Accred Qual Assur (2005) 10: 421–429 DOI 10.1007/s00769-005-0004-9
H. Jancke F. Malz W. Haesselbarth
Received: 11 September 2004 Accepted: 7 June 2005 Published online: 21 October 2005 C Springer-Verlag 2005
H. Jancke · F. Malz () · W. Haesselbarth Federal Institute for Materials Research and Testing (BAM), Department Analytical Chemistry, Reference Materials, Richard-Willstaetter-Strasse 11, 12489 Berlin, Germany e-mail:
[email protected] Tel.: +49-30-81045869 Fax: +49-30-81045599
GENERAL PAPER
Structure analytical methods for quantitative reference applications
Abstract The analytical methods mass spectrometry, UV/Vis, IR, Raman, Fluorometry, XRD, M¨ossbauer, and NMR used to elucidate chemical structure are evaluated regarding their capabilities to be used as primary analytical techniques in quantitative measurements, considering the criteria in the CCQM definition of primary methods. This includes a review of the respective measurement equations, the evaluation of the measurement uncertainty, and a discussion of evidence for the
Introduction A basic requirement for accurate and comparable measurements in science, technology, economy, trade, health, etc. is traceability to recognized references, in particular internationally agreed measurement units. The higher the demand for reliability of measurement results, the greater the effort devoted to establishing and demonstrating traceability. The basic system of units for all fields of measurement is the SI system. Among the seven base SI units the dedicated unit for chemistry is the mole as the unit for the amount of substance due to the fact that chemical reactions run proportional to the number of molecules of the substances involved. A measurement procedure that is traceable to the SI unit of the measurand may serve as reference for other measurement procedures, which are not traceable by themselves. Primarily, it is the purity of chemical reference materials (CRM) that is the most critical point in chemical measurements. Such materials should be characterized qualitatively and quantitatively, i.e. by structure as well as by composition. By tradition, qualitative and quantitative analyses are often conceived as largely separate fields. However, many of the measurement techniques commonly used for structure analysis also have capabilities for
“highest metrological level”, as obtained from intercomparisons in contest with other methods. It is shown that only few methods fulfill the CCQM criteria. Quantitative NMR spectroscopy is one of them and may be considered as a potential primary method as recommended by CCQM because of being free of empirical factors in the uncertainty budget. Keywords Metrology . Structure analysis . Quantitative analysis . Primary methods . Reference methods
quantitative analysis. The paper re-considers some of these techniques from a metrological view with the aim to elucidate their capability for being used as “primary” reference methods for quantitative chemical measurements, as done earlier for NMR [1, 2]. The SI system and traceability of measurement The Commit´e Consultatif pour la Quantit´e de Mati`ere (CCQM) is responsible for the SI unit “mol”. The use of the base unit mole, the “chemical” unit, is impeded by several specific problems. First, there are as many “moles” as chemical species. Second, it is not possible to realize the definition of the mole (the same number of entities as in 0.012 kg of pure carbon-12) in the laboratory. So the mole itself should be represented by a primary method of measurement. For chemical measurements there are several mechanisms by which results may be traced back to SI units [3], utilising reference measurements and reference materials. The EURACHEM/CITAC Guide “Traceability in chemical measurement” [4] provides comprehensive guidance for chemical laboratories on all aspects of traceability. A distinguished type of reference measurement procedures for this purpose are the so-called “primary methods of
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measurement”. Primary methods are intended to provide direct traceability of measurement results to the respective SI unit. A primary method is defined [5] as: “a method having the highest metrological properties, whose operation can be completely described and understood, for which a complete uncertainty statement can be written down in terms of SI units”. The crucial characteristic of primary methods is that they are “standard-free”, i.e. they do not require any calibration, neither for bias correction nor for determination of response behaviour. For chemical measurements, there are currently only a few methods which have been recognised as primary. Among those coulometry, gravimetry, titrimetry and colligative methods [6] are absolute methods, i.e. they do not require a standard of the measurand. A second category are relative methods (e.g. IDMS), which measure the ratio of related measurands, e.g. isotope contents. Converting these ratios into values of the target measurand requires a standard, e.g. a spike of known composition. This is the difference between a primary “direct” and a primary “ratio” method as defined by the CCQM [5]. A metrological approach to structure analytical methods
IA1 = K S1 n A ;
IA2 = K S2 n A ;
IA3 = K S3 n A
(2)
If one performs a quantitative analysis, i.e. if one analyses mixtures of different species A, B, C, . . . , the signals observed (for simplicity one for each component) have the same property: IA = K SA n A ;
IB = K SB n B ;
IC = K SC n C
(3)
where the proportionality constants KSj are not necessarily identical. Using several signals in parallel opens the possibility to increase the reliability and to reduce the measurement uncertainty by consistency checking and averaging. Again, if the constants are independently established and expressed in SI units, we may have an analysis of the primary direct type. If the constants are determined by calibration with a reference material, this would make for an analysis of the primary ratio type. The measurement equations
The structure determination of a chemical system includes the analysis of the chemical elements involved, the bonding between these elements and the spatial distribution of atoms and bonds. The main methods to accomplish this task are mass spectrometry (MS), X-ray powder diffractometry (XRPD), optical absorption spectroscopy (UV, Vis, IR, and Raman), M¨ossbauer spectroscopy and nuclear magnetic resonance (NMR) spectroscopy. Because of their special property to characterize the analyte structurally, they all can differentiate between different structures. This is done by different signals for different structures. “Signal” means an intensity function over a frequency (or mass, or angle or velocity) scale. Each signal intensity IA is proportional (at least in a certain range of linearity) to the amount n of the substance A observed. IA = K S n A
signment, may not follow the same dependence IA /nA , i.e. may have other individual constants KSi :
(1)
where I is given in volts or something equivalent, and n in moles. If the proportionality constant KS is defined by one or several fundamental constants, or exactly known from independent reference measurements (traceable to SI), such an equation fulfills the condition stated in the definition of a primary direct method. The usual measurement of content (n/m in mol kg−1 ) or concentration (n/V in mol l−1 ) includes a measurement of mass or volume, both in SI units. This is not in contradiction with the definition of a primary method [5]. For measurements of an amount-ofsubstance fraction (n/n in mol mol−1 ) or if the constant KS in turn can be evaluated experimentally by a second measurement, evaluating IA versus nA , the equation fulfills the condition for a primary ratio method. The different signals 1, 2, 3, . . . of the compound A, used for the structural as-
For each of the structure analytical methods, the connection of the signal intensity with the amount of substance of the analyte is defined by a measurement equation, based on the theory of the respective effect or experiment. Some of these will be discussed in the following. Mass spectrometry Mass spectrometry is one of the most valuable and most used techniques for chemical analysis. In the ion source the analyte substance is ionized and afterwards accelerated through the spectrometer. The analyte molecule and eventual fragments are registered in the receiver according to the m/e (mass per charge) ratio. The molecular peak is characteristic for the relative molecular mass and hence gives a confirmation on the molecular identity. More reliable is the identification using high resolution instruments. Structure information describing the spatial construction of the molecule is not provided in most cases. Some valuable hints may be gathered by interpretation of the masses of characteristic fraction peaks. Isomeric structures in most cases are not identified with complete certainty. In quantitative analysis, mass spectra are used mostly for identification after separation by any chromatographic method. Since different molecules undergo different molecular destructions in the ionic source, quantitative analysis of mixtures directly by their mass spectra is difficult to perform. However, in certain cases, e.g. for time or substance limited tasks, direct quantitative mass spectrometry, requiring careful calibration of every component (Eq. 3) of interest in the mixture, is in use [7].
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A special case concerns quantitative analysis of isotopomers (molecules that differ in the isotope ratio, e.g.12 C/13 C or H/D at one or several molecular positions). These molecules show the same behaviour in the ion source, and the ratio of the isotopomers remains constant over the whole route through the spectrometer and also in the receiver. This is the basis for one of the most powerful (because of sensitivity) methods of quantitative analysis, isotope dilution mass spectrometry (IDMS). The quantity of the unknown nX is given by the isotope ratios (i.e. signal intensity ratios) of the unknown RX , the quantity nY of a spike of a different isotope ratio RY , and that of a gravimetric mixture of both, RB , according to Eq. 4. RY − RB 1 + RX nX = (4) nY RB − RX 1 + RY where the reference to a neat compound of different isotopic composition and known purity is necessary. The metrological property of IDMS as a potential primary ratio method is described in [8]. Concerning applications in organic analysis, one may have the problem that an isotopomer of the analyte should be available and both the isotopomers should be equalibrated before analysis in the mass spectrometer. Absorption spectroscopy The usual application of quantitative absorption spectroscopy (UV/Vis, and IR) [9] comparing the intensities of radiation before (0 ) and after () it passed through an analyte medium in the spectrometer is based on Lambert– Beer’s law. The measurement equation applicable for a homogenous optical medium, i.e. a diluted solution, is as follows: 0 1 E = lg = lg = ελ cd T
(5)
where E extinction, T the transmission, ελ the extinction coefficient, c the analyte concentration and d the optical absorption path lenth. Since the extinction coefficient depends on the wavelength, the relationship between measured spectral intensity and analyte concentration is of the basic form of Eq. 3. The extinction coefficient is also concentration dependent, i.e. the relation between extinction and analyte concentration is non-linear, but for low concentrations the extinction coefficient may be taken as a constant. Several absorption spectroscopy methods are applied either as such or in combination with separation techniques (e.g. UV detectors of chromatographic systems), their main benefit being high sensitivity for analytes with chromophoric groups in the molecule. However, the chromophoric group often must be introduced by preparation prior to analysis and the analyte must be available in neat form to perform the calibration. This is a very demanding requirement and
may restrict the application for instance in pharmacy and bioanalysis. Only in the very seldom cases, when ελ is given from an independent primary measurement of high precision, the amount of substance of the analyte is directly available by an intensity measurement [3]. Raman spectroscopy A spectrometer designed in emission geometry (observation at 90◦ to the incident beam) registers the Raman spectrum, almost equivalent to the mid-infrared absorption spectrum [9]. The sample is irradiated by intense monochromatic laser light in the visible region and the diffused light is analysed. The measured Raman intensity Iν of a line in the spectrum can be expressed as: Iν = I0 K ν c
(6)
where I0 is the excitation intensity; Kν the constant; c the analyte concentration. The factor Kν includes the frequency dependent terms, i.e. the spectrometer response, the self absorption and the molecular scattering properties. Although there may be differences in Iν for different spectra due to intensity variations of I0 or the positioning of the sample, in certain cases Raman spectroscopy is a valuable tool in quantitative solid state analysis [10]. In any case, however, for obtaining reliable results multi-point calibration, tailored for specific applications, should be used instead of single-point calibration (calibration factors). Fluorometry Fluorometry is another mechanism of emission of light after exiting the sample with light of the intensity I0 . Light is emitted in accordance with the matrix dependent fluorescence quantum yield f [9]. Since this light is absorbed in the sample cell of the spectrometer as well, the measurement equation (valid for diluted solutions only) contains elements of Lambert–Beer’s law known from absorption spectrometry: If = 2.3I0 f ελ cd
(7)
The proportionality factor between measured intensity If and analyte concentration c is governed by experimental conditions of the respective spectrometer and is too complex to be calculated on a theoretical basis or measured by independent methods. Fluorometry is the most sensitive of the structure analytical methods and is applied for quantitative analyses after calibration with the analyte. Care must be taken of the fact that even small impurities may cause remarkable fluorescence intensity changes due to large differences in response behaviour or quenching effects.
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M¨ossbauer spectrometry M¨ossbauer spectroscopy is a well-established method to characterise solid phases containing M¨ossbauer active nuclei, e.g. iron, tin, antimony and gold [11]. The spectrum shows signals containing information on characteristic nuclear transitions yielding quadrupole doublets, magnetic dipole quartets or sextets of magnetic hyperfine splitting. In mixtures of several components, the respective patterns are superposed on each other. After fitting the atomic fraction of the M¨ossbauer active nucleus, for example 57 Fe, in each component, assigned by its position on the velocity scale (isomeric shift), the quadrupolar splitting and magnetic splitting is determined by the ratio SA Peak area of component A = S Total peak area
(8)
Since the total mass of iron is known for each component according to the chemical assignment, this ratio can be converted into amounts of substance according to Eq. 9 [12] nA =
m( Fetot )SA /S MA 57
(9)
Due to thermal motion of atoms and due to magnetic relaxation of small magnetic domains at higher temperatures, the peak area SA of a component is a function of temperature (f- or Debye–Waller factor) and the peak ratio must be calibrated for each component in the mixture using pure substances. Care must be taken concerning further influences on the signal intensities due to texture effects, the anisotropy of the f-factor and saturation of some absorption intensities when using thick absorbers. The quantitative application of M¨ossbauer spectroscopy is restricted to well-defined analytical problems. Powder diffractometry The great power of X-ray crystal diffractometry is the unambiguous determination of the structure of crystalline inorganic and organic solids. Powder diffraction [13], on the other hand, is used for phase analysis of crystalline powders by comparing intensities of characteristic reflections of components in the mixture. The intensity of the ith line of compound A, IiA , is given by Eq. 10: IiA =
KA wA ρA µ∗
(10)
where, KA is an experimental constant, ωA the mass fraction of the component A, ρ A the density of component A, and µ∗ the mass absorption coefficient of the matrix. This equation corresponds to the general form (2) relating a single signal intensity (the area, not the height [14]) to the amount of analyte. Depending on the number of compo-
nents, and whether the components have equal or different mass obsorption coefficients, three cases have to be considered [13]: (i) mixtures of components with the same µ∗ (polymorphs) can be analysed directly by the intensity ratio of corresponding lines, (ii) mixtures of two components with different µ∗ can be analysed by means of calibration curves of the pure components, and (iii) the general case of determination of one component in an unknown matrix requires a standard to be added in known amount. Several potential assay errors associated with quantitative X-ray powder diffraction were investigated by Campbell Roberts [15]. Especially the influence of particle size may be reduced by grinding and sample rotation. The effect of sample morphology should be studied in detail for the material in quantitative powder diffraction studies. A recent alternative is the Rietveld profile refinement. For quantitative applications not only few reflections are evaluated by intensity, but the whole diffractogram is calculated for each constituent of a mixture. The relative mass fraction of the pth phase in a mixture of N phases is given [16] by: Sp (Z M V )p W p = N i=1 Si (Z M V )i
(11)
where S, Z, M, and V are the Rietveld scale factors, the number of formula units per unit cell, the mass of the formula unit and the unit cell volume, respectively. When an internal standard is added by mass fraction wStd , the absolute mass fraction of the pth components is calculated according to wp =
wStd Sp (Z M V ) p SStd (Z M V )Std
(12)
There are some advantages of this so-called full-pattern analysis over traditional methods, in particular (i) the calibration constants Z, M, and V may be taken from the literature, (ii) all reflections are included, (iii) the background is better defined since a continuous function is fitted to the whole pattern, (iv) the effects of preferred orientation and extinction are reduced, and (v) crystal-structural and peak-profile parameters can be refined as part of the same analysis [16]. The sum of the determined mass fractions of the N identified components provides an estimate of the amount of amorphous material in the sample. However, the crystal structure of the components of the mixture must be known. The mass fraction of crystalline components can be determined with an accuracy of better than 0.5 wt%. Nuclear magnetic resonance Placing an ensemble of nuclei with a magnetic moment in a static magnetic field B0 , the nuclei arrange themselves in different, quantum mechanically controlled orientations in relation to the axis of the magnetic field.
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These orientations are energetically different. An oscillating high frequency magnetic field B1 perpendicular to B0 will cause transitions between these orientations. In the Fourier-transform method, B1 is irradiated in form of a radio frequency-impulse of the Larmor frequency ω0 with subsequent Fourier transformation of the decay of free induction. The NMR spectrum provides information as follows: kind of nuclei observed, number of chemically different groups of nuclei, relative numbers of resonance nuclei per group, chemical nature of the structure group observed, kind of coupling nuclei and geometry of the coupling path and others [17]. Each of the chemically different molecular groups is the source of an own signal separated from others by chemical shifts in the spectrum. The solution state NMR signals are narrow compared with the overall frequency region under observation, leading to a high structure resolution even in a complex (liquid) matrix. Most interesting molecules in organic chemistry contain hydrogen in the chemically interesting sites. This and the sensitivity of 1 H NMR, that is by far greater than that of all other nuclei, combined with the nearly 100% natural abundance of the spin 1/2 isotope 1 H makes 1 H NMR the easiest and most effective of all applications with comparably good signal-to-noise ratio in the spectra. Relatively short relaxation times and the lack of nuclear overhauser effect (NOE) [18] problems allow reliable registration of signal intensities. In NMR spectroscopy, at least in its easiest form of a single pulse experiment (SPE) like routine 1 H NMR, a signal voltage R is measured as response of the spinsystem after excitation by a radio frequency impulse at a certain frequency ω. The measurement equation may be given in the following form [18]: γ 2 I¯( I¯ + 1) N ω3/2 (T2∗ )1/2 R(ω) = 1 2 T 3/ 2 24k 3/2 µ /
0
2ξ 2 ρ QVC × λF
1/ 2
sin α
(13)
The first factor contains fundamental constants (γ is magnetogyric ratio, I¯ is spin number). The second factor characterizes the sample by T2 ∗ , T (transversal relaxation time, temperature) and N, the number of spins in resonance. The constants in the third factor contain the receiver parameters ξ : filling factor, ρ : ratio of effective to total inductance, Q: quality factor, VC : volume enclosed in the receiver coil, λ: Nagaoka’s constant, F: noise figure. α is the pulse angle of the FT experiment. Though most of the constants in the above equations can not be measured directly, they all may be put together in a “Spectrometer constant” KS , and one obtains an easy to handle expression for the integrated signal intensity (integration over the whole frequency region ω) similar to (1) as follows: IA = K S N A
(14)
where NA is the number of spins responsible for the signal under consideration. The outlined procedure has two consequences for the validity of Eq. 14: (i) one has to be sure that all observed spins underlie the same experimental conditions, i.e. the physical constants collected in (13) should be identical for all spins under observation, and (ii) since the constant KS is not known, no absolute number of observed spins but only ratios can be determined. In experiments for structure analysis, i.e. of a single substance, all molecules in the observation volume in the NMR spectrometer underlie exactly the same experimental conditions. Therefore the same KS applies for all nuclei at the various molecular sites. Taking ratios, the constant KS cancels, and the intensity ratios in the spectrum are directly related to the ratios of numbers of nuclei at different sites 1, 2, . . . (having different chemical shifts) of a molecule according to Eq. 15 I1 N1 = I2 N2
(15)
Since the numbers of nuclei are small integers, there is no high requirement on the accuracy of the measured intensities. On the other hand, Eq. 15 is the simple basis for each spectrometer calibration by means of any substance with at least two measurable signal intensities just by stoichiometry. Quantitative mixture analysis may be carried out according to the same principles. Here the accuracy of intensities is a crucial issue, and therefore signal selection is of paramount importance. Signals for quantitation have to be well separated from others, and care has to be taken to assure that they are pure, i.e. that they are not contaminated with impurity signals. Basically, the data obtained from an NMR spectrum directly provide relative amounts of substance in molar ratios. There are three different quantitative NMR procedures in use. These procedures differ with respect to the use of (internal) standards, but all procedures include the measurement of signal intensities Ik related to the number Nk of nuclei (protons) responsible for the respective signals in the molecules k =x, y, . . . 1. Ratio measurements. Mass (m) or amount of substance (n) ratios of two or more mixture components (solvent excluded) are determined according to Eq. 16: mx I x N y Mx = ; my I y N x My
nx Ix N y = ; ny Iy N x
(16)
Alternatively, the results of analysis may be expressed in =m / mi or amount-of-substance fracmass fractions ω x x tions xx =nx / ni . 2. Content measurements. In this case, a known amount (mass) of a standard is added to a known amount (mass) of mixture, and the results of analysis are expressed in contents, specifying the mass or amount of substance of a mixture component per mass of mixture (including the solvent) in g g−1 or mol g−1 , respectively. For best accuracy,
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this standard addition should be done gravimetrically. Most often the standard will be a neat substance of established purity PStd (in mol%), here expressed by a purity factor fStd (=PStd /100). Then Eq. 16 becomes Ix NStd Mx m Std mx = f Std ; m IStd Nx MStd m (17) nx Ix NStd 1 m Std = f Std m IStd Nx MStd m For the determination of concentrations (in mol l−1 or g l−1 ), instead of the mass m the volume V of the mixture (or rather the solution) is measured and inserted in Eq. 17. 3. Purity determination. Generally, the purity of a compound can be determined by measurements according to items (1) and (2). In the indirect approach, the content of
u(PX ) = PX
u(IX /IStd ) IX /IStd
2 +
u(MX ) MY
2 +
u(MStd ) MStd
all impurities is measured, and the sum is subtracted from 100%. To this end, it has to be assured that all impurities were identified and determined with sufficient accuracy. This is difficult for partly overlapping signals and often impossible, e.g. inorganic impurities. In the direct approach to purity determination, the content of the main component is measured directly. Using NMR, this can be done by addition of a standard of known purity. Expressing purity by mass content (or mass fraction) Px (in g g−1 ), the equation for this purpose is Px =
Ix NStd Mx m Std PStd IStd Nx MStd m
(18)
Uncertainty budgets The second precondition for a method to be of primary type is the availability of a complete uncertainty budget in terms of SI units. To this end, the measurement equation must be validated as to demonstrate that it properly accounts for all quantities and effects contributing to or impacting on the measurement result. Given that, the combined standard uncertainty of measurement results is calculated from the uncertainties associated with all input data to the measurement. For the methods described above, this amounts to (i) demonstrating that the measurement equations are complete, and (ii) applying uncertainty propagation according to the Guide to Expression of Uncertainty in Measurements (GUM) [19]. Where a constant KS (see Eq. 1) is determined by calibration, the uncertainty of the result depends on the uncertainty of the calibration. For the emission methods, Raman and Fluorometry, and for the solid state methods XRPD and M¨ossbauer, the uncertainty of measurement must be evaluated for the par-
ticular experiment, since the effects of experimental conditions, e.g. intensity of the excitation radiation, internal absorption, texture effects and others can not be estimated generally. Therefore the equations given for these techniques cannot be considred to be complete, and additional empirical factors accounting for these effects have to be included. In case of NMR, where KS always cancels in the determination of ratios, the measurement equation does not contain any empirical parameters to be determined by calibration. Therefore only uncertainties of signal intensities, masses and molar masses of analytes and standards have to be considered in the uncertainty budget.1 As a model example, for measurements of purity according to Eq. 18, the combined standard uncertainty is obtained as follows:
2 +
u(m) m
2
+
u(m Std ) m Std
2 +
u(PStd ) PStd
2 (19)
The uncertainty components may be obtained as follows: (1) For the ratio of signal intensities, as type A evaluation, the standard uncertainty may be determined as the empirical standard deviation of the mean of the result from p replicate measurements: u
IX s(Ix /IStd ) = √ IStd p−1
(20)
(2) The uncertainty of the relative molecular masses is calculated from the uncertainties of the relative atomic masses:
n (Nj u( j))2 (21) u(Mi ) = j=1
where n is the number of elements involved in the molecular formula, Nj the number of atoms of the jth element, and u(j) the standard uncertainty of its atomic weight (taken from IUPAC tables [21]). (3) The uncertainty of masses depends on the performance of the balance used. Using repeatibility R and linearity L as key performance measures, the standard uncertainty is obtained as: uL 2 u(m i ) = u 2R + 2 √ (22) 3 (4) The uncertainty associated with the purity (or purity factor, fB =PB /100) of the standard should be taken from 1 Note to Eq. 19: Due to the fact that the spectra of the analyte A and the internal standard Std are processed and evaluated alike, errors may be correlated, and a covariance term may have to be included in the uncertainty budget [20].
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the certificate of the provider, given that the standard is a certified reference material. The dominating contribution to the combined measurement uncertainty is the uncertainty of NMR signal intensities. This is, in turn, dominated by the quality of integration, which therefore should be carried out with utmost care. State-of-the-art uncertainties for signal intensities are about 0.5% relative.
Validation As mentioned earlier, quantitative applications of structure analytical methods for reference measurements require rigorous method validation, meaning comprehensive investigation of potential assay errors. Guidelines for the validation of methods based on mass spectrometric detection are given in [22]. A validation for the polymorph analysis of quantitative X-ray powder diffraction was given by Campbell Roberts [15]. A validation of the Rietveld analysis method of powder diffraction was published by Peplinski et al. [23]. In recent years, quantitative NMR spectroscopic applications (qNMR) received major attention, supported by the technichal progress of modern NMR techniques that overcame the problems of comparatively low sensitivity. This leads to a reduction of the previously wide-spread scepticism towards qNMR results. In [24] it was shown, that an exact sample preparation, spectra acquisition and signal integration can provide assays for simple model compounds with expanded uncertainties of about 1% relative. Maniara et al. [25] conducted a validation study of 1 H and 31 P NMR measurements in great detail, focussed on purity assays for model and agrochemical compounds, yielding standard uncertainties of about 0.5% relative. In a suite of papers Wells et al. [26–28] demonstrated the great power of modern qNMR when performed as a validated method. They assessed the purity of some technical grade agrochemicals with a detailed uncertainty budget 2 [29] on the basis of the GUM [18]. The great importance of quantitative NMR spectroscopic measurements using modern NMR techniques and validated procedures is demonstrated by three recent dissertations [31–33]. Trueness of results – intercomparisons In principle the reliability of quantitative analysis methods can be tested in every laboratory by means of gravimetrically prepared mixtures of pure substances. According to the policy of national metrology institutes, a higher level of evidence is provided by intercomparisons. Up to now, only 2
In the paper mentioned here [29] confusion arises with the formulas used to calculate the purity. It should be noted that the purity P and the purity factor f should be distinguished. Otherwise somewhere a factor of 100 is wrong as for instance in Eqs. 3 and 6. We would recomend to use the accepted symbols [30].
very few “public” intercomparisons involving structure analytical methods were performed. In several international intercomparisons in organic chemistry as well as inorganic chemistry organized by the CCQM, mass spectrometry was included, however, not as pure MS but in combination with chromatography. IDMS key comparisons were performed regularly, organized by the CCQM since 1998. The first intercomparisons for quantitative X-ray phase analysis were performed to investigate the inter-laboratory agreement of results, with a view to assess the metrological quality of this technique [23, 34]. Few NMR intercomparisons were published so far [35]. Since 1998, the CCQM entrusted the Federal Institute for Materials Research and Testing (BAM) NMR laboratory to organize NMR intercomparisons on the international level. Reports about these intercomparisons are available as CCQM documents, but will be published. It has been shown that experienced laboratories may reach levels of accuracy and precision of better than 1% relative, if carefully validated measurement and data handling parameters are used. The same result was obtained in parallel intercomparisons for German NMR laboratories during 1999–2001. Discussion Currently a growing interest in quantitative application of structure analytical methods can be observed. This results from a self consistent process: The methods reviewed here (and perhaps others not mentioned in this article, e.g. ESR and CD), when applied to the determination of the amount of a component in a mixture, need a reference material of known purity. The purity of reference standards should be assessed by primary methods of measurements because they guarantee the highest metrological quality of results. Some of the most widely used structure analytical methods combine a high potential for qualitative structure elucidation with a capability for quantitation. Their capabilities as primary quantitative methods, i.e. their metrological quality, are quite different as judged by the criteria taken from the definition given by CCQM. The spectrometer output of each structure analytical method consists of an electronic signal assigned accordingly and quantified by height or by area. The measurement equation relating the signal intensity to the amount of substance connects both data by a constant (KS in (1)) based on the specific theoretical and experimental background. This constant must be estimated by comparison with a suitable standard material, so all methods in question here are ratio methods according to the definition of CCQM. The absorption methods (IR, UV/Vis) and traditional XRDP use a measurement equation where the constants KS are concentration and frequency dependent and have to be determined by calibration. The reference to be used is the analyte itself. Direct MS is capable in priciple, but seldom used for quantitative tasks because of the complex processing of the mixture in the spectrometer. It may be
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used for very sensitive and rapid analysis under carefully calibrated experimental conditions. The emission methods (Raman, Fluorometry) have the disadvantage that the intensity of the exciting light, governed by the experimental arrangement of the sample in the spectrometer, influences the diffused light. The experimental efford is too high in most laboratories to use the method routinely for quantitative tasks. Comprehensive validation would be a difficult piece of work. The same is true for M¨ossbauer spectrometry. All these methods compare intensities of signals corresponding to the amount of substance of the respective components, but these measured intensities are based on different response factors which are only obtainable by costly experiments, if ever. The Rietveld variant of XRPD is a powerful tool for quantitative analysis of crystalline powders and can be considered as a primary ratio method since it delivers the internal ratio of the mixture components. In addition, if desired, absolute amounts of mixture components may be determined using an internal standard. The calculation of the complete diffractogram of each substance in the mixture, provided that the structure is known, is feasible, using dedicated computer software, for experienced laboratories. For IDMS methods a measurement equation of the type (1) is used. The experimental constant in Eq. 1 cancels because the response factors of the signal intensities for isotopomers are identical. This can be utilized, whenever isotopomers of the analyte are available and equilibrate in the sample preparation step. Sensitivity, trueness and precision are outstanding. The 1 H NMR spectrum can be used for simple and quick direct quantitative determination of amount ratios in mixtures of structurally different compounds, even stereoisomers. This is an almost unique fact in the field of spectroscopy. Since in most analytical applications the determination of amount of substance ratios is exactly what is required, NMR data do not suffer from the imprecision associated with volumetric determinations. For quantitative evaluations, the NMR spectrum must contain at least one signal assigned to a defined molecular structure group for each molecule in the mixture to be analysed. No weighing and no sample preparation steps (except dissolution) are necessary. If the absolute determination of the amount of substance of mixture components is required, an internal standard other than the analyte itself can be used. Besides
its extraordinary capability for structure analysis in solution, exclusively NMR enables to assess the purity of pure materials (up to 99.5%) without using the analyte itself as a standard. Among others, this is an obvious advantage for rare and expensive materials, e.g. in pharmacy, biology and medicine. Summarising, the measurement equation of 1 H NMR in solution and the associated uncertainty budget are given directly in SI units and all response factors are identical. Further, the high metrological quality is demonstrated by good agreement of results in inter-laboratory comparisons. The method is comprehensively validated and can be applied using the validated parameters in every laboratory on each NMR spectrometer. These features establish quantitative 1 H NMR as a potential primary method of measurement. Moreover the progress in modern NMR instrumentation with respect to sensitivity has recently leaded to an impressive increase of quantitative applications.
Conclusions Pure compounds are necessary for metrologically accepted quantitative chemical investigations. For this purpose, a comprehensive characterization of their chemical structure (constitution, configuration, and conformation) is highly demanded. All the methods of structure analysis considered here have their special field of application also in quantitative analysis. IDMS, 1 H NMR and the Rietvield variant of XRPD were identified as having features of a primary ratio method, capable to determine amounts of substance in mixtures and the purity of pure compounds. They may be used to provide references for other methods used in chemical laboratories that need pure compounds for tracing analytical results back to SI units. 1 H NMR has further methodical and practical advantages which make this technique one of the most capable modern measurement methods with a wide range of applications in chemical research. Acknowledgement The authors thank the Federal Ministry of Economics and Labour (BMWA), the German Federation of Industrial Cooperative Research Associations “Otto von Guericke” (AiF) and the German Research Association of Medicine Manufacturers (FAH) for supporting this work within the project AiF-No. 13843 N/1.
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