Relaxation (NMR)

Under relaxation is understood in nuclear magnetic resonance spectroscopy (NMR ) spectroscopy and magnetic resonance imaging ( MRI), the processes that make the nuclear spin magnetization (eg after a deflection or excitation ) back aspire to their equilibrium state. These processes are based on different relaxation mechanisms and are described by Relaxationsszeiten for the different magnetization components.

Different nuclear spin relaxation times in various tissues are the primary basis of image contrast in magnetic resonance imaging dar. NMR spectroscopy are the relaxation times, among other things of importance to investigate the micro- dynamics and microstructure of condensed matter at the molecular length scale, for example, in physics, physical chemistry, chemistry and materials research.

  • 4.1 Intramolecular homonuclear dipole -dipole relaxation mechanism
  • 4.2 Intramolecular heteronuclear dipole -dipole relaxation mechanism
  • 4.3 Intermolecular dipole -dipole relaxation mechanism
  • 4.4 Relaxation by the chemical shift anisotropy ( CSA)
  • 4.5 relaxation by spin- rotation ( SR )
  • 4.6 relaxation by scalar coupling (SC)
  • 4.7 Relaxation by nuclear quadrupole field gradient interaction ( QF )

Principle

In thermal equilibrium there is in a magnetic field ( by convention in the z- direction) an equilibrium nuclear magnetization along the field direction. Their size is determined by the Boltzmann statistics and is called this component of magnetization in the z direction, the longitudinal magnetization. The magnetization component perpendicular to the field, that is in the x- and y-directions are in the case of equilibrium in its zero value. It disturbs the thermal balance of the magnetic resonance system, such as by irradiation of a 90 ° - or 180 ° - high-frequency ( RF ) pulse, then the z-component of the magnetization is zero or. After failure, the longitudinal magnetization, an exponential law in time is the following, by the relaxation process back to the equilibrium value over. This is the longitudinal relaxation. By a 90 ° pulse, as " proof pulse ", after a time t, can be detected by the resulting relaxation time t back nuclear magnetization experimentally.

By a failure, for example, by the aforementioned 90 ° RF pulse, but also poses a precessing nuclear magnetization in the xy-plane ( transverse plane ) the amount, which is also exponentially, according to the disturbance to the equilibrium value for the transverse magnetization namely zero, goes. This is the transverse relaxation.

In the experimental determination of the nuclear magnetic relaxation times, the nuclear magnetization, measured over the NMR signal amplitude as a function of time t ( time interval between the " glitch " and the " detecting pulse"). Is measured from the exponential relaxation curve, the characteristic time constant, the " relaxation time " determined. Nuclear magnetization measurements as a function of time, therefore, provide a form of time-resolved NMR dar.

The nuclear magnetic relaxation processes associated with transitions between different energy levels of the nuclear spin system. Since there are virtually no spontaneous transitions in the frequency range of NMR spectroscopy, electromagnetic fields in the nuclear magnetic resonance frequency are required, which can induce transitions. These are internal substance, fluctuating magnetic ( in some cases electric ) fields. The emergence of these fluctuating fields and their interaction with the core may be different and therefore we speak of different relaxation mechanisms. Knowing the relaxation mechanism in particular for samples to be tested, then you can get valuable information about the environment of the observed nuclei, ie from the core of the matter from the measurement of the nuclear magnetic relaxation times.

Applications

One of the classic applications of Relaxationszeitstudien is the physico-chemical study of matter in a liquid state, such as the explanation of the micro- or dynamic microstructure of pure liquids, or electrolyte solutions. One possible molecular reorientation in the liquid, for example, in the picosecond range determine, short-lived, local molecular aggregates, such as studying the solvation shells of ions or ion associations, as well as, for example, short-lived hydrogen bonds between molecules.

In magnetic resonance imaging (MRI ) have different relaxation properties of various tissues and organs are the main basis for the high soft tissue contrast as compared to X-ray based techniques such as computed tomography. In addition, the MRI contrast agents are also often used, by means of which the Relaxationsunterschiede between different tissues can be selectively altered. The functional magnetic resonance imaging (fMRI ) to visualize physiological (brain ) functions based on relaxation effects ( by paramagnetic deoxygenated hemoglobin, see BOLD contrast).

The nuclear spin relaxation times are except by material properties determined by the magnetic field strength, in which the sample is located. From the determination of the dependence of the relaxation times of the applied magnetic field strength, additional information can be obtained. For the measurement of the relaxation time as a function of the frequency of a particular NMR measurement method has been developed, the so-called field cycle NMR ( english field -cycling NMR).

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

Relaxation times

In addition to the spin -lattice relaxation or longitudinal relaxation relaxation time characterizing the relaxation times are important, the transverse relaxation time and the time constant of decrease in the observed signal according to the NMR excitation free induction decay ( FID free induction decay ).

Always applies to the relative length of these three time constants

( Applicable in most cases. Add low-viscosity fluids, however, is common)

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 characterizing the longitudinal relaxation plays a limiting role in nuclear magnetic resonance in several ways:

  • It determines the one hand, the time that must elapse after an NMR excitation process until the sample is approached before re- excitation again sufficiently close to their equilibrium state ( normal waiting times in this case are about three to five times the longitudinal relaxation time, shorter waiting times example, be used in weighted or fast FLASH measurements).
  • You on the other hand determines the maximum time frame can be encoded in a nuclear spin system in the information. This has consequences for example in the study of exchange processes or diffusion processes, as well as considerations for the realization of a quantum computer by NMR.

Transverse relaxation time

The transverse relaxation time can also act as a limiting factor in the NMR experiments, since the achievable resolution in the NMR 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 about the same length as the respective time in simple liquids, such as water or acetone and may be several seconds. The greater the mobility of the molecules is restricted in a material, the shorter the time. In solids is usually in the range of some 10 microseconds.

Not only by the molecular dynamics the nuclear spin relaxation is also influenced by the presence of paramagnetic substances. Then, based on the effect of the usual in magnetic resonance imaging contrast agents and the use of chromium acetylacetonate to shorten the relaxation time in eg 29Si NMR.

Relaxation mechanisms

For a relaxation process to atomic nuclei (spins ) can be effective fluctuating magnetic fields with the " right " frequency ( NMR resonance frequency) and have a sufficient intensity occur for nuclei with nuclear spin inside the matter at the place of these atomic nuclei. Such magnetic fields are generated by magnetic dipoles of atomic nuclei in the molecular environment of the pins, for example. This field results from the fluctuation of the molecular motion, which permanently the relative orientation of the adjacent cores and intermolecular neighbors changes the relative orientation and their spacing in intramolecular neighbors. For nuclei with a nuclear spin fluctuating electric field gradients also be added as an additional, usually dominant, Relaxationsursache. From nuclear magnetic relaxation times, and in particular, their temperature dependence, information on the thermal motion of the particles can be obtained in the interior of a sample thus generally. If the core by neighboring magnetic core or relaxed Elektronendipole then one speaks of dipole -dipole ( DD ) relaxation mechanisms.

The relaxation mechanisms following cases are generally distinguished:

Intramolecular homonuclear dipole -dipole relaxation mechanism

Here is the interaction that results in the relaxation between two identical nuclei within a molecule instead of I. This relaxation mechanism for hydrogen nuclei in organic molecules usually dominant. By knowing the distance between the interaction partner of the molecule information, can be determined from measurement of the intramolecular DD relaxation time, for example, the reorientation correlation time in is liquid in the vicinity of room temperature is typically picosecond to nanosecond.

Intramolecular heteronuclear dipole -dipole relaxation mechanism

Find an interaction between two dissimilar nuclei, such as 1H and 13C instead, it is a heteronuclear DD interactions. Since the magnetic dipole moment, and therefore the intensity of the fluctuating field of 1H in the vicinity thereof is significantly greater than that of 13C is, the hydrogen nuclei through the adjacent carbon nuclei less than relaxed by homonuclear DD relaxation. Accordingly, the reverse is true for the relaxation of 13C nuclei.

Intermolecular dipole -dipole relaxation mechanism

Are the interacting nuclear dipoles on different molecules or macromolecules on different parts of the molecule, it is intermolecular DD relaxation. Then because of the greater distance between the nuclei compared with the case of intramolecular, intermolecular Relaxationsbeitrag small and in practice only for the 1H -1H- interactions ( due to the large dipole moment of 1H ) is measurable. However, the intermolecular relaxation, if you eg knows the dynamics of the system of self-diffusion data provide very interesting information about local structures of liquids and solutions. Intermolecular 1H-1H DD relaxation is also the basis of a major method of determining the three-dimensional structure of complex biomolecules, such as proteins in solution, that is in the natural state of the biomolecule.

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

Relaxation by anisotropy of the chemical shift ( CSA)

When the chemical shift of a nucleus in a molecule depends on the orientation of the molecule relative to the direction of the external magnetic field, then it is called anisotropic chemical shift ( chemical shift anisotropy English ( CSA) ). Due to the thermal wobbling motions of the molecules in fluids produced at the nucleus then a fluctuating small additional magnetic field which can influence the relaxation of the core. The CSA relaxation mechanism is for non- protonated X nuclei (eg 13C or 15N without hydrogen - neighbor) is the dominant relaxation mechanism.

Relaxation by spin- rotation ( SR )

In low-viscosity liquids and gases fast rotation movements can occur in molecules. Then magnetic fields may occur at a position of the nucleus in the molecule by the rotation and modulated through molecular collisions, acting as a spin -rotation relaxation mechanism. Experimental recognizable, the SR mechanism of its characteristic temperature dependence.

Relaxation by scalar coupling (SC)

This relaxation mechanism can occur when a core I is scalar- coupled spin-spin coupling to a second core, and S when the coupling (and thus the additional magnetic field which splits the lines in the spectrum ) is modulated, that varies over time. This modulation can be caused by the chemical exchange of the spin S bearing neighboring atom (SC- relaxation of the first type ) or relaxation of the spin (SC- relaxation of the second type ), which will change its orientation relative to the external field.

Relaxation by nuclear quadrupole field gradient interaction ( QF )

For the very common case where nuclei ( nuclides such as 2H, 7Li, 14N, 17O, 23Na, 35Cl and 133Cs ) have a nuclear spin, a special, namely a non-magnetic relaxation mechanism comes into play. is equivalent to a spherical distribution of the positive electric charge core while means that the charge distribution of the core ( the core -image shape ) no longer corresponds to a sphere, but an ellipsoid. Such cores have then, in addition to the magnetic dipole moment and an electric quadrupole moment eQ. This can Quadrupolment with electric field gradients, if they are present at the nucleus, interact; the nuclear spin can be reoriented and thus take place quadrupole field gradient (QF ) relaxation. This additional relaxation mechanism is usually very strong and therefore dominant for such nuclei. The usually short relaxation times and thus the broad NMR resonance lines are characteristic of nuclei.

Bonding electrons at the nucleus often produce an electric field gradient, which is characterized by the quadrupole coupling constant. In molecular reorientation, such as liquids, this intramolecular field gradient is constantly changing its direction, and the QF relaxation effect. Usually one knows the quadrupole coupling in molecules and can therefore excluded from the measurement of these intramolecular QF- relaxation rate very accurate molecular reorientation times, even in the picosecond range, determine. Important is the QF- mechanism is also at the core ion relaxation in electrolyte solutions, which is then is an intermolecular ( interatomic ) process. Electric fields of molecular electric dipoles or ionic charges in the closest vicinity of a core observed ions such as 23Na , generating the fluctuating electric field gradient, and so relax the ion core. The ion core QF- relaxation is an important source of information for the study of Ionensolvatation and association in electrolyte solutions.

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