Relaxation (NMR)
This field makes the magnetic dipole moments of the sample precess at the resonance (Larmor) frequency of the nuclei.
They become abruptly phase coherent when they are hit by radiofrequency (RF) pulses at the resonant frequency, created orthogonal to the field.
Spontaneous emission of energy is a radiative process involving the release of a photon and typified by phenomena such as fluorescence and phosphorescence.
[2][3] Rather, the return to equilibrium is a much slower thermal process induced by the fluctuating local magnetic fields due to molecular or electron (free radical) rotational motions that return the excess energy in the form of heat to the surroundings.
The decay of RF-induced NMR spin polarization is characterized in terms of two separate processes, each with their own time constants.
Values of T1 range from milliseconds to several seconds, depending on the size of the molecule, the viscosity of the solution, the temperature of the sample, and the possible presence of paramagnetic species (e.g., O2 or metal ions).
The longitudinal (or spin-lattice) relaxation time T1 is the decay constant for the recovery of the z component of the nuclear spin magnetization, Mz, towards its thermal equilibrium value,
T1 relaxation involves redistributing the populations of the nuclear spin states in order to reach the thermal equilibrium distribution.
Note that the rates of T1 relaxation (i.e., 1/T1) are generally strongly dependent on the NMR frequency and so vary considerably with magnetic field strength B.
By degassing, and thereby removing dissolved oxygen, the T1/T2 of liquid samples easily go up to an order of ten seconds.
Especially for molecules exhibiting slowly relaxing (T1) signals, the technique spin saturation transfer (SST) provides information on chemical exchange reactions.
[4] The transverse (or spin-spin) relaxation time T2 is the decay constant for the component of M perpendicular to B0, designated Mxy, MT, or
T2 relaxation is a complex phenomenon, but at its most fundamental level, it corresponds to a decoherence of the transverse nuclear spin magnetization.
In an idealized system, all nuclei in a given chemical environment, in a magnetic field, precess with the same frequency.
However, in real systems, there are minor differences in chemical environment which can lead to a distribution of resonance frequencies around the ideal.
For molecules that aren't moving, the deviation from ideal relaxation is consistent over time, and the signal can be recovered by performing a spin echo experiment.
The relation between them is: where γ represents gyromagnetic ratio, and ΔB0 the difference in strength of the locally varying field.
is the cross-product, γ is the gyromagnetic ratio and B(t) = (Bx(t), By(t), B0 + Bz(t)) is the magnetic flux density experienced by the nuclei.
They can be employed to explain the nuclear Overhauser effect, which is an important tool in determining molecular structure.
Following is a table of the approximate values of the two relaxation time constants for hydrogen nuclear spins in nonpathological human tissues.
Following is a table of the approximate values of the two relaxation time constants for chemicals that commonly show up in human brain magnetic resonance spectroscopy (MRS) studies, physiologically or pathologically.
The decay constant for the recovery of the magnetization component along B1 is called the spin-lattice relaxation time in the rotating frame and is denoted T1ρ.
Relaxation of nuclear spins requires a microscopic mechanism for a nucleus to change orientation with respect to the applied magnetic field and/or interchange energy with the surroundings (called the lattice).
This interaction depends on the distance between the pair of dipoles (spins) but also on their orientation relative to the external magnetic field.
The chemical shift anisotropy (CSA) relaxation mechanism arises whenever the electronic environment around the nucleus is non spherical, the magnitude of the electronic shielding of the nucleus will then be dependent on the molecular orientation relative to the (fixed) external magnetic field.
[12] The form of the spectral density functions depend on the physical system, but a simple approximation called the BPP theory is widely used.
These fluctuations produce transitions between the nuclear spin states in a similar manner to the magnetic dipole-dipole interaction.
In 1948, Nicolaas Bloembergen, Edward Mills Purcell, and Robert Pound proposed the so-called Bloembergen-Purcell-Pound theory (BPP theory) to explain the relaxation constant of a pure substance in correspondence with its state, taking into account the effect of tumbling motion of molecules on the local magnetic field disturbance.
This theory makes the assumption that the autocorrelation function of the microscopic fluctuations causing the relaxation is proportional to
s, while hydrogen nuclei 1H (protons) at 1.5 tesla precess at a Larmor frequency of approximately 64 MHz (Simplified.
