Instrumentation
Bernard C. Gerstein Departnmni of Chemisby Iowa State University and Ames Laboratory, U S . W E Am=, Iowa 50011
High-Resolution NMR Spectrometryof solids Part I Nuclei reside in houses of marvelous and fascinating architecture. The design of these residences is limited only by the variety of nature and by the scientist's imagination. The details of the plumbing, electricity, and house plans are responsible for processes as diverse as the response of the human eye to light and the lubrication of an automobile engine.
Ever since engaging in the first effort a t materials science, the production of pottery by dehydration of kaolinite, we have been attempting to put this molecular architecture to our own use. In doing so, we have continually attempted to understand the details of the static and dynamic behavior of ensembles of nuclei and electrons in a manner that would give us
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some predictive power over that behavior. Prior to the mid-19%, the chemist spent months and sometimes years of arduous synthetic activity validating the details of a particular molecular structure. The discovery of nuclear magnetic resonance (NMR) in 1946,and the subsequent realization that the transition frequency for a nucleus in a particular chemical environ-
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Figure 1. NMR powder patterns of nuclei me tollowing imeractlm are present: 1 ) dIp&r mupllng tatween two Isolated spins (a). dlpolsr cwpiing between Wee isolatedspins (b). and dipolar coupling among many spins (c):2) shieldinganlsobopy. nonsymmetrlc (d) and axially symmetric (e) penemo: 3) quadwpolar spllnlng. the central '12-'lttransition lor a Spin 3/2system (0:4) J capllng. sarm form as hvc-spin dlpolar psnan (9): and 5) IlkUme broadening (h). me mispemum of nuclei experiencingall 01 ths above lnteractlons will be a convolution(4 of all of ths abave specIra
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ANALYTICAL CHEMISTRY, VOL. 55, NO. 7, JUNE
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shielding anisotropies, dipolar broadening, and the current state of the art of high-resolution solid-state NMR. The second section, to he published in the July issue, will cover applications to polymers, biopolymers, fossil fuels, and technical achievements such as magic angle spinning (MAS, see below) a t low temperatures, slow spinning, recovery of shielding anisotropies in systems with many chemically distinct nuclei, high-resolution NMR in systems with quadrupolar nuclei, and multiple quantum NMR.
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Flgure 2. Static powder pattern and high-resolution NMR (under CPMAS) of 29Siin 1,l. 1-trimethyl-2.2.2-triphenyldisilane Top cwve t h Mme exptrimentai Wms is least squares lit to a suwposition of axially symmebk povder patterns (broad peaks. center). The high+%olution owmum is also shown
ment is an incredibly delicate probe of that environment, added a quantitative and qualitative analytical tool of enormous power to the chemist’s workshop. (The resolution attainable today corresponds to being able to distinguish from Earth two cats sitting 30 cm apart on the moon.) The use of synthesis and infrared (IR) and ultraviolet (UV)spectroscopy, in addition to NMR, made a structure determination of a molecule in the liquid state almost routine. With the advent of large, fast digital computers in the 19608, and appropriate algorithms for the solution of the phase problem, it became possible (hut not routine) to determine molecular architecture in Crystalline solids for systems as large as enzymes via X-ray methods (I). A rather large and important fraction of matter, however, is neither liquid, nor nicely crystalline solid, nor amenable to structural determination by standard liquid-state or solid-state probes. Such systems are “solids” that are not in thermodynamic equilibrium with respect to phase changes (e.g., glasses and glassy polymers) or in which the concept of “macroscopic phase” has no meaning (e.g., cell membranes, biopolymers, and coals). The NMR spectra of randomly oriented solids of such materials as well as of randomly oriented crystalline 782,.
solids are generally broad and featureless as a result of four interactions: dipolar coupling, shielding anisotropy, electric field gradients in nuclei with quadrupole moments, and scalar, or J-coupling, anisotropy. In addition to the above, there is lifetime broadening. The general forms of powder spectra associated with the above interactions are shown in Figure 1. For a nucleus experiencing all of the ahove broadening interactions, the total powder spectrum is a convolution (a) of all the above possible spectra. One of the real triumphs of high-resolution solid-state NMR is the deconvolution of such spectra so that the chemical and physical information available from each.interaction is obtained. Dipolar interactions yield internuclear distances and molecular geometries. Shielding anisotropies give information on coordination symmetries and relative nearest neighbor distances. Quadrupole splitting8 yield.the electric field gradient at the nucleus and thus are a probe of molecular wave functions. Scalar coupling is also a probe of molecular wave functions. Because of the explosive growth of applications of solid-state NMR to chemistry, it is not possible to adequately cover all developments in one article. For this reason, this feature will be published in two sections. The first will cover introductory concepts,
ANALYTICAL CHEMISTRY, V M . 55, NO. 7. JUNE 1983
Shielding Anisotropies The additional information available from solid-state NMR spectra comes as a blessing and a curse. The blessing is that more information is available for the chemist to correlate with trends in reactivity etc., so that we have more predictive power over our environment. The curse is that we must learn some new and perhaps unfamiliar concepts to be able to use this information. One of the new concepts needed to use this information is that of a shielding “powder pattern.” The basic idea is that a single chemical species, such as hydrogen, which exhibits one sharp NMR line in a liquid (ignoring scalar coupling), exhibits a spectrum in a powdered solid that can be as wide as 100 ppm ( Z ) , which is about 10 times the total range of isotropic chemical shifts of protons in organic liquids. I t is important to understand a t this point that the line broadening represented by shielding anisotropy is an inhomogeneous broadening associated with the fact that it is a superposition of spectra of randomly oriented individual nuclei. Each of these nuclei has an inherently sharp line for a particular orientation of nuclear environment with respect to the static field. This fact will be important later when we consider spectra obtained under MAS slower than the shielding anisotropy. For example, in the case of ”Si in trimethyl triphenyldisilane, the isotropic and anisotropic values of the shielding tensors of both silicons in this molecule have been determined in our laboratory. Figure 2 shows the high-resolution spectrum of the solid, obtained using combined cross polarization (CP),strong proton decoupling, and MAS, and the powder pattern of a nonspinning (static) sample fitted to a superposition of two axial powder patterns. Both shielding environments are axially symmetric. A fascinating feature of the shielding symmetries is that they are inverted with respect to each other, i.e., one shielding tensor is oblate, the other prolate. The shielding anisotropy of the silicon attached to the methyl groups is 18ppm. Similarly, the an-
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Figure 3. High-resolution NMR spectrum of protons in maleic acid ( 17) obtained under conditions of combined sample rotation and multiple-pulse proton-decoupling spectroscopy
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isotropy of the other silicon is a negative 31 ppm. Note that, in addition to an isotropic value of a shielding, the chemist no-’ has a symmetry, a sign, and a magnitude with which to characterize a shielding environment. The amount of available information from a high-resolution solid-state NMR measurement of a powder has been multiplied by a factor of four relative to a measurement of a liquid! There are three important points in the above discussion. The first is that “nonstandard” (in general, low ah=dance) nuclei such as BSi are readily measured with sensitivity enhancement techniques available to the solid-state NMR spectroscopist. The second is that even with severely overlapping tensor powder patterns, individual shielding anisotropies may be obtained via a number of available techniques developed recently. Third, certain nuclei, such as I13Cd, have isotropic and anisotropic shieldings that are relatively very sensitive to local environments. This fact promises to be of great use in studying active sites in enzymes in which metal ions may be replaced by CdZ+. A detailed list of I13Cd chemical shifts and some anisotropies of Cd in solids has been published by the author (3)and hy Mannitt et al. ( 4 ) . In addition to the added fingerprint of shielding anisotropies, it also becomes necessary ta learn how this information can be used to infer details of molecular behavior not readily available from high-resolution liquidstate NMR. We have seen that a nucleus in a particular liquid-state envi-
784A * ANALYTICAL CHEMISTRY, VOL. 55. NO. 7 , JUNE 1983
ronment has a characteristic isotropic shielding. In the solid, the anisotropy of the shielding is added information. However, in a solid in which there is nonisotropic motion, the ahove information becomes modified in a predictable manner. Examples of such solids are liquid crystals, membranes, and mobile surface-deposited species. A part of our subsequent discusion will deal with the effect of motion on the shielding powder pattern. Changes in the powder pattern characterizing the rigid lattice state of the system and the “motional” state can help to characterize both frequency and amplitude of motion in favorable cases. Dipolar Broadening Thus far, we have discussed some of the features of solid-state NMR that make attainable results exciting for the chemist. We now discuss one of the reasons why standard liquidlike techniques applied to solids yield relatively little information. In addition to the shielding anisotropy discussed above, there are two major broadening interactions for the NMR of solid-state species. These are dipolar interactions between different nuclei, a many-body phenomenon, and, for non-spin-llz nuclei, the quadrupolar interaction in a single spin of nuclei such as I4N. The anisotropy of both interactions can be described in tensor form (5).We defer discussion of quadrupolar species until later and concentrate here on the utility and removal of dipolar interactions between spin-’h nuclei, e.g., between ‘H and ISC. The premiere fact to be under-
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ANALYTICAL CHEMISTRY, VOL. 55, NO. 7, JUNE 1983
stood in this context is that a spin-lI2 nuclear moment, 12,produces a magnetic field (the dipole field), Bo, which has the same symmetry and spatial dependence as the magnetic field of a current through a loop of wire or the familiar pattern seen in iron filings arranged about a bar magnet. This magnetic field adds, or subtracts (since I2 can align with or against the dc field), from the static field seen by a neighboring nuclear magnet, 1 1 , producing the energy level scheme and spectrum for 11 that splits the single Zeeman line into a doublet (the Pake doublet). The dipolar splitting, Afo, is dependent upon the length of the internuclear vector, ryand the angle between the applied field, Boyand the internuclear vector, but not upon the magnitude of Bo. This means that a measurement of AfD as a function of 8, obtained by rotating a single crystal or from an NMR powder pattern of the spectrum of an isolated pair of spins, will yield the internuclear distance r. An example of such isolated pairs of spins is 1H in CaS062H20 ( 6 ) .This means that for an isolated pair of spins, NMR in the solid state has the capability of probing internuclear distances with about the accuracy inherent in an X-ray diffraction measurement. Unlike X-ray diffraction, however, there need not be a minimum crystalline size present for such a measurement. This means that structures of surface-adsorbed species can in principle be determined by NMR, even though they would be unattainable by X-ray diffraction. Extended X-ray absorption fine structure (EXAFS), of course, also offers this possibility. Another way of viewing this structural information attainable by NMR (which is not at all high resolution) is that for an isolated pair of spins, a single spin, I t , will precess in the dipolar field supplied by another spin, S, with a dipolar frequency that adds and subtracts from the Zeeman frequency, fo. A measurement of this additional dipolar frequency can yield the molecular geometry. The broad NMR line associated with a powder containing isolated spin pairs is, like the shielding powder pattern, an inhomogeneously broadened line. Nature, however, seldom gives without taking away. There are very few solids with isolated pairs of nuclear spins. This means that not only is the energy spectrum of spin I1 split into a doublet by the presence of the field of I2 or S, but it is also further split by the presence of additional 12's or 5"s. The resulting energy spectrum then becomes a rather broad featureless band of what is essentially a continuum of levels. The lines of each
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spin have been homogeneously hroadened. The NMR absorption spectrum is then a featureless hroad band, about 40 kHz wide for protons in the presence of many other protons or for carbon in the presence of many protons. Indeed this width, in terms of the second moment (7),contains average structural information, but the nicety of detail in the case of isolated pairs of spins has been lost. I t is to be noted, in addition, that even in solids with isolated pairs of spins, the presence of anisotropic shielding leads to confusion, such as in the simple spectrum of Figure 3. For ISC, the shielding anisotropy can be comparable to the magnitude of dipolar broadening between isolated C-C spin pairs, so the confusion in this case is particularly severe. Yannoni and Kendrick ( 8 ) and Zilm and Grant (9) have recently shown means of removing the shielding anisotropy broadening from the response of pairs of '3C nuclei in solid organic molecules to specific rf pulse excitations, while maintaining information on the dipolar splitting. The resulting dipolar powder patterns yield the C-C internuclear distances to an accuracy of 0.005 8, and can be used to orient dipolar vectors with respect to shielding tensors. Thus, internuclear distances of surface-adsorbed species may he determined. One of the triumphs of recent advances in high-resolution solid-state NMR has been that in systems of 788A
many (loz3)coupled spins, the dipolar frequencies of individual hetero-spin'12 pairs (e.g., 13C coupled to 'H in a system with many protons) may be measured, and molecular geometries can be determined. Among the major advances in solidstate NMR has heen the invention of time-dependent techniques to selectively remove one or more of the many interactions that nuclei see in a solid. It is an interesting fact that in 1950, the same year as the Proctor-Yu discovery of chemical shifts, Erwin Hahn (10) laid the basis for what we now call high-resolution solid-state NMR with the discovery of the s p i n echo. This experiment was an example of the decoupliug of a nuclear moment from external field inhomogeneities and from spins of different (heteronuclear) species. Eight years later Lowe (21)and Powles and Mansfield (12) realized that dipolar interactions of spins of the same type (e.g., 'H in the presence of 'H) could he decoupled with the attainment of the solid echo. The theory and techniques of achieving high-resolution NMR in strongly dipolar-coupled spin-'/* systems (e.g., 13Ccoupled to 'H, or IH coupled to 'H, but not '*N coupled to 'H) have heen extensively developed, as recently reviewed (13), to achieve resolution of NMR signals in solids approaching that in liquids. Recent advances in homonuclear decoupling include improved pulse sequences (14) and windowless sequences (15).
ANALYTICAL CHEMISTRY, VOL. 55. NO. 7, JUNE 1983
Rotations in Spin Space and in Real Space Homonuclear Dipolar Broadened Systems. A recent discussion of considerations pertinent to attainment of high-resolution NMR for randomly ordered strongly homonuclear-coupled dipolar systems has heen given (13)-both with regard to salient points of the theory and to experimental details-so no more than a brief summary will be presented here. The major broadening interactions considered in this case are shielding anisotropy and homonuclear dipolar coupling. Strong rf pulse decoupling (rotations in spin space) is used to attenuate the dipolar broadening, leaving shielding anisotropy as the major residual broadening interaction. Removal of the shielding anisotropy is accomplished with a rotation in real space, known as magic angle spinning (16). Minimum requirements are rf powers of a t least 400 W (1 kW is comfortable), with a broadband transmitter being desirable, hut not absolutely necessary, to obtain minimum interference from transients inherent in tuned circuits. The author's experience has been with protons a t 56 MHz, hut there is a t least one commercial spectrometer capable of performing these experiments a t 200 MHz, and the Jena group (17)has reported combined homonuclear decoupling and magic angle spinning a t 270 MHz for protons, with the resolution for protons in maleic acid shown in Figure 3. Easily attainable spinning speeds of 3 kHz are sufficient to avoid the artifact of sidebands, but in fact the problem of sideband interference may he avoided in other ways. However, sidebands contain useful information that may dictate the use of spinning speeds that are small compared to the shielding anisotropy. MAS a t frequencies larger than the shielding anisotropies will avoid spinning sidebands within the spectral width of interest. For protons, this means frequencies generally. larger than 15 ppm or greater than about 3 kHz a t 270 MHz. There are many descriptions of devices for achieving MAS. Basically they are all variations of the early conical designs of Beams (18) and the eylindrical configuration used by Lowe (19). Designs for achieving the homogeneous rf field necessary for homonuclear decoupling experiments have heen published by the author (20)and by the Jena group (17). One ofthe most important contributions to the understanding of rotor stability is that of Doty and Ellis (21). The reader is referred to that paper for some earlier designs in the field. A major contribution of the Doty-Ellis
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work is the recognition that rotors exhibit resonance frequencies (conical and cylindrical) beyond which it is hard to drive them. In the past, rotors have been driven through these resonances by means of physical stabilization with a cotton swab, a fingernail, or by some other artistic subterfuge. With the publication of the Doty-Ellis work, much of the magic has been removed from the field. Machining tolerances on stable cylindrical rotors sufficient to raise the resonance frequencies as high as possible are very tight, however, and require materials such as machinable ceramic for stators. I t is the author’s preference to use the Beams design or a variant for most work involving protons, because of the relatively forgiving nature of such systems to machining errors. Most commercial designs presently use a variation of the conical Beams configuration, but Doty is producing cylindrical rotors commercially. Of particular interest among rotor-stator systems for MAS are the conical designs of Zilm et al. (22),with achievable rotor frequencies of 10 kHz, and of Fyfe e t al. (23), which allows MAS at temperatures as low as 20 K. The critical reader might ask at this point, “Why rotations in spin space and in real space? Why can’t one remove shielding anisotropy and dipolar interactions by just spin-space pulsing or by just real-space spinning?” In fact, both are possible! I t might help the reader to realize that radiofrequency pulse sequences that remove shielding anisotropies also remove shielding differences. The differences in isotropic values of shielding of all chemical species of a particular nucleus are removed, so much chemically desirable information is lost. Pulse sequences that remove both dipolar coupling and shielding anisotropies, however, (13) are used to reveal residual broadening due to lifetimes and are an important probe. MAS, at a rotational frequency greater than either the dipolar interaction or the shielding anisotropy, will remove both broadening interactions. However, easily achievable spinning frequencies do not exceed 4 kHz, and dipolar line widths can he as large as 40 kHz. Hence the need for the Combination of rotations in spin and real space to achieve removal of both dipolar and shielding anisotropy broadening. Rare Nuclei: Spin %. High-resolution NMR of low-abundance nuclei such as 1 W d or generally involves a combination of rotations in spin and real space. The most commonly used combination is detection of the rare spin, using polarization transfer from the abundant spin, and MAS (24,25). Shielding anisotropies of rare spins are generally much higher than those ?BOA
of protons, so if one wishes to avoid dealing with spinning sidebands it is necessary to realize that shielding anisotropies scale as the dc field. This means that a I S C shielding anisotropy that is 5 kHz at a carbon NMR frequency of 14 MHz will become 2 1 kHz a t a carbon frequency of 60 MHz! In fact, as previously mentioned, one does not necessarily wish to avoid spinning sidebands, and there are means of dealing with them a t spinning speeds much lower than half the anisotropy; these will he discussed in Part I1 under “Slow Spinning.” A general discussion of the limits of resolution of 13C NMR signals in solids has been provided by Garroway et al. (26). Dominant line-broadening mechanisms (ignoring, for the moment, the presence of quadrupolar nuclei) are identified as anisotropic magnetic susceptibilities, magnetic inequivalencies present in solids hut not in liquids, and motion. Resolutions of 0.1 ppm have been attained for in some nicely crystalline solids, hut resolutions of 0.2-0.7 ppm are characteristic of crystalline solids and become worse by a factor of 10 for glassy polymers. A particularly important part of this discussion involves the influence of dc field strength on resolution. Some broadening interactions are found to increase with magnetic field, so larger (and more expensive) fields are not desirable for all possible systems under study. A prime example of the two extremes of resolution for rare spin-% nuclei in the solid state is supplied by NMR spectra of mSi in crystalline 1,1,1-trimethyl-2,2,2-triphenyldisilane (Figure 2). as compared with 29Siin an amorphous silicon-hydrogen alloy (Figure 4) (27). The high-resolution spectrum of silicon in the crystalline compound has a line width of about 0.2 ppm. On the other hand, the highresolution spectrum of 29Si in amorphous silicon alloys is found to have a line width of about 40 ppm, with some discernahle structure perhaps assignable to silicon, or to SiH, groups. In one case, there is little dispersion of local geometry about silicon, and the crystalline compound yields a sharp spectrum. In the case of the amorphous glassy material, the enormous dispersion of geometries and disorder inherent in the glassy state lead to relatively severe broadening. Somewhere between these two limits will lie possibilities for resolution of solid materials of interest to chemists. The above discussion does not take into account the case of heteronuclear dipolar interactions with quadrupolar nuclei, such as “N and ”CI. References (1) Hackert. M. L.; Ford. G. C.; Rossrnan,
ANALYTICAL CHEMISTRY. VOL. 55. NO. 7. JUNE 1983
M. G. J. Mol. B i d . 1976, 78,665-73. (2) Murphy. P. DuBois; Gerstem. B. C. J.
Chem. Phys. 1979.70,4552-56. (3) Murphy.
P. DuBois; Stevens,W.C.;
Cheung. T.T.P.: Lseelle, S.; Gerstein, B. C.; Kurtz. D. M. J. Am. Chem. Soc.
1981.103,4400-4405. (4) Mannitt. G.; Shatlock. M. P.; Bartuska. V. ,I.; Maciel. G. E. J. Phys. Chem. 1981. 85,2087-91. (5) Mehring, M. “High Resolution NMR
Spectroscopy in Solids”;Springer Ver-
la 1976. (6) cKnett. C. L.; Dybowski. C. R.; Vaughsn, R. W . J. Chem. Phya. 1975,63.
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(7) Van Vleck, J. H. Phys. Re”. 1948,14. 1168-83. (8) Yannoni. C. S.; Kendrick, R. D. J. Chem. Phys. 1981,74,74749. (9) Zilm. K. W.;Grant. D. M. J. Am. Chem. Soe. 1981,103,2913-22. (IO) Hahn. E. L. P h w Re”. 1950.80, 580-94. (11) Lowe, 1. J.8~11.Am. Phys. Soc. 1957. 2,344. (12) Powles, J. G.; Mansfield, P. Phys. Lett. 1962.2.5a59. (13) Gerstein. B. C. Phil. Trona. Ray. Soe. London 1981. A299,521-46. (14) Burum, D. P.; Rhim, W. K. J. Chem. Phys. l979,71.944-56. (15) Burum. D. P.; Linder. M.; Emst, R. R. Bull. MoRn. Res. 19RO. 2,413. (16) Andrew, E. R. Pmg. NUC.Mngn. Res. Spectrose. 1971.8.1-40. (17) Scheler. G.; Haubenreisser,V.; Rosenberger, H. J. Magn. Res. 1981.44, 13444. (18) Beams. J. W . Re”. Sei. Inatr. 1930.1.
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(19)
Lowe, I. J. Phys. Rev. Lett.
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1-R LR.7 -1
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Pembletan,R. G.; Ryan. L.M.; Gerstein, l “ 0 C 00 B. C. Reo. Sei. Imtr. 1977.48,
(20)
Ir”V.33.
Doty, F.David: Ellis, Paul D. Rev. Sei. Instr. 198l.52,1869-75. (22) Zilm. K. W.; Alderman. D. W.;Grant, D. M. J. Magn. Res. 1978,30,563-70. (23). Fyfe. C. A.; Mossbrugger.H.;Yannoni, C. S. J. Magn. Res. 1979.36.6148. (24) Pines. A.; Gibby, M. G.; Waugh. J. S. J. Chem. Phys. 1973.59.569-95, 125) Sehaefer. J.: Steisksl. E. 0. J. Am. ’ Chem. Soe. ‘1976.9k. 1031-32 (26) Garroway, A. N.; VanderHart. D. L.; Earl, W . L. Phil. Trans. Roy. Sot. London 1981. A299,609-28. (27) Reimer, J. A,; Murphy, P. DuBois; Gerstein. B. C.: Knights. J. C. J. Chem. (21)
Bernard Gerstein is professor of chemistry at Iowa State University, where he earned his PhD in 1960. His research interests include applications of pulsed magnetic resonance to chemistry; heterogeneous catalysis on semiconductors and insulators; and chemical structures and anisotropic motion in molecular solids, polymers, and biopolymers.
