Zeeman order

The temperature dependence of the spectral spin diffusion and crossrelaxation was examined by Mueller et a/.287,288 with spin- and spin-1 systems. They showed that the diffusion rate can be strongly temperature dependent if it is motionally driven. It is therefore, unreliable to discriminate spin diffusion and chemical exchange by variable-temperature measurement of 2D exchange spectra. Mueller et al. suggested that the dependence of the polarization transfer rate on the spectral difference of the relevant resonances should be measured in a single crystal to safely distinguish the two different polarization transfer processes (see also ref. 289). They also explained satisfactorily why the relaxation of the quadrupolar order is much faster than the Zeeman order. This... 

We now describe the concept of dipolar and Zeeman order and then discuss some experimental techniques which utilize the concepts. Dipolar order is a very useful concept to know when you are dealing with solids. 

The concept of Zeeman order has already been discussed in terms of relaxation in III.A. If a sample containing nuclear spins is introduced into an external magnetic field Hq, no magnetization appears immediately. However, as the sample is allowed to soak in the field, a magnetization parallel to the applied field develops. This happens because the spins, originally equally divided between the two energy states, i.e.,... 

There are two major means of transforming Zeeman order into dipolar order. The technique, mentioned in the previous section, of physically removing the sample from the magnet and then replacing it is quite slow and cumbersome to be practical in most cases although it was used in at least one interesting set of experiments (Jones and Daycock, 1967 Jones, et al., 1969). 

Any of the above ADRF methods, in principle, can convert Zeeman order into dipolar order with an efficiency approaching 100%. In contrast, the Jeener echo technique (to be discussed in IV.B.4.) can only achieve approximately 50% conversion. 

Figure 8.2 Basic 1-D pulse sequences (a) the quadrupole echo (b) the spin-alignment echo (c) inversion-recovery quadrupole echo and (d) quadrupole echo with pre-saturation for amorphous/crystalline selection, t is the quadrupole echo pulse spacing in each sequence, DE is a delay for spin-lattice relaxation, of either (b) quadrupolar order or (c) and (d) Zeeman order. Flip angles are labelled above the pulses.

The operator Qz represents quadrupolar order just like the Zeeman order is given by Iz, while Kz corresponds to double quantum coherence. It is possible to convert the larger Zeeman order into quadrupolar order by means of pulse techniques. The time-dependent a t) can be expressed as a linear combination of the basis operators... 

For an isolated spin-1 system, it is convenient to define sum and difference magnetizations [Eqs. (2.84)-(2.85)] in the J-B experiment. The decay of the difference (quadrupolar order) proceeds exponentially at a rate T q, while the sum (Zeeman order) recovers exponentially towards equilibrium at a different rate. The J-B experiment allows simulataneous determination of these rates from which Ji uJo) and J2 2ujo) can be separated. Table 5.1 briefly summarizes thermotropic liquid crystals in which spectral density measurements were reported. Figure 5.4 illustrates the temperature and frequency dependences of spectral densities of motion (in s by including the interaction strength Kq factor) for 5CB-di5. The result is fairly typical for rod-like thermotropic liquid crystals. The spectral densities increase with decreasing temperature in the nematic phase of 5CB. The frequency dependence of Ji uJo) and J2(2a o) indicate that molecular reorientation is likely not in the fast motion regime. However, the observed temperature dependence of the relaxation rates is opposite to what is expected for simple liquids. This must be due to the anisotropic properties (e.g., viscosity) of liquid crystals. 

A rather lovely aspect of this experiment is that there is a sense in which time is reversed, in that the experiment starts with the system being in a state of Zeeman order (all spins aligned along the external field), is caused to develop multiple quantum coherence, and then caused to reverse its evolution back into a state of Zeeman order again. NMR is a wonderful tool for the study of time-dependent quantum mechanics. 

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