The phenomenon of nuclear magnetic resonance was first observed in 1946, and it has been routinely applied in organic chemistry since about 1960. It has grown enormously in power and versatility since that time, conspicuously since the late 1970s with the introduction of Fourier transform (FT) NMR spectroscopy on a routine basis. NMR spectroscopy has grown so fast that it has become a scientific discipline in its own right, and this technology has been widely applied in chemistry and biology. Experiments in both solution and solid-state are extensively performed.
Some atomic nuclei have a nuclear spin (I), and the presence of a spin makes these nuclei behave rather like bar magnets. In the presence of an applied magnetic field the nuclear magnets can orient themselves in 2I + 1 ways. The most common nuclei observed in NMR experiments, including 1H, 13C, 15N, 19F, and 31P, have spins of Ω. These nuclei, therefore, can take up one of two orientations, a low energy orientation parallel to the applied field, and high energy orientation opposed to the applied field. The difference in energy is given by
where is the gyromagnetic ratio (a proportionality constant, differing for each nucleus, which essentially measures the strength of the nuclear magnets) and B0 is the strength of the applied magnetic field. The number of nuclei in the low energy state and the number in the high energy state will differ by an amount determined by the Boltzmann distribution:
The NMR absorption is then a consequence of transitions between these two energy levels, stimulated by the applied radio (RF) frequency field. To extend this picture to include the bulk description of the experiment, we need to consider the motions of the nuclear magnets more thoroughly. The nuclear angular momentum J and the magnetic moment µ arising from it can both be represented as vectors, and the constant of the proportionality between them has been introduced previously as gyromagnetic ratio . The interaction of the nuclear magnetic moment and angular momentum with the applied field B0 can be expressed in classical terms by the equation
The solution of this differential equation is an analog to the motion of a gyroscope. In a magnetic field the axis of the angular momentum precesses around the direction of the field. A single nucleus, then, gives rise to a magnetic moment which rotates at some speed around the applied field; this is reffered to as the Larmor frequency of the nucleus, and is just its NMR absorption frequency :
When the applied RF field matches the Larmor frequency at which the nuclear magnets naturally precess in the magnetic field B0, some of the nuclei are promoted from the low energy state to the high energy state, and increases. The Larmor frequency is dependent upon both the applied field strength and the nature of the nucleus in question.
In modern NMR experiments, the RF signal is applied as a single powerful pulse, which effectively covers the whole frequency range and lasts a time (tp) typically of a few microseconds. This pulse generates an oscillating magnetic field (B1) along the x axis, at the right angles to the applied magnetic field (B0) which is defined as being along the z axis. The effect of the pulse is to tip the magnetization through an angle given by:
Commonly, the time (tp) is chosen so that is 90°, and such pulses are called pulses. The magnetization, disturbed from its orientation along the z axis, precesses in the xy plane, generating an oscillating signal, which is to be picked up by a receiver coil. This signal is called the free induction decay (FID) and is a complicated wave pattern decaying away to zero. The decay takes place because the individual nuclei relax, though interaction with local fluctuating magnetic fields, back to their equilibrium states. Fourier transformation (FT) of the FID, which is said to be in the time domain, converts it into a spectrum, which is said to be in the frequency domain. The frequency domain spectrum is the normal NMR spectrum we are to observe.
The most commonly encountered nuclei with I = ±½ in organic chemistry and biological NMR are 1H, 13C, <sup15N, 19F, 29Si, and 31P. The common nuclei with I = 0, 12C and 16O, are completely inactive. Nuclei with spins I > ½ are called quadrupolar nuclei. 2H and 14N nuclei have spins of I = 1. Many other nuclei, 17O and 13Na as examples, have even higher spin numbers.
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