Absorbance spectra derivative

Fig. 4 Comparison between statistical measurement of Sn02 particle sizes by TEM and absorbance spectra derived distribution (21). On the inset, the obtained absorbance spectra, showing the sharp exciton peak [83]...

Another approach that can be taken is the use of derivative spectra, that is, plotting the first, second, or even higher derivatives of the absorbance spectra. Derivative spectra can enhance the differences among spectra, resolve overlapping bands, and reduce the effects of interference from other absorbing compounds. The number of bands increases with higher orders of the derivative. The increased complexity of the derivative spectrum may aid in compound identification. For example, the absorbance spectrum of testosterone shows a single broad peak centered around 330 nm the second-derivative spectrum has six distinct peaks (Owen). 

The above-mentioned bands are found at the same positions in the transmission spectrum of polyethylene, indicating that the recorded specular-reflection spectrum can indeed be converted, by using the KK relations, into a spectrum that is essentially the same as the absorbance spectrum derived from a transmission measurement. However, several bands observed in the region of 2000-1700 cm in the (v) spectmm of Figure 8.5 are not expected for polyethylene. A more careful examination is needed to clarify their origin. 

SEC-FTIR yields the average polymer structure as a function of molecular mass, but no information on the distribution of the chemical composition within a certain size fraction. SEC-FTIR is mainly used to provide information on MW, MWD, CCD, and functional groups for different applications and different materials, including polyolefins and polyolefin copolymers [703-705]. Quantitative methods have been developed [704]. Torabi et al. [705] have described a procedure for quantitative evaporative FUR detection for the evaluation of polymer composition across the SEC chromatogram, involving a post-SEC treatment, internal calibration and PLS prediction applied to the second derivative of the absorbance spectrum. 

Figure 54-1 Two Gaussian absorbance bands and their respective first and second derivatives (finite differences). The top spectrum represents a synthetic Gaussian absorbance spectrum, the middle a first derivative and the bottom a second derivative . Note that the ordinate of the first derivative has been expanded by a factor of 10 and the second derivative by another factor of 10. The wavelength spacing between data points is 1 nm. The narrow band has a bandwidth (FWHH) of 20 nm, the broad one is 60 nm.

The absorbance spectrum in Figure 54-1 is made from synthetic data, but mimics the behavior of real data in that both are represented by data points collected at discrete and (usually) uniform intervals. Therefore the calculation of a derivative from actual data is really the computation of finite differences, usually between adjacent data points. We will now remove the quotation marks from around the term, and simply call all the finite-difference approximations a derivative. As we shall see, however, often data points that are more widely spread are used. If the data points are sufficiently close together, then the approximation to the true derivative can be quite good. Nevertheless, a true derivative can never be measured when real data is involved. 

Details are given of the development of an on-line sensor using near IR spectroscoy for monitoring carbon dioxide concentration in polymeric extrusion foaming processes. The calibration curve relating the absorbance spectrum at 2019 nm to the dissolved gas concentration was derived so as to infer dissolved carbon dioxide gas concentration... 

UV spectrum of pseudoephedrine with its first and second derivative spectra. The minima correspond to the maxima in the absorbance spectrum. 

Many types of analyses would be improved by using this principle because the use of a derivative spectrum is no more difficult than the use of an absorbance spectrum. The amplitude between the minimum and maximum on the nth derivative curve is... 

Plots of the correlation coefficients obtained from the absorbance and its first and second derivatives (D1 and D2) are shown superimposed on the absorbance spectrum of the 100% Fe SWy in Figure 4a. Correlation coefficients for the full set, superimposed on the absorbance spectrum for 100% Fe Otay sample, are shown in Figure 4b. The quality of the correlation is significantly improved using 1st derivative data and improved still further using 2nd derivative data. This can be seen from Table III where a summary of the correlation coefficients obtained from absorbance and first and second derivatives of absorbance at several prominent wavelengths, including the computer optimum, are displayed. 

Figure 6.4 shows the peak position of the methylnitrophenol absorbance spectrum at different pHs. Displacement of the peak position with the pH follows a sigmoidal curve, pKa, determined at the inflection point of the curve is 6. This point corresponds to the maximum of the first derivative spectrum of the sigmoid curve and to the zero-crossing... 

Figure 21 shows the absorption spectra of diclofenac, a UV-B absorber (camphor derivative), a UV-A absorber (dibenzoylmethane derivative), and abroad-spectrum absorber (benzophenone derivative) (45). 

The aromatic nature of macrocycles 4.96a-4.99 was inferred from the large diamagnetic ring-current effect observed in their H NMR spectra. For instance, in the case of the octaethyl derivative 4.96a, the shift difference between the internal C-H protons and the external ones was found to be 25.3 ppm. This shift difference is over twice as large as that found for [18]annulene (A5 = 12.1 ppm). The UV-vis absorbance spectrum for 4.96a exhibits an intense Soret-like absorbance at 547 nm... 

Generally, the haptenic group has an absorbance spectrum that can allow one to differentiate it from the protein carrier. This is particularly true for azo derivatives, which absorb in the visible range. However, even if there is overlap in the two spectra, reasonably accurate determinations of the number of haptenic molecules per carrier protein can be determined from difference spectra. 

The curve of the second derivative matches the points of inflection in the zeroth order spectrum by regions of zero slope which correspond to maxima or minima (Figure 9.30). The fourth derivative reveals even further the weak absorbance variations in the initial spectrum. Numerous analyses would be improved by adopting this principle, knowing that to make a measurement from the derivative spectra is no more difficult than from the absorbance spectrum. The amplitude between the maxima and the minima of the nth derivative graph is proportional to the absorbance value of the solution. The calibration graph is established from a few standard solutions of different concentrations to which the same mathematical treatment has been applied, as to the sample solution. 

Another attempt to get structural information from UV spectra is described by Bartolome et al. [232], They invented the so-called "min-max distance", which is the distance in nanometers between the maximum and minimum absorbances between 220 nm and 280 nm. The minimum absorbance is derived from the second derivative of the original spectrum. It was found that this "min-max distance" decreased by 1.3 nm upon each additional monomer unit in the molecule. This regularity was demonstrated up to the tetrameric level. In routine analysis, the value of this spectral parameter is questionable because spectra must be recorded with a high resolution and blank spectra must be substracted. So far, it has only been applied to the analysis of procyanidins from Visnea mocanera [183]. 

TRIR measurements are obtained from three different recordings of the emission spectrum of the IR source. These include a spectrum of the IR source without the sample in the beam path (/q), a spectrum of the IR source with the sample in the beam path (/), and the infrared intensity changes induced by photoexcitation (A/). The absorbance spectrum of the unexcited sample is derived from /q and /, A=log (/q//). Because the IR detector is AC coupled, measurements of /q and / are performed with an optical chopper (Stanford SR540) to modulate the IR light. 

Figure 11.18. IR spectrum of indigo. Top absorbance spectrum bottom second derivative.

Activation spectrum for yellowing of the same PVC compositions on exposure to a filtered xenon source, determined by the cut-on filter technique, has also been reported. The wavelength interval % = 310-325 nm was identified as being the most effective in bringing about photoyellowing [37] of extruded PVC sheets with no titania and with 2.5 phr of titania. These findings are consistent with the conclusions from an earlier report of an activation spectrum derived from a monochromatic exposure experiment. For a similar source, the maximum degradation as detected by UV-visible spectral absorbance was found to be at X. = 320 nm [19]. 

Figure 1 Synthetic example demonstrating numerical derivative spectra up to third order derived from a synthetic absorbance spectrum - the lower left graph compares the Savitzky-Golay method to the noise sensitive difference approach [3].

Savitzky-Golay method This method determines a derivative spectrum by moving a spectral window comprising 2 +1 measurement points over an absorbance spectrum. Then a polynomial of order m... 

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