Infrared spectra curve-fitting

For the case of the frequency response of a real catalyst in which the number and magnitude of different types of adsorption is not known beforehand, the response may be interpreted by curve fitting to give a distribution of adsorption types versus rate constant. The interpretation of an experimentally determined frequency response curve would not be too dissimilar, in principle, from the interpretation of the output of an infrared spectrum where two or more unknown compounds are to be identified and quantitatively estimated from a single IR scan. 

Ibbitson and Moore (13) conclude that the maximum in the curve of polarization vs. concentration for ethanol in carbon tetrachloride is caused by linear multimers, and the subsequent fall in polarization is caused by an increasing amount of cyclic multimer (Figure 1). The concentration at which the maximum occurs coincides with that at which the 3350-cm.-1 band first appears in the infrared spectrum, so they have suggested that this band arises from cyclic multimers. They have fitted their data to a system containing linear dimer and trimer and cyclic tetramer only and have evaluated association constants for these species. 

Apart from the obvious variables of peak height and width, the type of bandshape needs to be considered. Ilie class of bandshape of an infrared spectrum depends on the type of sample. A choice of Gaussian, Lorentzian or a combination of these bandshapes, is usually considered. Figure 5.2f illustrates a typical. curve-fitting process. 

Fig. 3. Infrared spectra in the carbonyl stretching region for binary P(BA-co-BT)/TDP=90/10 blend (a) and ternary P(BA-co-BT)/PEO/TDP=45/45/10 blend (b) resolved by curve-fitting program Amor. amorphous component Crys. crystalline component Hydr. hydrogen-bonded component Fitt. omve-fitted Exp. experimental spectrum.

The various ways in which a spectrum can be manipulated in order to carry out quantitative analysis were examined. These included baseline correction, smoothing, derivatives, deconvolution and curve-fitting. The Beer-Lambert law was also introduced, showing how the intensity of an infrared band is related to the amount of analyte present. This was then applied to the simple analysis of liquid and solid samples. Then followed a treatment of multi-component mixtures. An introduction to the calibration methods used by infrared spectroscopists was also provided. 

The infrared spectrum of each sample was analyzed with a Fourier transform infrared (FTIR) microspectroscopy (IRT-5000-16/FTIR-6200, Jasco Co., Tokyo, Japan) equipvped with a mercury cadmium telluride (MCT) detector via a transmission technique (Gao Lin, 2010 Lin et al., 2006, 2010). All the FTIR spectra were obtained at a 4 cmi resolution and at 100 scans. The components and relative compositions of each sample were estimated quantitatively within the 1740-1600 cm-i region of FTIR spectra by a curve-fitting algorithm with a Gaussian-Lorenzian function (Cheng et al., 2008 Hu et al., 2002). The best curvefitting procedure was performed by iterative fits toward a minimum standard error. The relative composition of the component was computed to be the fractional area of the corresponding peak, divided by the sum of the area for all the peaks. 

A simple application of the multiple-oscillator theory is to fit measured reflectance data for MgO in the Reststrahlen region. In Section 9.1 we considered the electronic excitations of MgO, whereas we now turn our attention to its lattice vibrations. A glance at the far-infrared reflectance spectrum of MgO in Fig. 9.7 shows that it does not completely exhibit one-oscillator behavior there is an additional shoulder on the high-frequency side of the main reflectance peak, which signals a weaker, but still appreciable, second oscillator. The solid curves in Fig. 9.7 show the results of a two-oscillator calculation using (9.25) the reflectance data were taken from Jasperse et al. (1966), who give the following parameters for MgO at 295°K ... 

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