Pure component reference spectra

Figure 4.2 The pure component reference spectra of hexane (a), dissolved carbon monoxide (b), dissolved cyclooctene (c) and dissolved Rh4(CO),2 obtained after entropy minimization.

Partial chemical information in the form of known pure response profiles, such as pure-component reference spectra or pure-component concentration profiles for one or more species, can also be introduced in the optimization problem as additional equality constraints [5, 42, 62, 63, 64], The known profiles can be set to be invariant along the iterative process. The known profile does not need to be complete to be used. When only selected regions of profiles are known, they can also be set to be invariant, whereas the unknown parts can be left loose. This opens up the possibility of using resolution methods for quantitative purposes, for instance. Thus, data sets analogous to those used in multivariate calibration problems, formed by signals recorded from a series of calibration and unknown samples, can be analyzed. Quantitative information is obtained by resolving the system by fixing the known concentration values of the analyte(s) in the calibration samples in the related concentration prohle(s) [65],... 

Pure Component Reference Spectra. An ESCA Cls spectrum of the pressed PEEK wafer is shown in Figure la. An ESCA Ols spectrum of the pressed PEEK wafer is shown in Figure lb. The Cls spectrum can be resolved into peak components indicative of hydrocarbon-type environments (285.0 eV), carbons singly bound to oxygen (at approximately 286.5 eV), and a distinctly resolved peak indicative of carbon in a ketone environment at 287.3 eV. Since this Q=0 peak is expected at 288.0 eV, this suggests delocalization of electron density along the backbone chain. The PEEK surface stoichiometry is as expected (see Table I). This further supports the idea that the Q=0 peak is... 

The instrument uses three recordings stored in memory a spectrum of the sample (composed of the two compounds to be analysed) and a spectrum of each of the pure components in the same spectral domain (reference solutions of known concentrations). 

First, a reference background spectrum for the IR spectrophotometer was obtained then the reactor was charged with 35 mL of 0.1 M hydrochloric acid. The stirrer speed was set to 600 rpm and the reaction temperature, Tr, was set. Next, 2 g of a mixture of 10.7 mmol of acetic anhydride and 15.1 mmol of acetic acid was added at a constant dosing rate of 5 mL min-1. Three experiments were carried out at each of three reaction temperatures, Tr = 25, 40 and 55°C. For the determination of qoos, the heat capacity of the feed mixture (1.83 kj kg-1 K-1) was calculated using the mass fraction and the heat capacities of the pure components (acetic anhydride cp = 1.65kjkg-1 K-1 and acetic acid cp =2.05kjkg-1 K-1). 

Selectivity describes the degree of spectral interferences, and several measures have been proposed. Most definitions refer to situations where pure-component spectra of the analyte and interferences are accessible [19-21, 28]. In these situations, the selectivity is defined as the sine of the angle between the pure-component spectrum for the analyte and the space spanned by the pure-component spectra for all the interfering species. Recently, equations have been presented to calculate selectivity for an analyte in the absence of spectral knowledge of the analyte or interferences [25-27], These approaches depend on computing the NAS, defined as the signal due only to the analyte. Methods have been presented to compute selectivity values for N-way data sets (see Section 5.6.4 for the definition of N-way) [29, 30],... 

The AMDIS program analyses the individual ion signals and extracts and identifies the spectrum of each component in a mixture analysed by GC-MS. The software comprises an integrated set of procedures for first extracting the pure component spectra from the chromatogram and then to identify the compound by a reference library (Figure 3.18-3.23). 

The analytical mass spectrometer was introduced commercially in 1941. For two decades its main application was quantitative analysis of light hydrocarbon mixtures and similar samples, often with accuracies of 1% absolute. Such analyses depend directly on linear superposition of the spectra of the components, in the same way that Beer s law governs spectrophotometric mixture analysis. The low-pressure conditions for electron ionization cause each mixture component to contribute independently to the measured spectrum of the sample, so that the spectrum s abundances can be reflected by a series of simultaneous equations using data from reference spectra of the pure components. Thus, if you can identify correctly one component of an unknown mixture spectrum, you can then subtract out the reference spectrum of that component ( spectrum stripping ), and attempt to interpret the residual spectrum. Note, however, that spectral superposition will not necessarily be linear for Cl and other spectra obtained at pressures high enough for competitive ion-molecule reactions. Today, most MS mixture analysis utilizes combined instrumentation such as GC/MS (Karasek and Clement 1988 Evershed 1989 Catlow and Rose 1989). 

Cross-correlation is used to evaluate the similarity between the spectra of two different systems, for example, a sample spectrum and a reference spectrum. This technique can be used for samples where background fluctuations exceed the spectral differences caused by changes in composition. The cross-correlation technique also can be used to generate the spectra of the pure components from the mixture spectra when the pure component spectra are not available, or when the pure component spectra differ significantly from the isolated pure spectra because of interaction or matrix effects. 

As mentioned previously, the complex emission spectrum F (l) of samples containing multiple fluorophores is assumed to be the linear sum of individual component spectra Ffl), F2(X), FfX), weighted by their abundance xu x2, x3. Let Fj(X) and F2(X) be the reference emission spectra of pure samples of fluorophore (e.g., Cerulean and Venus). The term reference emission spectra is used because these spectra describe the emission at excitation wavelength /. x of a defined concentration of fluorophore (e.g., 10 /rM) acquired using the same excitation light intensity as was used to acquire an emission spectra of an unknown sample mixture. Under these conditions, the shape and magnitude of the fluorophore mixture spectra will be ... 

A more complex situation is a multi-component mixture where all pure standards are available, such as a mixture of four pharmaceuticals.3 It is possible to control the concentration of the reference compounds, so that a number of carefully designed mixtures can be produced in the laboratory. Sometimes the aim is to see whether a spectrum of a mixture can be employed to determine individual concentrations, and, if so, how reliably. The aim may be to replace a slow and expensive chromatographic method by a rapid spectroscopic approach. Another rather different aim might be impurity monitoring,4 how well the concentration of a small impurity may be determined, for example, buried within a large chromatographic peak. 

An exploratory analysis performed by FSIW-EFA provides an estimate of the number of components in each pixel. For resolution purposes, only those pixels in the partial local rank map will be potentially constrained, because these are the pixels for which a robust estimation of the number of missing components can be obtained. However, the FSIW-EFA information is not sufficient to identify which components are absent from the constrained pixels. For identification purposes, the local rank information should be combined with reference spectral information, the ideal reference being the pure spectra of the constituents, although in most images not all of these are known. For the image components with no pure spectrum available, the reference taken is an approximation of this pure spectrum. These approximate pure spectra can be obtained by pure variable selection methods, or they may be the result of a simpler MCR-ALS analysis where only non-negativity constraints have been applied. 

The differential method is often important for the identification and determination of impurities in a natural product, for the assay of a pharmaceutical preparation, or for the detection of adulterants in foods and other substances. One places the impure sample in the sample beam of a double-beam spectrophotometer and the pure major component in the reference beam. One adjusts the thickness of the reference sample until the absorption bands of the major component are blanked out, and obtains a difference spectrum produced by the impurity in the mixture. A calibration curve of absorbance against concentration of impurity can be made from a series of such difference spectra. The advent of ordinate scale expansion in modem instruments has helped considerably in the study of impurity bands and weak bands generally, as well as in microanalysis. 

---