Nuclear Magnetic Resonance NMR

the resonance absorption of electromagnetic energy by matter owing to the reorientation of the magnetic moments of atomic nuclei. NMR is a method of radio-frequency spectroscopy.

NMR is observed in a strong static magnetic field H₀ onto which a weak radio-frequency magnetic field H⊥H₀ is superimposed. The resonant nature of the phenomenon is determined by the properties of nuclei that have an angular momentum of J = ħ I and a magnetic moment of μ, = γI, where I is the spin of a nucleus, γ is the gyromagnetic ratio (a quantity with a characteristic value for a given nuclear species), and ħ is Planck’s constant. The frequency at which NMR is observed is ω₀ = γH₀. For protons in a field of H₀ = 10⁴ oersteds, ω/2π = 42.57 megahertz (MHz); for most nuclei, the resonance frequencies lie in the range from 1 to 10 MHz. The order of magnitude of the resonance absorption is given by the equilibrium nuclear magnetization, or nuclear paramagnetism, of a substance: μ₀ = X₀H₀, where X₀ is the nuclear magnetic susceptibility.

As is the case with other types of magnetic resonance, NMR may be described by a classical model of a gyroscope. In a static magnetic field H₀, a couple due to a magnetic moment μ causes a precession of the magnetic moment and of momentum that is analogous to the precession of a top under the influence of gravity. The magnetic moment μ precesses around the direction of H₀ at a frequency of ω₀ = γH₀; in this case, the angle of precession θ remains constant (Figure 1). A radio-frequency field H₁ of resonance frequency ω₀ causes the angle θ to change at a rate of γH₁ radians/sec, resulting in a substantial change in the projection of μ, on the direction of the field H₀ in even a weak field H₁.

From the standpoint of quantum theory, NMR is caused by transitions between energy levels for the interaction of nuclear magnetic dipole moments with the field H₀ In the simplest case of isolated nuclear spins free of other effects, the condition ℰ = –γħH₀m—where m = I, I – 1, . . ., –I—yields a system of (2I + 1) equally spaced nuclear energy levels in the field H₀. The frequency ω₀ corresponds to a transition between two adjacent levels.

The concept of isolated nuclear spins is an idealization. In reality, nuclear spins interact with one another and with their surroundings, for example, with a crystal lattice. Such interactions result in the establishment of thermal equilibrium, or in relaxation.

Relaxation processes are characterized by two constants, T₁ and T₂. The constant T, describes changes in the longitudinal component of the nuclear magnetization, while T₂ describes changes in the transverse component. A change in the longitudinal component is associated with a change in the energy of a nuclear spin system in the field H₀, that is, with spin-lattice relaxation. Changes in the transverse component are governed

Figure 1. The precession of the magnetic moment μ of a nucleus in a field H₀: (θ angle of precession, (H₁) radio-frequency magnetic field

mainly by interactions within the spin system itself, that is, by spin-spin relaxation. The values of T₁, range from 10^–4 sec for solutions of paramagnetic salts to several hours for very pure diam-agnetic crystals. The values of T₂ range from 10^–4 sec for crystals to several seconds for diamagnetic liquids.

T₁ and T₂ are associated with the structure of a substance and with the nature of the thermal motion of the substance’s molecules. As a rule, T₁ and T₂ have similar values for liquids. However, they become markedly different upon solidification, which is always accompanied by a substantial decrease in T₂. The large values of T₁ in very pure diamagnetic crystals are due to the weakness of the magnetic fields in such crystals. In a crystal that contains paramagnetic impurities, only a few nuclei make thermal contact with the lattice; such nuclei are located near impurity atoms, where the local field is considerably stronger. The equilibrium distribution that is formed near an impurity atom spreads throughout the crystal owing to the interchange of states between neighboring nuclear spins as a result of the magnetic dipole interaction. In metals and alloys, the main relaxation mechanism is the interaction of conduction electrons with nuclear magnetic moments. The interaction results in a shift of the resonance frequencies (seeKNIGHT SHIFT).

A resonance line has a width of Δω = 2/T₂ (Figure 2). In strong fields H₁, saturation occurs. Accompanied by a decrease in nuclear magnetization, saturation is characterized by an increase in the width of a resonance line and a decrease in the amplitude of the line at ǀγǀH₁ > (T₁T₂)^–½. The equalization of the populations of energy levels as a result of transitions caused by the field H₁ corresponds to saturation.

Figure 2. An NMR line

The width of resonance lines in crystals is determined by the magnetic field of neighboring nuclei. For many crystals, the nuclear spin-spin interaction is so great that it results in the splitting of a resonance line.

The interaction of the electric quadrupole moment Q of nuclei with the local electric field in a substance has a large effect on the relaxation times and on the width and shape of NMR lines. In the case of liquids, NMR for nuclei with a large Q can be observed only in substances with a symmetric molecular structure, which prevents the occurrence of the quadrupole interaction. An example is the case of the ⁷³Ge nucleus in the tetrahedral molecule GeCl₄. In crystals, the quadrupole interaction often gives rise to a splitting of NMR levels that is approximately equal to μH₀. In this case, the absorption of energy is governed by nuclear quadrupole resonance.

In mobile liquids, NMR spectra for nuclei with a spin of I = 1/2 and Q = 0 are distinguished by narrow lines. Such nuclei are investigated by means of high-resolution NMR. High-resolution spectra are obtained for protons and for such nuclei as ¹⁹F, ¹³C, and ³¹P. In this case, single lines are obtained only if the NMR of chemically equivalent nuclei is observed. An example of such lines is the hydrogen lines in spectra of water, benzene, and cyclohexane. All compounds with a more complicated structure yield spectra that consist of many lines (Figure 3). The formation of such spectra is associated with two effects, called the chemical shift and the indirect spin-spin interaction.

The chemical shift results from the interaction between the electrons that surround a nucleus and the field H₀. A perturbation of the electron states causes a decrease in the static component of the field that acts on the nucleus; the decrease is proportional to H₀. The magnitude of the chemical shift depends on the structure of the electron shells and, hence, on the nature of the chemical bonds, making it possible to evaluate the structure of molecules on the basis of NMR spectra.

A direct magnetic interaction between nuclei in a mobile liquid is difficult owing to the Brownian movement of the molecules. The indirect spin-spin interaction, or spin-spin splitting, is caused by the polarization of the electron shells by the field of the nuclear magnetic moments. In this case, the magnitude of the splittings is independent of H₀.

NMR spectra are observed by slowly changing either the frequency ω of the field H₁ or the strength of the field H₀. Modulation of the field H₀ by an audio-frequency field is often used. In investigations of crystals, the technique of “fast modulation” provides the best resolution. In this case, the field H₀ is modulated by an audio-frequency signal so that the processes that determine the relaxation time T₁ cannot be completed in the modulation period and the spin system is not in a steady state. Pulse methods are also used. In such methods, the action of the field H₁ is limited in time by means of short pulses. The most important pulse methods are the spin echo technique and Fourier-transform spectroscopy.

An induced electromotive force (emf) is proportional to H²₀. Therefore, experiments are usually carried out in a strong magnetic field. The main component of a radio-frequency instrument used to observe NMR is a circuit tuned to the precession frequency. The substance to be studied is placed in the induction coil of the circuit. The coil fulfills two functions. First, it generates the radio-frequency magnetic field H₁ that acts on the substance to be studied. Second, it detects the emf’s that are induced by the precession of the nuclear magnetic moments. The circuit is connected either to a radio-frequency bridge or to an oscillator that operates at the oscillation threshold.

Figure 3. The NMR spectrum of protons in pure ethyl alcohol. The splitting of the resonance lines of the OH, CH₂, and CH₃ groups is due to the indirect spin-spin interaction.

NMR has been used to measure nuclear moments and was employed in the first studies of energy states with an inverted population. Studies of relaxation processes and of the width and fine structure of NMR lines have yielded much information about the structure of liquids and solids. Together with infrared spectroscopy, high-resolution NMR is a standard technique for determining the structure of organic molecules. The close relationship between the shape of NMR signals and internal motion in a substance makes it possible to use NMR to study hindered rotation in molecules and crystals. NMR is also used to study the mechanisms and kinetics of chemical reactions. Instruments for the extremely accurate measurement or stabilization of magnetic fields are based on NMR (seeQUANTUM MAGNETOMETER).

In 1946, F. Bloch and E. Purcell discovered and explained NMR. For their achievement, they received the Nobel Prize in physics in 1952.