Spectrum derivative

It is equivalent, when an ftk spectrometer is used, to re-apodization of the data. Curve fitting is a method of modeling a real absorption band on the assumption that it consists of a series of overlapped peaks having a specific lineshape. Typically the user specifies the number of peaks to attempt to resolve and the type of lineshape. The program then varies the positions, sizes, and widths of the peaks to minimize the difference between the model and the spectmm. The largest difficulty is in knowing the correct number of peaks to resolve. Derivative spectra are often useful in determining the correct number (18,53,54). 

A solvent free, fast and environmentally friendly near infrared-based methodology was developed for the determination and quality control of 11 pesticides in commercially available formulations. This methodology was based on the direct measurement of the diffuse reflectance spectra of solid samples inside glass vials and a multivariate calibration model to determine the active principle concentration in agrochemicals. The proposed PLS model was made using 11 known commercial and 22 doped samples (11 under and 11 over dosed) for calibration and 22 different formulations as the validation set. For Buprofezin, Chlorsulfuron, Cyromazine, Daminozide, Diuron and Iprodione determination, the information in the spectral range between 1618 and 2630 nm of the reflectance spectra was employed. On the other hand, for Bensulfuron, Fenoxycarb, Metalaxyl, Procymidone and Tricyclazole determination, the first order derivative spectra in the range between 1618 and 2630 nm was used. In both cases, a linear remove correction was applied. Mean accuracy errors between 0.5 and 3.1% were obtained for the validation set. 

Derivative spectra can be recorded by means of a wavelength modulation... 

Likewise, record the second derivative spectra of the four standard pseudo-ephedrine hydrochloride solutions and record the peak heights DL at 258-259 nm plot the results against concentration and confirm that a straight line is obtained. 

Because of peak overlappings in the first- and second-derivative spectra, conventional spectrophotometry cannot be applied satisfactorily for quantitative analysis, and the interpretation cannot be resolved by the zero-crossing technique. A chemometric approach improves precision and predictability, e.g., by the application of classical least sqnares (CLS), principal component regression (PCR), partial least squares (PLS), and iterative target transformation factor analysis (ITTFA), appropriate interpretations were found from the direct and first- and second-derivative absorption spectra. When five colorant combinations of sixteen mixtures of colorants from commercial food products were evaluated, the results were compared by the application of different chemometric approaches. The ITTFA analysis offered better precision than CLS, PCR, and PLS, and calibrations based on first-derivative data provided some advantages for all four methods. ... 

Fig. 4. ESR spectra at 298 K. A Curves 1-4 refer to CuAc, Cu-H-Y, Cu-MCM-22 and Cu-VPI-5. B Curves 1-4 refer to the second derivative spectra of curves 1-4 of A. C Curves 1-4 represent the absorption curves of CuCl,4Pc, CuCI,4Pc-Na-Y (0.26), Cu(N02)4Pc and Cu(N02)4Pc-Na-Y (0.16), respectively.

The amount of information, which can be extracted from a spectrum, depends essentially on the attainable spectral or time resolution and on the detection sensitivity that can be achieved. Derivative spectra can be used to enhance differences among spectra, to resolve overlapping bands in qualitative analysis and, most importantly, to reduce the effects of interference from scattering, matrix, or other absorbing compounds in quantitative analysis. Chemometric techniques make powerful tools for processing the vast amounts of information produced by spectroscopic techniques, as a result of which the performance is significantly... 

Figure 1-3. Comparison between experimental and theoretically derived spectra for prephenate anion in solution. The vertical lines correspond to the theoretical spectrum for 12 conformers (3 lines for each) with intensities computed as described in the main text. The experimental spectrum is presented as a dark line (with the highest energy intensity also normalized to 1). The inset shows the near-UV absorption in greater detail. Adapted from Ref. [18]...

Fig. 7. Effect of pH on the EPR spectrum recorded at —100° of sulphite oxidase reduced by sulphite. The species present at low pH values, which shows proton splitting, is replaced by another species at high pH. The pH. for the transformation is about 8.2, In (A), maxima and minima in the derivative spectra are denoted by the numbers 1—7. In (B) changes in the spectra are plotted as a function of pH. with values at pH 7.2 taken as 100% and those at pH 9.2 taken as 0%, or vice versa. The features in the spectra measured were height of the 1 and 2 doublet (open circles) height of the peak at 3 (squares) distance between 4 and 5 (triangles) and height of 7 (diagonal crosses). (Reproduced from ref. 15, with the permission of Dr. K. V. Rajagopalan.)...

It takes a little practice to get used to looking at first-derivative spectra, but there is a distinct advantage first-derivative spectra have much better apparent resolution than do absorption spectra. Indeed, second-derivative spectra are even better resolved (though the signal-to-noise ratio decreases on further differentiation). Figure 1.6 shows the effect of higher derivatives on the resolution of a 1 2 1 triplet arising from the interaction of an electron with two equivalent 7=1/2 nuclei. 

Reeder and Rieger6 used ESR spectra to identify complex ions and to estimate formation constants for aqueous oxovanadium(iv) complexes with lactic acid, thiolactic acid, glycolic acid, and thioglycolic acid. Through the use of second-harmonic detection, which produces second-derivative spectra, the resolution was good enough that several of the individual species could be separately... 

In first-derivative spectra, it is most convenient to describe the line width as the separation between derivative extrema. This width may be computed by taking the second derivative and finding the zeros, obtaining ... 

Spectrophotometric determination of niclosamide and thiabendazole in their binary mixtures (e.g., tablets) was realized by precipitating thiabendazole with ammonium reineckate at pH 3.0 selectively and reading the absorbance of the solution of the precipitate in acetone at 525 nm for thiabendazole and by measuring the dA/dA values at 405.8 nm in the first-derivative spectra of the remaining solution for niclosamide [52]. 

Since in EPR we usually observe first-derivative spectra as a consequence of phase-sensitive detection (see 2.7) it is relevant to note that the first derivatives of the two distributions are features with a positive and a negative peak. The peak-to-peak separation App in field units for the two distributions is... 

The H NMR derivative spectra of natural clinoptilolite sample CT and two modified clinoptilolite samples CT ODA 2 and CT ODA 5 are at Fig. 4. The NMR signal arose from hydrogen in OH groups of water that are placed along the clinoptilolite channel walls, from the CH3, CH2 and —NH3+ groups that are in the ODA chains and also from free water molecules that are always present in natural clinoptilolites. 

Another variation on the fermentation of alcohol was the work done in a rice vinegar broth by Yano et al.34 Using second derivative spectra from 1600 to 1760 ran, the ethanol and acetic acid concentrations were easily determined in the culture broth. Gas chromatography was used as the reference method. 

In the first method, derivative spectrophotometry, the amplitudes in the first derivative spectra at 287 and 260 nm were selected to determine caffeine. The concentration range of application is 3-15 pg mL for caffeine. 

The eahbration samples were prepared in 10 mL cahbrated flasks eontaining 3-15 pg mL of eaffeine and were diluted with distilled water. The peak amplitudes of the first-derivative spectra was measured at 287 and 260 mn. 

In analysing the caffeine of energy drinks, an accurately weighed amount of 15 mL of sample to 50 mL volumetric flask containing 25 mL water. Two milliliters of basic lead acetate solution was added to this solution and diluted the mark with distilled water. After filtering, 25 mL of filtrate was taken and 0.25 g of NaHCOj was added to this solution. Then, the solution was filtered. Five milliliters of filtrate was transferred to a 25 mL volumetric flask and adjusted to volume with distilled water. The peak amplitudes of the first-derivative spectra was measured at 287 and 260 nm. The sample preparation procedure was also used for PLS-1 method and the absorbances of this solution were recorded between 240-320 mn. 

The absorption spectra and first derivative spectra of 9 )ig mL solution of caffeine and energy drinks samples are given in Figs. 31.1 and 31.2. Upon examining the first spectra of two samples, it can be noticed that caffeine can be determined 287 and 260 nm. 

Figure 1.6 The absorption spectrum and first and second derivative spectra of a natural colorless diamond. The marked wavelengths indicate characteristic bands of N3 centers (reproduced with permission from Lifante et at., 1990).

Infrared derivative spectra for different isotopic mixtures of C 0/ C 0 in the c(2 x 2) structure at lOOK on Cu(lOO). Reproduced by permission from Persson and Ryberg. )... 

Frake et al. compared various chemometric approaches to the determination of the median particle size in lactose monohydrate with calibration models constrncted by MLR, PLS, PCR or ANNs. Overall, the ensuing models allowed mean particle sizes over the range 20-110/tm to be determined with an error less than 5 pm, which is comparable to that of the laser light diffraction method nsed as reference. Predictive ability was similar for models based on absorbance and second-derivative spectra this confirms that spectral treatments do not suppress the scattering component arising from differences in particle size. 

The use of second-derivative spectra eliminated the baseline shifts observed during the reaction (which could be due to changes in the amounts or size distribution of particles, or small amounts of probe fouling). 

Polymer type All of the polymers have very distinct, easily distinguished NIR spectra except N66 and N6 which are very similar. The use of second-derivative spectra is necessary to reliably distinguish the small spectral differences between N66 and N6. 

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