Relaxation (NMR)

Under relaxation is understood in the nuclear magnetic resonance spectroscopy (NMR) spectroscopy and magnetic resonance imaging (MRI), the operations that the nuclear spin - magnetization (for example, after a deflection or excitation.) In its equilibrium state can seek back. These processes are based on different relaxation mechanisms and are described by relaxation times for the various magnetization components .

Different nuclear spin relaxation times in different types of tissue represent the most important basis of image contrast in magnetic resonance imaging. In terms of NMR spectroscopy, the relaxation times are important for examining the microdynamics or microstructure of condensed matter on the molecular length scale, for example in physics , physical chemistry , Chemistry or materials research .

principle

In thermal equilibrium there is an equilibrium nuclear magnetization along the direction of the field in a magnetic field (according to convention in the z-direction) . Its size is determined by the Boltzmann statistics and this magnetization component in the z-direction is called the longitudinal magnetization. The magnitude of the magnetization components perpendicular to the field, i.e. in the x and y directions, is zero in the case of equilibrium. If the thermal equilibrium of the nuclear spin system is disrupted, e.g. B. by irradiating a 90 ° - or 180 ° high frequency (RF) pulse, then the z component of the magnetization is equal to zero or . After the disturbance, the longitudinal magnetization, following an exponential law in time , returns to the equilibrium value through the relaxation process . This is the longitudinal relaxation. A 90 ° pulse, as a “detection pulse”, after a time t , can be used to experimentally demonstrate the nuclear magnetization that has arisen again due to relaxation at time t . ${\displaystyle {\vec {M}}=M_{0}{\vec {e}}_{z}}$ ${\displaystyle M_{0}}$ ${\displaystyle M_{z}}$ ${\displaystyle -M_{0}}$ ${\displaystyle t}$ ${\displaystyle M_{z}=M_{0}}$

Due to a disturbance, e.g. B. by the mentioned 90 ° RF pulse, but also a precessing nuclear magnetization in the xy-plane (transverse plane) with the amount which also goes exponentially towards the equilibrium value for the transverse magnetization, namely zero, after the disturbance. This is the transverse relaxation. ${\displaystyle M_{\perp }\neq 0}$

In the experimental determination of the nuclear magnetic relaxation times, the nuclear magnetization is measured using the NMR signal amplitude as a function of time t (time interval between the “interference pulse” and the “detection pulse”). The characteristic time constant, the “relaxation time”, can be determined from the measured, exponential relaxation curve. The nuclear magnetization measurements as a function of time therefore represent a form of time-resolved NMR spectroscopy .

The nuclear magnetic relaxation processes are associated with transitions between different energy levels of the nuclear spin system. Since there are practically no spontaneous transitions in the frequency range of NMR spectroscopy , electromagnetic fields are required at the nuclear magnetic resonance frequency, which can induce the transitions . These are substance-internal, fluctuating magnetic (in some cases also electric) fields. The origin of these fluctuating fields and their interaction with the nucleus can be different and one therefore speaks of different relaxation mechanisms . If one knows the relaxation mechanism in certain samples to be examined, then from the measurement of the nuclear magnetic relaxation times one can obtain valuable information about the environment of the observed atomic nuclei, i.e. from the innermost part of the matter.

Applications

One of the classic applications of relaxation time studies is the physico-chemical research of matter in the liquid state, such as B. the elucidation of the microdynamics or microstructure of pure liquids or electrolyte solutions. One can use molecular reorientation times in the liquid, e.g. B. in the picosecond range, determine short-lived, local molecular aggregates, such as the solvation shells of ions , or study ion associations , as well as z. B. short-lived hydrogen bonds between molecules.

In magnetic resonance tomography (MRT), different relaxation properties of different types of tissue and organs are the most important basis for the high soft tissue contrast, for example in comparison to X-ray-based methods such as computed tomography . In addition, contrast media are often used in MRI , by means of which the relaxation differences between different tissues can be changed in a targeted manner. Also, the functional magnetic resonance imaging (fMRI) to visualize physiological (brain) functions based on relaxation effects (by paramagnetic deoxygenated hemoglobin , s. BOLD-contrast ).

The nuclear spin relaxation times are determined not only by the material properties but also by the magnetic field strength in which the sample is located. Additional information can be obtained from the determination of the dependence of the relaxation times on the applied magnetic field strength. For the measurement of the relaxation time as a function of the frequency of a specific NMR measuring method has been developed, the so-called field cycle-NMR ( English field-cycling NMR ).

In materials research, nuclear spin relaxation times can convey information about the dynamic properties of materials on the molecular length scale. This is important in polymer research, in the development of electrochemical functional materials for batteries and fuel cells, and in the characterization of porous materials.

Relaxation times

In addition to the relaxation time , the spin-lattice relaxation characterized or longitudinal relaxation, the main relaxation times the transverse relaxation time and the time constant , according to the NMR excitation signal of the observable free induction decay (with the FID , free induction decay ) decreases. ${\displaystyle T_{1}}$ ${\displaystyle T_{2}}$ ${\displaystyle T_{2}^{*}}$

The following always applies to the relative length of these three time constants

${\displaystyle T_{2}^{*}\leq T_{2}\leq 2T_{1}}$

(In most cases this applies . In low-viscosity liquids, however, it is common ) ${\displaystyle T_{2}<T_{1}}$ ${\displaystyle T_{1}=T_{2}}$

${\displaystyle 1/T_{1}}$is called the longitudinal relaxation rate and it has the meaning of a transition probability between the nuclear spin energy levels.

Longitudinal relaxation time

The relaxation time that characterizes longitudinal relaxation plays a limiting role in nuclear magnetic resonance in several ways: ${\displaystyle T_{1}}$

• On the one hand, it determines the time that has to be waited after an NMR excitation process until the sample has come sufficiently close to its equilibrium state before renewed excitation (usual waiting times in this case are about three to five times the longitudinal relaxation time; shorter waiting times are used, for example, in -weighted or fast FLASH measurements). ${\displaystyle T_{1}}$
• On the other hand, it determines the maximum time window in which information can be encoded in a nuclear spin system. This has consequences, for example, when examining exchange processes or diffusion processes as well as for considerations regarding the implementation of a quantum computer using NMR.

Transverse relaxation time

The transverse relaxation time can also act as a limiting factor in NMR experiments, since the achievable resolution in NMR spectroscopy experiments is proportional to the reciprocal of the time due to the frequency-time uncertainty . Short relaxation times mean broad resonance lines in the NMR spectrum. The -time is approximately the same length as the respective in simple liquids, such as water or acetone several seconds and can -time. The more restricted the mobility of the molecules in a material, the shorter the time. In solids it is usually in the range of a few 10 µs. ${\displaystyle T_{2}}$ ${\displaystyle T_{2}}$ ${\displaystyle T_{2}}$ ${\displaystyle T_{1}}$ ${\displaystyle T_{2}}$

In addition to the molecular dynamics, the nuclear spin relaxation times are also influenced by the presence of paramagnetic substances. This is based on, among other things, the effect of the contrast media customary in magnetic resonance imaging and the use of chromium acetylacetonate to shorten the relaxation time in z. B. ²⁹ Si NMR.

Relaxation mechanisms

In order for a relaxation process on atomic nuclei (spins) to be effective, fluctuating magnetic fields with the "appropriate" frequency ( NMR resonance frequency ) and sufficient intensity must occur for nuclei with nuclear spin inside the matter at the location of these atomic nuclei . Such magnetic fields are z. B. generated by magnetic dipoles of atomic nuclei in the molecular environment of the spin. The fluctuation of this field results from the molecular movement, which in the case of intramolecular neighbors constantly changes the relative orientation of the neighboring nuclei and in the case of intermolecular neighbors their relative orientation and distance. In nuclei with a nuclear spin , fluctuating electrical field gradients are added as an additional, mostly dominant, cause of relaxation. Information about the thermal movement of particles inside a sample can generally be obtained from nuclear magnetic relaxation times, and in particular their temperature dependence. If the nucleus is relaxed by neighboring magnetic nucleus or electron dipoles, one speaks of dipole-dipole (DD) relaxation mechanisms. ${\displaystyle I={\tfrac {1}{2}}}$ ${\displaystyle =\gamma B_{0}=\omega _{0}}$ ${\displaystyle I\geq 1}$

A distinction must be made between the following cases for the relaxation mechanisms:

Intramolecular homonuclear dipole-dipole relaxation mechanism

Here the interaction that leads to relaxation takes place between two identical nuclei I within a molecule. This relaxation mechanism is mostly dominant for hydrogen nuclei in organic molecules. If you know the distance between the interaction partners from molecular data, you can measure the intramolecular DD relaxation time z. B. determine the reorientation correlation time , which in liquids near room temperature is typically in the picosecond to nanosecond range.

Intramolecular heteronuclear dipole-dipole relaxation mechanism

Finds an interaction between two dissimilar nuclei, e.g. B. ¹ H and ¹³ C instead, then it is a heteronuclear DD interaction. Since the magnetic dipole moment and thus the intensity of the fluctuating field of ¹ H in its vicinity is significantly greater than that of ¹³ C, the hydrogen nuclei are less relaxed by the neighboring carbon nuclei than by the homonuclear DD relaxation. The opposite applies to the relaxation of the ¹³ C nuclei.

Intermolecular dipole-dipole relaxation mechanism

Are the interacting nuclear dipoles on different molecules or macromolecules on different parts of the molecule, it is inter -molecular DD relaxation. Because of the larger distances between the atomic nuclei compared to the intramolecular case, the intermolecular relaxation contribution is smaller and in practice only measurable for ¹ H- ¹ H interactions (because of the large ¹ H dipole moment). However, the intermolecular relaxation, if one considers the dynamics of the system z. B. from self-diffusion data, provide very interesting information about local structures of liquids and solutions. The intermolecular ¹ H- ¹ H-DD relaxation is also the basis of an important method for determining the complicated spatial structure of biomolecules, such as proteins in solution, i.e. in the natural state of the biomolecule.

In paramagnetic systems such as solutions in which there are paramagnetic particles, a nuclear dipole-electron dipole interaction occurs. Since the magnetic moment of the electron is about three orders of magnitude stronger than that of the nuclei, this DD relaxation is extremely strong. Such paramagnetic particles are used as contrast agents in MRI . This relaxation mechanism is also the basis of fMRI . Depending on the concentration and type of paramagnetic centers, NMR lines can be extremely broadened. This means that the transverse relaxation time becomes very short and the NMR signal can no longer be measured.

Chemical Shift Anisotropy Relaxation (CSA)

If the chemical shift of a nucleus in the molecule depends on the orientation of the molecule relative to the direction of the external magnetic field, then one speaks of anisotropic chemical shift ( English chemical shift anisotropy (CSA)). The thermal tumbling movements of the molecules in fluids then create a fluctuating small additional magnetic field at the core location, which can influence the relaxation of the core. The CSA relaxation mechanism is the dominant relaxation mechanism for non-protonated X nuclei (e.g. ¹³ C or ¹⁵ N without a hydrogen neighbor).

Spin-Rotation Relaxation (SR)

Molecules can rotate rapidly in low-viscosity liquids and gases. Then alternating magnetic fields can arise at a core location in the molecule through rotation and modulated through molecular collisions, which act as a spin-rotation relaxation mechanism. The SR mechanism is experimentally recognizable from its characteristic temperature dependence.

Scalar Coupling Relaxation (SC)

This relaxation mechanism can occur when a nucleus I is scalarly coupled to a second nucleus S via spin-spin coupling and when the coupling (and thus the additional magnetic field that splits the lines in the spectrum) is modulated, i.e. changes over time. This modulation can be brought about by chemical exchange of the neighboring atom carrying the spin S (SC relaxation of the first type) or by relaxation of the spin (SC relaxation of the second type), which thereby changes its orientation with respect to the external field. ${\displaystyle S\geq {\tfrac {1}{2}}}$

Relaxation through nuclear quadrupole field gradient interaction (QF)

For the very common case that nuclei ( nuclides such as ² H, ⁷ Li, ¹⁴ N, ¹⁷ O, ²³ Na, ³⁵ Cl and ¹³³ Cs) have a nuclear spin , there is a special one, namely a non-magnetic relaxation mechanism in the game. is also synonymous with a spherical distribution of the positive electrical charge in the nucleus , while means that the charge distribution of the nucleus (figuratively the nucleus shape) no longer corresponds to a sphere, but to an ellipsoid . Such nuclei then have, in addition to the magnetic dipole moment , an electrical quadrupole moment eQ . This quadrupole can interact with electric field gradients , if they are present at the nucleus; the nuclear spin can be reoriented and thus quadrupole field gradient (QF) relaxation can take place. This additional relaxation mechanism is usually very strong and therefore dominant for such nuclei. The mostly short relaxation times and thus the broad NMR resonance lines are characteristic of nuclei with . ${\displaystyle I\geq 1}$ ${\displaystyle I={\tfrac {1}{2}}}$ ${\displaystyle I\geq 1}$ ${\displaystyle I\geq 1}$

Binding electrons often generate an electric field gradient at the nucleus, which is characterized by the quadrupole coupling constant . In the case of molecular reorientation, e.g. B. in liquids, this intramolecular field gradient constantly changes its direction and the QF relaxation takes effect. The quadrupole coupling constant in molecules is usually known and can therefore determine molecular reorientation times very precisely from the measurement of this intramolecular QF relaxation rate, even in the picosecond range . The QF mechanism is also important for ionic core relaxation in electrolyte solutions, which is then an intermolecular (interatomic) process. Electric fields from molecular, electric dipoles or ion charges in the closest vicinity of an observed ion nucleus, such as B. ²³ Na ⁺ , generate the fluctuating electrical field gradients and relax the ion core. Ion nucleus QF relaxation is an important source of information for studying ion solvation and association in electrolyte solutions.

literature

• Rainer Kimmich: NMR. Tomography, diffusometry, relaxometry. Springer, Heidelberg et al. 1997, ISBN 3-540-61822-8 .

Individual evidence

1. ^ ^{A b} Manfred Holz : Electrolytes. In: David M. Grant, Robin Kingsley Harris (Eds.): Encyclopedia of Nuclear Magnetic Resonance. Vol. 3: Con - F. Wiley, Chichester u. a. 1996, ISBN 0-471-93871-8 , pp. 1857-1864.
2. ↑ Malcolm H. Levitt: Spin Dynamics. Basics of Nuclear Magnetic Resonance. 2nd Edition. John Wiley & Sons, Chichester et al. 2008, ISBN 978-0-470-51117-6 , section 11.9.2.
3. ↑ James McConnell: The theory of nuclear magnetic relaxation in liquids. Cambridge University Press, Cambridge et al. 1987, ISBN 0-521-32112-3 .
4. ^ HG Hertz Structure and Dynamics of Liquids from NMR Relaxation. In: Journal chimie physique et de physicochimie biologique 82, 1985, ISSN  0021-7689 , pp. 557-563.
5. ↑ M. Holz, M. Mayele Influence of Additives on Hydrophobic Association in Polynary Aqueous Mixtures. In: Gerd Maurer (Ed.): DFG Research Report. Thermodynamic Properties of Complex Fluid Mixtures. Wiley-VCH, Weinheim 2004, ISBN 3-527-27770-6 , pp. 150-183.
6. ^ A. Abragam : The principles of nuclear magnetism . Clarendon Press, Oxford, 1961, pp. 313-316.