Magnetisation equilibrium

Relaxation refers to all processes which regenerate the Boltzmann distribution of nuclear spins on their precession states and the resulting equilibrium magnetisation along the static magnetic field. Relaxation also destroys the transverse magnetisation arising from phase coherenee of nuelear spins built up upon NMR excitation. 

Spin-lattice relaxation is the steady (exponential) build-up or regeneration of the Boltzmann distribution (equilibrium magnetisation) of nuelear spins in the static magnetic field. The lattice is the molecular environment of the nuclear spin with whieh energy is exchanged. 

FID Free induction decay, decay of the induction (transverse magnetisation) back to equilibrium (transverse magnetisation zero) due to spin-spin relaxation, following excitation of a nuclear spin by a radio frequency pulse, in a way which is free from the influence of the radiofrequency field this signal (time-domain) is Fourier-transformed to the FT NMR spectrum (frequency domain)... 

By the term state we refer to such data as the chemical composition of the parts of the system (including allotropy and isomerism), their state of electrification, magnetisation, stress or strain, their state of division, temperature, and the like, and the second condition generalises the statement of equilibrium. 

There is a second relaxation process, called spin-spin (or transverse) relaxation, at a rate controlled by the spin-spin relaxation time T2. It governs the evolution of the xy magnetisation toward its equilibrium value, which is zero. In the fluid state with fast motion and extreme narrowing 7) and T2 are equal in the solid state with slow motion and full line broadening T2 becomes much shorter than 7). The so-called 180° pulse which inverts the spin population present immediately prior to the pulse is important for the accurate determination of T and the true T2 value. The spin-spin relaxation time calculated from the experimental line widths is called T2 the ideal NMR line shape is Lorentzian and its FWHH is controlled by T2. Unlike chemical shifts and spin-spin coupling constants, relaxation times are not directly related to molecular structure, but depend on molecular mobility. 

Figure 9.7—Change of the magnetisation vector Af0 with irradiation and relaxation of the system after resonance. Schematic representation showing only the individual vectors resulting from the non-equilibrium of populations ( numerical). An independent observer rotating at the same frequency as the precession would see the magnetisation vector tilted by an angle of a. Relaxation to the original position is also shown.

The equilibrium bulk magnetisation comes from the net moment on summation of contributions from individual spins. A sample containing spin- /2 nuclei has two states (energy levels) with the nuclear spins distributed between these according to the Boltzmann distribution which gives the probability of occupation of the different states. 

Figure 2.4. In the vector model of NMR many like spins are represented by a bulk magnetisation vector. At equilibrium the excess of spins in the a state places this parallel to the +z-axis.

Figure 2.8. An rf pulse applies a torque to the bulk magnetisation vector and drives it toward the x-y plane from equilibrium. 9 is the pulse tip or flip angle which is most frequently 90 or 180 degrees.

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