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Nuclear Magnetic Resonance

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Pulse Techniques in NMR

In the early days of NMR spectroscopy, it was common to hold the magnetic field at a constant strength and then irradiate the sample with highly monochromatic electromagnetic radiation (i.e. electromagnetic radiation spanning only a small frequency range). This radiation could then be swept through different frequencies, and the frequencies at which nuclei in the sample came into resonance could be noted. However, this was a time-consuming process, with much time being wasted scanning through frequencies at which no nuclei resonated.

Relaxation times and Linewidths in NMR Spectra

We have already established that a bulk sample containing numerous spin ½ nuclei in a static magnetic field possesses a net magnetisation in the z direction (as defined by the direction of the magnetic field). Application of a brief electromagnetic pulse in the xy plane produces a magnetisation component in the xy plane which decays with time.

Practical aspects of NMR

High resolution NMR spectra are routinely obtained today, but there are various requirements which must be fulfilled to produce high quality spectra from which a great deal of useful data can be obtained.

Electron Spin Resonance (ESR) Spectroscopy

This is a spectroscopic technique related to NMR that makes use of the fact that electrons also have an intrinsic spin angular momentum. For electrons, the spin quantum number, S, is equal to ½. This number specifies the magnitude of the total spin angular momentum for an electron to have the numerical value / 2 (in precisely the same way that a spin angular momentum quantum number of I = ½ specifies the spin angular momentum of a proton or other spin-½ nucleus to have magnitude / 2.)

Patterns of Splitting in an NMR Spectrum

It is also necessary to consider the interactions of a nucleus A with two or more magnetic nuclei. The other nuclei with which A interacts can either be equivalent (identical isotopes occupying equivalent sites in a molecule, such as the CH2protons or the CH3 protons in ethanol) or inequivalent. Inequivalent nuclei can be of the same isotope, if the positions they occupy in the molecule are such that they couple differently to any particular atom.

Fine Structure in an NMR Spectrum

As mentioned previously, it is most common for the lines in an NMR spectrum to be split into several components. This is referred to as the fine structure of the spectrum, and it leads to the NMR spectrum of ethanol (C2H5OH) having the following appearance

Energies of Nuclei in Magnetic Fields

The nuclear magnetic moment of a nucleus is denoted μ, and the component of this magnetic moment on the z axis, μz, is proportional to the component of the nuclear magnetic moment along this axis, mI.

Chemical Shift

Nuclear magnetic moments interact with the local magnetic field, which will not necessarily be identical to the applied magnetic field. The applied field can induce motion of electrons in orbitals, which gives rise to an additional magnetic field at the nucleus.

Contributions to the Chemical Shift

Broadly speaking, we have established that protons in inequivalent positions in a molecule will have different resonancefrequencies. This explains the appearance of the NMR spectrum of ethanol

Spin Angular Momentum

Spin angular momentum is a specific type of angular momentum possessed by some nuclei. As such, it obeys all the relations given for angular momentum under the quantum mechanics of rotation, here. i.e. there are two quantum numbers associated with the spin angular momentum momentum that determine its properties.