Second - derivative absorption spectroscopy

Figure Bl.4.7. Top THz generation by optical-heterodyne conversion in low-temperature GaAs. (a) The three DBR laser system that synthesizes a precise difference frequency for the THz photomixer spectrometer, (b) the MOPA system and the set-up for spectroscopy. Bottom second-derivative absorption spectrum of the...

Absorption Spectroscopy. Second derivative absorption spectra were recorded using a Perkin-Elmer Model 554 absorption spectrophotometer. Film samples were analysed by transmission on optically transparent quartz flats. 

Zero-order first and second derivative UV absorption spectra of 18 purines and pyrimidines were determined in aqueous solution at 298 K. The procedure, based on the direct comparison of the derived maximum and minimum wavelengths and of the sequences of relative amplitudes, can be used for concentrations of purines as low as 5 x 10-6 M <85MI 7li-0l>. A similar study has shown that second derivative spectra can be used for the identification of eight mixtures of purines and pyrimidines <88TAL513>. The structure and equilibrium of purine in ethanol has been studied by UV spectroscopy which indicates the existence of annular automery in purine and the presence of associated species of only one of its tautomers <88JST(174)83>. Both polarized UV and Raman... 

The properties are most useful when there are several closely overlapping peaks, and higher order derivatives are commonly employed, for example in electron spin resonance and electronic absorption spectroscopy, to improve resolution. Figure 3.11 illustrates the first and second derivatives of two closely overlapping peaks. The second derivative clearly indicates two peaks and fairly accurately pinpoints their positions. The appearance of the first derivative would suggest that the peak is not pure but, in this case, probably does not provide definitive evidence. It is, of course, possible to continue and calculate the third, fourth, etc., derivatives. 

Electro-absorption (EA) spectroscopy, where optical absorption is observed under the application of an electric field to the sample, is another method that can distinguish between localised and inter-band excitations. The electric field produces a Stark shift of allowed optical absorptions and renders forbidden transitions allowed by mixing the wavefunctions of the excited states. Excitons show a quadratic Stark (Kerr) effect with a spectral profile that is the first derivative of the absorption spectrum for localised (Frenkel) excitons and the second derivative for charge transfer excitons, i.e. 

Figures 8B and 8C illustrate the use of second-derivative spectroscopy and FSD, respectively, to resolve the overlapping component bands of the amide I band profile in the FTIR spectrum of p-lactoglobuhn (Figure 8A). Both of these techniques should only be applied to spectra that exhibit a high signal-to-noise ratio (>1000 1), or otherwise artefacts may be introduced by resolution enhancement. The presence of water vapour in the region of the spectrum of interest will also produce features in the processed spectrum that may be misinterpreted as absorption bands of the sample (Figure 9).

Even derivative spectra do not produce an increase in information compared to zero order absorption spectra. Differentiation can visualise the wavelength regions in which spectral changes are exceptional. For this reason derivative spectroscopy has been applied to kinetic analysis [87]. Fig. 4.20 demonstrates an example of a derivative reaction spectrum given for the above mentioned photoreaction of stilbene. The second derivatives are shown. The advantage in selection of characteristic wavelengths improves the kinetic evaluation as discussed in Chapter 5. However, in each application the optimum between increased noise and extracted information has to be found. 

The estimation of the concentration of polyenes from their absorption spectra requires prior empirical calculation of the absorption coefficients [512]. A very sensitive method for the registration of polyene structures in degraded poly(vinyl chloride) is second derivative spectroscopy (cf. section 10.16) [1792, 1888]. 

As can be seen from these figures, the polyene chromophores are much more easily detectable by second derivative spectroscopy, from the commencement of irradiation, than by normal absorption spectra. 

The first term on the right is non-zero only when the initial and final states are identical - which relates back to Rayleigh scattering. It is the second term which is significant for the Raman process and its detailed form establishes two rules governing Raman-allowed transitions, since both of its factors must then be non-zero. For the Dirac bracket to be non-zero dictates v =v l as in infrared absorption spectroscopy. For the polarizability derivative to be non-zero, the polarizability must change... 

Multidimensional spectroscopy and derivative spectroscopy When bands of reactants and reaction products overlap in the fundamental UV-visible absorption spectra the reaction kinetics cannot be followed by the classic UV method. In many cases, the second derivative UV-visible spectrophotometry (D-2) provides an alternative method to solve the problem. Even-order derivatives are suitable to follow kinetics because the maxima in the UV-visible derivative spectrum can be associated with the minima and a low-noise online spectra is obtained which can be computed up to the 6th order derivative and even up to the 10th order with the newly developed computers. On the other hand, the first derivative does not provide the above association and other higher odd-order derivatives are less precise, though in practice it has proved valuable to work with spectra of the 3rd and 5th order. 

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