Nuclear Magnetism

F. Bloch*)

In recent years a new field of research has arisen, which has received the name “nuclear magnetism.” This unusual combination of two words that at first sight are incompatible requires some explanation.

The word “nuclear” refers to the nucleus of the atom—its central part, where almost all the mass of the atom is concentrated. The second word, “magnetism,” evokes more familiar notions, since the magnetic properties of matter have long been known and we know of them from everyday experience. It will be useful, however, to set forth briefly the basic facts and concepts relating to this well-known type of magnetism, in order to prepare the ground for understanding the magnetism of a new type, to which the present article is devoted.

It is necessary to recall that the properties of a magnetized substance, for example an iron magnet, are created as the result of the joint action of a very large number of small magnets contained within this substance. This very important conclusion is based on the observation that every fragment obtained when a magnet is broken itself possesses the property of a magnet; the process of fragmentation can in principle be continued until we reach “elementary magnets,” which evidently are atoms or molecules. Thus there arises the need to explain the existence of “elementary magnets.”

The essential aspects of this explanation were revealed more than 100 years ago by Ampère, who showed that a wire loop through which an electric current flows behaves like a magnet. By analogy he supposed that the behavior of atoms and molecules as elementary magnets can be explained by weak electric currents circulating in them. Although this postulate was widely disseminated for a complete explanation of “Ampère currents,” it was necessary—

*) F. Bloch, Amer. Scientist 43, No. 1, 48–62 (1955). Translated from the English by D. Voskoboinik.

clear understanding of the structure of the atom, achieved only in the last forty years. Fig. 1 schematically illustrates our modern conceptions of the structure of the atom. Its central part is a massive nucleus. The circles and ellipses symbolize the orbits of electrons, whose mass is considerably smaller than the mass of the nucleus. Each electron carries a negative electric charge, and the motion of these charges is equivalent to an electric current in a wire loop. These motions are, in essence, “Ampère currents,” giving atoms the properties of elementary magnets; they are the primary cause of ordinary magnetism.

Fig. 1. Schematic representation of an atom. The relative dimensions of the nucleus are greatly exaggerated. On the same scale it should be 10,000 times smaller than shown.

Labels in the figure: scale \(10^{-8}\) cm; nucleus; electron trajectory.

FUNDAMENTALS OF NUCLEAR MAGNETISM

Turning now to nuclear magnetism, we encounter elementary magnets of an entirely different nature. Unlike ordinary, or “atomic,” magnetism, nuclear magnetism is caused by Ampère currents flowing inside the nucleus, and therefore it is necessary briefly to outline their origin. Unfortunately, at present much less is known about the structure of the nucleus than about the structure of the atom, and the central task of modern physics consists precisely in explaining this question as far as possible. Fig. 2, representing the structure of the nucleus, is even more schematic than Fig. 1; however, in its main features it is based on firmly established facts. First of all, it is necessary to recall that nuclei are not simple systems, but themselves consist of several particles called nucleons. Two types of nucleons are known: protons—positively charged particles with a mass approximately 2000 times greater than the mass of the electron—and neutrons—neutral particles with a mass close to the mass of the proton. Particles of both types are in a state of rapid motion within a small region of space, schematically bounded by the circle in Fig. 2. The details of this motion still have to be studied, but one of its characteristics is well known and is of the greatest importance for us: whatever the trajectories of the individual nucleons may be, this motion is such that for at least half of the total number of nuclei known to us one may speak of the rotation of the nucleus, as a whole, about an axis passing through its center of gravity.

It is necessary to note that the nucleus, like any rotating body, possesses a mechanical angular momentum, directed—

...directed along the axis of rotation. According to the laws of quantum mechanics, the magnitude of the angular momentum can take only the following values \((0,\ ^1/_2,\ 1,\ ^3/_2\), etc.) \(\times \dfrac{h}{2\pi}\), where \(h\) is Planck’s constant, and the values in parentheses indicate the magnitude of the “spin” of the nucleus. For all spin values different from zero, i.e., in all cases where we are dealing with intrinsic rotation, there appears yet another property of the nucleus, connected with the participation in the rotation of electric charges. The rotation of nuclear charges, analogous to the rotation of electrons in an atom, is equivalent to Ampère currents, and we may expect that nuclei will also possess the properties of elementary magnets.

Although there is a qualitative similarity between nuclear and atomic magnetism, at the same time there is also an enormous quantitative difference between them in the strength of the elementary magnets. It is customary to measure the strength of a magnet by a quantity called the “magnetic moment,” which for a macroscopic bar magnet is defined as the product of the strength of the north or south magnetic pole by the distance between them. Comparing an atom and a nucleus with equal angular momenta, one may expect that their magnetic moments will be approximately inversely proportional to the masses of the electron and the nucleon. Indeed, the magnetic moment of a rotating nucleus is approximately a thousand times smaller than the magnetic moment of an atom.

Scale \(10^{-13}\) cm
● Proton
○ Neutron

Fig. 2. Schematic representation of a nucleus. Neutrons and protons are in a state of rapid motion within the region whose dimensions are shown by the outer circumference.

In describing the nature of nuclear magnetism we not only confined ourselves to purely qualitative notions, but also omitted another essential fact. From the description given above it might seem that the motion of nucleons is a necessary requirement for the existence of a nuclear magnetic moment, and that a proton at rest makes no contribution whatever to the magnetic moment of the nucleus. In reality this is not so, since the proton itself possesses a spin equal to \(^1/_2\), and a magnetic moment. The “intrinsic” spin of an elementary particle, by analogy with the daily rotation of the Earth, may be ascribed to the rotation of the particle about an axis passing through it. At present we know almost nothing about the Ampère currents which, apparently, circulate inside the particle and lead to the appearance of its intrinsic magnetic moment. The peculiar nature of these currents is manifested, for example, in the fact that the neutron, having spin \(^1/_2\), also possesses a magnetic moment, despite the fact that it has no electric...

charge. A quantitative consideration of the magnetic moment of the nucleus is possible only when the intrinsic moments of the nucleons are taken into account. The nucleus of the simplest atom—hydrogen—consists of only a single proton, and in this case we are dealing only with properties due to the intrinsic spin and magnetic moment of the nucleon. The nucleus of the hydrogen atom is of special interest, since a considerable part of the research on nuclear magnetism has so far been carried out on substances containing hydrogen.

NEW METHODS OF INVESTIGATION

The circumstance that nuclear elementary magnets are considerably weaker than atomic ones leads to the necessity of creating new sensitive methods of investigation. In order to explain the essence of these methods, we shall first consider a single nucleon situated between the poles of a laboratory magnet (see Fig. 3). Owing to the existence of a magnetic moment, the rotating nucleus behaves like a compass needle rigidly bound to the nucleus and oriented in the direction of the axis of rotation. The north pole \((N)\) of this needle is repelled by the north pole of the magnet downward; the south pole of the needle \((S)\) is repelled by the south pole of the magnet upward. These two equal and oppositely directed forces form a mechanical moment acting on the nucleus. The result of its action is shown in Fig. 4 as applied to an analogous system—a spinning top, where the downward-directed force is caused by the weight of the top, while an equal and oppositely directed force acts at the point of contact of the top with the floor and represents the reaction of the support. Everyday experience shows us that in this case the axis of the top begins slowly to rotate about the vertical. This rotation, which must be distinguished from the rotation of the top about its own axis, is called “precession.” By analogy, one should expect the same behavior of a rotating nucleus, i.e., the precession of its magnetic moment.

Fig. 3. Nuclear precession. The drawing illustrates the precession of a nucleus, caused by the mechanical moment arising from the action of the magnetic field on the magnetic moment of the nucleus. The latter is represented in the drawing in the form of a compass needle directed along the axis of rotation.

The frequency of precession is proportional to the intensity of the magnetic field created by the laboratory magnet, or, more precisely, to the field strength ...

of the magnetic field at the point in space where the nucleus is located. The coefficient of proportionality is a quantity characteristic of the given nucleus; it is called the “gyromagnetic ratio” and is equal to the ratio of the magnetic moment to the angular momentum of the nucleus. If a constant magnetic field has a magnitude attainable under ordinary conditions, for example 1000 oersteds, and if we are dealing with the simplest nucleus, i.e., the nucleus of the hydrogen atom, then the precession frequency is approximately four million hertz.

Fig. 4. Precession of a spinning top. The drawing illustrates the precession of a top. The mechanical moment here arises owing to the action of the force of gravity, applied at the center of gravity of the top, and of an equal and oppositely directed reaction force applied at the point of support.

This frequency, although much higher than the precession frequency of a macroscopic top, is small in comparison with the frequency of motion of nucleons inside the nucleus. It must be noted, however, that it lies in the radio-frequency region—a fact of enormous importance for experimental technique. Experiments are carried out, of course, not on a single nucleus, but on a macroscopic specimen containing an enormous number of nuclei. For experiments on protons, for example, a noticeable amount of hydrogen is required, contained, say, in \(1\ \mathrm{cm}^3\) of water.

The method of observation is shown schematically in Fig. 5. The direction of the constant magnetic field here, in contrast to Fig. 3, is horizontal. This field serves two purposes. First, it produces a weak nuclear magnetization of the specimen. In the absence of the magnetic field we would have a random distribution of the directions of the magnetic moments of the nuclei, and their action would mutually cancel. Owing to the existence of a mechanical moment caused by the magnetic field, a preferential orientation of the magnetic moments in the direction of the magnetic field arises. This “nuclear polarization” of the specimen is very weak. Whereas the corresponding polarization in the case of ordinary magnetism leads to the appearance of measurable forces acting on other magnetized bodies, in the present case the forces are so small that their direct measurement is very difficult.

The detection of nuclear magnetism becomes possible thanks to the supplementary influence of the magnetic field discussed above, namely, thanks to the precession of the magnetic moment of the nucleus. If one depicts the nuclear polarization in the form of a compass needle, one must imagine that this needle precesses with a frequency equal

frequency of precession of the corresponding nucleus. In the case when the direction of polarization coincides with the direction of the magnetic field, precession cannot be detected, since it occurs at a “zero angle” and does not change the direction of polarization. In order to produce the measurable effect, it is necessary to deflect the direction of polarization

Fig. 5. Schematic diagram of the experiment. Under the action of the field between the poles of the magnet, the water contained in the test tube experiences weak nuclear magnetization and behaves like an equivalent magnetic needle, schematically shown inside the test tube. The small dotted circle indicates the precession of this needle, occurring at the same rate as the precession of an individual nucleus (see Fig. 3). The precession induces an alternating current in the receiving coil wound on the test tube. After amplification and rectification this current is observed on the screen of a cathode-ray oscilloscope

by some angle with respect to the direction of the magnetic field. This can be achieved most simply if, in addition to the constant magnetic field, an alternating magnetic field directed at right angles to the constant one is superposed. In Fig. 5 it is assumed that the alternating field is directed perpendicular to the drawing. If the frequency of the alternating field is equal to the frequency of nuclear precession, then “magnetic resonance” arises—an effect analogous to mechanical resonance. Owing to this phenomenon, the desired inclination of the vector of nuclear polarization can be obtained.

The vector of nuclear polarization, inclined with respect to the direction of the magnetic field and precessing about it, behaves like an invisible magnetic needle rotating in the medium under study—in the present case, in a small portion of water. This phenomenon is indeed invisible in the sense that it has no relation to visible light, but this circumstance does not prevent its detection by other means. In fact, it can be detected by means of the well-known phenomenon of electromagnetic induction, discovered long ago by Faraday, who found that a change in the magnetic flux penetrating a wire coil leads to the appearance of a potential difference at its terminals. In order to make use of this effect, it is sufficient to wrap the test tube containing the substance under investigation with several turns of wire, as shown in Fig. 5. The turns of wire form a “receiving coil.” The precession of the inclined polarization vector induces in the receiving coil (between terminals \(A\) and \(B\)) an alternating voltage with a frequency equal to the frequency of precession. Measurement of the voltage appearing as a result of “nuclear induction” is the basis of all studies of nuclear magnetism.

The experimental technique of these studies is in many respects reminiscent of the technique of receiving radio signals. It consists in receiving radio signals from the nuclei present in the sample by means of a receiving coil, which in this case performs the role of an antenna. The received signal of nuclear induction is fed to an ordinary radio receiver, amplified and detected, after which it may be supplied, for example, to a loudspeaker. Usually, instead of making the received signal audible, it is made visible on the screen of a cathode-ray oscillograph. This last stage of signal detection is shown schematically in Fig. 5, which also depicts the typical form of the signal obtained under conditions of magnetic resonance.

There is still one important element of the circuit, essentially necessary for observing nuclear induction. It consists of an alternating-current coil which creates the alternating magnetic field required for the occurrence of magnetic resonance. This coil is called the “transmitting coil”; its axis is perpendicular to the plane of the drawing in Fig. 5. The transmitting coil usually consists of two halves, so that the test tube with the sample can be inserted into it as simply as possible. Looking at Fig. 5, we must imagine that one half of the coil is located above the plane of the drawing, the other below it, and that their projections onto the plane of the drawing are shown by the dotted circle.

The following figures illustrate only the methods just described for studying nuclear magnetism. Figure 6 shows the “head”—the main part of the whole apparatus, placed between the poles of a laboratory electromagnet, whose field is perpendicular to the plane of the drawing. The test tube with the sample under examination is inserted through an opening in the head into a cylinder made of insulating material, surround-

...with the receiving coil. The alternating magnetic field created by the alternating current flowing through both halves of the transmitting coil alternately changes its direction (from right to left and back) and acts on the nuclei of the substance under investigation, located at the center. Special precautions must be taken so that changes in the magnetic flux caused by the alternating field do not induce in the receiving coil a voltage greater than the voltage of the nuclear induction signal and do not suppress the latter.

Labels in the figure: “Transmitting coil”; “Receiving coil”; “Flag” (left and right).

Fig. 6. The “head” of the apparatus. Test tubes with the substance being examined can be introduced into the cylinder located at the center. The receiving coil is wound on the cylinder. By rotating the “flags” located to the left and right of the cylinder, the coupling between the receiving and transmitting coils can be reduced to a minimum.

This is achieved in part by the fact that the axes of the receiving and transmitting coils are perpendicular to one another. Precise compensation of the pickup of one coil on the other is ensured by the two “flags” shown in the figure. They consist of copper semicircles mounted on rotating rods made of insulating material. By rotating the copper flags, the alternating magnetic field can be directed in such a way that its flux through the receiving coil is substantially reduced. Two cables approach the bottom of the head: one supplies alternating current from the generator to the transmitting coil; the other connects the receiving coil to the amplifier.

On Fig. 7 is shown the head, half inserted into the gap between the poles of the electromagnet, with a test tube containing the substance under investigation. The lower tube, supporting the head, at the same time serves as the supply cable for the transmitting coil. The bent cable above the tube runs from the receiving coil to the receiver.

Fig. 7. The assembled “head” with a test tube containing the test substance inserted into it before installation in the gap of the electromagnet.

In Fig. 8 is presented the shape of the nuclear-induction signal from protons of water placed in a magnetic field of about 2000 oersteds, in the form in which it is observed on the screen of a cathode oscilloscope. The vertical displacement is proportional to the amplitude of the signal; the horizontal displacement is proportional to the strength of the magnetic field, which slowly increases with time. The value of the field strength corresponding to the maximum of the signal corresponds to resonance, i.e. to equality of the frequency of precession of the protons and the frequency of the applied alternating current. As the field deviates in one direction or the other from its resonance value, the signal becomes weaker and gradually disappears. The “half-width” of the resonance curve, i.e. the width measured between the two points at which the intensity of the signal is equal to one half of its maximum value, corresponds to a change in the field strength equal to approximately \(1/2\) oersted.

Fig. 8. Shape of the absorption signal from protons in water.

In Fig. 9 is shown a signal obtained from the same sample as in Fig. 8, but differing in that the phase difference of the signal

nuclear induction and the alternating field has a different meaning. If one uses the terminology adopted in optics, then the curves in Figs. 8 and 9 correspond to two closely related phenomena—absorption and dispersion, respectively. By applying a phase-sensitive detector, it is possible to obtain either phenomenon in pure form, or a combination of both.

Fig. 9. Shape of the dispersion signal from protons in water.

Let us now proceed to consider the results obtained in the study of nuclear magnetism.

MEASUREMENT OF NUCLEAR MAGNETIC MOMENTS

The most significant results were obtained in the measurement and comparison of nuclear magnetic moments. We said above that the magnetic moment of a nucleus is caused by internal Ampère currents. Therefore, by studying the magnetic moments of nuclei one can obtain important information about the structure of the nucleus and about the motion of the particles composing it. The data obtained in this way testify to the “shell structure” of the nucleus, in a certain sense analogous to the shell structure of the atom, which is so clearly manifested in the periodic properties of the elements.

If the presence of nuclear magnetic resonance is established from the presence of a nuclear-induction signal, it remains only to measure the intensity of the magnetic field and the frequency of the alternating field. Both of these quantities give us directly the value of the gyromagnetic ratio and, if the spin value is known, the value of the magnetic moment of the nucleus under investigation. There are several independent methods for measuring nuclear spins; therefore measurement of the gyromagnetic ratio is equivalent to measurement of the magnetic moment. But even if we do not know the nuclear spin from independent measurements, we can still determine this quantity by using only the observation of nuclear magnetic resonance, since the magnitude of the observed signal gives us some additional information from which the spin value of interest to us can be determined.

A particularly important characteristic of the method under consideration for determining magnetic moments is its high accuracy, limited only by the accuracy with which the resonance conditions are realized. The accuracy of the method is illustrated by the absorption curve shown in Fig. 8. It might seem that exact resonance corresponds to the exact maximum of the absorption curve; this conclusion, however, is not sufficiently reliable, since the position of the maximum is sensitive to all sorts of weak perturbations of unknown nature. It is much more correct to assume that resonance occurs somewhere between the two points of the curve corresponding to a signal intensity equal to half its maximum intensity, and to take the half-width of the curve as a measure of the experimental error. Since the magnitude

experimental error in the case of Fig. 8 is \(1/2\) oersted at a field of 2000 oersteds; this means that in this case it is possible to determine the magnetic moment of the proton with an accuracy of \(1/4000\). With such accuracy the magnetic moments of many nuclei have been determined, and in most cases this is sufficient for interpreting the values obtained from the point of view of nuclear structure.

There are, however, cases where higher accuracy can provide very substantial information, especially if we are dealing with isotopes of one and the same element, i.e., with nuclei differing in the number of neutrons while having the same number of protons. If the ratio of the magnetic moments is measured with high accuracy and the measured value is compared with data from other experiments, then direct conclusions can be drawn about the distribution of Ampère currents inside the nucleus.

In such cases, as well as in some others considered below, it is desirable to obtain a sharper resonance curve. The width of such a curve is determined partly by the physical and chemical nature of the substance under investigation (“natural width”), and partly by the apparatus used (“instrumental width”). The principal cause of instrumental broadening of the resonance curve is the variation of the magnetic-field strength in the region of the sample; therefore the instrumental width can be reduced by improving the homogeneity of the field. In studies of liquids it often happens that the natural line width is extremely small, so that the observed width is determined primarily by the homogeneity of the field. As an example, let us consider the results obtained with water. It proved possible to obtain for protons a resonance curve with a half-width of the order of \(1/1000\) oersted in a field of 7000 oersteds, which corresponds to an accuracy of \(1/7\,000\,000\). Approximately this accuracy was achieved in measuring the ratio of the magnetic moments of the proton and the deuteron—the nucleus of heavy hydrogen, consisting of a neutron and a proton. This isotope is of special interest for nuclear physics because of its simplicity, and the measurement of the above-mentioned ratio contributed much to the understanding of its properties.

NATURAL WIDTH AND STRUCTURE OF RESONANCE LINES

Above we said that the natural width of resonance lines depends on the substance under investigation. It can be shown that it is due to the internal fields created by neighboring atoms and molecules, which exert a perturbing effect on the precession of the nuclear moment. Thus, studies of the width of resonance lines can be used to solve the inverse problem, namely, to obtain information about the molecules surrounding the nucleus. Such studies have been carried out on solids, liquids, and gases, and data have been obtained on their structure and molecular motion.

Internal fields lead not only to a broadening of resonance lines, but also to their splitting into several components. Such a phenomenon is observed, in particular, in crystals, where it is due to the regular arrangement of atoms in the crystal lattice. Two main causes of line splitting are known. One of them consists in the interaction of the nuclear magnetic moment with the moments of neighboring nuclei; in this case the various components of the line structure are due to the superposition, on the external magnetic field, of an additional weak magnetic field from neighboring nuclei and depend on the different possible orientations of these nuclei. The other cause of line splitting is connected with the existence in the crystal of nonuniform electric fields; these fields create an additional mechanical moment acting on the nucleus, which depends on the distribution of charges within the nucleus and on the orientation of the nucleus. In this way it is possible to study the deviation of the charge distribution in the nucleus from spherical symmetry, which is measured by the magnitude of the “electric quadrupole moment” of the nucleus.

CHEMICAL SHIFT AND RESONANCE STRUCTURE OF LINES IN LIQUIDS

Other factors affecting the structure of lines are also known, and some of them, pertaining to liquids, will be discussed below. There exist, however, modifications of resonance lines that are of an entirely different character and reveal a connection between nuclear magnetism and chemistry. These are shifts of the resonance lines of the nucleus of one and the same element depending on the chemical compound of which it is a part. The “chemical shift” is caused by the influence of the electrons revolving around the nucleus. It may be considered that the electrons exert a shielding action, as a result of which the magnetic field acting on the nucleus becomes somewhat weaker than the field that would act in the absence of the surrounding electrons. Since the chemical bond between atoms is effected by the outer “valence” electrons and this bond manifests itself in a change of their orbits, it is possible that these changes affect the shielding effect and, consequently, the magnitude of the magnetic field acting on the nucleus. Chemical shifts are of the order of \(1/1000\) in magnitude. If a considerably greater resolving power is achieved, they can easily be detected, measured, and subjected to quantitative analysis.

The existence of a chemical shift raises the following question: is it necessary, in order to observe it, to use different chemical compounds, or can analogous effects also occur for one and the same compound? Surprisingly, it turned out that the second possibility is realized, and we shall illustrate this “internal chemical shift” with the example of ethyl...

NUCLEAR MAGNETISM

alcohol, with which a large part of the investigations of this effect was carried out. The structure of the ethyl alcohol molecule is well known (see Fig. 10). Three hydrogen atoms are bound to one carbon atom, two other hydrogen atoms (H) are bound to the other carbon atom (C), and, finally, the fifth hydrogen atom is bound to the oxygen atom (O). The lines connecting the various atoms represent “valence bonds” and symbolize the fact that the bond between neighboring atoms is established only by means of a single valence electron. In this structure the electrons form different environments for the hydrogen atoms belonging to the three different groups CH₃, CH₂, and OH; it may therefore be expected that these electrons will shield in different ways the magnetic field acting on the corresponding protons.

Fig. 10. Structure of the ethyl alcohol molecule.

Fig. 11 demonstrates the real existence of internal chemical shift. The figure shows the form of the signal on the screen of a cathode-ray oscilloscope, obtained in the investigation of ethyl alcohol by means of an apparatus analogous to that shown in Fig. 8. Instead of one resonance maximum we have here three, corresponding to the protons in the groups CH₃, CH₂, and OH. The areas encompassed by these maxima are in the ratio 3:2:1, in accordance with the number of hydrogen atoms in each group.

Fig. 11. Form of the signal from protons in ethyl alcohol. The maxima from left to right and from the center to the right are due to resonances in the groups CH₃, CH₂, and OH, respectively. The half-width of these resonance curves is equivalent to a change of field by 1/1000000.

The curve was obtained at a constant magnetic-field strength of about 7000 oersteds, and the distance between the maxima corresponding to CH₃ and CH₂ is equal to 20 millioersteds, i.e. amounts to \(1/350000\). The relative line width which permits the maxima to be resolved must, of course, be still narrower—in the present case, apparently about \(1/1000000\). Being almost exclusively instrumental, i.e. caused by variations of the field in the region of the specimen under study, such a small line width testifies to the high degree of homogeneity of the field. The latter was achieved by careful shimming of the magnet and by using a very small specimen, whose linear dimensions amounted to only a few millimeters.

It would seem difficult to obtain still narrower lines by further increasing the resolving power and thereby to reveal any further details by this method. Fig. 12 shows that these doubts are unfounded. The figure shows the form of the signal of Fig. 11,

taken at a resolving power of about \(1/10\,000\,000\). At such high resolving power it was possible not only to separate all three resonance maxima, but also to show that each of them contains several closely spaced components.

Fig. 12. Shape of the signal from protons in ethyl alcohol under conditions of high resolution. The three groups of lines are structures of the three, seemingly simple, resonance maxima whose photographs at low resolving power are shown in Fig. 11. The half-width of an individual line here is equivalent to a field change of \(1/10\,000\,000\).

The observed structure can be explained by the action on the protons of one group of atoms of magnetic fields created by the protons of another group of atoms in the same molecule. The orientation of these protons with respect to the external field is different in different molecules, and this leads to splitting of the corresponding resonance lines.

The splitting caused by the interaction of magnetic moments in crystals can reach several oersteds, whereas in the case of ethyl alcohol it is of the order of millioersteds. Such a sharp decrease in the magnitude of the splitting can be explained by the fact that in crystals the positions of the atoms remain, for the most part, fixed, while in a liquid the molecules participate in molecular motion, in which they not only change their position but also rotate rapidly in various random directions about their center of gravity. Owing to these rotations, the field acting on the magnetic moment of the proton is averaged to a considerable extent; however, the small changes in the field caused by the valence electrons are not averaged and lead to the formation of the observed structure.

One can be convinced that this mechanism leads to a splitting of the same order of magnitude as that observed, but it is very difficult to calculate its magnitude in advance. There are, however, several simple rules concerning the number of components in each group. These rules follow from the mechanism of the phenomena under consideration and are confirmed experimentally. In the present case they indicate that, when the splitting is due to the influence of other protons, each of which has spin \(1/2\), a group containing \(n\) protons causes the splitting of an otherwise single resonance maximum into \(n+1\) components. Thus, for example, the \(\mathrm{CH_3}\) group, as well as the \(\mathrm{OH}\) group, has as its neighbor in the molecule a \(\mathrm{CH_2}\) group containing two protons, and therefore its resonance curve consists of three components. The \(\mathrm{CH_2}\) group has as its neighbor, on one side, a \(\mathrm{CH_3}\) group with three protons and, on the other side, an \(\mathrm{OH}\) group with one proton. The first causes splitting of the resonance curve into four components, and the second a further splitting of each of these components into two; thus,

In the group CH$_2$ there appear altogether 8 components. A detailed investigation of the central part of the resonance curve of the CH$_2$ group shows that each of the three central maxima in reality consists of two closely spaced lines, which, together with the two small maxima at both edges, gives a total of 8 components.

Structures analogous to ethyl alcohol have been found in many other organic liquids. In particular, molecules containing hydrogen and fluorine have been investigated. Fluorine nuclei also have spin equal to $1/2$, and their behavior is qualitatively similar to that of protons, with the difference that the splitting of the components of the resonance lines is greater here and therefore the requirements on resolving power are considerably lower.

The detailed investigation of ethyl alcohol described here has only confirmed the structure of its molecule, which has long been known. There are, however, many compounds whose molecular structure is still unknown to us. The fact deserves attention that the number of components in the resonances of various groups of atoms depends on the structure of neighboring groups. Thus, the study of nuclear magnetism is an important tool in the hands of chemists in their attempts to establish and verify the structure of complex molecules.

References

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