Normalisation techniques

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]. 

It is well known that the trace metal content of a sediment is often to a large extent a function of its chemical and mineralogical characteristics. It is, therefore, very important to use a reliable normalising technique for reporting trace metal concentrations. The key sediment characteristic is surface area or particle size since many of the trace metal binding components (e.g. organic matter, Fe and Mn oxides and hydroxides) are very well correlated with both characteristics. 

In Table 5.2,1 compare different normalisation techniques through an example of traffic risk between different ASEAN countries and Sweden. 

Table 5.2 Traffic risk as an example of using different normalisation techniques...

As shown in the table the traffic risk is scaled between 0 to 100 by applying formula (5.2). The normalisation techniques can be tested to show whether the results are highly influenced by any of the methods used in this normalisation. For this empirical sample (11 countries), aU countries did not show any change by using any of the techniques. I prove this by comparing the correlation between each pair of methods as illustrated in Figure 5.2. The correlations are perfect (R-sq=100%) and we can therefore generalise that the results obtained in this study are not influenced by any normalisation method choices. 

This is the easiest case for NMR (and other analytical techniques). What we are looking for is the relative proportion of compounds in a mixture. To do this, we identify a signal in one compound and a signal in the other. We then normalise these signals for the number of protons that they represent and perform a simple ratio calculation. This gives us the molar ratio of the two compounds. If we know the structure (or the molecular weight) of these compounds, then we can calculate their mass ratio. 

The carbonyl index is not a standard technique, but is a widely used convenient measurement for comparing the relative extent and rate of oxidation in series of related polymer samples. The carbonyl index is determined using mid-infrared spectroscopy. The method is based on determining the absorbance ratio of a carbonyl (vC = 0) band generated as a consequence of oxidation normalised normally to the intensity of an absorption band in the polymer spectrum that is invariant with respect to polymer oxidation. (In an analogous manner, a hydroxyl index may be determined from a determination of the absorbance intensity of a vOH band normalised against an absorbance band that is invariant to the extent of oxidation.) In the text following, two examples of multi-technique studies of polymer oxidation will be discussed briefly each includes a measure of a carbonyl index. 

Direct determination of portal blood flow rate is difficult and would generally require placement of an electronic flow probe in each animal. However the technique proposed by Hoffman et al. utilised tritiated water as an absorption probe (i.e. internal standard) [89], By dosing and sampling drug/ absorption probe concurrently, factors such as variable portal blood flow rate are normalised between experiments. 

Fig. 6.31 Normalised intermediate scattering function from C-phycocyanin (CPC) obtained by spin-echo [335] compared to a full MD simulation (solid line) exhibiting a good quantitative matching. In contrast the MD results from simplified treatments as from protein without solvent (long dash-short dash /me), with point-like residues (Cpt-atoms) (dashed line) or coarse grained harmonic model (dash-dotted line) show similar slopes but deviate in particular in terms of the amplitude of initial decay. The latter deviation are (partly) explained by the employed technique of Fourier transformation. (Reprinted with permission from [348]. Copyright 2002 Elsevier)...

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%. 

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]. 

Both these concerns were addressed by the development of modified IR techniques. In the technique of Subtractively Normalised Fourier Transform IR Spectroscopy (SNIFTIRS) or Potential Difference IR (SPAIRS or PDIR) [37], the increased stability and sensitivity of Fourier Transform IR is exploited, allowing usable spectra to be obtained by simple subtraction and ratioing of spectra obtained at two potentials without the need for potential modulation or repeated stepping. A second technique which does not call for potential modulation, but actually modulates the polarisation direction of the incoming IR beam is termed Photo-elastically Modulated Infra-Red Reflectance Absorption Spectroscopy (PM-IRRAS) this was applied to the methanol chemisorption problem by Russell and co-workers [44], and Beden s assignments verified, including the potential-induced shift model for COads. 

The main objective of this technique is to reduce the dimensions of data without losing important information, starting with the correlation between variables, to explore the relationship between variables and between observations. The aim is to obtain p new variables (Ti, I2, , Yp), that we will call principal components, which are (1) a normalised linear combination of the original variables (Yi = aijXi fl2,iX2 -I-. .. -I- apjXp J2k< k,i = 1 X (2) uncorrelated ones (cov(T , Yj) = OVt j), (3) with progressively diminishing variances (var(Yi) > var(Y2) >. .. > var Yp) ), and (4) the total variance VT) coincident with that... 

Another commonly-used normalisation procedure is to use the relative flow technique. In this method the elastic differential cross section for a particular species may be obtained by comparing the scattered intensity under the same conditions with that from another target with a known cross section. It is important to ensure, for both the gas under study and the reference gas, that the electron flux density and distribution, the detector efficiency, and the target beam flux distribution are the same for both gases during the measurement. 

Using DAD or scanning detectors it is possible to determine the purity of a peak by spectral peak purity analysis. Peak homogeneity can be demonstrated by a variety of methods. However, the most commonly used technique normalises and compares UV spectra from various peak sections. 

Methods for correcting for grain-size effects in studies on heavy metal concentrations in estuarine and coastal sediments have been discussed by Ackermann (1980). There is, unfortunately, no one standard method for particle-size normalisation and a wide range of techniques are in use (Table 2.3). The method which often involves the least effort is the correction which uses comparison with rubidium (Rb) as a conservative element (Ackermann, 1980). This technique relies on the fact that Rb has a similar ionic radius to potassium (K) and so substitution of Rb for K will take place in clay minerals. Furthermore, Rb is present in the sand fraction in very much smaller concentrations than in the clay or silt fraction and concentrations of the element in sediments are rarely influenced by anthropogenic activity. Another advantage of the use of Rb is that it is often routinely analysed by X-ray fluorescence along with a suite of pollutant trace metals. 

The introduction of in-situ infrared spectroscopy to electrochemistry has revolutionised the study of metal/electrolyte interfaces. Modnlation or sampling techniques are applied in order to enhance sensitivity and to separate snrface species from volume species. Methods such as EMIRS (electrochemicaUy modulated IR spectroscopy) and SNIFTIRS (subtractively normalised interfacial Fonrier Transform infrared spectroscopy) have been employed to study electrocatalytic electrodes, for example. There have been surprisingly few studies of the semiconductor/electrolyte interface by infrared spectroscopy. This because up to now little emphasis has been placed on the molecnlar electrochemistry of electrode reactions at semiconductors because the description of charge transfer at semiconductor/electrolyte interfaces is derived from solid-state physics. However, the evident need to identify the chemical identity of snrface species should lead to an increase in the application of in-situ FTIR. 

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