Dipolar order

As witli tlie nematic phase, a chiral version of tlie smectic C phase has been observed and is denoted SniC. In tliis phase, tlie director rotates around tlie cone generated by tlie tilt angle [9,32]. This phase is helielectric, i.e. tlie spontaneous polarization induced by dipolar ordering (transverse to tlie molecular long axis) rotates around a helix. However, if tlie helix is unwound by external forces such as surface interactions, or electric fields or by compensating tlie pitch in a mixture, so tliat it becomes infinite, tlie phase becomes ferroelectric. This is tlie basis of ferroelectric liquid crystal displays (section C2.2.4.4). If tliere is an alternation in polarization direction between layers tlie phase can be ferrielectric or antiferroelectric. A smectic A phase foniied by chiral molecules is sometimes denoted SiiiA, altliough, due to the untilted symmetry of tlie phase, it is not itself chiral. This notation is strictly incorrect because tlie asterisk should be used to indicate the chirality of tlie phase and not tliat of tlie constituent molecules. 

C. Jeener-Broekaert dipolar order relaxation sequence 464... 

C. Jeener-Broekaert Dipolar Order Relaxation Sequence... 

The classical Jeener Broekaert sequence (133) is used to determine the dipolar-order relaxation time (in systems of spin 1/2 nuclides) and the Tiq relaxation time (in systems with spin 1 nuclides) of spin 1 nuclides with quadrupolar contributions to 7. Its FFC version is similar to the Inversion Recovery, except that the first 180° pulse is replaced by the sequence 90, — 5 — 45, the detection pulse becomes 45 and a special phase cycle is required. We shall not dwell on the details and purpose of the sequence since they go beyond the scope of this chapter. We wish to underline, however, the fact that sequences of this type require a close coordination of the preparatory sub-sequence with the signal-detection sub-sequence in order to isolate not just a particular magnetization component but a particular relaxation pathway. 

Discussions with D. L. VanderHart have helped to identify the role of dipolar order in carbon rotating frame studies. This work is sponsored in part by the Naval Air Systems Command. 

Fig. 11. Dipolar generalized order parameters squared (S dc) determined using the DIDC approach for the protein ubiquitin (solid lines and circles). The shaded region represents the generalized order parameters squared determined using 15N spin relaxation methods.137 Due to the extended timescale sensitivity of RDCs, the overall scaling for the dipolar order parameters was chosen such that S. values were equal to or less than the corresponding spin relaxation order parameters.

An alternative to the REREDOR experiment is the REcoupled polarization transfer-heteronuclear dipolar order (REPT-HDOR),27 shown in Fig. 18(b). This experiment uses initial 1H transverse magnetization, rather than 13C as in the REREDOR experiment, to create a heteronuclear 1H-13C coherence (corresponding to dipolar order, described by a term 3IZSZ - IS in the density operator, where / = JH and S = 13C) in tx after dipolar... 

One such analysis in the review period involves the characterization of the rotation of the methyl groups in pyridoxine (vitamin B6).49 The temperature dependencies of the 1H spin-lattice relaxation time T, and Tld (the relaxation time constant characterizing the relaxation of dipolar order, a population distribution over the Zeeman spin levels, which corresponds to a density operator component T20, he. I z - Ii. I2, to equilibrium) at three different applied field strengths and for a variety of temperatures were determined, yielding the curves in Fig. 30. The only motion that could affect... 

There are two requirements for the use of multiple-pulse sequences to speed up the spin-diffusion process First, the scaling factor of the homonu-clear dipolar coupling should be as large as possible and, second, the effective spin lock has to be larger than the homonuclear dipolar interactions between the S-spins [19] to prevent loss of sum magnetization into dipolar order [15]. 

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 dipolar order is less obvious. Consider the following experiment A sample with a long T which has... 

Provided that the system is in a high field Hq, and that no rf fields are applied on resonance, the dipolar ordered system and the Zeeman system are isolated from each other, the only connection being through the lattice. The dipolar... 

Note that one could have transitions of a nucleus up one Zeeman level and another nucleus down one Zeeman level to maintain the magnetization while altering the dipolar order. Because the dipolar reservoir is usually isolated from the Zee-man reservoir, a system can be prepared so that its Zeeman spin temperature is different from its dipolar temperature... 

For further insights and examples of dipolar order, see, for example, Anderson and Hartmann, 1962, sections IV.B.2. and IV.B.4. of this book, and references therein. 

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. 

The requirements on the phases of the pulses is somewhat less stringent than implied by the sequence above. The second pulse must be in quadrature with the first but the third pulse can have any arbitrary phase because the dipolar order is not referenced by any external directions. To observe the Jeener echo, the reference phase of the receiver must be 90° out of phase with the third pulse. When the detector reference phase is identical with that of the third pulse, a Zeeman signal can be observed which is simply the FID resulting from the magnetization which has relaxed back to the z direction in the time since the first pulse. 

The most obvious application of the Jeener echo is to measure T by plotting echo amplitude vs. time spent in a state of dipolar order. If the system under study is homogeneously broadened, then the location on the echo where the amplitude is measured, provided it is chosen consistently, is immaterial for the measurement of T - In an inhomogeneously broadened system, such as a poly crystalline material, the Jeener echo may be a superposition of Jeener echoes with different shapes and different T- s. If so, it may matter where the echo amplitude is sampled. The most obvious test is to plot relaxation curves from different parts of the echo to determine whether the echo is relaxing uniformly. For a crystalline material, one expects that the dipolar relaxation time T p will be independent of the crystal orientation in the external field because the state of dipolar order is independent of this external field. 

In an inhomogeneously broadened system, such as the bulk sample of a lamellar phase, there will be a superposition of FID s with different Tg s depending on the angle the lamellae s normal makes with Hq. As the effectiveness of the transformation from Zeeman to dipolar order depends upon the slope of the FID at the point of application of the second pulse, at short times one preferentially selects those lamellae with short FID s and at long x s those lamellae with long decays, namely those with orientations close to the magic angle. 

We have discussed two ways in which spin-lattice relaxation rates can be measured at fields much smaller than the usual laboratory fields. In section IV.B.l. we introduced the concept of dipolar order in fields of neighboring nuclei and in IV.C.l. we talked about the spin-lattice relaxa-... 

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