Quantitative NMR

In this particular case where the molecules of the two compounds each have six protons, the ratio of the areas of the two peaks is representative of the ratio njn of the respective numbers of molecules of A and B (given that the response factors are equal for A and B). Assuming that the mixture only contains these two components, and designating as the area of the acetone signal and 5g that of benzene, it follows that  

If Cp and Cg are the concentrations expressed in percentage mass of A and B, of which the molar masses are Mp and Mg respectively, then  

A more general case is that in which the signal (or signals) selected for each compound to be measured do not correspond globally to the same number of 

Supposing for example, that the signal selected for compound A corresponds to a protons and the signal chosen for compound B corresponds to b protons (A and B do not represent acetone and benzene as in above section). When the spectrum of the mixture of A and B is recorded each molecule of B leads to a signal whose intensity is different to that of a molecule of A. The expressions in 15.15 will remain valid provided corrections are inserted to take into account these differences. Each area must be divided by the number of protons that are at the origin of the selected peak, in order to normalize the relative area to one proton of either A or B. Then substituing Sj and 5g by the corrected areas S/ /a and S /b, the two preceding expressions become  

Expression 15.16 can be transposed to the case where n constituents are visible on the spectrum. By using labels such as A, B,. .., Z and in locating each consti-tuant by a specific area, ca. A, for i protons for the component I, the general equation 15.16 giving the mass per cent of each one can be formulated  

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Attard J J, Doran S J, Flerrod N J, Carpenter T A and Flail L D 1992 Quantitative NMR spin-lattice-relaxation imaging of brine in sandstone reservoir cores J. Magn. Reson. 96 514-25... 

It is also clear from Eq. (2.5.1) that the linewidth of the observed NMR resonance, limited by 1/T2, is significantly broadened at high flow rates. The NMR line not only broadens as the flow rate increases, but its intrinsic shape also changes. Whereas for stopped-flow the line shape is ideally a pure Lorentzian, as the flow rate increases the line shape is best described by a Voigt function, defined as the convolution of Gaussian and Lorentzian functions. Quantitative NMR measurements under flow conditions must take into account these line shape modifications. 

Hartmann-Hahn match, and cross-polarization mixing time are discussed in relation to obtaining quantitative NMR results. 

Quantitative NMR analysis may also be applied to water-soluble polymers or copolymers in some cases. Polymers usually have large molecular weights and are heterogeneous in size. However, the proton NMR signals of some polymers... 

Precision and accuracy Quantitative analysis by NMR is very precise with relative standard deviations for independent measurements usually much lower than 5%. The largest errors in NMR measurements are likely due to sample preparation, not the NMR method itself. If a good set of standards is available and all NMR measurements for the test and standard samples are performed under the same acquisition conditions, the quantitative results can be readily reproduced on different instruments operated by different analysts at different times. Therefore, good intermediate precision can also be achieved. An accurate quantitative NMR assay will require accurately prepared standards. The accuracy of an NMR assay can be assessed, for example, by measuring an independently prepared standard or an accurate reference sample with the assay. In many cases, a spike recovery experiment can also be used to demonstrate the accuracy of an NMR assay. 

NMR is a remarkably flexible technique that can be effectively used to address many analytical issues in the development of biopharmaceutical products. Although it is already more than 50 years old, NMR is still underutilized in the biopharmaceutical industry for solving process-related analytical problems. In this chapter, we have described many simple and useful NMR applications for biopharmaceutical process development and validation. In particular, quantitative NMR analysis is perhaps the most important application. It is suitable for quantitating small organic molecules with a detection limit of 1 to 10 p.g/ml. In general, only simple one-dimensional NMR experiments are required for quantitative analysis. The other important application of NMR in biopharmaceutical development is the structural characterization of molecules that are product related (e.g., carbohydrates and peptide fragments) or process related (e.g., impurities and buffer components). However, structural studies typically require sophisticated multidimensional NMR experiments. 

Quantitative NMR examination of the hydrolysis of dimethyl phosphonate (245) using 0-enriched water under base-catalysed conditions supports a mechanism involving P—O rather than C—O bond cleavage. 

In the systems that I have examined, I can satisfy the dynamic requirements with a ten second pulse delay. The longest methyl T] may be 3 seconds. In general, the longer the side chain, the longer will be the methyl Tj. We will hear more about this subject later on. We need not be too concerned about NOE factors because they are usually full under the experimental conditions (T = 120-130°C) used for polymer quantitative measurements. The Tj problem can be handled, even under non-equilibrium conditions, by utilizing resonances from the same types of carbon atoms in a quantitative treatment. Such an approach can sometimes lead to more efficient quantitative NMR measurements. Adequate pulse spaclngs will have to be used whenever one wishes to utilize all of the observed resonances. Quantitative measurements in branched polyethylenes are very desirable because this is one of the best applications of analytical polymer C-13 NMR. 

All too frequently, researchers perform experiments beyond the means of the spectrometer used. The most common problem involves concentrations exceeding the linear response limits of the spectrometer. When this happens, solution of Eq. (2) becomes intractable. The most common mistake in infrared spectroscopy is when samples with absorbance greater than ca. 2-3 are measured with a DGTS detector [56]. At this point, the response of the spectrometer is no longer linear, and quantitative information is no longer accessible. The same type of situation exists in NMR, except it is perhaps a little more severe. The difficulties encountered when performing quantitative NMR work are well known [57, 58]. Most other types of spectrometers have similar limitations. 

Figure 4.22. Pareto chart of the contributions to the uncertainty of the quantitative NMR analysis of Profenofos. The effects are a (intra), the intralaboratory precision P(std), the purity of the proton standard w, weighings of unknown and standard MW, the molecular weights of unknown and standard. (Data kindly supplied by T Saed Al-Deen.)...

It is important not to assume that this or that effect always has negligible uncertainty each factor must be assessed for a particular result. For example, in the quantitative NMR work in my laboratory, we could just see the effect of the uncertainty of molar masses. As a rule of thumb, if the uncertainty component is less than one-fifth of the total, then that component can be omitted. This works for two reasons. First, there are usually clear major components, and so the dangers of ignoring peripheral effects is not great, and second, components are combined as squares, so one that is about 20% of the total actually contributes only 4% of the overall uncertainty. There is a sort of chicken-and-egg dilemma here. How do you know that a component is one-fifth of the total without estimating it and without estimating the total And if you estimate the contribution of a factor to uncertainty,... 

As an example, consider the measurement of the purity of a chemical by quantitative NMR, using the peak of an added CRM as an internal standard. The purity of the test material (Ptest) is given by... 

Spreadsheet 6.3. Values and uncertainties for quantities used in the calculation of the purity of a sample by quantitative NMR using equation 6.3 7. 

Consider the example of quantitative NMR. Spreadsheet 6.3 gives the standard uncertainties and relative standard uncertainties of the components of the combined uncertainty. It is usual to graph the relative standard uncertainties, the standard uncertainties multiplied by the sensitivity coefficient [dy/dx uc(x)], or the squares of the latter expressed as a percentage contribution to the combined uncertainty (see equation 6.23). A horizontal bar chart for each component in decreasing order is one way of displaying these values (figure 6.9). 

Figure 6.9. Bar charts of the uncertainty components in the quantitative NMR example.

Several methods have been proposed to estimate the oil distribution, such as the integration of surface area of images [68] and quantitative NMR analysis... 

Bis(pentamethylcyclopentadienyl)zirconium dichloride is prepared readily in 50-60% yield following Reactions 4 and 5. Although (ry5-CsMes Zrb (7) can be obtained by treating ( -CsMes ZrC with Li+fBH Hs ]- or with Na+[AlH2(0CH2CH20CH3)2] in THF or benzene, respectively, its isolation from these reaction mixtures is extremely difficult. We therefore used an indirect synthesis (Reactions 6 and 7). Compound K -CsMes Zr fe (8) is obtained as a pure crystalline material in 60% yield its structure is reported elsewhere (13). Structure 8 reacts quantitatively (NMR) with H2 at 0°C according to Reaction 7. 

The use of this quantitative NMR technique, allowed identification, quantification, and characterization of bioactive natural compounds, while the use of a regression method, like PLS, was proposed for the quantification of partially overlapped NMR signals (Fig. 4.21). 

In the NMR spectrum integrated signals are exactly proportional to the number of contributing nuclei. The Comite Consultatif pour la Quantite de Matiere (CCQM) has started international comparison of quantitative NMR experiments. In the first round the possible reproducibility should be established. The composition of a mixture of organic compounds has been determined by integration of the NMR signals. Already the first experiments (Fig. 9) have shown the problems arising by isomerization (ethyl-4-toluene sulphonate), decomposition (1,3-dimethoxybenzene), purity of standard compound and superimposition of isotopic satellites. Additional experiments with a new composition are necessary. 

Quantitative NMR measurements always require a number of precautions159. The well-known unfavourable properties of silicon nuclei are a further aggravation. Quantitative measurements of 29Si NMR require the use of IGD to eliminate NOE, long delays between scans (5-10 times the longest T in the sample) and/or addition of a relaxation reagent [e.g. chromium or iron triacetylacetonate, Cr(acac)3 or Fe(acac)3], to enhance relaxation... 

Henderson, T.J., Quantitative NMR spectroscopy using coaxial inserts containing a reference standard purity determinations for military nerve agents, Anal. Chem., 74, 191-198 (2002). 

Gellerstedt G, Robert D (1987) Quantitative NMR analysis of kraft lignins Acta Chem Scand B 41 541-546... 

Chini, M. G. Jones, C. R. ZampeUa, A. D Auria, M. V. Renga, B. Fiorucci, S. Butts, C. P Bifulco, G. Quantitative NMR-derived interproton distances combined with quantum mechanical calculations of chemical shifts in the stmeochemical determination of conicasterol F, a nuclear receptor ligand from theonella swinhoei, ... 

Turner et al. used this technique to prove that the unresolved peak in the gas chromatograms of Toxicant A consisted of the two components B8-806 (P-42a) and B8-809 (P-42b) [79], The second approach is quantitative NMR. This technique can be used to calculate the amount of a component in a solution since the integrals of proton resonances are in the first order independent of the component structure and proton position. Nikiforov et al. studied the composition of toxaphene in this way. Toxaphene components with geminal chlorine atoms on primary carbons have proton signals in the range of 6-7 ppm. Monitoring this ppm range allows the determination of the number of components in a mixture [69]. 

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