Nuclear magnetic resonance spectroscopy frequency dependence

Nuclear magnetic resonance spectroscopy first aroused the chemist s Interest when the discovery was made that the exact nuclear precession frequency is dependent upon the chemical environment of the nucleus. The displacement of the resonance frequency relative to an arbitrary standard is commonly referred to as chemical shift. Without this property, NMR would be without practical utility to the chemist as an analytical tool and it would probably long be extinct. 

The foregoing spectral absorption methods can yield quantitative results, although calibration is required. With nuclear magnetic resonance spectroscopy (NMR) (Koenig, 1999 Stuart, 2002 Cheng, 1991 Kinsey, 1990 Wang et al., 1993), the absorption intensity is directly proportional to the amount of the particular isotope present consequently, ratios of absorption intensities in proton NMR, for example, can be used to determine the number of chemically distinct protons in a sample. The characteristic NMR resonance frequency (e.g., chemical shift ) depends on chemical environment, and therefore the specific chemical nature of the material can be identified. 

The isothermal time dependence of relaxation and fluctuation due to molecular motions in liquids at equilibrium usually cannot be described by the simple linear exponential function exp(-t/r), where t is the relaxation time. This fact is well known, especially for polymers, from measurements of the time or frequency dependence of the response of the equilibrium liquid to external stimuli such as in mechanical [6], dielectric [7, 33], and light-scattering [15, 34] measurements, and nuclear-magnetic-resonance spectroscopy [14]. The correlation or relaxation function measured usually decays slower than the exponential function and this feature is often referred to as non-exponential decay or non-exponentiality. Since the same molecular motions are responsible for structural recovery, certainly we can expect that the time dependence of the structural-relaxation function under non-equilibrium conditions is also non-exponential. An experiment by Kovacs on structural relaxation involving a more complicated thermal history showed that the structural-relaxation function even far from equilibrium is non-exponential. For example (Fig. 2.7), poly(vinyl acetate) is first subjected to a down-quench from Tq = 40 °C to 10 °C, and then, holding the temperature constant, the sample... 

In a paper that appeared in 1979, R.P.J. Merks and R. DeBeer pointed out that the sinusoidal dependence of the stimulated echo ESEEM experiment on x and T (equation 8), presented the opportunity to collect ESEEM data in both time dimensions and then apply a two-dimensional EFT to derive two important benefits. The first benefit was that suppression-free spectra should be obtained along the zero-frequency axis for each dimension while the second benefit would be the appearance of cross-peaks at (tUo, cofs) and (tw, co ) that would allow one to identify peaks that belonged to the same hyperfine interaction. This ESEEM version of the NMR COSY experiment (see Nuclear Magnetic Resonance (NMR) Spectroscopy of Metallobiomolecules) would prove invaluable for ESEEM analysis of complex spin systems. However, the disparity in spin relaxation times in the x and T time dimensions precluded the general application of this method. 

Nuclear magnetic resonance (NMR) spectroscopy is a powerful and widely used tool for the examination of samples for chemical or atomic composition and, to some extent, for the relative amounts of the component substances. If a particular nucleus has a spin, then it has a magnetic moment that is subject to a torque if an external magnetic field is applied. Depending on the frequency of the applied field, certain nuclei or functional groups will resonate, thus yielding a signal spectrum that can be compared with the spectra of known substances. Additionally, NMR spectroscopy can be used to determine the chemical dynamics of a sample, such as a protein. 

In conventional spectroscopy, measurements are carried out in the frequency domain. The intensity of radiation is recorded in dependence on the frequency or reciprocal wavelength. Some analytical methods, such as Fourier transform infrared (FT-IR) or pulsed nuclear magnetic resonance (NMR) spectroscopies, provide the information in the time domain. There, the opposite transformation into the frequency domain is of interest. 

Some transitions require more energy than others, so we must use radiation of the appropriate frequency to determine them. In this chapter, we will discuss three types of spectroscopy that depend on such transitions. They are nuclear magnetic resonance (NMR), infrared (IR), and ultraviolet-visible (UV-vis) spectroscopy. Table 12.1 summarizes the regions of the electromagnetic spectrum in which transitions for these three types of spectroscopy can be observed. We will begin with NMR spectroscopy and nuclear spin transitions, which require exceedingly small amounts of energy. 

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