Quantitative solid-state NMR

Throughout the cross-polarization pulse sequence, a number of competing relaxation processes are occurring simultaneously. The recognition and understanding of these relaxation processes are critical in order to apply CP pulse sequences for quantitative solid state NMR data acquisition or ascertaining molecular motions occurring in the solid state. 

Despite the obvious benefits of quantitative solid-state NMR via single pulse excitation methodology (SPE) (see Section 3), cross-polarisation combined with magic-angle spinning (CP/MAS) [1] has many intrinsic advantages which... 

Quantitative analysis is a very important component of pharmaceutical analysis. In a number of the publications describing the use of solid-state NMR, the majority of the work has dealt with qualitative studies with brief references to the possibility of quantitative analysis. Under proper data acquisition conditions, solid-state NMR is a quantitative technique that typically provides sufficient selectivity and sensitivity. An excellent guide to the utilization of magic angle spinning and cross-polarization techniques for quantitative solid-state NMR data acquisition has been outlined by Harris (34). 

Ramanathan, C. and Ackerman, J.L. (1999) Quantitative solid-state NMR imaging of synthetic calcium phosphate implants. Magn. Reson. Med., 41 (6), 1214-1220. 

Solid-state NMR using MAS NMR has been utilised to determine the DMAIC (Define, Measure, Analyse, Improve and Control) framework and associated statistical tools have been applied to both identify and reduce variability observed in a quantitative solid-state NMR analytical method in pharmacy. 

A low-tcmpcraturc, dynamically driven structural transition observed in a polypeptide by solid-state NMR spectroscopy has been reported by Bajaj et At low temperatures, proteins and other biomolecules are generally found to exhibit dynamic as well as structural transitions. This includes a so-called protein glass transition that is universally observed in systems cooled between 200 and 230 K, and which is generally attributed to interactions between hydrating solvent molecules and protein side chains. However, there is also experimental and theoretical evidence for a low-temperature transition in the intrinsic dynamics of the protein itself, absent any solvent. In the study by Bajaj et al., low-temperature solid-state NMR was used to examine site-specific fluctuations in atomic structure and dynamics in the absence of solvents. In particular, they employed MAS NMR to examine a structural phase transition associated with dynamic processes in a solvent-free polypeptide lattice at temperatures as low as 90 K. Several quantitative solid-state NMR experiments were employed to provide site-specific measurements of structural and motional features of the observed transition. 

Solid state NMR is a relatively recent spectroscopic technique that can be used to uniquely identify and quantitate crystalline phases in bulk materials and at surfaces and interfaces. While NMR resembles X-ray diffraction in this capacity, it has the additional advantage of being element-selective and inherently quantitative. Since the signal observed is a direct reflection of the local environment of the element under smdy, NMR can also provide structural insights on a molecularlevel. Thus, information about coordination numbers, local symmetry, and internuclear bond distances is readily available. This feature is particularly usefrd in the structural analysis of highly disordered, amorphous, and compositionally complex systems, where diffraction techniques and other spectroscopies (IR, Raman, EXAFS) often fail. 

The problems involved in quantitative analysis using NMR spectroscopy, have been discussed by several authors and it is evident that it still causes a lot of problems as especially pointed out by Hays55 in his excellent review on the subject. Thus in liquid state NMR spectroscopy the quantitative estimation of atoms and groups involves the use of normal analytical method. In the case of solid state NMR spectroscopy, however, the application of the cross-polarization technique results in signal enhancements and allows repetition rates faster than those allowed by the carbon C-13 Tl. Therefore, the distortion of relative spectral intensities must always be considered a possibility, and hence quantitative spectra will not always be obtained. 

Once the proton Tx and Tcli values are determined for a polymorphic system, physical mixtures of the two polymorphs can be generated (calibration samples). Subsequent acquisition of the solid state NMR spectra under quantitative conditions yields signal intensities representative of the amount of each solid state phase... 

In some cases, CP is not necessary to obtain a suitable solid state NMR spectrum. In these cases, the SPE/MAS sequence may be used and for quantitative analysis only the X-nucleus T time needs to be determined. The standard inversion-recovery experiment (Fig. 10C) can be used to measure this... 

Quantitative solid state 13C CP/MAS NMR has been used to determine the relative amounts of carbamazepine anhydrate and carbamazepine dihydrate in mixtures [59]. The 13C NMR spectra for the two forms did not appear different, although sufficient S/N for the spectrum of the anhydrous form required long accumulation times. This was determined to be due to the slow proton relaxation rate for this form. Utilizing the fact that different proton spin-lattice relaxation times exist for the two different pseudopolymorphic forms, a quantitative method was developed. The dihydrate form displayed a relatively short relaxation time, permitting interpulse delay times of only 10 seconds to obtain full-intensity spectra of the dihydrate form while displaying no signal due to the anhydrous... 

Within various pharmaceutical laboratories (industrial and academic), the mul-tinuclear technique of solid state NMR has primarily been applied to the study of polymorphism at the qualitative and quantitative levels. Although the technique ideally lends itself to the structure determination of drug compounds in the solid state, it is anticipated that in the future, solid state NMR will become routinely used for method development and problem solving activities in the analytical/materials science/physical pharmacy area of the pharmaceutical sciences. During the past few years, an increasing number of publications have emerged in which solid state NMR has become an invaluable technique. With the continuing development of solid state NMR pulse sequences and hardware improvements (increased sensitivity), solid state NMR will provide a wealth of information for the physical characterization of pharmaceutical solids. 

In the present work, we use quantitative solid-state 13C NMR spectroscopy to study the polymerization process of multiacrylates and the effects of thermal history/aging on the free radical life in polymultiacrylates. 

Figure 1. Schematic diagram of the solid-state NMR pulse sequences for (a) quantitative single pulse 13C observe with gated decoupling and (b) Ti and (c) 13C Ti determinations via cross polarization.

We have found that combined solid-state NMR spectroscopy and DPC results can be used to calculate reaction enthalpies which are in close agreement with Moore (15). Furthermore, we find that the degree of conversion can be significantly affected by post reaction thermal processing. We conclude that the single pulse solid-state NMR spectroscopy can provide reliable, reproducible, and quantitative information about these highly crosslinked, insoluble, polymer networks. 

The exact nature of the alkylidenes formed on various oxide surfaces is still uncertain, as is the nature of the alkylidenes responsible for the often observed metathesis activity. Mo(N)(CH2CMe3)3 also has been employed as a precursor to a surface-bound species believed to be of the type Mo(NH)(CHCMe3)(CH2CMe3) (Osurf) [115]. Although the alkylidene carbon atom could not be observed in solid state NMR spectra, which is typical of surface supported alkylidenes, reaction with acetone to give 2,4,4-trimethylpent-2-ene quantitatively confirmed the presence of the reactive neopentylidene complex. Such species would initiate various metathesis reactions when prepared on partially dehydroxylated silica. 

Beyond the qualitative molecular information afforded by NMR, one can also obtain quantitative information. Depending on the sample, NMR can measure relative quantities of components in a mixture as low as 0.1-1% in the solid state. NMR limits of detection are much lower in the liquid state, often as low as 1000 1 down to 10,000 1. Internal standards can be used to translate these values into absolute quantities. Of course, the limit of quantitation is not only dependent on... 

Molecular motion in solids has been the object of many studies in the field of physical chemistry of polymers , but dynamic processes in molecular crystals of organic and inorganic compounds are less well investigated. In fact, the average chemist is not aware of the fact that processes like internal rotation or ring inversion proceed in solids quite often with barriers which are not very different from those found for these types of internal motion in the liquid state. Thus, for the equatorial axial ring inversion of fluorocyclohexane values of 42.4 and 43.9 kJ mol have been measured in the liquid and the solid, respectively. The familiar thermal ellipsoids of individual atoms obtained from X-ray studies are qualitative indicators of molecular motion in the crystal, but a more quantitative study of such processes is only possible after appropriate solid state NMR techniques are applied. 

The technique of solid-state NMR used to characterize supported vanadium oxide catalysts has been recently identified as a powerful tool (22, 23). NMR is well suited for the structural analysis of disordered systems, such as the two-dimensional surface vanadium-oxygen complexes to be present on the surfaces, since only the local environment of the nucleus under study is probed by this method. The nucleus is very amenable to solid-state NMR investigations, because of its natural abundance (99.76%) and favourable relaxation characteristics. A good amount of work has already been reported on this technique (19, 20, 22, 23). Similarly, the development of MAS technique has made H NMR an another powerful tool for characterizing Br 6nsted acidity of zeolites and related catalysts. In addition to the structural information provided by this method direct proportionality of the signal intensity to the number of contributing nuclei makes it a very useful technique for quantitative studies. 

MRI to characterize hydrodynamics within reactors is already established. The extent to which the potential of MR to study both hydrodynamics and chemical conversion is fully realized will depend on our ability to integrate the well-established MR spectroscopy techniques in liquid- and solid-state NMR into imaging pulse sequences, and still provide quantitative data in the magnetically heterogeneous environments typical of catalysts and reactors. 

Smernik, R. I, Baldock, J. A., Oades, J. M., and Wittaker, A. K. (2002). Determination of rlpH relaxation rates in charred and uncharred wood and consequences for NMR quantitation. Solid State Nucl. Magn. Reson. 22, 50-70. 

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