners of solution NMR of polymers. After a brief introduction to using one-dimensional (1D-) NMR for quantitative analysis of polymers, the presentation covers recent developments in pulse sequences/software, hardware developments and methodology that combines the two. For the benefit of novice NMR users, an introduction to some basic NMR methodology is incorporated into these discussions. The work cited includes NMR papers on polymers as well as recent work on small-molecule NMR that has potential for helping with polymer analysis.

Introduction The most important aspect of polymer synthesis is to identify the structures of the newly synthesized materials. Once a material with desirable properties is prepared, it is important to know the structures present and their quantities, so that the synthesis of the desired material can be reproduced. If properties of synthesized materials are not reproducible, the polymer chemist must determine whether the structure and composition of the material has changed to cause the change in properties. Furthermore, systematic changes in polymer structure can often be correlated with changes in mechanical and physical properties. This in turn can lead to educated choices in designing the structures of new polymers with desired properties. Finally, it is desirable to identify the nature and quantity of adulterants which undesirably alter the properties of materials.

© 2011 American Chemical Society In NMR Spectroscopy of Polymers: Innovative Strategies for Complex Macromolecules; Cheng, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2011.


Solution state NMR is ideally suited for determining the structures and compositions of organic materials. There are a wealth of pulsed 1D- and 2DNMR techniques for resolving the resonances of many unique atoms (especially hydrogen and carbon) present in the mixtures of organic structure components that make up a polymer. These methods can be used for determining how these atomic components are linked to form molecules. In most cases, the structures of unknown compounds can be determined by straightforward examination and interpretation of NMR spectra. Once the structures have been identified and NMR resonances have been attributed to the structures present, NMR spectra can be used to quantitatively determine the compositions of these structures in the polymer. In fact, NMR is unique among spectroscopic methods in that a correctly acquired and processed NMR spectrum has a simple one-to-one relationship between the strengths of signals and the number of atoms producing those signals. Other spectroscopic methods require calibration procedures to determine extinction coefficients for different functional groups before they can be used for quantitative analysis. For the benefit of novice NMR users, this work contains a brief introduction to polymer structure and some general comments on collection of quantitative 1DNMR spectra. It is followed by a description of some recently available (last 5 years) NMR methods which will have an impact on the field of solution NMR of polymers. For more comprehensive descriptions of polymer NMR, the reader is refered to some recent works (1, 2). For an excellent introduction to the use of 1D- and 2D-NMR for characterization of organic structures, the reader is referred to an excellent textbook on the subject (3). Polymer Structure It is desirable to identify a number of structure elements in polymers. These include: chain-ends, monomer composition, monomer sequence, sequences from inverse monomer addition, stereosequence effects, branches and cross-link points and polymer block junctions. It is also desirable to identify structure defects that might be caused from side reactions during the polymerization, and to determine the presence and amount of adulterants such as low molecular weight impurities like solvents and unreacted monomer.

Chain-Ends Equations (1)−(6) outline the general mechanism for polymerization including initiation, propagation and termination steps.

38 In NMR Spectroscopy of Polymers: Innovative Strategies for Complex Macromolecules; Cheng, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2011.

Termination:


Chain transfer:

The relative rates of propagation and termination pathways determine the molecular weights of the polymers produced. From a knowledge of the various termination processes, the chemist can alter the reaction conditions to control the polymer’s molecular weight. Additionally, many polymer degradation processes start by reactions at the chain terminus. If the structures of the predominant chain-ends are known, the reaction chemistry can be altered, or chain-end capping reactions can be performed, to reduce the number of reactive chain-ends, leading to a stable polymer.

Monomer Sequence When a polymer is synthesized from two monomers, A and B, the monomers can add in an alternating fashion (1), in a statistical manner (2), in a manner to form blocks of A and blocks of B (3), or such that sequences of B can be grafted to a chain of A sequences (4).

The prevalence of these various structures is dependent upon the relative reactivities of A and B monomer with themselves or with each other, and on the 39 In NMR Spectroscopy of Polymers: Innovative Strategies for Complex Macromolecules; Cheng, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2011.


reaction conditions. The prevalence of these various structures has a dramatic influence on polymer properties and is of intense interest to polymer chemists. The relative reactivities of A/B monomers with themselves and with each other can be derived from the analysis of n-ad sequences. Often, the resonances of triads (AAA, AAB/BAA, BAB, ABA, ABB/BBA, BBB) can easily be resolved, even at relatively low field. From an analysis of the relative compositions of these triads, the predisposition of a particular copolymer to form alternating, random or block structures can be quantitatively described (4). With the routine availability of instruments with 1H resonance frequencies as high as 700 to 800 MHz, it is sometimes possible to resolve resonances from heptads or even nonads. When it is possible to resolve and measure the intensities of signals from different n-ads, accurate information about relative reactivities is obtainable.

Stereosequence When certain monomers such as 1-substituted ethylenes (e.g. styrene) polymerize, they create stereogenic centers on alternating carbons along the polymer backbone. In most cases the absolute stereochemistry is not important, as a racemic mixture of polymer chains is created. However, the relative stereochemistry of adjoining stereogenic centers is important, and has a dramatic effect on polymer properties. If the backbone of a vinyl polymer is drawn in a planar zig-zag orientation as in structures 5−7, two relative orientations are seen: the meso (m) structure has two adjoining R substituents on the same face of the polymer as in the two dyads in 5; and the racemic (r) structure has two adjoining R substituents on opposite faces of the polymer as in the two dyads in 6. If triads are considered, isotactic polymers have the same orientations of all R substituents to produce polymers with all m dyad placements. Syndiotactic polymers have alternating orientations of R substituents to produce polymers with all r dyad placements. Atactic polymers have random orientations of R substituents to produce polymers with equal numbers of randomly placed m and r dyads.


Since the properties of polymers are related in part to their tacticity, measurement of m and r dyad composition is crucial. NMR is ideally suited to this measurement, as the NMR resonance positions are influenced by relative stereochemistry (5).


Other Defects NMR is ideally suited for determining the structures and quantities of polymer defects, whether they are incorporated intentionally or accidentally. These include branch points, junctions between two polymer blocks, cross-link junctions and other defects. Finally, adulterants such as residual solvents or monomer, and additives such as antioxidants can usually be detected and identified. Structure proofs can usually be accomplished by comparison of resonance positions with those in the spectra of authentic material. When authentic materials are difficult to obtain or are not available, combinations of 2D-NMR methods can be used to determine atomic attachments, prove structure elements and simultaneously assign resonances.

Quantitative One-Dimensional NMR Once the presence of the above structure elements is determined and their resonances identified, it is desirable to quantitatively evaluate the amounts of these structures present in the polymer. This is usually accomplished with 1D-NMR experiments. While NMR is unique among spectroscopic methods in that peak areas can be directly related to the number of atoms of each type, it is important to properly obtain NMR spectra in order to get reliable and accurate analysis of composition and purity. Accurate quantitative analysis of polymers requires attention to the details at the data acquisition stage as well as the data processing stage. Data Acquisition The most important factor in generating good quality 1D-NMR spectra for quantitative analysis it to measure the T1 relaxtion times for the nuclei whose signals are to be measured. This is accomplished using an inversion recovery experiment (relaxation delay-180o-τ-90o-acquire, where τ is a variable relaxation delay) experiment. By fitting the exponentially decaying peak intensity variation vs. τ from a series of spectra obtained with varying τ delays, the exponential recovery time constant T1 for each peak in the spectrum is determined (1). In setting up a quantitative 1D-NMR experiment, the relaxation delay should be 5-10 times the longest T1 among the signals of interest. If decoupling is performed (as is the case when 13C NMR is used) then in most cases, the nuclear Overhauser effect (NOE) resulting from saturation of the decoupled nuclei must be suppressed, since signals of different 13C atoms are differentially enhanced depending upon the unique relaxation characteristics of 41 In NMR Spectroscopy of Polymers: Innovative Strategies for Complex Macromolecules; Cheng, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2011.


each nucleus. To accomplish NOE suppression, a gated decoupling experiment must be used, where the 1H decoupler is turned off except during the acquisition time, and a 90o excitation pulse is used. Under these circumstances complete suppression of the NOE requires a relaxation delay (during which the 1H decoupler is turned off) of at least 10xT1. In rare instances, when signals of very similar atoms are compared, spectra with NOE enhancement can be used if the enhancement is the same for all signals to be compared. Data accumulation should be performed with an acquisition time such that the NMR signal decays (at least 3xT2*, the apparent transverse relaxation of the NMR signal). In selecting the spectral window, the effective excitation window of the pulse should be considered. A square pulse produces an excitation window in which peak height vs. offset from the transmitter (center of the spectral window) is defined by a sin(x)/x function. A good rule of thumb is that for a 5μs pulse only the middle 50 kHz of the spectral window experiences uniform excitation. Outside of this window, the peak heights will be attenuated by incomplete flipping of the spins. If the pulse width is doubled (10 μs) then the useable spectral window will be halved (25 kHz). A second factor to consider when setting the spectral window is hardware filtering of the audio signal. Older NMR instruments mix the rf signal down to the audio frequency range where it can be digitized by older analog-to-digital converters (ADC’s). To prevent aliasing of high frequency signal components from outside of the spectral window (thus maintaining good signal-to-noise) audio filters are used. These hardware filters have non-ideal response and can attenuate signals outside of the middle half of the spectral window; attenuation of signals near the edges of the spectral window is often 50% or more, depending on the age of the instrument. Thus, only the middle half of the spectral window is useable for quantitative analysis. Instruments manufactured in the past five years use digital manipulation over a much larger portion of the signal receiver path. In these newer instruments, the NMR signal is digitized in the rf range, and mathematical filtering is used to prevent aliasing of signals from outside of the desired spectral window. Mathematical filters have more desirable “brick wall” behavior; completely attenuating signals from outside of the spectral window, while leaving signals within the spectral window unperturbed. In these newer digital instruments, signals in the middle 90% or more of the spectral window can be used for quantitative analysis. Once the spectral window is determined, the delay between the end of the pulse and start of data acquisition should be adjusted such that in the final spectrum all peaks can be phased correctly with adjustment of only the zero order phase correction. The spectrum should be properly phased without the use of first order phase correction. The optimum preacquisition delay is spectral window dependent, so that once analysis parameters are determined, it is unnecessary to make further adjustments and the parameters can be used for subsequent analyses. If the spectrum is collected with an incorrect preacquistion delay, then a sinusoidal roll will be introduced into the baseline. The intensity and number of cycles will be dependent on the extent of the misset, and the spectral window. The problems introduced will be more severe for data collected with larger spectral windows. 42 In NMR Spectroscopy of Polymers: Innovative Strategies for Complex Macromolecules; Cheng, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2011.

Finally, for good quantitative analysis, spectra with good signal-to-noise (S:N) are required. Analytical criteria specify that a minimum S:N of 10:1 is required before quantitative measurements can be performed. However, for accurate analyses, S:N levels an order of magnitude or greater should be used.


Data Processing In order to accurately measure a peak integral, the peak must be accurately represented in the digital domain. Typically, it is desirable to have approximately 10 points to define the top half of the peak shape. A good rule of thumb is to zero fill a properly collected time domain signal (free induction decay, FID) to 2 or 4 times the original dataset size. To improve S:N and to further contribute to sufficient digital resolution of the peaks, it is also useful to apply an exponentially decaying function to the decaying FID. Optimum S:N is achieved when the decay of weighting function matches the decay of the FID. Often, in real spectra there will be a mixture of broad and sharp peaks from polymer backbone and side-chain resonances, respectively. Therefore, it is usually desirable to examine the spectral with different weighting functions. A properly phased spectrum is essential for good quantitative analysis. As mentioned above, if the data are properly collected, it should be possible to phase the spectrum solely by adjustment of the zero order phase parameter. Often the operator will phase spectra by zooming in on the peak and attempting to make the peak symmetrical. If the peak is inherently asymmetric due to a signal component producing a shoulder on the main peak, or due to an asymmetric shape from incorrect shimming, then integration error will result. There are many published protocols for phasing. Some of these involve phase adjustments to produce a maximum peak integral and numerically monitoring the baseline on either side of the peak. When phasing, it is useful to examine the true baseline regions on either side of the peak and to adjust the phase so the extensions of these baseline components to the peak center, intersect at the same vertical point. Distortions in the baseline should be removed with the operator’s favorite baseline correction algorithm. For properly collected data, the distortions should not be too severe and a spline fit is effective. Other more involved procedures involve fitting the baseline to an nth order polynomial, or to a sum of sinusoidal functions. In all cases the baseline (peak-free regions of the spectrum) needs to be identified. This is often accomplished by dividing the integral regions of the spectrum (e.g. such that odd regions are peak-free). When defining the baseline regions it is important to consider the fact that Lorenzian peaks typically found in NMR spectra extend for quite a distance from the frequency of the peak maximum. Approximately 99% of the peak area is found over a region 20 times the peak width at half height (Δυ1/2); 98% of the peak area is found within a region with 10 times Δυ1/2; and only 95% of the peak area is found within a region with 5 times Δυ1/2. While it might be desirable to integrate the spectra with narrower integral regions surrounding the peak maxima, it is necessary to select baseline regions of the spectrum that do not fall within 10-20 peak widths of the intense signals in the spectrum. If this is not done, baseline correction will shift the baseline offsets due to the presence of real signals, and lead to inaccurate peak integrals. 43 In NMR Spectroscopy of Polymers: Innovative Strategies for Complex Macromolecules; Cheng, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2011.


Accurate quantitative analysis requires that all of the resonance assignments be known and properly counted. Some particular problems include contributions from 13C satellites and the outer wings of AB patterns in 1H and 19F NMR spectra. Failure to count these signals properly can cause errors in quantitative analysis, especially if the intensities of weak and strong signals are being compared. Figure 1 shows an excellent example of how both of these factors can cause complications in quantitative analysis. This region of the 19F spectrum of poly(hexafluoropropylene oxide) (pHFPO) contains two AB patterns, labeled a2 and a’2 from the two diastereotopic CF2 fluorines shown on the two structures at the bottom of the figure. The structures differ by inversion of the central –CF(CF3)CF2 monomer unit. The central parts of these AB pattern are off scale. They are components of the AB patterns from the chain-ends groups of pHFPO containing CF2 signals from normal (a2) and inverse addition (a2’) of the second monomer unit in the chain. The two weak signals at the outer edges of this spectral region are the outer satellites of the AB pattern from the a2 fluorines. The measured couplings in this AB pattern are 2JFF = 285 Hz, which is typical of a two-bond 19F-19F homonuclear coupling. The corresponding outer parts of the AB pattern from the a’2 fluorines are too weak to detect; they are ca. 10 fold weaker due to the lower concentration of structures from monomer inversion.

Figure 1. Section of the 470 MHz 19F 1D -NMR spectrum from pHFPO showing the region containing the a2 and a′2 CF2 resonances as labeled on the structures at the bottom of the figure. The ratio of the two structures is ca. 100:12. Satellites of the a2 resonance from 1.1% 19F-13C and 2.2% 19F-C-13C are seen with couplings of 1JCF = 270 and 2JCF = 40 Hz, respectively. The center of the doublet from 1JCF is shifted upfield by ca. 0.1 ppm by a 13C istotope shift. The center of the doublet from 2JCF is shifted upfield by ca. 0.01 ppm by a 13C istotope 44 In NMR Spectroscopy of Polymers: Innovative Strategies for Complex Macromolecules; Cheng, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2011.


shift. Additionally, the latter doublet (from 2JCF ) is twice as large as the former doublet (from 1JCF ) because the probability of coupling to 13C is twice as large (13C’s can be present at two sites, CF2 and CF3, which are two bonds away from the a2 fluorines). These signals from coupling to 13C could easily be misinterpreted as weak resonances from other minor chain-end structures, especially because they are asymmetrically spaced around the central 19F resonance. Corresponding 13C satellite signals from the weaker a′2 resonances are not seen in the spectrum because these structures are present in ca. 10-fold lower concentration. Also, if these satellites had fallen beneath weaks signals of minor structure components, they could easily lead to enormous errors in compositional calculations. If very accurate compositional calculations are needed, one should compare integrals which are a similar multiple of the peak width. Usually, 10 peak widths is acceptable. However, one must also consider overlap of neighboring resonances and the effect of J-couplings on the width of multiplets in deciding integral reset positions. When doing compositional calculation with a high degree of accuracy, one must also decide whether to incorporate 13C satellites, and to be consistent in their inclusion or omission. Once the peak areas are determined, there are several strategies for calculating compositions of various monomer- or stereo-sequences. The traditional strategy involves determining the relationship between peak areas and various n-ad structure elements (monomer sequences or stereosequences). A set of linear equations is obtained which can be solved for n-ad compositions. In many cases some of the resonances are associated with odd-numbered n-ads such as triads, and other resonances are associated with even number m-ads such as dyads and tetrads. These can be related to each other through necessary relationships, which also provide additional linear relationships (2). On occasion problems with incorrectly counting structure units occur when more than one n-ad is considered in the compositional analysis. Researchers from Dow proposed an alternative method for extracting polymer compositions from NMR data (6). Their method involves examining resonances and attributing them to the central monomer of odd-numbered n-ads, thus counting atoms only once. From these assignments, a set of linear equations can be obtained that relate peak integrals to a set of structures. The compositions can be solved by numerically fitting calculated peak areas to those experimentally determined. Recently, Momose et al. (7) described the use of multivariate analysis as a method for studying the compositions of copolymers and homopolymer blends.

New Experiments and Pulse Sequences Over the past decade, 2D-NMR methods have become routine for studying the structures of complex polymers and producing the unequivocal resonance assignments that are needed for quantitative analyses. Complete spectral analysis usually involves collection of two or more 2D-NMR spectra and using complementary information from the spectra to construct an entire structure. 45 In NMR Spectroscopy of Polymers: Innovative Strategies for Complex Macromolecules; Cheng, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2011.

2D-NMR Methodologies for Determining Polymer Structure Various methodologies have been developed for determining polymer structure. Reference (3) serves as an excellent initial source for learning how to determine organic structure and resonance assignments from NMR data. Two commom methodologies for extracting structures from multidimensional NMR spectra involve the use homonuclear or heteronuclear 2D-NMR methods.


Homonuclear 2D-NMR In the case where sample quantity and/or sensitivity is an issue, methodologies involving 1H - 1H (or 19F - 19F) correlation 2D-NMR experiments are useful. Such situations include cases where sub-milligram quantites of material are available, or where very weak signals from structures such as chain ends are to be studied. In these homonuclear experiments the natural abundance of both nuclei is 100%, and high sensitivity detection of nuclei with large magnetic moments (1H or 19F) is performed.

Figure 2. Schematic representation of homonuclear 2D-NMR experiments and the structure information available from them: a) COSY, b) DQCOSY, c) TOCSY, and d) NOESY. Reprinted with permission from reference (1). The structure information available from homonuclear 2D-NMR experiments is illustrated schematically in Figure 2. The atomic connectivities in the structure in Figure 2 are highlighted by colored boxes that match the color codes of the experiment names which provide that structure connectivity information. The COSY (correlation spectroscopy, highlighted in yellow) 2D-NMR experiment produces a spectrum schematically illustrated by Figure 2a with the 46 In NMR Spectroscopy of Polymers: Innovative Strategies for Complex Macromolecules; Cheng, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2011.


identical homonuclear chemicals shifts plotted along the two axes. Peaks are found along a diagonal at the shifts of the resonances in the spectrum. If there is germinal or vicinal coupling between protons, cross-peaks appear off the diagonal at the intersection of the two shifts indicating atomic connectivity highlighted in the yellow box (i.e. the vicinal relationship between HA and HB) on the chemical structure in the figure. Similar information from the COSY spectrum identifies the vicinal relationship between HB and HC (not shown on the figure). The DQCOSY (double quantum filtered COSY, also highlighted in yellow) NMR experiment produces a 2D spectrum (Figure 2b) similar to that in COSY, but with signals from singlets (resonance not coupled) filtered from the spectrum. These signals do not produce useful information in COSY spectra and only serve to hide cross-peaks that fall near the diagonal, so their absence from the 2D spectrum is an advantage. TOCSY (total correlation spectroscopy, highlighted in blue) 2D-NMR spectra (Figure 2c) have an appearance similar to COSY spectra, but with correlations among resonances of all protons that are part of the same spin system as illustrated by the structure elements highlight in blue on the structure in the figure. Note crosspeaks between HA and HC in this spectrum, even though they are not coupled to each other. These TOCSY crosspeaks are produced because they are part of the same spin system, where HA is coupled to HB and HB in turn is coupled to HC. NOESY (NOE spectroscopy) 2D-NMR experiments produce spectra (Figure 2d) with cross-peak patterns similar to those found in COSY spectra, but with cross-peaks appearing at the intersection of the chemical shifts of protons that are close (usually within 0.5 nm) in space. They provide structure information about the spacial proximity of groups (regardless of coupling) like those shown by the red arrow on the structure in the figure. From a set of homonuclear experiments, it is usually possible to determine chemical structures. However, these experiments suffer from the limited chemical shift dispersion of 1H (10 ppm). If many structures are present with slight environmental differences, such as those found from stereosequence effects, it can be difficult to resolve all of the cross-peaks needed to determine structure. Furthermore, the distinction/resolution between cross-peaks is complicated by the fact that the cross-peak pattern are a cluster of (n x m) peaks where n and m are the multiplicities of the coupled peaks in the 1D-NMR spectrum. For example, the cross-peaks between HA and HB resonances in Figure 2a are a 2x4 set of peaks. The projection of these cross-peaks produce a 2-line pattern at the chemical shift of the HA resonance, which is a doublet; and a 4-line pattern at the chemical shift of HB, which is a doublet of doublets. If two sets of cross-peaks occur at similar shifts, it is often difficult to distinguish between them. Finally, the individual peaks within a cross-peak pattern are a series of positive and negative contours, determined by the relative signs of the J-couplings. In low resolution 2D-NMR spectra, overlap between adjoining anti-phase peaks can lead to signal cancellation, especially if the J-couplings are small compared to the digital resolution and/or the peak width. In these circumstances it is easy to miss cross-peaks, leading to misassignments and incorrect interpretation of the spectra. This is especially true with spectra of polymers, which contain broader lines than those found in the spectra of small molecules. 47 In NMR Spectroscopy of Polymers: Innovative Strategies for Complex Macromolecules; Cheng, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2011.

For these reasons, when adequate signal is present, it is often preferable to study structures using a methodology involving two or more heteronuclear 2DNMR experiments.


Heteronuclear 2D-NMR

In the case where ample quantities of material are available (1-100 mg depending upon the abundance of the structure to be detected and the field strength of the instrument used) heteronuclear 2D-NMR experiments can be performed. These experiments most commonly involve sensitive detection of a nucleus such as 1H or 19F, which has a large magnetic moment and is also present in high natural abundance. However, the shifts of these nuclei are correlated with a low abundance nucleus such as 13C (1.1% abundance), so that NMR signal is detected from one molecule in 100. These experiments have the advantage that the chemical shift dispersion in the indirectly detected dimension is determined by the shift range of the heteronucleus (200 ppm in the case of 13C). Also, the correlation is a (1 x n) pattern as there is usually no coupling in the 13C dimension (unless there is a third NMR-active nucleus in the structure). Thus, it is possible to resolve many resonances from chemically similar structure fragements. Figure 3 schematically illustrates the most useful heteronuclear 2D-NMR spectra. As in the previous section, the connectivities on the structure in the figure are highlighted with colored boxes to match the colors of the boxes around the experiment names from which the atomic connectivities are derived. The HSQC (heteronuclear single quantum coherence, colored in yellow) and HMQC (heteronuclear multiple quantum coherence) experiments use one-bond C-H couplings to produce spectra (Figure 3a) with cross-peaks indentifying direct C-H attactment, as illustrated by the fragments highlighted by the yellow boxes on the structure in the figure. The HMQC experiment was originally used for this purpose, but has been replaced by the HSQC experiment which produces more intense signals and less complicated cross-peak patterns. Variations of the HSQC experiment that use adiabatic 180o pulses usually give better signal to noise levels than spectra from HSQC experiments using simple 180o pulses (8). The HSQC experiment is usually used in combination with data from the HMBC (heteronuclear multiple bond correlation, highlighted by the blue boxes) experiment which produces spectra similar to that illustrated by Figure 3b. The HMBC spectrum shows correlations between 13C and 1H atoms coupled through 2- and 3-bonds. Structure fragments highlighted in blue on the structure in the figure are identified. Complications arise in distinguishing between 2- and 3-bond C-H correlations. One method to enhance one or the other set of cross-peaks is to perform the experiment twice with different delays optimized for 2- and 3-bond couplings (80 and 50 ms usually work for the former and the latter). Some judgement of relative cross-peak intensity in the two spectra is necessary, and the results are often ambiguous. 48 In NMR Spectroscopy of Polymers: Innovative Strategies for Complex Macromolecules; Cheng, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2011.


Figure 3. Schematic illustration of heteronuclear correlated 2D-NMR spectra from the hypothetical structure fragment shown at the top of the figure: a) HSQC or HMQC, b) HMBC, c) H2BC, d) HSQC-TOCSY. Reproduced with permission from reference (1). The advantage of this experiment is that correlations across heteratoms and quaternary carbons can be detected (e.g. in this case a correlations can be seen between the resonances of the methoxyl protons and CC). Distinction between 2and 3-bond correlations in the HMBC spectra is usually the “Achilles heel” of this heteronuclear 2D-NMR methodology. Many variations of the HMBC experiment have been devised to help differentiate between between 2-bond and 3-bond correlations. Most of these work nicely for small molecules, but because polymers give spectra with broader lines from shorter relaxation times, these experiments rarely work well for polymers. The exception is the H2BC (heteronuclear two-bond correlation) experiment which produces spectra illustrated by Figure 3c (9). This experiment uses a combination 1JCH and 3JHH to produce correlations among the atoms in the structure fragment highlighted by the red box on the structure in the figure. In this example a 2-bond correlation is seen between CA and HB. The H2BC cross-peak patterns are considerably simpler that those in the HMBC spectra because 13C decoupling can be used during the acquisition time in the former experiment. Furthermore, the cross-peaks are independent of 2JCH; 49 In NMR Spectroscopy of Polymers: Innovative Strategies for Complex Macromolecules; Cheng, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2011.


two bond C-H couplings are often small leading to inefficient coherence transfer between nuclei in the HMBC experiment. When polymers are studied, for the same experiment time, signals in H2BC spectra are considerably more intense than signals in HMBC spectra. The drawback of H2BC is that correlations to quaternary carbons are not detected. In the HSQC-TOCSY spectrum (Figure 3d), at the shift of each proton bearing 13C, a C-H correlation is detected at the intersection of the chemical shifts of directly bound carbon and hydrogen (e.g. between CA and HA). In addition, at this 13C shift, additional TOCSY correlations are observed to the shifts of all the other protons (HB and HC in this case) that are part of the consecutively coupled proton spin system. The experiment is usually run to produce positive contours (red spots) to indicate correlations between the resonances of directly bound carbons and hydrogens, and negative contours (blue spots) to indicate correlations between the resonances of the initial C-H carbon and protons not directly bound to that carbon but part of the same coupled proton spin system. Figure 4 shows selected regions from the heteronuclear 2D-NMR spectra of poly(lactate-co-glycolate)-b-poly(ethylene glycol) capped with folate end groups on the polyester chain-end (PLGA-PEG-FOL). These data show the regions which support the assignments of resonances from the lactate portion of polymer, as shown on the structure in the figure. Figure 4a contains the HSQC data showing a one-bond correlation for the methyl group. Figure 4c shows the portion of the HMBC spectrum containing correlations from lactate methyl protons to the lactate methine and ester carbonyl carbons (correlations A1 and A2, respectively), twoand three-bonds away, respectively. On its own, this spectrum does not permit distinction between the two- and three-bond correlations. Figure 4b shows the relevant region from the H2BC spectrum; it identifies the A1 cross-peak as the one associated with the two-bond HMBC correlation.

Figure 4. Polylactic acid regions from the 2D-NMR spectra of PLGA-PEG-Folate: a) HSQC, b) H2BC, and c) HMBC of PLGA-PEG-folate. 50 In NMR Spectroscopy of Polymers: Innovative Strategies for Complex Macromolecules; Cheng, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2011.

Quantitative NMR The spectral dispersion provided by 2D-NMR methods is enormously powerful for resolving and assigning resonances in complicated polymer structures. However, once resonance assignments are made, it is desirable and often necessary to use this information to perform quantitative analysis of polymer composition. This can be a problem if resonances are not resolved in standard 1D-NMR spectra. There are alternatives for getting resolved peaks for quantitative analysis.


2D-NMR The utilization of 2D-NMR peak integrals for quantitative analysis is complicated by several factors that produce non-linear instrument response which hampers quantification. These include: 1) resonance offset effects on both transmitter and decoupler channels; 2) inconsistent polarization transfer efficiency due to ranges of J-couplings; 3) variations in 1H T1 causing inconsistent return of the magnetization to its equilibrium state during the relaxation delays; 4) differential polarization transfer due to variations in T2’s; 5) effects from inadequate digital resolution; and 6) multiplicity effects (CH, CH2 and CH3 signals do not provide identical responses). Lemaster et al. (10) first used quantitative 2D-NMR analysis for the study polymers by examining the spectra of polyester urethanes from 1,4-butanediol/ 4,4’-diphenylmethane diisocyanate and adipic acid. They used 2D-HSQC and 3DTOCSY-HSQC spectra to obtain resonance assignments. They then used HSQC spectra under conditions so that the resonance offset effects were insignificant. They determined relative 1H T1’s and corrected for shorter T1’s of the backbone protons relative to the chain-end groups. They compared the 2D-NMR integrals of CH2 groups which were expected to have similar 1JCH couplings. They determined that inconsistent T2’s did not contribute to the integration errors. Digital resolution problems were eliminated by collecting higher resolution 2D-NMR data, and by using signal processing methods to extend the acquired signal (especially in the evolution time dimension). Only signals of CH2 groups were compared. After accounting for these issues, they obtained excellent results when they were able to determine the monomer distribution ratio and the ratio of backbone to chain-end units. Most often, inadequate resolution in 1D-NMR spectra occurs when comparing resonances of similar structures, as these are the resonances most likely to overlap. This was the case in research reported by Qiu et al. where they were concerned with the composition of poly(ethylene-co-octene) (6). 1D- and 2D-NMR data from the αα-CH2 region of one of their samples of poly(ethylene-co-1-octene)s (polyEO) containing 64 mole% 1-octene are shown in Figure 5. The quantitative 13C 1D-NMR spectrum is shown across the top of the corresponding region from the HSQC spectrum collected under conditions where the 2D-peak volumes are expected to be quantitative. Since the αα-CH2 resonances are being compared, identical JCH couplings are expected, identical 51 In NMR Spectroscopy of Polymers: Innovative Strategies for Complex Macromolecules; Cheng, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2011.

relaxation is expected, effects of resonance offset are identical in both the 1H and 13C dimensions, and multiplicity effects are identical. 1H T1 could not be measured directly because the αα-protons are not resolved; however, T1’s for these protons (0.2s) could be measured indirectly through detection of the resolved αα- 13C resonances. The bar graph at the bottom compares the 1D-(blue) and 2D-(purple) peak integrals for the three resolved resonances. Excellent comparisons are seen, indicating the utility of 2D-NMR spectra for quantitative analysis.


Diffusion NMR diffusion measurements have played an increasingly important role in characterizing components in polymer systems. Although the first NMR diffusion measurement using pulsed magnetic field gradients was described by Stejskal and Tanner (11), the development of a 2D-pulsed field gradient NMR method, DOSY (diffusion ordered spectroscopy), really sparked applications of diffusion measurements (12). A good summary of applications and methodology can be found in reference (13).

New Hardware Over the past decade, hardware improvements have been made in several areas. Modern instruments provide precise and accurate control of the rf amplitude, phase and frequency. After decades of incremental improvements in instrument sensitivity, new detection circuitry has provided a quantum jump in signal-to-noise level. Incorporation of multiple receivers permits simultaneous detection of two or more spectra. Control of Rf Modern instruments provide unimaginable control of the rf signals to permit flexible and arbitrary schemes for manipulating the states of nuclear spins. Many of these schemes reduce the demands of collecting high resolution 2D-NMR data by accomplishing selective excitation of the information containing regions of the spectrum, while ignoring other uninteresting regions of the spectrum. There are a number of options for accomplishing this; only a few of these will be discussed here.

Selective Excitation The COSY pulse sequence is the most basic 2D-NMR experiment, consisting of only two rf pulses separated by an evolution period. It is simple to perform, tolerant of miscalibrations, has good sensitivity, and requires very little expertise to perform. When dealing with hydrocarbon-based structures, it is the first 2D-NMR experiment performed and it generally provides useful structure information. 52 In NMR Spectroscopy of Polymers: Innovative Strategies for Complex Macromolecules; Cheng, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2011.


Figure 5. Backbone αα-CH2 region from the quantitative 1D-13C and 2D-HSQC NMR spectra poly(ethylene-co-octene) containing predominantly racemic relative orientations (top of figure). A bar graph is shown comparing compositions of monomer sequences OOOO, EOOO and EOOE determined from 1D- (blue) and 2D- (purple) integrals (bottom part of figure). Reproduced with permission from reference (6). When working with fluoropolymers, the huge 19F spectral window (200 ppm compared with 10 ppm for 1H) is an advantage in that the resonance positions are well dispersed and sensitive to the chemical environment of the fluorine atoms. 53 In NMR Spectroscopy of Polymers: Innovative Strategies for Complex Macromolecules; Cheng, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2011.


When COSY experiments are perfomed with 19F, many FID’s with different values of the t1 evolution period must be collected to digitize the indirectly detected dimension of the 2D-NMR spectrum. Figure 6a shows a small fraction of the entire 19F-19F COSY spectrum (ca. 1% of the total spectrum area) from tetrameric(hexafluoropropylene oxide) T(HFPO), which is a model compound for Krytox® fluoropolymer, a poly(hexafluoropropylene oxide) P(HFPO). To obtain this data, a spectrum with several thousand t1 increments was collected over the course of a weekend. The experiment was long because many FID’s were needed, not because signal averaging was required to obtain good signal-to-noise. Only the region shown was needed to obtain the desired correlation information between the CF2-O-CF structure fragments illustrated by the red arrows on the structure in the figure. Despite the long experiment, spectral detail in the multiplets is not resolved. Figure 6b shows the entire 2D-NMR spectrum from a selective COSY (14) experiment in which shaped pulses were used to produce a spectrum containing only CF resonances in the f1 dimension and CF2 resonances in the f2 dimension, corresponding to the same spectral window shown in Figure 6a. The experiment required less than 30 minutes of instrument time in which several hundred FID’s were collected (15, 16). The experiment required hardware to produce arbitrary rf pulse shapes with arbitrary frequency offsets, not just the simple square pulses centered at the frequency in the center of the spectral window as are commonly used in NMR. Note that the selective COSY spectrum contains far more detail than is seen in the corresponding region from the standard COSY spectrum. Figure 6c contains a spectrum obtained from a selective COSY spectrum collected with inversion pulses centered in the middle of the evolution period, in order to remove homonuclear couplings. The flexible hardware permits resolution of unprecedented spectral detail. The cross-peaks all appear as singlets in the f1 dimension; multiplet pattern containing coupling information are retained in the f2 dimension where collection of high resolution data has little impact on the total experiment time. Two sets of four cross-peak patterns are observed; one set showing the B2-C1 correlation between fluorine resonances from the central CF2OCF groups, and a second set showing A2-B1 correlations between the fluorine resonances of the CF2OCF fragment on the left part of the structure at the top of the figure. Four cross-peak patterns are observed for each C-F group because the three stereogenic centers in the structure produce four diastereomers and their mirror images.

Homonuclear Decoupling Once multidimensional NMR experiments provide resolution and resonance assignments, the next immediate need is to measure how much of each structure component is present using peak area integration. 13C 1D-NMR experiments are ideally suited for this purpose since all of the protons can be decoupled with broadband irradiation, to produce a spectrum with a single line for each unique carbon atom. Since the natural abundance of 13C is only 1.1 %, homonuclear 54 In NMR Spectroscopy of Polymers: Innovative Strategies for Complex Macromolecules; Cheng, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2011.


coupling between 13C atoms does not complicate the spectrum because coupled 13C-13C spin pairs occur in only 1/104 molecules.

Figure 6. 2D-COSY spectra of hexafluoropropylene oxide tetramer: a) segment from a standard COSY spectrum; b) full spectrum from a selective COSY experiment; and c) full spectrum from a selective COSY experiment with homonuclear decoupling in the f1 dimension. 55 In NMR Spectroscopy of Polymers: Innovative Strategies for Complex Macromolecules; Cheng, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2011.


When doing NMR of abundant spins such as 1H or 19F, homonuclear coupling produces spectra with complex multiplets. In complex molecules, these multiplets result in overlapping patterns which can’t be resolved from one another, and can’t be easily integrated. Although many attempts have been made, until now it has not been generally possible to accomplish broadband decoupling of homonuclear spins to produce 1D-NMR spectra with integrable singlets. Until recently, it has only been possible to obtain spectra with single frequency irradiation of the resonance of a single atom, or at best to perform homonuclear decoupling of a narrow multiplet. Recently, Espindola et al. (17) described the use of state-of-the-art rf hardware to produce shaped inversion pulses. These capabilities were used to decouple an arbitrary combination of nuclei with resonances in various spectral windows, and produce a spectrum of singlets with broadband decoupling of the rest of the nuclei in the spectrum.

Figure 7. Selected (CF containing) regions from the 470 MHz 19F 1D-NMR spectra of hexafluoropropylene oxide tetramer: (bottom) standard spectrum; (top) spectrum with broadband decoupling of CF2 resonances. This is illustrated with the spectra of T(HFPO) shown in Figure 7, where the C-F containing regions of the 470 MHz 19F spectra are shown. In the bottom spectrum, coupled C-F multiplets from the middle (B and C) monomer units shown in the structure at the top of the figure (Bn and Cn designate the fluorines of CFn groups in monomer units B and C in the structure). These resonances were resolved and assigned with the aid of the selective COSY spectra shown above. It is impossible to resolve and integrate the 8 separate sets of resonances due 56 In NMR Spectroscopy of Polymers: Innovative Strategies for Complex Macromolecules; Cheng, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2011.


to large couplings with the CF2 groups. In structure such as this, the four-bond couplings are usually large (20-40 Hz), compared with the three-bond couplings to the CF3 groups. The top spectrum was collected with shaped inversion pulses between data point samplings in the FID, such that the CF2 atoms (resonances between -75 and -90 ppm) are inverted. As a consequence, homonuclear couplings that evolve during the first half of the dwell time (period between sampling of two data points in the FID) are refocused during the second half of each dwell time. From the homonuclear decoupled spectrum, shown in the top of the figure, it is possible to separately integrate most of the resonances. At worst, it is possible to perform peak deconvolution on some of the overlapping resonances to obtain quantitative information.

Sensitive Detection As with most spectroscopic techniques, in NMR there has been a constant struggle to improve the receptivity of instruments so that spectra can be obtained with smaller quantities of material. Over the past 60 years, this improvement has been incremental, and resulted from improvements in instrument stability, magnet homogeneity, magnetic field strength, rf electronics, solid state circuitry and probe design. The exception has been the introduction of Fourier transform techniques in the late 1960’s and early 1970’s, which lead to a quantum leap in receptivity. The cumulative effect of these many incremental improvements has been a 105-106 fold gain in receptivity such that with the most sensitivie NMR instruments it is now possible to get 1H NMR spectra from 10-100 ng of material compared with 100mg of material required to obtain spectra from instruments available in the early 1960’s. After many years of instrument improvements, the major sources of noise in the NMR experiment are now the detection coil and the sample itself. In the past decade, probes with the detection coil cooled to cryogenic temperatures have become commercially available. In these probes the detection coil is typically cooled to 200K, while the sample located a few mm away, remains at ambient temperature. Such probes provide a factor of 4-5 gain in receptivity compared to older style probes in which the coil remains at ambient temperature. Most of these commercial probes are designed to operate with the sample near ambient temperature, using 5mm sample tubes for sensitive detection of 1H, while decoupling 13C and 15N. These probes are primarily designed and used for biological applications. For polymer applications we are not usually sample limited, so that it is desirable to study larger samples. Also, often polymers require high temperature to dissolve or swell the material for high resolution solution NMR studies. Zhou et al. (18) describe a new commercial “cryoprobe” designed for 13C detection using 10 mm sample tubes, heated at temperatures up to 420oK, while the coil temperature remains at 20oK. Under these conditions, they observed almost 6-fold increase in receptivity compared to a standard 10 mm probe designed for 57 In NMR Spectroscopy of Polymers: Innovative Strategies for Complex Macromolecules; Cheng, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2011.

13C


detection. This new cryoprobe permitted them to study the minor structure components in poly(propylene-co-1-octene) using 13C NMR.

Figure 8. 100 MHz 13C NMR spectra of poly(propylene-co-1-octene): a) INADEQUATE spectrum showing correlations of the major structure components; b) vertical amplification of the spectrum in (a) revealing additional correlations from minor structure components; and c) 1D-NMR spectrum. Reproduced with permission from reference (18). In this copolymer, the major structure component is polypropylene; the next major component is derived from insertions of 1-octene units within the polypropylene backbone; and finally the smallest component is derived from inverse addition of propylene units. The study of this polymer’s structure 58 In NMR Spectroscopy of Polymers: Innovative Strategies for Complex Macromolecules; Cheng, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2011.


requires sensitive detection of the weakest signal components. The 100 MHz 13C 1D-NMR spectrum is shown in Figure 8c; the three signals that are off scale (labeled (CH2)PP, (CH2)PO, (CH)P and (CH3)P) are derived from CH, CH2 and CH3 carbons of “normal” polypropylene segments; the set of signals that fall near half scale (labeled 1B6 – 6B6 and (CH)O) are from 1-octene units incorporated into the polymer; and the weak signals that are labeled with capital letters (C, D and F-N) are derived from inverse addition of propylene units. The latter labels indicate resonance assignments corresponding to the labels on the structure at the top of Figure 8. The 2D-INADEQUATE experiment provides correlations among the resonances of carbons related by 13C-13C attachments in a structure. Because these spins occur together in only 1/104 molecules, obtaining an INADEQUATE spectrum is 100 times more difficult than performing a simple 13C 1D-NMR experiment. Their plot of an INADEQUATE spectrum in Figure 8a, showing correlations identifying the major structure fragments in the polymer, represents the capabilities of most state-of-the-art NMR spectrometers. The vertical amplification of this spectrum, shown in Figure 8b, reveals additional correlations identifying low concentration structures from inverse propylene addition. These structures are present in 3-5 times lower concentration. Their 2D-INADEQUATE spectrum took 2.6 days to collect using a “cryoprobe” with a 10 mm coil. They estimated that it would take 2.6 months to collect a similar spectrum on a 400 MHz spectrometer using a standard probe with a detection coil at ambient sample temperature. If quantitative 13C 1D-NMR experiments are to be performed with senstitive detection of weak signals, cryoprobes like the one described here could boost an instrument’s productivity by 30-fold when long-term signal averaging is necessary. Alternatively, it might be possible to detect weak signals in a weekend using this cryoprobe, when another lab with a standard probe would never be able to dedicate 3 months to collection of a single spectrum.

Multiple Receiver Systems Multiple receiver systems have been used to speed up collection of image data in magnetic resonance imaging (MRI) applications. These multiple receiver systems are beginning to appear in labs doing high resolution NMR in chemistry related applications. In one paper, representative of one application area, Kupce et al. (19) were able to nest 1H{13C}-HSQC and 19F{13C}-HSQC 2D-NMR experiments and to use an instrument with two receiver channels to simultaneously detect the 1H and 19F signals (Figure 9). Such work had not been reported with a polymer sample so the illustration here is with data from a small molecule. Two separate experiments were performed simultaneously to double the productivity of the instrument. The reader is encouraged to look at the cited literature in this paper to learn of other possible variations. These experiments can increase the productivity of instruments that are dedicated to routine screening of samples. 59 In NMR Spectroscopy of Polymers: Innovative Strategies for Complex Macromolecules; Cheng, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2011.


Figure 9. Nested HSQC pulse sequences (left) to produce 1H (black) and 19F detected HSQC spectra (right). Reproduced with permission from reference (19).

Alternative Lock Channel Another valuable use of instruments with a second receiver systems is as an alternative to the field-frequency locking system. In order for the NMR signal to add coherently, the peak frequencies must remain fixed from one transient (and one spectrum) to the next. To compensate for magnetic field drift, instruments have a third complete rf channel to monitor the frequency of a third nucleus and to adjust Bo to maintain a constant resonance frequency. In almost all cases, this third nucleus is 2H from a deuterated solvent. Deuteration of the solvent also has the fringe benefit of reducing the solvent signal strength, especially in 1H NMR. In solution NMR studies of polymers, it is often necessary to use exotic solvents to dissolve the material, or to heat and swell the polymer. For example, chlorinated solvents such as tetrachloroethylene or dichlorobenzenes are often used to study polyolefins, because they permit heating the sample to 120-140oC. At these temperatures, the polymers swell and produce high resolution spectra. Often deuterated forms of these solvents are expensive or unavailable and alternatives are needed to provide the needed lock signal. These range from incorporating a small amount of a deuterated cosolvent, to addition of a capillary containing a high boiling deuterated solvent to the center of the NMR tube. Kupce and Freeman (20) used their second receiver system to monitor the frequency of an independent NMR signal and to calculate a correction factor to be applied to the spectrum during the data processing stage. Their results are shown in Figure 10. In Figure 10a and b, the results from plotting a 13C NMR signal from a 0.1 M solution of sucrose are shown without and with compensation for field drift, respectively. Figure 10c and d show the effects of field drift on the HMBC spectrum without and with compensation, respectively.



Figure 10. Results from using a second receiver as an alternate lock channel while collecting HMBC spectra of 0.1 M sucrose in D2O: a) 13C signal monitored without lock and b) the same signal as in (a), but with digital compensation for field drift; c) HMBC spectrum without lock and d) same spectrum as in (c), but with compensation for field drift. Reproduced with permission from reference (20). 61 In NMR Spectroscopy of Polymers: Innovative Strategies for Complex Macromolecules; Cheng, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2011.


Summary This paper presents a small sampling of the new NMR capabilities that can potentially impact polymer NMR spectroscopy. There are many advances in NMR hardware, software and methodology that could not be mentioned here. Space limitations require that the list stop at some point. If anything, the NMR field seems to be advancing at a more rapid pace than ever before. Advancements continue to contribute to improving the sensitivity of the NMR experiment so that it is possible to work with smaller samples (or detect lower occurrence structure components). New NMR methodologies help to provide information about new structure components so that detailed structure information can be resolved. New computers and software automate experiment setup so that once methodology is developed, it can be applied by users who are not expert in NMR. Development of powerful computers and software will make it easier to extract information from complicated spectra or groups of spectra. For new workers in this field, the times are as exciting as ever.

Acknowledgments The author wishes to thank the National Science Foundation (DMR-0905120) for financial support during the preparation of this work. The author also wishes to thank current and former research group members, University of Akron NMR Center staff members (past and present) and collaborators who are too numerous to mention here. They have contributed in countless ways to exciting research and learning experiences over the past few decades.

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