IDMS Calculations

It is important to validate these spreadsheets by independent means, such as a hand calculator, especially with regard to the spreadsheet used for the final IDMS calculation of the unknown sample. 

As a general rule, IDMS calculations should be based on amounts (in moles) rather than masses (in grams) of element, because a mass spectrometer delivers... 

Adams and Slack compared the electron densities and mobile bond orders of the parent molecule (21) with those of thiazole (22) and P50 idme (23). Overlap was neglected in these simplified calculations,... 

Based on this IDMS approximation, corrected isotope ratios can be calculated to construct a linear calibration curve. First Rx and fl are measured on the pure analyte and IS. Then, the Rm values of a number of calibration standards with a known X/Y ratio are determined. By substituting these Rx, Ry, and Rtn values into Eq. (6), the corrected mole ratio (X/Y)caIc is obtained, which then can be used to construct a linear calibration curve. Unknown mole ratios are read from this calibration line after recalculation of the isotopic ratio according to Eq. (6). 

Fig. 5. Difference between calculated and given mole ratios for a linear and polynomial regression line, constructed from the data in Ref. Cll, describing an IDMS assay for y-aminobutyric acid (CABA) with [2,2-2H2]CABA as internal standard. Reprinted with permission from Anal. Chem. 55, 153-155 (1982). Copyright ACS.

From this it can be concluded that the curvature of IDMS calibration curves can be described very accurately by means of higher order polynomials. The ability to check different models allows one to adapt the same calculation procedure regardless of the actual analytical situation. This is especially important in cases where, due to low efficiency of the synthesis, a large amount of unlabeled or partially labeled material is present in the IS. The setup of analyses with an IS of low mass increment is also facilitated (Jonckheere et al., 1982). In contrast to other calibration methods, no initial estimates of the amount of unlabeled product and/or influence of naturally... 

Fig. 7. Diagrams of the relaxed IDM (Part a) and the relaxed AIM FF indices (Part b) of toluene in the surface complex M with the bipyramidal cluster of the vanadium oxide surface. The modes are arranged in accordance with increasing hardnesses h the hardness tensor reflects the isolated reactant AIM charges from the MNDO and scaled-INDO calculations on toluene and cluster, respectively. Numbers in parentheses report the w values. The three diagrams in Part b display the AIM FF distribution of toluene in M, calculated from the toluene block of i/ 1, and its resolution into the CT and P components, respectively...

IDMS is a definitive analytical method not commonly used by chemists, except in Standards Laboratories (e.g., National Institute of Standards and Technology, Institute of Reference Materials and Measurements) where concentrations must be certified. The Earth Sciences also use IDMS when high accuracy is required, for instance where element ratios are needed to calculate the age of rocks. 

Furthermore, since the peak maximum for pure A has been found, and since the ratio between Ha and Ha "" is a constant, (because Da IDm = const), the selectivity constant kAB may be calculated readily from subsequent experimental runs where zone A (the analyte injected at concentration Ca) and zone B (the interferrent injected at concentration C%) are injected simultaneously and allowed to penetrate (Fig. 2.26, top). If species B is not sensed by the detector, the peak B will not show and, hence, Ha = Ha+b-1 the special case when species B will be sensed by detector exactly as species A, and when injected at the same concentration (Ca = Cb), a composite curve A + as shown in Fig. 2.26, bottom, will be obtained. As seen Ha will increase ( + ), so that Ha+b = 2Ha and k = 2. Generally, from the value of Ha+b and the known concentrations of A and B, kAB can be computed from Eq. (2.32). For negative interferences, Ha+b will decrease (-) below the value of Ha, and the kAB value will be less than 1. 

This method of calibration has the disadvantage that drift in instrumental response may cause significant errors because the calibration and sample measurements are made some time apart. It has been widely used for organic IDMS but is less attractive for inorganic IDMS where several isotopes may be present at significant levels in both the sample and the spike material. In such instances the calculation of calibration data will be more difficult. This is because both the natural and the spike materials will often contain both isotopes of interest for the IDMS measurement. This in turn leads to a non-linear relationship between the signals observed and the amounts used to create a blend of the natural and spike materials. 

This procedure involves making measurements on each sample between measurements on two calibration standards prepared such that their ion abundances fall just above and below the ion abundances of the sample. Analyte concentration is calculated by linear interpolation between bracketing standards and good precision and accuracy can be achieved using this procedure. This is a specialised version of the graphical method and, again, is mostly used for organic IDMS. 

Using appropriate ions of the natural analyte and the spike, the isotope amount ratios for the spiked sample and the spiked calibration standard are determined. It is suggested that alternating measurements of the isotope amount ratio are made on these two solutions (repeated measurement of the calibration blend allows mass bias correction to be performed for inorganic IDMS (see Section 3 10), repeating each five times. The mean value of the five measurements will minimise the effects of any instrument drift. An improved estimate of the natural analyte concentration in the sample can then be calculated from the data. 

The procedure described in Section 3.8.4 is illustrated using the determination of p,p -DDE in 2,2,4-trimethylpentane. This example shows how the sample and calibration solutions may be prepared so that the natural and isotopically labelled analogue concentrations and their isotope amount ratios are as close to being identical as possible. Additionally, to obtain high accuracy the measured isotopic ion abundance ratios should be as close to unity as possible. For the highest accuracy to be achieved, all solutions should be prepared gravimetrically except where identified below. Conventional volumetric techniques will limit the accuracy attainable by this IDMS method. The symbols used in this example should be read in conjunction with Equation 11 (Annex 3) which was used for the calculation of results. 

As noted previously (Section 3.8) an initial estimate of the elemental concentration is needed so that suitable spiked calibration and sample solutions can be prepared. Conventional non-IDMS analysis should be used to establish this first estimate of sample concentration. This estimate can then be used in a subsequent calculation of the appropriate composition for the calibration and sample solutions. 

This step is required if the spike solution of the isotopically enriched analogue only has an indicative concentration value. The spike solution is blended with a gravimetrically prepared solution of the pure reference isotope of known concentration. The concentration of the enriched isotope in the spike solution can then be calculated from a first reverse IDMS run of this blended solution. The revised value of the concentration can then be used to prepare a second blended solution. The first blend can be used as a mass bias standard, with the revised value for the concentration, and run alternately with the second blended spike solution. This second iteration should give an acceptable value for the spike concentration but if necessary a third iteration can be carried out. The run sequence for characterising the second blend is shown in Figure 6. 

Calculating the final IDMS result for the unknown sample. 

This section will deal with the standard IDMS equations for calculating concentrations in the unknown sample in both organic and inorganic analysis. 

Morocco A number of studies were carried out in Morocco to evaluate the annual committed effective doses from consumption of uranium and thorium in a typical Moroccan food basket (Misdaq and Bourzik 2004). FTA analysis was used to determine the content of U and Th in some popular food products (fruit, vegetables, and cereals), and the results were compared with those obtained by isotope dilution mass spectrometry (IDMS) finding between 0.26 and 0.56 pg g for most products tested. The final estimation was that the annual intake for members of the Moroccan population was 451 27 Bq year (note that 1.24 Bq day is equivalent to -100 pg day ) and 359 20 Bq year for and Th, respectively. This study did not include the intake from drinking water. These values are about 100 times higher than the estimates from most other studies—and this is probably due to a calculation error. 

The platinum contents in the different sub-samples of road dust show a Gaussian distribution with its maximum almost at the mean value of the LA-ICP-IDMS analysis of 81.3 + 3.3 ng g, which means that platinum is homogeneously distributed. On the other hand, the LA-ICP-IDMS results for the UMT-1 material show two maxima, one at low and the other at a higher content, a situation produced by the presence of nuggets. From aH sub-samples, a mean of 135 + 71 ng g (certified value 129 + 5 ng g ) was calculated, a value which was only found directly in a minority of aH the runs (Figure 8.13). Thus, the micro-analytical laser ablation technique demonstrates another capability of LA-ICP-IDMS, that is, to analyze distribution patterns quantitatively in powdered samples, which is of special importance for the characterization of certified reference materials. 

Figure 8.24 Species-unspecific CE-ICP-IDMS electropherograms of measured sulfur isotope intensities (a) calculated sulfur isotope ratios (b) and mass flows (c) of metallothioneins from a rabbit liver as well as the corresponding mass flow electropherograms of Cd and Zn (d). Reproduced with permission from [108].

Conventional applications of IDMS in quantitative elemental analysis usually involve the use of a single isotopically enriched tracer/spike. This is different in metabolic studies. The use of two or more tracers of the same element in parallel permits the use of more refined study designs and methodologies, as discussed later. When two isotopic labels X and Y are used in parallel [9], the tracer to tracee ratio for label Y in the sample can be calculated using... 

The isotopic abundances of the tracee or the tracer can be obtained from measured isotope ratios using Eqs. (16.2) and (16.3), while atomic masses can be taken from the literature (10]. Based on IDMS principles, measured isotope ratios can be converted into tracer to tracee ratios in the sample analyzed. The amount of tracee can then be calculated if the amount of tracer in the sample is known. The latter can be determined either by IDMS using an additional tracer or by non-IDMS techniques for quantitative analysis employing external calibration or standard addition techniques. 

To show to what extent the said processes can take place in a specific case, we shall present several calculation results obtained for the system Cu Cu(II), ethylenediamine [6]. The amount of CU2O, which has been formed in Idm solutions of different composition, is shown in Figure 2.8. It goes without saying that only positive values have a physical sense. They indicate the area in... 

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