Nuclear magnetic resonance

Nuclear magnetic resonance, and nuclear magnetic resonance or nuclear magnetic resonance (hereinafter abbreviated to English NMR Nuclear Magnetic Resonance ) is a (core) physical effect which absorb and emit electromagnetic alternating fields in which atomic nuclei of a sample in a constant magnetic field. The nuclear magnetic resonance is the basis of both the nuclear magnetic resonance (NMR ) spectroscopy, one of the standard methods in the study of atoms, molecules, liquids and solids, as well as magnetic resonance imaging ( Magnetic resonance imaging, MRI) for medical diagnostic imaging.

Nuclear magnetic resonance relies on the Larmor precession of the nuclear spins about the axis of the constant magnetic field. Due to the emission or absorption of AC magnetic fields that are associated with the Larmor precession into resonance, the nuclei change the orientation of their spins to the magnetic field. If the emitted alternating field observed by an antenna coil, one also speaks of nuclear induction. The absorption of an incident alternating field is observed on the basis of the energy transfer to the nuclear spins.

The resonant frequency is proportional to the strength of the magnetic field at the location of the core and the relationship of the magnetic dipole moment of the core to its spin ( gyromagnetic ratio). The amplitude of the measured signal is, inter alia, proportional to the concentration of the species of seeds ( nuclide ) in the sample. The amplitude and the frequency of the particular nuclear magnetic resonance can be measured with very high accuracy. This allows detailed conclusions on both the structure of the nuclei as well as on their other interactions with the near and atomic environment.

Requirement of a nuclear spin magnetic resonance is equal to zero. Most often, the cores of the isotopes 1H and 13C are used to monitor the nuclear spin resonance. Other investigated nuclei are 2H, 6Li, 10B, 14N, 15N, 17O, 19F, 23Na, 29Si, 31P, 35Cl, 113Cd, 129Xe, 195Pt and v. a, ​​each in their ground state. Excluded are all nuclei with an even number of protons and neutrons, provided they are not in a suitable excited state with spin equal to zero. In some cases, nuclear magnetic resonance of nuclei were observed in a sufficiently long-lived excited state.

For analog observation in electron see electron spin resonance.

• 2.1 polarization
• 2.2 Zeeman levels
• 2.3 relaxation
• 2.4 Bloch equations
• 2.5 Transverse alternating field and absorption of energy

History and Development

Before 1940: Zeeman effect and Rabi method

In 1896 it was discovered that optical spectral lines split in the magnetic field ( Zeeman effect). Hendrik Antoon Lorentz interpreted this soon after, so that the (circular ) frequency of the light wave is shifted by the amount of the Larmor frequency, because the atom a magnetic gyroscope, which is excited by the magnetic field to precess at the Larmor frequency.

According to the hypothesis of light quanta ( Einstein 1905), the frequency shift corresponds to a change of energy, which could be explained by the turn in 1916 by Arnold Sommerfeld discovered space quantization of angular momenta. The angular momentum vector and the magnetic dipole parallel to the atom has only discrete allowed setting angle to the magnetic field and correspondingly different discrete values ​​of the magnetic energy. Thus, the magnetic field causes the splitting of energy levels in several so-called Zeeman levels. This picture was taken in 1922 confirmed directly in the Stern-Gerlach experiment. There was shown that the smallest possible ( non-zero ), the angular momentum (i.e. quantum number ) may only have two possible adjustment angle to an external field.

In the late 1920s it was discovered that atomic nuclei possess an approximately 1000 times smaller magnetic moment than atoms, which is why they cause splitting of the energy levels are referred to as hyperfine structure. The transition frequencies between adjacent hyperfine levels are in the range of radio waves (MHz). Isidor Rabi in 1936 succeeded the experimental proof that the precession of atoms flying through a constant magnetic field in the atomic beam is disturbed by the irradiation of an alternating magnetic field when its frequency is with such a transition frequency in resonance. As a result, the magnetic moments of many nuclei with high accuracy could be determined, which, inter alia, the development of more accurate core models enabled.

1940s: nuclear magnetic resonance in liquids and solids

Nuclear magnetic resonance in the strict sense, ie the change in the pitch of the nuclear spins with the static external magnetic field with no significant involvement of the nuclear envelope at the precession movement, was founded in 1946 for the first time realized in two different ways. Edward Mills Purcell used for the detection of the resonance energy transfer from the alternating magnetic field on the nuclear spins and further atomic in their vicinity. Felix Bloch observed that the AC voltage is induced by the precessing of the dipole moment of nuclei in a coil, if this is no longer parallel to the direction of the static field is in the case of resonance ( method of the " nuclear induction "). The prerequisite is that the static magnetic field causes the strongest possible polarization of the nuclear spins, which has oriented device development to ever stronger magnetic fields down (now with superconducting coils to 24 Tesla). These methods now enabled measurements on liquid and solid matter and to further increase the measurement accuracy on soon 6-8 decimal places. According to exactly were the so obtained measured values ​​for the nuclear magnetic moments. In reversing the question of the nuclear magnetic resonance was also the conventional method in the precision determination of magnetic fields. In addition, several additional influences of the atomic environment on the action at the site of magnetic cores were measured, which are small, but allow detailed conclusions about the structure and bonding of the molecules and their mutual influence. Therefore, the nuclear magnetic resonance spectroscopy is still a standard method in the chemical structure research.

1950s: radio-frequency pulses and spin-echo

The measurement capabilities of nuclear induction method expanded in the 1950s, when the direction of polarization of the nuclei was manipulated through the use of the alternating field in the form of brief pulses. It is the first polarization parallel to the constant magnetic field, the dipole moment of the entire sample can be rotated in a particular direction perpendicular to the field direction, for example, by a " 90 ° pulse ". This allows the direct observation of the subsequent free Larmor precession of the dipole moment to the field direction, because it induces (like the rotating magnet in a generator of electrical engineering) in an antenna coil, an AC voltage ( " free induction decay ", FID, for engl. Free induction decay ). The amplitude then decreases over time, because the degree of alignment of the nuclear spins along the common direction perpendicular decreases toward the field, partly because the parallel to the static magnetic polarization restores ( longitudinal relaxation ), and partly by field inhomogeneities and fluctuating interference ( transverse relaxation ). Both processes are here observable separately, especially by means of the spin-echo method first described by Erwin Hahn.

1970s: NMR tomography and imaging

From the 1970s to the nuclear magnetic resonance was based on work by Peter Mansfield and Paul C. Lauterbur to an imaging method, magnetic resonance imaging, further developed. Upon application of an inhomogeneous static field, the resonance frequency in a controlled manner from the place of cores dependent ( field gradient NMR ), but only in one dimension. From this, a three-dimensional image of the spatial distribution of the nuclei of the same isotope can be obtained if the measurements are repeated successively with different directions of the inhomogeneous static fields. To create an information-rich a picture as possible, such as for medical diagnosis, then not only the measured values ​​for the concentration of the isotope to be recycled, but also for the relaxation times.

Special developments

Of principal physical interest are two less frequently used methods:

• As early as 1954 it was possible after the FID method, the Larmor precession of the hydrogen nuclei (protons) to demonstrate a sample of water in the Earth's magnetic field (about 50 μT ). The protons were polarized by a stronger field perpendicular to the Earth's field, which was quickly switched off at a certain time. The immediate onset of Larmor precession induces an alternating voltage with a frequency of about 2 kHz, which is used for example for accurate measurement of the Earth's magnetic field. Absorption of a resonant alternating field is not required. Therefore, it is here to the purest case, the observation of nuclear induction.
• On cores in a sufficiently long-lived excited state ( shortest life far 37 microseconds ) has been successfully shown that nuclear magnetic resonance, wherein the detection of this change in the angular distribution of the light emitted from the cores of γ radiation was used.

Physical Basics

In the nuclear magnetic resonance, macroscopic explanations, according to classical physics and microscopic observations, according to quantum mechanics can be smoothly combined with each other (in this precise reason). The decisive factor is that the Larmor precession is independent of the orientation of the nuclear spin magnitude and direction. The corresponding effect of the static field may therefore by changing over a frame of reference rotating at the Larmor frequency for the field direction be completely transformed away, irrespective of the state of the individual examined cores of the sample and the magnitude and direction of them fabric ended macroscopic magnetic moment.

Polarization

A core with the magnetic moment in a magnetic field has an angle dependent on the potential energy. The lowest energy belongs to the parallel position of the moment to the field, the highest energy applies to anti-parallel setting. In thermal equilibrium at temperature the moments are distributed according to the Boltzmann factor to the different energies (: Boltzmann constant ). In typical nuclear moments eV / T and typical thermal energies, the Boltzmann factors differ although by less than 10-4, but expressed the statistical preference for the small entering angle against the major by a non-zero mean value of. The result is a polarization and thus a macroscopic magnetic moment parallel to the external field ( which: number of cores ). As far as the classic explanation of polarization by (core) para magnetism.

Zeeman levels

According to quantum mechanics acts in states of definite angular momentum vector of each operator parallel to the angular momentum operator, one writes

The constant called gyromagnetic ratio, it has for each nuclide a characteristic value (see also Landé factor).

Therefore, the cosine of the pitch to the field direction in the energy eigenstates For the vector and the known from the angular momentum space quantization, after a given angular momentum quantum number only can assume the values ​​, the magnetic quantum number goes through the values. The maximum component of the longitudinal field also referred to as the amount of the magnetic moment is so.

Consequently, the field for the parallel component of the moment has one of the values

And the magnetic energy according to:

(. Amount of ) This formula is the energy of the Zeeman levels resulting from the equidistant division of the levels of nuclear spin. The distance between adjacent Zeeman levels corresponds exactly to the Larmor frequency, ie the frequency, precesses with a ( classical and quantum ) magnetic centrifugal field:

The occupation numbers of the Zeeman levels decrease in thermal equilibrium up from ( if positive, otherwise vice versa ), but the order of magnitude by no more than 10-4 relative.

Relaxation

The setting of the equilibrium polarization of the nuclear spins parallel to the external field is called longitudinal relaxation. You take in liquid and solid samples up to several seconds ( in gases it can take weeks ), when the sample contains no paramagnetic impurity, ie atoms with permanent magnetic dipole moment which caused by fluctuating magnetic transitions between the Zeeman levels and thus the energy exchange accelerate with the nuclear spins. The time constant is referred to. The reduction of the field perpendicular polarization to the equilibrium value of zero is called transverse relaxation and is (usually) more quickly (time constant), because this is no energy conversion is needed; It is sufficient that the transverse to the magnetic field aligned nuclear spins by small fluctuations in their constant Larmor precession about the field direction lose their common orientation. Time follows the approach to equilibrium in a good approximation of a simple decaying exponential.

Bloch equations

The Bloch equations summarize the Larmor- precession and the longitudinal and transverse relaxation in a single equation of motion for the vector of the magnetic moment together ( with the magnetic field and equilibrium magnetization, both parallel to the z -axis):

Describes therein the cross product of the Larmor precession at the angular velocity. In the second term, the relaxation process is grouped phenomenologically as first order (i.e., a simple exponential decay ), with the time constant for the field to the parallel component is different from the transverse. The Bloch equations are valid according to quantum mechanics for the expectation value of the magnetic moment of each core

Transverse alternating field and absorption of energy

A weak supplemental AC field, such as in the x direction, can be always regarded as the sum of two circularly polarized alternating fields, for example about the z axis (i.e. the direction of the strong field constant ) in the opposite sense rotate.

• In quantum-mechanical consideration of this alternating field induced at resonance transitions between the Zeeman levels in one direction or the other, because his circularly polarized quanta have the correct angular momentum ( z component ) and then with just the right energy. These transitions disturb the thermal equilibrium, because they reduce existing differences in the occupation numbers. This means a net energy input because before more cores at lower energy states were higher than, the thermal equilibrium accordingly. This flow of energy from the alternating field in the system of nuclear spins would come with achievement of equal occupation to a halt. The thermal contact of the spin system to the environment, which already for the bringing forth of the original equilibrium magnetization is indeed crucial, but deprives the so perturbed spin system running energy. It turns at a slightly reduced magnetization a steady one. The necessary critical parameter is the longitudinal relaxation time. On this continuous wave method, the first proofs and applications of nuclear magnetic resonance is based on the method of Purcell.
• In macroscopic observation can be overlooked easily, results which movement of the macroscopic dipole moment of it: The co-rotating with the Larmor precession of the two components of the alternating field is at resonance in the co-rotating reference system a constant field perpendicular to the z - axis dar. on the dipole does it with a torque that another Larmor precession around the ( in the xy - plane co-rotating ) axis imposes him this additional field. Since this has to change the setting angle of the much stronger static field, the dipole energy absorbs from the alternating field or are those from. Was previously parallel to the field direction of the dipole, it can itself induce an AC voltage in a receiver coil in the twisted state. Is the alternating field pulsed, depending on the exposure time, the dipole moment can be targeted accurately rotated eg 90 ° or even completely reversed ( as far as the relaxation time of the permitting). Hence the number of different pulse methods result with its versatile measurement capabilities (eg, the spin- echo for the separate determination of and ).

Apparatus and methods

NMR apparatus typically comprises a magnet for generating a homogeneous static magnetic field and strong as possible, in which the sample can be introduced, and each having a small magnetic coil for generating and detecting a high-frequency transverse magnetic field (see Fig.) Bloch and Purcell used in their first successful apparatuses a static field of the order of 1 T, generated by an electromagnet. To improve the spatial constancy of the field and its fine control small auxiliary coils were installed. At the resonance frequency of protons. The coil for receiving the radio frequency magnetic field was perpendicular to the Bloch apparatus transmitter coil to eliminate the direct reception of the alternating field generated by it. The output of the receiver coil AC is then causes only the protons that rotate the magnetic moments with the Larmor precession about the field direction, after they have been successfully turned away by the radiated alternating field at resonance from the direction of the static field. Purcell used in his apparatus only one coil for transmission and reception, the resonance can become evident that the induced by the nuclei in the coil AC voltage is opposite to the applied AC voltage, thus more energy is extracted from the transmitter. In an intentionally weak designed transmitter that leads to a readily detectable decrease in the oscillation amplitude. To find the resonance without having to adjust the frequency of the transmitter, the field strength of the static field was varied by the auxiliary coils. Therefore, the resonance curves were not coated by the Purcell method in the NMR spectra over the frequency, but to the applied magnetic field.

At the present time ( magnetic resonance spectroscopy), for time-resolved NMR ( relaxation time ) and for spatially resolved NMR ( field gradient NMR ) are used almost exclusively NMR pulse spectrometer for energy-resolved NMR. The first commercial and " quartz- controlled " pulse spectrometer were developed in the 1960s in Germany by a group of physicists Bertold Bludgeon and Manfred Holz in Bruker and manufactured. In this case, the cores are excited with high-frequency pulses and the NMR signal as a free induction decay (FID ), spin echo or measured. In the " quartz- controlled " devices all transmitting frequencies and all times in the pulse program ( pulse spacing, pulse duration, etc. ) derived in the NMR experiment by a single mother quartz and there is a quartz- stable, but variable phase relationship between transmitter - high frequency and eg the start of the pulse. This allows the setting of the Hf - Hf phase and thus the irradiation direction of the individual radio-frequency transmission pulses in a complex series of pulses, which is an essential requirement in most modern NMR experiments. In the, also developed in the 1960s, Fourier transform ( FT) spectrometers recorded in the time domain signals are then (eg FID) by computer into signals in the frequency domain (spectrum) transformed. Now work almost all nuclear magnetic resonance apparatus on this basis.

Applications

• Chemistry: Nuclear Magnetic Resonance Spectroscopy
• Physical Chemistry: diffusion, micro dynamics and structure of liquids
• Medicine: magnetic resonance imaging, diffusion tensor imaging
• Geophysics: proton magnetometer, pore sizes and shapes in rocks and sediments
• Quantum computing: quantum simulation