Characterization of Materials with NMR Spectro - American Chemical

Chapter 9

Characterization of Materials with NMR Spectroscopy Downloaded by UNIV OF FLORIDA on November 7, 2017 | http://pubs.acs.org Publication Date (Web): November 2, 2017 | doi: 10.1021/bk-2017-1258.ch009

Cecil Dybowski* Department of Chemistry and Biochemistry, University of Delaware, Newark, Delaware 19716, United States *E-mail: [email protected]

NMR spectroscopy is a major characterization technique. With modern technology addressing the state of solids, it provides a tool for understanding the character and function of materials. Examples are given from work at the University of Delaware.

Introduction Beginning in the 1940s and continuing after World War II, an era of application of new technology to characterize substances brought a panoply of new ways to address the identities of molecules. Among the spectroscopic techniques to which chemists had access was the newly discovered technique of nuclear magnetic resonance (NMR) spectroscopy (1, 2). The dependence of NMR parameters on chemical state pointed the way to the ultimate importance of the technique for chemical analysis (3, 4). The use of NMR spectroscopy of protons revolutionized chemical analysis, particularly of organic materials (5). Later, the application of 13C NMR spectroscopy added a new dimension to organic analytical capabilities in the late 1960s and early 1970s. Over the decades, Professor Eliel contributed materially to the use of NMR spectroscopy, particularly 13C NMR spectroscopy, to study conformation and dynamics of organic molecules in solutions (6). In the 1960s and thereafter, chemists began to study other nuclei than 1H and 13C, which added to the versatility of analysis with NMR spectroscopy. Today the analytical capabilities of NMR spectroscopy are applied to problems involving a wide variety of chemical systems because of the ease of studying many different nuclei.

© 2017 American Chemical Society Cheng et al.; Stereochemistry and Global Connectivity: The Legacy of Ernest L. Eliel Volume 2 ACS Symposium Series; American Chemical Society: Washington, DC, 2017.

Downloaded by UNIV OF FLORIDA on November 7, 2017 | http://pubs.acs.org Publication Date (Web): November 2, 2017 | doi: 10.1021/bk-2017-1258.ch009

In the early period, most applications of NMR spectroscopy by chemists involved either neat liquids or dilute solutions of solids. Although physicists had continued to study the NMR spectroscopy of solids since its discovery, chemists tended to focus on the NMR spectroscopy of liquids and solutions during that era. By the early 1970s, however, chemists had begun to study the chemical properties of solids with NMR methods (7–10). Examples began to be seen in the chemical literature of applications of NMR spectroscopy to technologically relevant solid-like materials, such as polymers, zeolites, and catalysts (11–18). The distinction, from the viewpoint of NMR analysis, between a solid and a solution is the time scale on which the major dynamics of constituent molecules/atoms occur. In a solution at room temperature, fast isotropic random motions on the sub-nanosecond time scale produce substantial dynamical averaging of magnetic interactions, with the result that spectra contain only dynamically averaged information. The relatively fixed positions of the confined molecules/atoms of a solid (or the anisotropic rapid motions) limit that averaging. Thus, NMR spectra of soluton and solid samples often appear noticeably different, even though they arise from the same interactions. Starting in the 1960s and continuing to the present, the use of computational techniques in chemistry also has had a considerable impact on NMR spectroscopic analyses. The prediction of NMR parameters such as magnetic shielding and spin-spin coupling from known or expected structures was at first limited by speed and memory of computers, but as the computational techniques became more efficient and reliable, the ability to characterize materials by comparing experimental results to theoretical predictions has added to the arsenal of techniques for understanding chemical identity with NMR spectroscopy. Very often, calculations of NMR properties have been performed on isolated-molecule models, with the extra-molecular local environment being treated, if at all, in some mean-field approximation. In this article, I describe the application of NMR spectroscopy to materials, which are naturally mostly solid or solid-like. Many materials are more readily characterized by NMR spectroscopy of nuclei other than protons and carbons. As a consequence, the spectroscopy appropriate to “unusual” nuclei and to solid-state structures is important in these experiments. These problems further demonstrate how, to make a computational prediction based on known structure, one must treat nuclei embedded in a solid, rather than in an isotropic fluid or an isolated molecule.

Solid-State NMR Spectroscopy With NMR spectroscopy, one determines the magnitudes of magnetic interactions of nuclei with their environments (19). The various interactions are specified by an expansion of the nuclear magnetic Hamiltonian, with terms appropriate to the interactions, as indicated in equation 1.

136 Cheng et al.; Stereochemistry and Global Connectivity: The Legacy of Ernest L. Eliel Volume 2 ACS Symposium Series; American Chemical Society: Washington, DC, 2017.


where the various terms represent typical interactions of the nuclear spins with the environment. The first is the Zeeeman coupling to the applied magnetic field, followed by the coupling to the radio-frequency magnetic field, the magnetic shielding of nuclei by coupling to electronic motion, the indirect spin-spin coupling, the coupling of the quadrupole moment of the nucleus (if it is non-zero) to the electric-field gradient, and the direct through-space dipole-dipole coupling of nuclear spins. In some cases, terms may be added to represent other interactions that may affect the NMR spectrum, but these in Eq. 1 are the common interactions typically affecting NMR spectroscopy. Each is characterized by a parameter or parameters that define the engagement of the nucleus with its environment, and it is these characteristic parameters for a particular material that give information on the state of the material. Not all terms in the Hamiltonian in Eq. 1 are accessible in all NMR experiments. In particular, the fast, isotropic random motion of liquids often results in averaging of effects for common experiments on solutions. The effects of the dipolar and quadrupolar terms average (in first order) to zero, and their effects are not apparent in first-order solution-state NMR spectra. Similarly, under fast, isotropic, random motion, the effects of other terms are limited only to those parts that are non-zero. The magnetic shielding and the spin-spin coupling only display isotropic average effects. (In experiments at sufficiently high magnetic fields, the influence of the field can be strong enough to encourage the rapid motion to be anisotropic, the result of which is reintroduction of the effects of averaged tensor properties such as magnetic shielding and dipolar coupling, but we shall not discuss these in this chapter.) To detect the effects of these anisotropic interactions, one must carry out the spectroscopy on nuclei whose nuclear environment is fixed during the time of the experiment, and that usually means examination of solids. There are two basic means of examining solids: (1) with a sample that is a single crystal; and (2) with a powder of microcrysallites. In the first case, one detects only signals of molecules at one or a few specific orientations of the molecular framework relative to the magnetic field; in the second case, one simultaneously detects the signals from molecules having many different orientations of the molecular axes relative to the magnetic field. In either case, one is able to extract information on the parameters describing the interactions, including how they depend on the structural relation between the molecular framework and the magnetic field. An example of the spectroscopy of a solid subject only to the full magnetic shielding Hamiltonian is given in Figure 1. The 13C NMR spectrum of a solid consisting of microcrystals of CO2 is a band, the shape of which is characteristic of materials having the nuclear center sitting on an axis of cylindrical symmetry. Each point on the spectrum corresponds, in this case, to a specific orientation of the cylinder axis relative to the magnetic field. The intensity at each point is determined by the number of ways in a random distribution of orientations that particular chemical shift is found. From this band, one determines two characteristic parameters of the interaction, the two unique principal components of the 13C chemical-shift tensor. (The magnetic-shielding tensor and the chemical-shift tensor are related, and differ by an additive constant, determined by the reference point for defining the chemical shift.) 137 Cheng et al.; Stereochemistry and Global Connectivity: The Legacy of Ernest L. Eliel Volume 2 ACS Symposium Series; American Chemical Society: Washington, DC, 2017.


Figure 1. Schematic depiction of the 13C NMR spectrum of a random powder of microcryalline CO2. At the top is shown a depiction of how molecules in the sample are oriented relative to the applied magnetic field, B0, for the two extreme chemical shifts.

For a general solid, all of the sub-Hamiltonians of Eq. 1 may be active. The spectrum may be much more complex than that of CO2, in which the magnetic shielding is, by far, the dominant effect. Such situations often call for more complex experiments to extract information. For example, a common organic material is likely to contain many more than a single carbon type. As a consequence, the spectrum of a static powdered sample consists of the overlap of the signals from the various sites, which may mean loss of information. Performing the spectroscopy with magic-angle spinning (MAS) causes the dispersion of the spectral line shape to be suppressed, resulting in a spectrum that is similar to that of a solution for identification of materials, as seen in Figure 2 for the 13C in α-glycine (11). One technical issue is that the 13C nuclei are usually strongly affected by the direct dipole-dipole interaction with adjacent protons in many organic materials. The spectrum in Figure 2 was not only taken while spinning the sample, but also with concurrent irradiation of the protons to suppress the effects of that direct dipole-dipole interaction, allowing observation of the average magnetic shielding that distinguishes each resonance from the other (dipolar decoupling, DD). 138 Cheng et al.; Stereochemistry and Global Connectivity: The Legacy of Ernest L. Eliel Volume 2 ACS Symposium Series; American Chemical Society: Washington, DC, 2017.


Figure 2. The 13C CP-MAS-DD NMR spectrum of α-glycine. There are two carbon resonances. The small resonances are the sidebands of the carboxyl resonance, a phenomenon that occurs in the MAS experiment. A second technical issue is the fact that the natural abundance of 13C is low. To enhance that 13C signal, one uses a technique in which the magnetic moment of the carbon is made larger by transfer of magnetization from the protons in a process called cross polarization (CP) (20). The spectrum in Figure 2 has been obtained by enhancement of the 13C magnetization. This process is made possible by the non-zero direct dipole-dipole interaction with the protons. Such experimental techniques are commonly used in NMR spectroscopy. There is another technical issue that must be resolved when obtaining NMR spectra of other nuclei such as 207Pb. For a nucleus like 13C the whole range of resonance positions spans only about 300 ppm. With current techniques, it is possible to excite all of the various 13C resonances with commonly used techniques using reasonably short pulses, but for nuclei like 207Pb that have ranges of several thousand ppm, that may not be possible (21). In these cases, it is necessary to design excitation protocols to take account of that facet of the spectroscopy. There are several ways to carry out excitation. For example, one can obtain the overall spectrum as a series of subspectra taken to ensure coverage of part of the NMR line shape. This technique is sometimes automated by summing responses with the so-called variable-offset-chemical-shift technique. One may attempt to excite over a much wider range than usual by incorporating elements into the excitation scheme that spread the energy. The success of the application of a technique largely depends on the specific situation. In Figure 3 are shown three 207Pb NMR spectra of a random powder of lead acetate. In Figure 3a, the spectrum is determined while spinning the sample about the axis canted at the magic angle to the magnetic field. The sideband pattern arises from the fact that the spinning rate is low compared to the width of the spectrum in hertz. From fitting of the intensity profile, one obtains the three principal components of the 207Pb chemical-shift tensor. In Figure 3b, the 139 Cheng et al.; Stereochemistry and Global Connectivity: The Legacy of Ernest L. Eliel Volume 2 ACS Symposium Series; American Chemical Society: Washington, DC, 2017.


spectrum is obtained by use of the wideband-uniform-rate-smooth-truncationwith-Carr-Purcell-Meiboom-Gill-detection (WURST-CPMG) experiment, which spreads the excitation to excite across a range of several thousand ppm uniformly. The envelope of the spikelets clearly indicates the three principal components of the chemical-shift tensor. In Figure 3c is shown the result of a similar experiment, called the Carr-Purcell-Meiboom-Gill (CPMG) experiment. In this spikelet spectrum, one sees excitation across a reasonably wide range, but the shape shows that the excitation is not as uniform as it is in the WURST-CPMG experiment of Figure 3b. Of note is the fact that the excitation trails off quickly in the region between -2800 and -3000 ppm, with the result that one might misinterpret the position of the sharp edge and, therefore misstate the value of the δ33 component. Additionally, the line shape in the CPMG experiment depends on where the central carrier frequency of the NMR experiment is set.

Figure 3. 207Pb NMR spectra of a powdered sample of lead acetate. (a) Taken with MAS spectrometry; (b) taken with the WURST-CPMG experiment; (c) taken with the CPMG experiment. For mild distortion of the excitation, one may characterize the excitation profile independently. Knowing the empirical distortion function, one may correct for the non-uniform excitation with the “transfer function” (22, 23). Although 140 Cheng et al.; Stereochemistry and Global Connectivity: The Legacy of Ernest L. Eliel Volume 2 ACS Symposium Series; American Chemical Society: Washington, DC, 2017.


the procedure has been shown to work well when the excitation profile is only slightly non-uniform, the use of wideband excitation experiments, such as the WURST-CPMG experiment, is preferred (24). Even with WURST-type excitation, if the NMR spectrum is sufficiently wide, the WURST excitation can be non-uniform over the spectral window. Under such conditions, one may take recourse to the idea of variable-offset-cumulativespectroscopy (25). The idea is straightforward. For very wide bands, one uses an experiment in which a portion of the data is taken with one setting of the carrier frequency. A second portion is taken with a different setting of the carrier frequency to excite another portion of the spectrum. That procedure is repeated until all areas of the NMR line shape are excited. Combining these subspectra into a single spectrum produces the full spectrum. The accumulation may be done before or after Fourier transformation. In our laboratory, we proceed after Fourier analysis of the individual subspectra, requiring matching of intensities at the overlap of two regions. There are many “tricks” used to obtain information in NMR spectroscopic experiments. The use of specific excitation sequences to suppress the action of certain parts of the Hamiltonian is typical, yielding a spectrum that emphasizes only part of the information available. The development and use of multidimensional NMR techniques allows one to correlate separate pieces of information about a system, such as how close two nuclei are with what sites they are. A discussion of the various ways in which experiments are designed to emphasize particular information or deal with the effects of unusual interactions could easily fill a book. The important point is that the parameters extracted from any spectrum give a picture of the state of the system. In the end, one must rationalize these bits of information with other ways of describing the material to provide as complete a description of the system under study as possible.

Computational Chemistry and NMR Spectroscopy One facet of NMR spectroscopy (as with other forms of analysis) is the assignment problem. One may detect NMR features, such as the two peaks in Figure 2 arising from the two different carbon sites of α-glycine. But, how does one a priori link a specific parameter (in this case, the chemical shift) to a specific site? In the early days (and to some extent, still today), assignment was carried out by analogy. The spectra of many different carboxylic acids with 13C NMR spectroscopy always showed an absorption peak in the region between 170 and 180 ppm relative to tetramethylsilane, which was assigned to a transition involving carbon nuclei in that environment. Over the years, many assignments have been made so that there are now libraries that show consistent trends with variation of environment. Such assignments are aided, in some cases, by observation of the spin-spin coupling to adjacent nuclei. Almost immediately after their development, two-dimensional NMR techniques for solutions had shown the benefits of correlation of various resonances through the spin-spin coupling. Whatever the NMR technology, the 141 Cheng et al.; Stereochemistry and Global Connectivity: The Legacy of Ernest L. Eliel Volume 2 ACS Symposium Series; American Chemical Society: Washington, DC, 2017.


assignment of resonance positions in unknown materials has been empirical, relying on analogies to NMR absorptions in molecules of similar known local structure, i.e. the “group effect”. NMR parameters are descriptors of the quantum mechanical state of a system consisting of nuclei and electrons. A knowledge of the quantum mechanical wave function of such a system allows one to relate those NMR descriptors to other parameters such as positions of atoms and strengths of bonds. The theory of the effects of electrons on NMR magnetic shielding was, for example, given only a few years after the discovery of NMR. In principle, calculation of magnetic shielding for known structures should be a means to define systems. Although there had been efforts to provide the link between the measured quantities and computationally derived quantities, the full capability of calculation had to await the development of fast, multiprocessor computers to begin to provide a meaningful implementation of calculation. For molecular systems, one may model the molecule as an isolated entity. In principle, this model of a gas-phase molecule works rather well for molecules in the gas phase or in dilute solution. If the environment outside of the molecule in solution is included, it is often treated in some mean-field approximation such as the conductor-like screening model (COSMO) or the polarizable continuum model (PCM), particularly when there is evidence of interaction with the solvent. For molecular solids, the nucleus-bearing molecule is embedded in a fixed structure of surrounding molecules, and the structure persists for a significant time, rather than being dynamically averaged to some sort of continuous distribution throughout the surrounding space. In this case, a proper model must include those intermolecular interactions when making predictions of the electronic state (from which one predicts the NMR parameters such as magnetic shielding). There are at least two ways to model such systems. The first type of model is based on the known periodicity of the solid lattice. A widely used method is the gauge-including projector augmented wave (GIPAW) approach of Mauri and Pickard in the density functional theory formalism (26). In this approach, the orbitals are expanded in a plane-wave basis that describes the lattice structure. Calculations of NMR parameters follow directly from the knowledge of the electron density as a function of the position. The second type is the cluster model (27–29). In this formalism, the lattice is described relative to the nucleus of interest. A cluster of atoms describing the environment is determined relative to the nucleus of interest. Ultimately, the cluster ends at some terminal atoms (usually forming a molecule for molecular solids). The important point is that NMR effects such as the magnetic shielding and the quadrupolar coupling are relatively short-range, and as one increases the size of the cluster modeling the environment, the predicted NMR parameters converge to a limit. Knowing the local symmetry of the nuclear site in a solid, one may choose as models clusters that have symmetry elements in common with the site in an infinite solid. For example, in Figure 4 is a cluster of 15 β-D-fructopyranose molecules which has the point symmetry elements at the central site in common with the space group P212121. Such symmetry-adapted structures are used to ensure that calculations reflect the known structural features of a solid object. 142 Cheng et al.; Stereochemistry and Global Connectivity: The Legacy of Ernest L. Eliel Volume 2 ACS Symposium Series; American Chemical Society: Washington, DC, 2017.


Figure 4. Cluster of 15 molecules of β-D-fructopyranose, such that the central point has the point symmetry of a similar point in the space group P212121. (Reproduced, with permission, from reference (29). Copyright 2017 by Sean T. Holmes.) In certain cases, the material is a network solid. In such materials, although the stoichiometry may be simple, e.g. PbO, the local structure of the material may have a general Pb site with strong interactions with more O sites than implied by the stoichiometry. Often, under these conditions, it is not possible to choose a truncation that creates an uncharged cluster and also maintains the point symmetry at the nuclear site. Approximations that allow one to carry out calculations must be made for such materials. By a judicious choice of computational method, including in some cases treatment of some or all electrons as relativistic objects (e.g. those associated with heavy nuclei like Pb or Hg), one may reliably predict the NMR properties of solid materials, essentially in agreement with measured NMR parameters. The combination of computational chemistry with NMR spectroscopy of solids allows one to specify the material and its structure to the point that some have suggested that NMR analysis with structure incorporation is a means of specifying structure, in a technique complementary to traditional diffraction-based techniques.

Examples of NMR Characterization of Materials Orientation in Polymeric Materials In processes like extrusion, extension, or compression, a material that originally had no macroscopic orientation of molecular or crystallographic axes 143 Cheng et al.; Stereochemistry and Global Connectivity: The Legacy of Ernest L. Eliel Volume 2 ACS Symposium Series; American Chemical Society: Washington, DC, 2017.


can commonly be induced to form an oriented material. Whether the orientation is transitory or permanent or what the extent of the orientation turns out to be depends on many variables. Thus, measures of the orientation of molecular structures in such a macroscopic sample are aids in determining the effects of these processes. One may address the question of the orientation with a variety of structure-sensitive techniques, such as X-ray analysis or electron microscopy or optical birefringence. The strong dependence of the NMR response on the orientation of a molecule in the magnetic field provides a means to use NMR to infer the distribution of oirentations in an oriented material (30). The band shape of a nucleus in a polycrystalline material, such as that of CO2 in Figure 1, depends on the manner in which the principal axes of the chemical-shift tensor (which specify how the position of resonance depends on the orientation of molecular axes relative to the direction of the magnetic field) are laid out in space. The schematic band shape in Figure 1 results when there is a random distribution of these molecular axes for CO2 relative to the magnetic field direction. Should the sample be macroscopically oriented, the shape of the band is distorted from that ideal shape in a manner characteristic of the orientation process. By careful analysis of the band shape and how it depends on the orientation of macroscopic sample axes to the magnetic field, one may specify the orientation distribution of the chemical-shift axes relative to the macroscopic axes (which are generally determined by how forces are applied in the process that produces orientation). As an example, Figure 5 shows two theoretical spectra. The chemical-shift tensor has only two unique principal components in this case. In (a), the characteristic spectrum of a random polycrystalline sample, i.e. the usual case for a system not subject to orienting forces, is shown. In (b) is shown the spectrum of a sample that has been subject to some uniaxial orienting force. Generally, for a sample subject to a uniaxial stress, the distribution can be described relative to the direction of that uniaxial stress. Thus, the spectral shape depends on the orientation of the axis of stress relative to the magnetic field. Figure 5b shows the theoretical spectrum of a uniaxially deformed sample for one particular orientation of the stress axis relative to the magnetic field direction. Placing the sample in the magnetic field at some other orientation of the stress axis results in a different, but related, spectrum (31, 32). An analysis of the band shape for a known orientation of the two axes such as Figure 5b can, in principle, allow a specification of how the stress produces orientation of the chemical-shift principal axes. However, there are other effects that may also cause dispersion of the resonance that are folded into this spectrum. To compensate for other non-orientation-dependent effects, a study of the variation of the band shape with the orientation of a macroscopic axis of the sample (often the direction of stress in a uniaxially deformed material) relative to the magnetic field direction is often performed, as was done in a study of the uniaxial orientation of poly(tetrafluoroethylene) (30). In that case, the chemical shifts were known for the situations in which the microcrystallite axes were oriented parallel to and perpendicular to the magnetic field. The analysis produced a specification of the orientation distribution function (relative to the stress direction) in several uniaxially deformed materials (Figure 6). 144 Cheng et al.; Stereochemistry and Global Connectivity: The Legacy of Ernest L. Eliel Volume 2 ACS Symposium Series; American Chemical Society: Washington, DC, 2017.


Figure 5. Simulated spectra of an NMR band for an axially symmetric chemical-shift tensor. (a) The band shape for a random distribution of microcrystallite axes relative to the magnetic field direction. (b) The band shape for a nonrandom distribution of microcrystallites in a uniaxially oriented object. Note that the non-random distribution tends to overemphasize certain resonance positions relative to the random distribution, and that others are de-emphasized relative to the random distribution. The NMR-based orientation analysis can also be applied to cases in which the material is subject to a more complex force field. For example, one may interrogate the distribution due to biaxial orientation of a film. The major requirement is that one must link the orientation of the chemical-shift principal axes to axes of interest that define the molecular frame. It is often the case that the chemical shift symmetry reasonably follows the symmetry of the electronic structure, thereby allowing one to specify the orientational effects on these electronic co-ordinates. It is also possible to address orientational effects at various points in a molecule by use of specific NMR probes at those points of interest in the molecule. One may study other processes such as disorientation, for example by subjecting the sample to heating with free ends (32). Identification of Species at Catalytic Surfaces The principal use of NMR spectroscopy has been the identification of molecular species. It has been used repeatedly over the last seven decades as a means to specify the outcome of organic reactions because of the straightforward relationship between NMR parameters and structure. In the last 40 years or so, the development of multidimensional NMR techiques that correlate parameters has added tools to allow the study of ever-more-complicated materials (33). 145 Cheng et al.; Stereochemistry and Global Connectivity: The Legacy of Ernest L. Eliel Volume 2 ACS Symposium Series; American Chemical Society: Washington, DC, 2017.


Initially, and perhaps still usually, the material of interest is dissolved in some solvent and dynamical averaging limits one to the study of dynamically averaged NMR parameters. However, the application of NMR to other forms of matter and other situations also provides information on structure and electronic states, such as molecules in crystalline solids, molecules dissolved in ordered liquids (liquid crystals), and species in surface phases (34–36). Since the early days of proton NMR spectroscopy, it has been applied to solid phases, as well. The line shape is often dominated by dipolar interactions, and this may be used to give information on internuclear distances, such as the measurement of the proton-proton distance in gypsum (37). The presence of dynamics in solids also affects NMR line shapes, because the averaging of the dipolar effects depends on the geometry and time scale of such motions (38, 39). The application of NMR spectroscopy to surface phases, such as one might find in studies of catalytic processes, has a number of disadvantages. For one, the species of interest are often dilute because they comprise only a small volume of the sample. For another, the other material may have interfering resonances that appear in the spectrum. For yet another, the electronic structure at the surface of particle (usually where the phases of interest reside) may give rise to a large variation of the magnetic environment, including inhomogeneties that wipe out the distinctions normally expected among different functional group that are the key to distinguishing various phases with NMR spectroscopy.

Figure 6. Simulations of NMR-derived orientation distribution functions for poly(tetrafluoroethylene). The three colors represent samples stretched to three different extension ratios. The distribution function can be divided into two parts, one that aligns with a specific distribution width and the other being a disordered random phase. Upon longer extension, the amount of ordered phase increases and the amount of disordered phase becomes smaller. [After reference (31).] 146 Cheng et al.; Stereochemistry and Global Connectivity: The Legacy of Ernest L. Eliel Volume 2 ACS Symposium Series; American Chemical Society: Washington, DC, 2017.


These disadvantages notwithstanding, it has been possible to analyze surface phases with NMR spectroscopy. For example, early on, hydrogen species on the surface of supported metal catalysts were extensively studied with NMR spectroscopy (14, 15, 40, 41). The use of carbon NMR spectroscopy, usually with 13C-enriched materials extended the usefulness of the technique to address questions about the involvement of organic materials in catalytic processes (42–51). These studies often involved the observation of the conversion of one organic species into a second species, as well as the observation of species unique to the surface environment. Because of the binding at surfaces that may affect orientational information about the species at the surface, NMR properties such as dipolar couplings (48, 52) and quadrupolar couplings (53) have been used to determine geometric factors. For example, in chemisorbed benzene at room temperature, the resonance line shape is consistent with bonding onto small platinum clusters in which the centroid of the benzene ring lies over a platinum atoms, as opposed to lying over the bridge site or the threefold-hollow site, and the magnitude of the coupling suggested that, at room temperature, the benzene ring was rapidly spinning about its six-fold axis (52). Adsorption of phenanthrene into a porous zeolite at low concentrations, showed the presence of a two-phase system in which one phase was bound and the other was highly mobile, as if in a gas phase. The temperature dependences of the relative amounts of the two phases suggested that an equilibrium was established been the two phases, from which one could estimate the enthalpy of transition (53). Comparison to gas-phase binding to ions suggested that the process was the binding of phenanthrene molecules to counterions in the zeolite. Reactions can be probed because NMR spectroscopy is sensitive to the local environment (54–56). The power of obtaining structural information from dipole-dipole interaction strengths of nuclei at surfaces provides imilar information to that for a solid or anisotropic liquid (57, 58). For example, specification of distances determined with NMR spectroscopy in adsorbed benzene relied heavily on the interaction between the protons of benzene and 195Pt nuclei in supported platinum catalysts (52). The effect of motion on the dipolar coupling affecting 13C in enriched benzene, indicated that benzene was sorbed on a supported platinum catalyst in a variety of energetically distinct sites (48). The use of the SEDOR technique to determine proximity of sites that contain NMR-active nuclei, as was the case in measurement of Pb-Al distances in Pb-exchanged zeolites, can allow the determination of structure or placement of ions on catalytic structures (59).

Use of NMR as a Probe To Study Porous Materials A commonly used technique for investigation of materials is through the use of a probe that senses the local environment, but does not participate too strongly to perturb the system. One probe that gained popularity for studying porous materials such as zeolites or clathrates is sorbed xenon gas (60–64). The weak interaction of xenon atoms with the local environment is reflected by changes in the NMR parameters of 129Xe. For example, the chemical shift is sensitive 147 Cheng et al.; Stereochemistry and Global Connectivity: The Legacy of Ernest L. Eliel Volume 2 ACS Symposium Series; American Chemical Society: Washington, DC, 2017.


to the collision rate and the type of partner with which the xenon atom collides. For example, xenon sorbed in a faujasite at low concentrations has a resonance frequency that is about 60 ppm from the low-pressure resonance position of xenon in a macroscopic space (64). The study of the influence of the environment on the xenon NMR parameters has led to its use in characterizing porous materials (62). The resonance position relative to the resonance position of the gas in a macroscopic space depends on the size of the space in which the xenon is trapped, first shown for zeolite adsorption of xenon. Similarly, xenon trapped in small cages in clathrates show a dramatic shift relative to low-pressure xenon in a macroscopic space (65). Of course, other effects may be present. In certain cases, paramagnetic counterions in the zeolite also affect the NMR parameters such as resonance position (66). The temperature at which spectroscopy is carried out may affect the spectroscopic parameters, giving information on the dynamical state (67). In cases where dynamics of the porous material are important, one may investigate the change in NMR parameters of sorbed xenon to determine elements of the dynamics of the porous material (68). Xenon can probe the void volumes of other materials, such as polymers to yield information on the space (69). In fact, one may use the NMR of noble gases like 129Xe and 3He in porous spaces such as lungs to investigate the pore spaces in such materials by MRI (70).

Study of Chemical Changes in Art Masterworks The study of solids with NMR spectroscopy is particularly well exemplified by the investigation of a problem in art conservation (71–73). It has been noticed that, in many masterworks, slow reactions between free fatty acids and pigmentderived ions produce soaps (often lead soaps, when the pigments are lead-based) that cause the appearance of protrusions (soap aggregates), clear spots in paintings, and crazes. A combination of 13C, 207Pb and 119Sn ssNMR has given information on the reactivity of lead-tin yellow type I with palmitic acid (74, 75). Comparison of 207Pb spectra show that the lead coordination in lead palmitate is similar to that of lead stearate, but the structures of both are different from that of lead azelate, and that carboxylates with chain lengths from C6 to C8 are in one structural class, whereas those of C9 or higher fall into a separate class (76). X-ray measurements of lead nonanoate indicate that the local structure around the lead site is quite different from that around lead in lead azelate and lead heptanoate (77). Figure 7 shows a comparison of the 207Pb NMR spectra of three of the pure lead soaps implicated in the deterioration of masterworks. The spectra had to be obtained with a NMR technique specially designed to spread the excitation as uniformly as possible across the region where resonance absorption occurs. Hence, the spikelet appearance. 13C NMR spectra of the lead soaps (Figure 8) also indicate a difference between the short-chain and the long-chain lead carboxylates, in the magnitude of the separation of the two carboxylate resonances. For the long-chain carboxylates (C9, C10, C11, C16, and C18), the separation of the two carboxylate peaks is in 148 Cheng et al.; Stereochemistry and Global Connectivity: The Legacy of Ernest L. Eliel Volume 2 ACS Symposium Series; American Chemical Society: Washington, DC, 2017.


the range of 1.13-1.25 ppm. For the short-chain carboxylates (C6, C7, and C8) and lead azelate, the separation of the two carboxylate peaks is in the range of 0.50 – 0.69 ppm. For the α-carbon, the resonance is doubled, with chemical-shift separations in the range of 2.0-2.1 ppm for C9, C10, C11, C16 and C18, and in the range of 0.50 – 0.69 ppm for C6, C7, and C8. The separation of the peaks for lead azelate is similar to that of the short-chain lead carboxylates. Another spectroscopic distinction between the two groups of lead monocarboxylates is that the 13C methyl resonance is doubled for the short-chain materials, whereas for the long-chain group, the resonance is a singlet.

Figure 7. The local lead coordination environment and the 207Pb WURST-CPMG spectra for (a) lead heptanoate, (b) lead azelate and (c) lead palmitate. Shown at the left of each is a representation of the local Pb co-ordination in each. 149 Cheng et al.; Stereochemistry and Global Connectivity: The Legacy of Ernest L. Eliel Volume 2 ACS Symposium Series; American Chemical Society: Washington, DC, 2017.


Figure 8.

13C

ssNMR spectra of (a) lead heptanoate, (b) lead azelate, (c) lead palmitate.

These observations imply the existence of two conformations of the chain end for the short-chain soaps, whereas for the long-chain soaps there is only a single conformation. The structure of a lead soap depends on the length and the saturation of the fatty acid chain, as well as other factors that affect the local environment (76). In particular, the presence of other materials such as the binding medium may have a measurable effect on the dynamic state. Some studies of soap formation suggest that water can increase reactivity (78). The reaction can readily be monitored with ssNMR 13C spectroscopy because the carboxyl resonances of free palmitic acid and lead palmitate can be distinguished easily (Figure 8). One may observe the slow transformation from the free acid to the soap, as shown in Figure 9. The appearance of lead palmitate in this reaction is a result of diffusion of the reactants, plus reaction. In Figure 10 is shown the half-time, T50, for samples conditioned by contact with different relative humidities before contact with the free palmitic acid. Although there is quite a bit of scatter, the figure shows that the reaction depends on the exposure to humidity. 150 Cheng et al.; Stereochemistry and Global Connectivity: The Legacy of Ernest L. Eliel Volume 2 ACS Symposium Series; American Chemical Society: Washington, DC, 2017.


Figure 9. Product build-up by reaction of free palmitic acid with a lead white paint layer as a function of time for a sample with ~10% (w/w) of the acid. The sample was equilibrated with water at 60% relative humidity before contact with the free acid.

Figure 10. T50 versus relative humidity for the formation of lead palmitate from palmitic acid in a lead white paint film. The trend line is presented to aid the eye in following the data, and does not represent a prediction of the dependence on humidity. Calculation of NMR Chemical Shifts of Solid Materials The exact resonance frequency of a nucleus (whether 1H, 13C, 31P, 207Pb or some other nucleus) in a magnetic field is determined by, among other things, the local electronic structure in the vicinity of the nucleus (79). This facet of the 151 Cheng et al.; Stereochemistry and Global Connectivity: The Legacy of Ernest L. Eliel Volume 2 ACS Symposium Series; American Chemical Society: Washington, DC, 2017.


technique is what gives NMR spectroscopy such a strong analytical utility. In principle, precise knowledge of the electronic structure in the region of a nucleus can be used to predict the resonance frequency (or what is often described as the “local field”) through relationships described in the early years of NMR study (5, 80). However, the resolution of experimental chemical shifts is so great that it only becomes possible to predict the resonance frequencies sufficiently accurately with the extremely precise computational protocols that rival the resolution of the experiment. Differences in experimental frequencies of a part per million require extremely accurate depictions of the electronic structure to allow similarmagnitude predictions of magnetic shieldings. The interpretation of NMR spectra necessarily requires this level of calculational accuracy to allow the association of the NMR parameters with other descriptors of the molecular state. In the early days of NMR spectroscopy, the association was often done by analogy with known spectroscopic characteristics of similar materials. With the development of computational chemistry, it has become ever more possible to link the experimental results to model structures by combining experimental NMR spectroscopy with calculations of NMR parameeters based on the structures. The agreement, for example, between experimental chemical-shift tensor components and calculations of them give confidence that the model structure represents the real structure, to the point that some practitioners refer to the combination of NMR experiment with calculated results as NMR crystallography. There are a number of problems that must be overcome to ensure that the the calculation is sufficiently accurate to allow reasonable comparison with experimental data. Prediction of NMR magnetic shielding requires a precise knowledge of the electronic state, at least in the near vicinity of the nuclear species. That requirement involves several issues, including the requirements of gauge invariance as well as properly including the relativistic nature of electrons, particularly in systems containing heavy nuclei such as 207Pb. The reference problem (making a connection between the theoretical magnetic shielding and the practical chemical-shift scale) also must be addressed. Chemical-shift tensors represent not only the local environment, but also the extended structure of a material, because the extended structure may influence the local electronic structure, as well as have direct effects through susceptibility effects. Inclusion of solid-state structure in calculations of NMR properties is important to model the solid state. For example, it has been shown that NMR chemical shifts are sufficiently sensitive to local environment that agreement of calculated parameters with experimental NMR data on materials like naphthalene allow one to specify a more precise set of structural parameters (81). A major development that opened the possibility of accurate predictions of magnetic-shielding tensors was the implementation of gauge-including atomic orbitals with density functional theory (DFT) (82). The same group would also later include relativistic effects through the inclusion of the zero-order regular approximation (ZORA) in DFT, which opened the possibility of calculation of magnetic shielding of heavy NMR-active nuclei (83). The intermolecular contributions to NMR magnetic shielding have long been appreciated, but it has been difficult to include them because of the limitations 152 Cheng et al.; Stereochemistry and Global Connectivity: The Legacy of Ernest L. Eliel Volume 2 ACS Symposium Series; American Chemical Society: Washington, DC, 2017.


of handling models of the electronic system that contain many electrons (84). For modelling a solid, there are two principal means of including the effects of structure. The first is to use periodic boundary conditions to specify the arrangement of atoms in the unit cell of a solid (26). The second involves the construction of a cluster that represents the region around a nucleus of interest (84, 85). The cluster may be chosen to emphasize a particular effect, such as hydrogen bonding, which may result in a relatively small cluster. To include more intermolecular effects systematically, one creates ever-larger clusters, but there is a practical limit to increasing the size of the cluster for model calculations (27). A careful choice of cluster properties should include such factors as the local rotational symmetry of the nuclear site (29) and the compensation of charge on the cluster, if any. The primary effects come from the electron distribution near the site of the nucleus, so adding or modifying elements further from the nuclear site may not affect the results of magnetic-shielding calculations as much as neglecting the near atoms in a cluster (28). For network solids such as PbO, the bonding is essentially an infinite network. Truncation of the network at any point, for example to create a cluster having the rotational symmetry elements, may leave charge on the cluster that gives a systematic error in calculations of the magnetic shielding. In such cases, it is necessary to compensate for the excess charge on the cluster to create a model that more closely represents the electronic state. This can be accomplished systematically through a bond-valence method developed by Brown (86), which can be applied to reduce the charge on a cluster by modification of the charge on the terminal atoms of the cluster (28, 87). In DFT calculations that provide NMR properties, the inclusion of exchange and relativistic effects have a great effect on the predicted values. For heavy nuclei or lighter nuclei bonded to heavy nuclei, one must take account of the fact that the electrons must be treated as relativistic particles. The inclusion of these relativistic effects by the zero order regular approximation, ZORA, has provided a means to estimate resonance frequencies of nuclei like 43Ca, 207Pb, and 199Hg with a relative accuracy sufficient to distinguish various sites in a solid (27, 28, 88–90). Of course, the amount of exchange incorporated into a calculation has noticeable.effect on the values of parameters like chemical shifts. Holmes has pointed out this effect is particularly strong for fluorine (91). The developments in calculational methods in recent years, both in computational power and in improvements in algorithms, has led to a situation in which comparison of predicted values of NMR parameters with experiment, when carefully done, can form the basis for specifying structure, or to refinement of structure determined by other means.

Conclusions Many materials, particularly technologically important materials, are complex solids. Characterizing these materials requires analytical techniques that are sensitive to the local environment. Solid-state NMR spectroscopy, with its multiple experimental techniques, is particularly well-suited to probe chemical 153 Cheng et al.; Stereochemistry and Global Connectivity: The Legacy of Ernest L. Eliel Volume 2 ACS Symposium Series; American Chemical Society: Washington, DC, 2017.


structure, geometric structure, and dynamics of solid materials. As with liquids or solutions, the identity of a solid may be inferred from the NMR parameters and their similarity to parameters of similar materials. With the advent of multinuclear NMR, the technique can address questions about complex situations. More importantly, the combination of measurements with the predictive ability of calculational chemistry allows on to provide detailed information about structure, for example of active pharmaceutical ingredients. In this article, I have concentrated on examples from work at the Universtiy of Delaware, often in collaboration with others. Whether it is the state of a catalytic material, the effects of macroscopic deformation on polymers, the probing of porous solids, or reaction in a film such as one finds in masterworks of art, NMR spectroscopy provides a means to answer questions of identity and activity. One may find many other examples of the use of these techniques in the literature. The application of solid-state NMR techniques to the study of complex biological systems has provided many examples (92). Applications to such technologically important materials as metal-organic-framework systems has led to a more complete understanding of the nature of these materials, as well (93). Applications to electronic materials have increased understanding of the electronic state of these materials (94). The list continues to expand with time. It appears that what started as an NMR novelty 40 years ago now provides a significant amount of information on solids.

Acknowledgments I am indebted to many students, postdoctoral associates, and collaborators who have provided me with ongoing enjoyment as we have strived to understand nature. I am particularly indebted to funding agencies like the Research Corporation, the Petroleum Research Fund of the American Chemical Society, and the National Science Foundation for support over my career.

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