True integrated intensity

This method of determining the true integrated intensity is based on integration ... 

Extrapolation of the absorbance to zero leads to the true integrated intensity A of the absorption band ... 

However, of greater theoretical significance than the maximal molecular extinction coefficient is the integrated absorption intensity A. (This can be referred to as the true integrated intensity.) This is the area under the absorption curve and is most commonly defined in terms of the absorption coefficient o... 

The apparent absolute intensity is what we would measure in practice and it will always be equal to or less than a, the true integrated intensity. The smaller the ratio Av/y, where y is the spectral slit width, the closer B approaches A,... 

The integral true fluorescence intensity is obtained again by Eq. (8.15). Also the partial intensities emerging from the front and back surface are accessible with the Kubelka-Munk formalism in closed analytical form. In order to solve the system of coupled differential equations, the source function... 

The integrated intensity data of Table III are shown plotted as a function of composition in Figure 4. Each peak intensity shows a smooth variation over the whole range. These data contain information about the local order of A1 atoms about Si. In the case of faujasite a structural model has been developed that successfully explains the NMR data over the whole range of composition (7). Comparision of the Si NMR spectra for ZK4 and faujasite at the same composition, Figure 5, shows that the relative intensities of the five peaks are different. Therefore, the local order of A1 about Si is different in the two materials. This is true over the whole range of composition as demonstrated by comparison of the relative intensities of the Si(2Al) and Si(OAl) peaks in Figure 6. 

Assuming the true absorptions to have Lorentzian form and assuming a triangular slit function, Ramsay 121, 122) investigated the effect of finite resolving power upon these band shapes for the vibrations of a variety of compounds. This approach reproduced satisfactorily the observed band profiles. However, he did not obtain a simple relationship between true and apparent integrated intensities. Ramsay found that bands are best characterized by their apparent peak intensities [loge(J o/r) J and their apparent half-intensity band widths These quantities are related to... 

Having established both a probable mathematical form of the true shape of an infrared absorption band and its relationship to its apparent or observed profile, Ramsay outlined three methods for determining true integrated absorption intensities. As these methods have been used exclusively in all reported studies of absolute intensities of metal carbonyl stretching vibrations, they are now described in some detail. ... 

Since the two ratios of the right-hand side of Eq. (14) have been tabulated, it is easy to present K in the same form so that by measuring the apparent peak intensity and the apparent half-intensity band width of an absorption band and consulting the relevant tables, the true integrated absorption intensity can be calculated from Eq. (13). 

If a spectrometer with a linear wavelength scale is used, the experimental absorption curve has to be replotted as fractional absorption (Tq — T)ITq against v in cm , and the area under the band for a range (r — i g) determined. A correction for the band wings is applied to obtain A, and then the true integrated absorption intensity is calculated from Eq. (20). Wing corrections are presented in tabular form in terms of the quantity (i — and are to be found in the original paper 121). 

Strictly speaking, Eq. (14-16) is valid only for integrated intensities, and the same is true of all other intensity equations in this chapter. Yet it has been found possible to determine the quartz content of dusts with satisfactory accuracy by simply measuring maximum intensities. This short cut is permissible here only because the shape of the diffraction lines is found to be essentially constant from sample to sample. There is therefore a constant proportionality between maximum and integrated intensity and, as long as all patterns are made under identical experimental conditions, the measurement of maximum intensities gives satisfactory results. Quite erroneous results would be obtained by this procedure if the particle size of the samples were very small and variable, since then a variable amount of line broadening would occur, and this would cause a variation in maximum intensity independent of sample composition. 

It has been repeatedly reported that silver stained methods are not suitable for computerized quantitation because of their capriciousness and nonlinearity. This is apparently true of the stains based on reduction with citric acid and weak carbonate because there is no predicting the slope of a plot of integrated intensity versus protein concentration without the use of a reliable and reproducible color. Thus, in order to use quantitation with these two methods one must perform a standard curve with each protein as its own standard or accept some relative standard for normalization. The relative approach has been successfully used with GELCODE and allowed measurement of protein changes within an experimental protocol (1 ). These disadvantages have discouraged the acceptance of silver staining to its full potential application. 

Lorentzian line shape, with an intensity variation that decreases slowly away from the specular condition). Unfortunately, this method is also subject to systematic error. In addition to changes in peak shape, the sample orientation may drift with time (due to thermal stresses) resulting in a measured reflectivity that is systematically reduced with respect to the true integrated reflectivity. 

In order to make quantitative measurements. Miles (1958f)) has determined integrated infrared absorption intensities for some nucleosides, nucleotides, and polynucleotides in DjO solution (Fig. 12.8 and Table 12.2) by application of Ramsay s method I (Ramsay, 1952). When there is a well-resolved band, the application of Ramsay s method encounters no difficulty, but when overlapping bands occur, as in uridine and its derivatives, some uncertainty exists in determining the halfband width of a particular band. (The half-band width is a factor in Ramsay s equation and is defined as, Av, 2 = the width of the band in cm" at half-maximum intensity.) The equation as used by Miles to obtain A, the true integrated absorption intensity... 

The reproducibility of quantification of additives with GC-QMS ion scan mode is unacceptable with RSDs of 5-20%, as opposed to 0.5-2.5% for GC-FID. Various alternatives for quantitation may be considered (i) simultaneous FID and QMS detection (ii) separate GC-FID and GC-QMS analysis and (Hi) verification in scan mode and quantification in SIM mode. For quantification by means of FID peak purity is important. Quantification in SIM mode is more sensitive than by means of FID. ToF-MS detection systems are inherently efficient in the true integral of the ion intensity from GC peaks of any width, compared to scanning instruments, where the ability to characterise narrower GC peaks falls off sharply as peak widths come within an order of magnitude of scan time (post-processing required). 

Due to the finite width of the slit function g(v,v ) the measured intensity at a setting v will not be equal to the true absorption intensity 1. An apparent intensity T(v ) will be in fact determined. It is given by the integral... 

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