Quadrupole echo lineshape

NMR is ideally suited to explore molecular motions in the polymer. Different types of motion can be discriminated on behalf of their timescale and geometry of exchange. One-dimensional quadrupole echo lineshapes (see Section 6.2.7.1) are particularly sensitive to segmental dynamics [1-6, 9-12], when there is either fast exchange between discrete geometries (with Tc <1/Avq) or when the motion occurs on the intermediate timescale (tc= 1/Aj q). Dynamic processes in the intermediate to slow motional limit (tc > l/Ar Q) are addressed by 2D exchange spectroscopy (see Section... 

In addition to spin relaxation, there are the methods that measure molecular motion. The spectra reflecting the quadrupolar interaction are sensitive to the mid-range of frequencies. Therefore, NMR spectroscopy is a powerful tool to examine the molecular motion of polymers in the solid state. Different types of motion can be di.scriminated on the basis of their time scale and their exchange geometry. The one-dimensional quadrupole echo lineshape of "H NMR is sensitive to dynamics in the range 10 s < r < 10 s. where is the... 

Quadrupole echo lineshapes for the phenylene ring-flip motion (or any jump model) are simulated with an n-site exchange calculation one must also include the exchange-caused relaxation between the pulses (echo distor-... 

The 2-site 120° jump motion for the basal molecules switches between these two hydrogen bonding arrangements and clearly requires correlated jumps of the hydroxyl groups of all three basal molecules. On the assumption of Arrhenius behaviour for the temperature dependence of the jump frequencies, the activation energies for the jump motions of the apical and basal deuterons were estimated to be 10 and 21 kj mol-1, respectively. This dynamic model was further supported by analysis of the dependence of the quadrupole echo 2H NMR lineshape on the echo delay and consideration of 2H NMR spin-lattice relaxation time data. 

The temperature dependence of the quadrupole echo 2H NMR lineshape and 2H NMR spin-lattice relaxation time measurements demonstrated that the hydrogen bonding arrangement is dynamic. 

A quadrupole echo is generated similar to a Hahn echo by two pulses which are separated by half the echo time t = t /2 (Fig. 3.2.6(a)). However, the second pulse is a 90° and not a 180° pulse, and it is shifted in phase by 90° with respect to the first. The quadrupole echo appears at a time t2 = t j2 after the second pulse. The spectra shown in Fig. 3.2.5 have been simulated for the quadrupole echo technique with acquisition of the echo decay during h — t. Clearly, the lineshape strongly depends on type and time scale of the motion. In this way, molecular reorientation with correlation times in the range of 10 s < Tc < 10 s can be characterized by H NMR [Laul, Wehl]. Faster motion with correlation times in the range of 10 s < < 10" s can be investigated... 

H quadrupole powder patterns are generally fairly straightforward to record. Usually, a solid- or quadrupole-echo pulse sequence (90 v i 90, -t-FID) is used in order that dead time losses do not occur these would otherwise severely distort the lineshapes.2... 

Fig. 25. Random walk simulations for static 2H NMR powder lineshapes arising from a quadrupole echo 90°x-t-90°v-t-FID pulse sequence for the model of an isotropic 3° jump.36 (a) Jump correlation time, tj = 411 gs correlation time for the motion, xc = 100 ms, echo delays x as given in the figure. Dotted line is the spectrum for an isotropic random jump with xj = xc = 100 ms and an echo delay x — 200 gs. (b) Jump correlation times xj and motional correlation times xc as given in the figure, echo delay x = 100 gs.

One-dimensional quadrupole echo NMR lineshape analysis of powder samples is particularly informative when fast, discrete jumps occur between sites of well-defined geometry as, for example, in a phenyl group undergoing two-site exchange. In this case, the characteristic Pake-pattern is transformed into an axially asymmetric lineshape with an apparent asymmetry parameter r] 9 0 (see Equation (6.2.3)) [1-8]. The asymmetric lineshapes, shown on the left in Fig. 6.2.2, can be derived by considering how the individual components of the principal EFG tensor become averaged by the discrete jumps. Within the molecular frame, and in units of as defined by Equation (6.2.2), the static axially symmetric tensor consists of the components = 1, = — 1/2, and V y = — 112. This traceless tensor satisfies the... 

Fig. 23.20. A series of NMR speetra taken at 76.77 MHz of mouse KIF and mouse macrofibrils where, in both creases, the keratin chains have been labeled with l-[4,4,5,5- H4]lysine. Each spectrum was acquired using the quadrupole-echo sequence and is an average of 50000 acquisitions. The temperatures at which these equilibrium spectra were taken are (a,f) 25, (b,g) -10, (c,h) -20, (d,i) -35, (e,j) -45°C. Even at the lowest temperature, variations in the lineshapes indicate that the onset of the quenching of side chain motions is occurring more significantly for the lysines of the macrofibrils than for those of the KIF.

The sensitivity of typical NMR experiments to the type and time scale of various motions is illustrated in Fig. 7. For simplicity, we have chosen equal correlation times for all motions, namely = 1 x 10 s, = 1 x 10 s and Xg = 5 x 10 s. The powder spectra refer to quadrupole echo sequences [57], and characterize two-site jumps (a, b), three-site jumps (c), planar rotational diffusion (d), tetrahedral jumps (e) and isotropic spherical diffusion (f), respectively. The significant differences of the lineshapes arise from the different motional anisotropies. Evidently, quadrupole echo spectra [57] contain valuable information on the type of motion [10,48,49, 58]. 

M.S. Greenfield, A.D. Ronemus, R.L. Void, R.R. Void, P.E. Ellis, T.E. Raidy, Deuterium quadrupole-echo NMR spectroscopy. III. Practical aspects of lineshape calculations for multiaxis rotational processes,. Magn. Reson. 72 (1987) 89—107. 

In the past, this has been studied semi-quantitatively by means of NMR second moments and NMR quadrupole echoes (5,6,7). Here we show that at high temperatures ( -iyOK) and NMR lineshapes can be obtained with sharp, well-defined features, so that quadrupole coupling or nuclear shielding (chemical shift) tensor components can be measured directly to yield information on guest molecule orientation in the clathrate hydrate cages. 

To conclude this section on 2D NMR of liquid crystals, some studies of more exotic liquid crystalline systems are pointed out. Polymer dispersed nematic liquid crystals have attracted much attention because of their applications as optical display panels. Deuteron 2D quadrupole echo experiments have been reported [9.28] in the isotropic and nematic phases of / -deuterated 5CB dispersed in polymers. A similar technique was used [9.29] to study two model bilayer membranes. Both studies allow determination of the lineshape F(u ) due to quadrupolar interactions and the homogeneous linewidth L(u ) of the individual lines [9.28]. The 2D quadrupole echo experiment has also been used [9.30] to separate chemical shift and quadrupolar splitting information of a perdeuterated solute dissolved in a lyotropic liquid crystal. The method was compared with the multiple-quantum spectroscopy that is based on the observation of double-quantum coherence whose evolution depends on the chemical shift but not on the quadrupolar splitting. The multiple-quantum method was found to give a substantial chemical shift resolution. The pulse sequences for these methods and their treatment using density matrix formalism were summarized [9.30] for a spin 1=1 system with non-zero chemical shift. Finally, 2D deuteron exchange NMR was used [9.31] to study ring inversion of solutes in liquid crystalline solvents. 

An important shortcoming of the two-pulse methods is the difficulty of balancing the echo and antiecho amplitudes to obtain undistorted two-dimensional lineshapes, especially for nuclei with spin larger than 3/2. The two coherence-transfer pathways being different, it has been shown that their amplitude depends on the quadrupole couphng and the orientation of the crystallites. In a powder, it is nearly impossible to reach a perfect equalisation of these amplitudes. 

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