Normalised analysis

ANALYSIS OF A MIXTURE USING THE INTERNAL NORMALISATION METHOD 9.7... 

To obtain an accurate quantitative analysis of the composition of a mixture, a knowledge of the response of the detector to each component is required. If the detector response is not the same for each component, then the areas under the peaks clearly cannot be used as a direct measure of the proportion of the components in the mixture. The experiment described illustrates the use of an internal normalisation method for the quantitative analysis of a mixture of the following three components ethyl acetate (ethanoate), octane, and ethyl n-propyl ketone (hexan-3-one). 

Figure 4 [29] shows the (s) versus profiles for potato amylose and the amylose/amylopectin mixture from wheat starch corresponding to the concentration versus radial displacement data of Fig. 3. The s data used in the concentration dependence plot of Fig. 3 for wheat amylopectin comes from (s) vs. s analysis data of Fig. 2b and similar. The concentrations shown in the abscissa in Fig. 4 have been obtained from the total starch loading concentration normalised by the weight fraction of the amylopectin component estimated from the (s) vs. s profiles.

Scaling is a very important operation in multivariate data analysis and we will treat the issues of scaling and normalisation in much more detail in Chapter 31. It should be noted that scaling has no impact (except when the log transform is used) on the correlation coefficient and that the Mahalanobis distance is also scale-invariant because the C matrix contains covariance (related to correlation) and variances (related to standard deviation). 

To allow for this, before the peak areas are normalised we must first correct each area so as to get the area we would have obtained had the detector response been the same for each of the three compounds. We will now use the results from our mixture to determine calibration factors (relative response factors) for the detector, and then use these for the analysis of a commercial tablet. 

A kinetic analysis of the data gave k22/k22 = 1.7 x 10-3, k22/k14. = 7.9 x 10 4 and k22/kA6 = 7.9 x 10-3. The dependence of G(H2) on the solute concentrations is shown in Fig. 6, where the chlorine and ethylene concentrations have been normalised by multiplying them by the values of k23fkl4t and k46/k1A respectively. These were calculated from the experimental ratios given above. They are summarised in Table 8. 

Figure 2.12 Correlation plots of (A) transporter expression and (B) metabolic enzyme expression in duodenum between rat and human. The expression levels of transporters and metabolic enzymes are normalised by GADPH expression, transformed by natural logarithm and absolute values were used in the correlation analysis [121].

Minerals Treated with Polyacrylamide. Minerals were treated with HPAM as outlined in Section 2. Any unadsorbed or weakly bound HPAM was removed from the mineral by washing and rinsing. Adsorption on the mineral surface was monitored by the N Is photoelectron peak from the HPAM. To compare HPAM adsorption between minerals, peak integration was used to obtain surface atomic % of N Is, Si 2p and Al 2p. The ratio Nis (Si2p -1- A12p) was used to normalise all the samples, which eliminates the contribution of C 7s hydrocarbon contamination from the analysis. 

Since in the case of an isolated pair of spin nuclei the dipolar dephasing, and hence the REDOR evolution curve, is exclusively governed by the dipolar Hamiltonian, the data analysis proves to be straightforward employing a universal REDOR curve, in which the normalised difference intensity AS/Sq is plotted as a function of the dimensionless product NTRxd.2 ... 

Standard methods of analysis published by bodies such as the American Society for Testing and Materials (ASTM), de Normalisation (CEN), or ISO are rigorously tested and validated in method performance, or validation, studies. These interlaboratory trials can establish reproducibility and method bias and also give some confidence that the method can be used in different environments. Laboratories are chosen with an expectation that they can competently follow the proposed method, which will have already been extensively validated before an interlaboratory trial is contemplated. To this end, a pilot trial is sometimes undertaken to ensure the method description can be followed and to give an initial estimate of the precision of the method. 

For certain samples, the radioelement under analysis can be isolated using its stable isotope and a training technique. A similar treatment carried out on the reference sample allows the extraction yield to be determined. The result is then normalised to 100%. 

Fig. 3.13. Partial least-squares (PLS) calibration of the API data set (5 s accumulation time). Spectra were baseline corrected, normalised to unit length and mean centred. The data set was randomly split into a calibration set (two-thirds) and a prediction set (one-third) obvious outliers from the PCA analysis were excluded from the analysis. The graph shows predicted versus measured API concentration of the prediction set. The straight line represents the 45° diagonal (this figure was published in [65], Copyright Elsevier (2008))...

Other sources of error, particularly in quantitative Raman analysis, include laser self-absorption effects leading to attenuation of some spectral bands. Similarly diffuse reflectance of the laser light, which is dependent on the particle size of the formulation components, may increase or decrease the collection volume. However, normalisation techniques can be used to overcome some of these effects [35]. 

New methods for non-destructive quantitative analysis of additives based on MIR spectra and multivariate calibration have been presented [67, 68], One of the limitations in the determination of additive levels by MIR spectroscopy is encountered in the detection limit of this technique, which is usually above the low concentration of additive present, due to their heavy dilution in the polymer matrix. The samples are thin polymer films with small variations in thickness (due to errors in sample preparation). The differences in thickness cause a shift in spectra and if not eliminated or reduced they may produce non-reliable results. Methods for spectral normalisation become necessary. These methods were reviewed and compared by Karstang et al. [68]. MIR is more specific than UV but the antioxidant content may be too low to give a suitable spectrum [69]. However, this difficulty can be overcome by using an additive-free polymer in the reference beam [67, 68, 69, 70]. On the other hand, UV and MIR have been successfully applied to quantify additives in polymer extracts [71, 72, 66]. 

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