Bulk Magnetisation

In a linear isotropic material B = where p, is the permeability of the material. The relative permeability p-r = p./po or = 1 + x is a measure of how much magnetisation a material will generate. The molar and specific susceptibilities are also quoted in the literature. 

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. 

AE = 7ftBo. The z-component of the magnetic moment is given by p,2 = yfim and 

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Rotating frame model A means of visualising the processes taking place in an NMR experiment by observing these processes as if you were riding on a disc describing the movement of the bulk magnetisation vector. 

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.

For those spins further from resonance, the angle 0 becomes greater and the net rotation toward the x-y plane diminishes until, in the limit, 0 becomes 90 . In this case the bulk magnetisation vector simply remains along the -f-z-axis and thus experiences no excitation at all. In other words, the nuclei resonate outside the excitation bandwidth of the pulse. Since an off-resonance vector is driven away from the y-axis during the pulse it also acquires a (frequency dependent) phase difference relative to the on-resonance vector (Fig. 3.6). This is usually small and an approximately linear function of frequency so can be corrected by phase adjustment of the final spectrum (Section 3.2.8). 

Figure 9.9. The adiabatic inversion pulse. An rf frequency sweep during the pulse causes the effective rf field experienced by the spins to trace an arc from the +z-axis to the -z-axis, dragging with it the bulk magnetisation vector.

Before moving forward, the chemical biology reader should appreciate that Mz(f) polarisation and recovery towards steady state bulk magnetisation Mby spin-lattice relaxation are primarily indicative of changes in the levels of spin state occupancy. By contrast, My(f) coherence and evolution by spin-spin relaxation are both primarily indicative of transitions between spin state energy levels. In this context, the nuclear Overhauser effect (NOE) is a very important through-space effect in NMR spectroscopy that results directly from dipolar coupling-mediated spin-lattice relaxation. 

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