NMR

NMR is a technique based on the behavior of atomic nuclei in magnetic fields. It is used in medicine for magnetic resonance imaging, and in chemistry/biochemistry for determining the structure of chemical compounds.

The basic theory behind NMR is that protons, which spin and have charge, have a magnetic dipole (a north and south pole, like miniature magnets themselves). When protons are subjected to a magnetic field from a very powerful electromagnet, they reorient in the direction of the magnetic field. The reorientation causes them to release radio waves, which can be detected.

For medical applications, this effect is sufficient, as different tissues have differing water content, and will return different signals. However, for more sophisticated chemical studies, there are several other effects which take place that allow structure determinations to be made. Protons that are very near to each other, or on adjacent atoms, cause resonance effects that create characteristic peaks. With computer modeling and knowing the sequence of a protein, it becomes possible to obtain very clear structures of proteins and other organic molecules in solution.

You make an NMR magnet in the following general way. Wind an electromagnet from niobium tin alloy wire. This wire should be very thin and very long, as you want to make a very strong magnet. The energy of the magnet comes from the electrons held within the coil of wire, in NMR magnets you have a lot of electrons, 100 amperes of more. (Also see coulombs.) The magnet does not have many volts though. Then cool this electromagnet until it exhibits superconductivity this will happen at about 4 degrees kelvin, very near to absolute zero. You do this by immersing the magnet into a vaccuum flask of liquid helium, which is at less than 4 kelvin. In order to keep the helium from boiling away too quickly, you need another vacuum vessel around this containing liquid nitrogen. The vacuum spaces are pumped down to about 10^-5 atmospheres pressure and this coupled with very effiecent insulation (which consists of many layers of molecule thick silvered mylar; like a 'space-blanket') can enable a magnet to keep it's helium for up to a year or more! This gives the external appearance of a big silver flask about 2.5 metres tall and 1 meter in diameter.

Once the coil of the magnet is cooled to liquid helium temperature, you can then slowly charge the magnet up to it's full strength. You have to do this carefully as any instabilities can cause a 'hot spot' in the coil, which boils away the helium, causing that bit of the wire to stop superconducting, which then causes the wire to heat up, boiling more helium off, heating up more wire....And in a matter of seconds all the energy you put into the coil has transferred itself as heat into the liquid helium, which turns into a gas expanding about 1000 times as it does so.

The strength of the magnet is usually expressed at the frequency hydrogen resonates at the magnetic field, for a field strength of 21.1 tesla the resonant frequency is 900 MHz. Modern designs of magnet have huge forces acting on them. If you consider the magnetic fields running through the magnet will actually work to collapse the magnet in on itself, and the design must take this into account. The wire is made hexagonal in cross-section so as to prevent movement of the individual strands. (A circular cross-section would have gaps, which could allow the wires to move). The magnet as a whole has to be designed to withstand forces of up to 200 tons and stresses of 250 MPa, that the current density of 200 Amps per mm² can generate. Pecision engineering results in a collosal magnetic field strength, homogenous to parts per million.

Once you have the correct amount of energy in the magnet coil, and it's stable, you can flick a switch to close the circuit of current flowing through the magnet, and as it's superconducting the electrons always flow, and the magnet is said to be persistant! The magnet can stay charged for several years, with no drop in performance as long as the cryogens are replenished.

The basic idea behind is that nucleons with a spin also have a magnetic moment. Now when a small magnetic field is applied this magnetic moment could be aligned with the field or aligned against it. The energy of these two configurations is slightly different.

Now when you apply a radio frequency pulse of just the right frequency this causes transitions between these two energy states. This precisely defined frequency depends not only the nucleus but also the chemical atmosphere which the nucleus is in and by determining it you can make a lot of deductions.

In its early days NMR was done by applying a radio frequency pulse and constantly modifying its frequency till maximum absorption was observed. Nowadays with Fourier Transform NMR you just apply one pulse(Which might have a rectangular or Gaussian or some other frequency spread). Now you Fourier transform the observed signal and this lets you determine the frequency of maximum absorption.

While it is probably true that the majority of experiments are solution-state, proton (¹H) NMR, there are many other types of NMR experiments available. First, almost every chemical element has at least one NMR-active isotope. Isotopes are categorized by their ground state nuclear spin quantum numbers, I, which are always n/2 where n is an integer. I is equal to zero for isotopes that have even atomic numbers and even mass numbers (e.g. ¹²C) and these nuclei do not have NMR spectra; isotopes with odd atomic number but even mass numbers have n even (e.g. ¹⁴N), while an isotope with odd atomic number and odd mass number has n odd (e.g. ⁹Be, ³⁵Cl). The most commonly studied group is the I = 1/2 nuclei, particularly ¹H and ¹³C.

Other NMR-useful isotopes include ¹⁹F, ³¹P, ⁵⁷Fe, ¹¹⁹Sn, ¹⁹⁹Hg (all I = 1/2); ⁷Li, ³³S, ⁷⁹Br, ¹³¹Xe, and ¹⁷⁷Hf (I = 3/2); ¹⁷O, ²⁷Al, ¹²⁷I (I = 5/2); ¹⁰B (I = 3); ⁴³Ca, ¹²³Sb (I = 7/2); ⁷³Ge, ⁹³Nb (I = 9/2). Nuclei with I > 1/2 are called quadrupolar.

The chemical shifts of the resonances (peaks) in an NMR spectrum are normally reported relative to a reference compound, in units of ppm. The chemical shift depends on the shielding constant which, in turn, depends on the electron density (i.e. the other atoms and their arrangement) around the nucleus being studied. Each chemically distinct nucleus in the sample will produce a unique resonance, and the pattern of these gives detailed structural information. Most NMRs today are Fourier transform instruments, in which a radiofrequency pulse of a few microseconds is applied to the sample followed by data collection as the nuclei relax to their ground states. This is repeated many times to average out the noise. The voltages induced in the receiver coil by the relaxing nuclei produce the free induction decay spectrum and Fourier transformation of this FID gives the more readable frequency domain spectrum.

If two nuclei are near each other (i.e. usually three chemical bonds apart or less), they may couple, which causes the resonances of each nucleus to be split. The spectrum of a spin 1/2 nucleus will be split into a (q + 1) multiplet by q equivalent spin 1/2 nuclei. The relative intensities of the multiplet for equivalent spin 1/2 nuclei follow the pattern of Pascal's triangle. In a system AtBw, where A and B are spin 1/2 nuclei and t and w are the numbers of each nuclei, the spectrum of A will be split into a (w + 1) multiplet and the spectrum of B will be split into a (t + 1) multiplet. Therefore, observation of both spectra enables one to count how many of each nuclei are present in the system.

Coupling to quadrupolar nuclei may also occur, in which case a spin of n/2 causes splitting into n +1 lines of equal intensity.

In addition to the normal, single resonance, experiments, many other NMR techniques have been developed. By applying a second radiofrequency at right angles to the magnetic field, the observed spectrum may be perturbed, from which more information about the system may be gathered indirectly. Internuclear double resonance (INDOR) is especially useful when a multinuclear NMR instrument is unavailable, because it gives details about one type of nucleus while irradiating only a different type. Other techniques include spin-tickling, spin decoupling (reduces the complexity of the spectrum by removing the effects of the irradiated nuclei), triple resonance, and multi pulse methods. Two dimensional NMR spectra are also obtainable. Correlated spectroscopy (COSY) gives details about couplings between nuclei of a single isotope. Heteronuclear correlation (HETCOR or HCOR) spectroscopy represents the couplings of two nuclei, with each axis corresponding to chemical shifts of one of the nuclei. The NOESY (Nuclear Overhauser Effect spectroscopy) and HOESY (heteronuclear NOESY) techniques are two others.

Besides spectra of liquid compounds and solutions, NMR can be used to gain information about the structures of gaseous molecules, liquid crystals and solids. Solid samples are associated with additional difficulties, however, due to the immobility of the nuclei. First, long range couplings produce very broad resonances. Since chemical shifts depend on the orientation of the molecule to the magnetic field, anisotropy in solids also produces broadened lines. Third, long nuclear relaxation times decrease the signal-to-noise ratio. In a liquid, the random orientation and movement of molecules with respect to each other cancels out most long range couplings and chemical shift anisotropy; relaxation times are generally shorter, too.

One way to reduce the linewidths of a solid sample is by using magic angle sample spinning (MASS or MAS). The effects of chemical shift anisotropy are averaged out by rotating the sample about an axis that is tilted at an angle of 54.7 ° to the magnetic field. (The equation for line broadening due to chemical shift anisotropy includes a term (3cos²θ - 1) which vanishes when θ = 54.7 °.) In some samples, especially those with heavy elements, the mechanical strength of the sample container does not allow the sample to be rotated fast enough to completely eliminate line broadening caused by chemical shift anisotropy. In this case, each resonance in the spectrum will be replaced by a central line and several spinning sidebands.

MAS can also remove long range couplings by averaging them to zero. The rotation rate must be greater than the linewidth or the couplings will not be completely eliminated.

The problem of long relaxation times can only be overcome for some nuclei using the technique of cross-polarization (CP). Other, more complicated techniques are necessary in most cases.

References:

Ebsworth, E. A.; Rankin, D. W. H.; Cradock, S. Structural Methods in Inorganic Chemistry, 2nd ed.; CRC Press: Boca Raton, FL, USA; 1991; Chapter 2.

Skoog, D. A.; Leary, J. J. Principles of Instrumental Analysis 4th ed.; Saunders: Fort Worth, TX, USA; 1992; Chapter 14.

Solomons, T. W. G. Organic Chemistry, 5th ed.; John Wiley and Sons: New York, NY, USA; 1992; Chapter 14.