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Hello. What is the best definition to the state of "saturation" in the context of NMR? No phase coherence in the transverse plane and no net Mz seem to be important requirements. Can dephasing with a field gradient count as "saturation"? Is there anything else? What methods can be used to achieve saturation - are there better/worse ones? Thanks! |
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I'll second Evgeny's suggestion and Scott's answer and amplify on them a bit. In a classical (avoiding quantum for the moment) context the definition of saturation is MX = MY = MZ = 0, where the Ms refer to macroscopic magnetization. (see "Pulse and Fourier Transform NMR", Farrar and Becker, 1971, p14, Academic Press) This state can be obtained by a number of different methods some of which are more suitable for the liquid state, others for the solid state and some in between. In a case where T2 << T1, saturation can be obtained through waiting for several T1s, applying a pi/2 RF pulse and then waiting for several T2s. At this point in time the macroscopic magnetization is zero. This is typically a broadband saturation, that is, all of the spins are affected, irrespective of their individual resonance offset. Another method is to apply a single, long and typically weak RF pulse. The frequency width over which this saturation pulse is effective (that is, the bandwidth of the pulse) depends upon the length (in units of time) of the pulse. It is often used to saturate a single signal rather than the entire ensemble. Alternately and perhaps more generally, a series of pi/2 RF pulses can be applied to the spin system which relaxes the above restriction. The series of pulses may be applied with constant or varying inter-pulse spacing. The phases of the RF pulses may be constant or varying. The effect of this irradiation can be narrow band or broadband, depending upon the experimental details. (see "Selective Excitation in Fourier Transform Nuclear Magnetic Resonance" Morris and Freeman, J Mag Res, 1978, v29, p433) NMR spectroscopists often have their personal favorite schemes (sometimes for certain situations) and many excellent/heated debates have been had over them (late night at ENCs). Now, considering the microscopic magnetization, it is possible for the macroscopic magnetization components to all equal zero while there can remain a "memory" of the history each microscopic moment has endured. It is because of this memory that an echo can be evoked from a spin system which appears for a moment in time to have no net macroscopic magnetization. (see for example, "Atomic Memory", Hahn, Scientific American, 1984, v251, p50 and yes, there used to be articles like this in Sci Am) So while it isn't, strictly speaking, part of the concept of saturation it is, practically speaking, often important to also destroy the "coherence memory" of the spins when saturating them. Doing so will suppress echo formation and other undesirable phenomena. In the liquid state, a favorite method is to apply a (B0) field gradient for a short time after applying one of the aforementioned RF pulse schemes. The net effect of this "gradient pulse" is to cause rapid evolution of the spins (under a resonant offset (hamiltonian)). Colloquially speaking, a large amount of phase is wound up into each spin. Since these spins are in the liquid phase they can diffuse freely throughout the sample. This diffusion carries them away from their initial (relative to the gradient pulse) position and makes it extremely unlikely that the phase they have accumulated can ever be unwound. In the solid state, specifically when there are (homogeneous) dipolar interactions present, no gradient pulse is required. Evolution under the dipolar interaction(s) will cause a comparable winding up of phase. For those so inclined there is a beautiful paper on this phenomenon and how to unwind these spins. ("Time-Reversal Experiments in Dipolar-Coupled Spin Systems", Rhim, Pines and Waugh, Phys Rev B, 1971, v3 p684) In a non-spinning solid context it is often found that the spacing between subsequent RF pulses in a series of them is most effective when it is on the order of the spins' T2. If that piece of data isn't known then T2* can be used which is roughly equal to the reciprocal of pi times the width of the signal (full width at half maximum, FWHM), depending upon the line shape. It's a good place to start. In a MAS (Magic Angle Spinning) context in the solid state (or for HRMAS in the semi-solid state) the MAS imposes a coherent modulation on the spin system and it is especially convenient to coordinate the timing of the series of RF pulses with the rotation. Often, one pi/2 RF pulse delivered every one-quarter rotation is most effective at saturating the spins. |
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I think there is an important difference between "saturation" and loss of phase coherence by a gradient pulse. A gradient pulse only dephases spacially. So at any arbitrary point in a sample, nearby nuclei would still have phase coherence with each other (gradually becoming less coherent as the distance between them increases along the Z axis). A truly saturated sample has lost all phase coherence everywhere. Also, the loss of phase coherence by a gradient can easily be reversed, again suggesting that this is different from true saturation in which phase decoherence can not be reversed (without restoring Mz first). |
