Principles of Nuclear Magnetic Resonance (NMR)

Principles of Nuclear Magnetic Resonance (NMR)

Nuclear Magnetic Resonance! You’re more familiar with this term than you may think. You’ve probably heard of Magnetic Resonance Imaging, or MRI. This is the technique used in hospitals to acquire images inside the human body. MRI is based on the principles of Nuclear Magnetic Resonance (NMR).

The NMR magnet

This is the most common use of NMR outside of research. In the medical field, MRI is used for acquiring images inside the human body. And to acquire the images we make use of very large superconducting magnets. Similarly, to run NMR experiments we use large superconducting magnets.

Bruker NMR magnet
NMR magnet

The sample, which is either a liquid or a powdered solid, is placed inside the magnetic field created by a superconducting coil, which is what we refer to when we talk about the NMR magnet. A superconducting material is a material that can transport the electrons without any resistance. And the continuous circulation of electrons then creates the magnetic field. To keep the coil superconducting, we have to keep it very cold. We have to keep the superconducting coil in a bath of liquid helium. The temperature of liquid helium is 4.2 Kelvin, which is -269 degrees Celsius, or -452 degrees Fahrenheit. There’s also a liquid nitrogen dewar surrounding the liquid helium dewar. This acts as a buffer between the very cold temperature of the liquid helium and the room temperature where the instrument is kept to slow down the liquid helium from boiling off and having to refill it often, which is a problem because of the high costs of liquid helium and the scarce helium resources. Some of the newer magnets no longer use liquid nitrogen; instead they have a system of liquid helium reliquefaction, thus reducing the need to refill the magnet with liquid helium. 

The sample goes inside a probe head that contains a radio-frequency coil which is used to send radio frequency pulses inside the sample. The probe head then goes inside the bore at the center of the magnet.

The nuclear spin

To understand the basic principles of Nuclear Magnetic Resonance we have to look at the nuclear spin. Let’s take the hydrogen atom for example. We’ve learned previously, when we talked about the atomic structure, that the hydrogen atom has one proton in the nucleus. And since the proton is a positively charged particle, that means that the nucleus is positively charged. The spinning charge then creates a magnetic field. So these nuclear spins act like tiny bar magnets.

nuclear spins in an external magnetic field
nuclear spins in an external magnetic field

In the absence of an external magnetic field, the nuclear spins in a sample have random orientations. When we place the sample in an external magnetic field, such as that created by the superconducting magnets we use in NMR and MRI, the spins align with the external magnetic field, denoted as B0 and shown by the purple arrow. The spins align either parallel or antiparallel with this external magnetic field. The spins that are parallel with the external magnetic field are at a lower energy, and the spin population at the lower energy is slightly higher than half. The spins that are anti-parallel are at a higher energy and the spin population at the higher energy is slightly lower than half. And the higher the magnetic field, the higher the energy separation between the parallel spins and the antiparallel spins. 

Another important thing to know about the nuclear spins in an external magnetic field is that, besides the fact that they are aligned with the magnetic field, they also precess around the direction of the magnetic field with a frequency that is dependent on the magnetic field. This precession frequency is called the Larmor frequency. This is similar to the precession of a spinning top.

The "resonance" in nuclear magnetic resonance

When we place the sample in the magnet, it is also inside another, smaller coil which can be used to send radio-frequency pulses into the sample. The electromagnetic waves in the radio region have the lowest energy and the lowest frequency of the entire electromagnetic spectrum. When we send radio-frequency pulses to the sample, if the frequency of these pulses matches the Larmor frequency, so the energy of those pulses is equal to the energy difference between the parallel and the anti-parallel state, then we have the phenomenon of resonance. Then we’ll have a transition of a spin from the lower energy state to the higher energy state. This spin transition is then detected, and as the magnetization returns to equilibrium, the signal is detected by the coil and it appears as a a free induction decay. This is the NMR signal as function of time and if we apply to this signal a mathematical transformation called a Fourier transform, we can transform the signal from the time domain to the frequency domain. Here we have peaks that appear at different frequencies, and this is called an NMR spectrum.

NMR signal recorded as a free induction decay in nuclear magnetic resonance
NMR signal recorded as a free induction decay in nuclear magnetic resonance

The NMR spectrum

The different peaks that we observe in an NMR spectrum correspond to the resonance frequency of atoms in a sample that have different local environments. These are atoms of the same type, let’s say hydrogen atoms, in a molecule where these atoms have different environments. Since the local environment for each hydrogen atom in a molecule could be different, this will be reflected in the NMR spectrum by the frequency at which the peak corresponding to that atom appears. Atoms in different chemical groups have characteristic resonance frequencies, which can be found in chemical shift tables. All the NMR spectra are referenced to the resonance frequency of the atoms in a reference sample, whose resonance frequency is known. An example of reference sample is tetramethylsilane (TMS), but there are other references used in NMR. 

chemical shifts in an NMR spectrum
chemical shifts in an NMR spectrum

The resonance frequency of an atom in a sample with respect to the reference sample is called a chemical shift, and the units that are used are parts per million, or ppm, of the frequency with respect to the reference. We can record these kinds of spectra for many other nuclei, not just hydrogens. Another one that is often use, especially for studying organic molecules is carbon, but we can use many other nuclei.

Applications of Nuclear Magnetic Resonance

NMR has many applications, varying from pharmaceuticals, to energy materials, to polymers, food, cosmetics, to biological research on proteins, DNA and RNA, and to the MRI applications of scanning the human body to acquire images inside the body.

In cultural heritage, NMR can be used to study the materials that cultural heritage objects are made of and it can be used to look at the degradation of objects of cultural heritage.

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