Fourier common absorption spectrum

The principle of Fourier transform (FT) NMR spectroscopy is the observation of the so-called free induction decay (FID) after the application of radio frequency (rf) pulses to the resonating nuclei. The carrier frequency of the rf-pulses is the Larmor frequency. In many cases, the FID is observed after single-pulse (SP) excitation, e.g., after application of a so-called 7r/2-pulse which rotates the magnetization by 90° from the direction of the external magnetic field (z-direction) into the x,y-plane. The characteristic time constant for the free induction decay is the transverse relaxation time, T2, which is given by T2=(2/M2) =0.53 (A Vi/2)" for Gaussian lines. Fourier transformation of the FID yields the common absorption spectrum. 

It is common practice to speak of the Fourier coefficients as the representation of the signal in the Fourier domain, or, alternatively, the frequency domain. The signal itself is then said to be a representation in the time domain. This is confusing when our signal is not a function of time, but, e.g. an absorption spectrum. In Fourier and Wavelet literature, however, these notions of time and frequency are so common that they are unavoidable. 

The instrument that determines the absorption spectrum for a compound is called an infrared spectrometer or, more precisely, a spectrophotometer. Two types of infrared spectrometers are in common use in the organic laboratory dispersive and Fourier transform (FT) instruments. Both of these types of instruments provide spectra of compounds in the common range of 4000 to 400 cm" Although the two provide nearly identical spectra for a given compound, FT infrared spectrometers provide the infrared spectrum much more rapidly than the dispersive instruments. 

More frequently than chemical techniques, the spectroscopic methods of analysis are used for the determination of polymer chemical composition. Among these techniques the use of infrared (IR) absorption spectra as fingerprints for polymer identification is probably the most common. The IR absorption is produced tjy the transition of the molecules from one vibrational quantum state into another, and most polymers generate characteristic spectra. Large databases containing polymer spectra (typically obtained using Fourier transform infra-red spectroscopy or FTIR) are available, and modern instruments have efficient search routines for polymer identification based on matching an unknown spectrum with those from the library. For specific polymers, the IR spectra can reveal even some subtle composition characteristics such as interactions between polymer molecules in polymeric blends. 

Both Fourier-transform (FT) and continuous-wave (CW) EPR spectrometers are available. The FT-EPR instrument is like an FT-NMR spectrometer except that pulses of microwaves are used to excite electron spins in the sample. The layout of the more common CW-EPR spectrometer is shown in Fig. 13.38. It consists of a microwave source (a klystron or a Gimn oscillator), a cavity in which the sample is inserted in a glass or quartz container, a microwave detector, and an electromagnet with a field that can be varied in the region of 0.3 T. The EPR spectrum is obtained by monitoring the microwave absorption as the field is changed, and a typical spectrum (of the benzene radical anion, CgHj) is shown in Fig. 13.39. The peculiar appearance of the spectrum, which is in fact the first... 

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