Solid echoes

Pulsed deuteron NMR is described, which has recently been developed to become a powerftd tool for studying molectdar order and dynamics in solid polymers. In drawn fibres the complete orientational distribution function for the polymer chains can be determined from the analysis of deuteron NMR line shapes. By analyzing the line shapes of 2H absorption spectra and spectra obtained via solid echo and spin alignment, respectively, both type and timescale of rotational motions can be determined over an extraordinary wide range of characteristic frequencies, approximately 10 MHz to 1 Hz. In addition, motional heterogeneities can be detected and the resulting distribution of correlation times can directly be determined. 

Fig. 6. The generalized Jeener-Broekaert three pulse sequence. Note that FT of the solid echo and the alignment echo starts at times delayed by the pulse separation r, after the second and third pulse, respectively...

In absence of motion the formation of the solid echo is limited by T only, in presence of motions, however, the NMR frequencies in the periods of destructive interference and constructive refocussing, respectively, may be different. The signal following the refocussing pulse is given by27)... 

Fig. 8. Calculated solid echo 2H NMR powder spectra for jumps between two sites related by the tetrahedral angle for ij =0, i.e. true absorption spectrum and Tj = 200 ps. xc is the correlation time of motion. R is the reduction factor, giving the total normalized intensity of the spectra for x, = 200 ps. (For x, = 0 all the spectra have total intensity 1)...

In polymers one will often particularly be interested in very slow dynamic processes. The solid echo technique just described is still limited by the transverse relaxation time T being of the order of a few ps at most. The ultimate limitation in every NMR experiment however, is not T but the longitudinal relaxation time T, which for 2H in solid polymers typically is much longer, being in the range 10 ms to 10 s. The spin alignment technique (20) circumvents transverse relaxation and is limited by Tx only, thus ultraslow motions become accessible of experiment. 

Fig. 13. Calculated 2H solid echo spectra for log-Gaussian distributions of correlation times of different widths. Note the differences of the line shapes for fully relaxed and partially relaxed spectra. The centre of the distribution of correlation times is given as a normalized exchange rate a0 = 1/3tc. For deuterons in aliphatic C—H bonds the conversion factor is approximately 4.10s sec-1...

Fig. 14.2H NMR spectra of LPE, isothermally crystallized from the melt at 396 K (Mw as 100000, Mw/Mn as 10, Merck, Darmstadt) at 55 MHz obtained from a complex FT of the solid echo for various temperatures...

Fig. 15. 2H FT NMR spectra of the mobile amorphous fraction of LPE for various temperatures. The total magnetization was saturated first by a series of 90° pulses and then the solid echo was created after a waiting period r0 T, (amorphous) ranging from 25 to 200 ms...

Smectic liquid crystalline polymer 51 Solid echo 32 ---spectra 37, 39... 

The slice selection procedure can be combined with a number of pulse sequences to spatially resolve NMR parameters or to contrast the profiles with a variety of filters. The most commonly used acquisition schemes implemented to sample echo train decays are the CPMG [(jt/2)0—(Jt)90] or a multi-solid echo sequence [(jt/ 2)0-(jt/2)9o]. In these instances, the complete echo train can be fitted to determine... 

Fig. 2.4.7 Profile of a PE gasoline tank wall. T-, and T2 were measured across the sample, and uniform values of about 90 ms and 300 ps, respectively, were obtained, except for EVOH where T2 drops to 30 [is. The profile amplitude is the coefficient at zero frequency of the FT of the signal obtained as the direct addition of the first 8 echoes generated with a solid-echo train.

Figure 2.4.11 Profiles of paintings where different layers can clearly be resolved. A solid-echo train was used with tE = 40 (is, and the first 4 echoes were used to calculate the amplitude. The profiles were reconstructed by moving the sensor in steps of 50 pm in the paint and canvas regions, and 100 pm in the gypsum and wood layers. Using 128 scans per point and a repetition time of 100 ms the total acquisition time per point was 16 s. Profiles of paint based on tempera ( ) and oil ( ) binders show appreciable difference.

NMR relaxometry Free induction decay (T2 ) or solid echo Spin echo decay (T2) Magnetization recovery curve (7)) Eads (1998)... 

Users of any NMR instrument are well aware of the extensive employment of what is known as pulse sequences. The roots of the term go back to the early days of pulsed NMR when multiple, precisely spaced RF excitation pulses had been invented (17,98-110) and employed to overcome instrumental imperfections such as magnetic field inhomogeneity (Hahn echo) or receiver dead time (solid echo), monitor relaxation phenomena (saturationrrecovery, inversion recovery, CPMG), excite and/or isolate specific components of NMR signals (stimulated echo, quadrupole echo), etc. Later on, employment of pulse sequences of increasing complexity, combined with the so-called phase-cycling technique, has revolutionized FT-NMR spectroscopy, a field where hundreds of useful excitation and detection sequences (111,112) are at present routinely used to acquire qualitatively distinct ID, 2D, and 3D NMR... 

Figure 10.15 The decay of the transverse magnetisation (points) for ethylene-octene copolymer at different temperatures [136]. The decay was measured using the solid-echo pulse sequence. The solid lines represent the result of a least-squares adjustment of the decay using a linear combination of Weibull and exponential functions. The dotted lines represent the relaxation component with a long decay time. In the experiments the sample was heated from room temperature to 343 K (70 °C)...

Figure 14.3 Deuterium solid-echo spectra of unfilled (a) and filled (b) polyfdimethylsiloxane] networks at 305 K with and without mechanical stress as given by the parameter X [23]. This example demonstrates the sensitivity of the NMR lineshape and thus of the spin interactions to internal and external conditions...

Figure 7. Typical pulse sequences applied for obtaining an 2H NMR solid echo (top) and a stimulated echo (bottom).

Figure 38. (left) Solid-echo 2H NMR spectra of glycerol-/ (7 = 189 K) [305]. A collapse of the solid-state spectrum is observed upon heating the corresponding time constants of the a-process are indicated, (right) Hahn-echo 31P NMR spectra of w-tricresyl phosphate (m-TCP, Tg = 210K) determined by the anisotropic chemical shift interaction [324]. 

While cooling, when the limit xa = 1 /, (cf. Eq. 15) is reached, the central Lorentzian NMR line, which is characteristic of a liquid (t-,8, solid-state spectrum, in the case of 2H NMR the Pake spectrum. The breadth of the solid-state spectra makes it difficult to measure the corresponding (short) free induction decay (FID), so that it is necessary to use echo-techniques (cf. Section II.D.2). Figure 38 (left) shows solid-echo 2H NMR spectra of glycerol-. The crossover from a Lorentzian line to the Pake spectrum is observed some 20% above Tg. Below Tg the spectrum is independent of temperature. In Fig. 37 (right), the corresponding 31P NMR spectra of m-tricresyl phosphate (m-TCP) are displayed. The characteristic spectral shape is now determined by the anisotropic chemical... 

It has been usually argued that the NMR fine-shape reaches the solid-state, rigid-lattice limit at temperatures around Tg (cf. Fig. 38), and consequently no dynamical effects are expected when measuring solid-echo spectra. While such... 

Figure 54. 2H NMR spectra for the type A glasses glycerol-, polystyrene-, and picoline-rfy at T/Ts ss 0.85. Results for solid-echo delays tp = 20, 100, and 200 ps are shown. In the case of picoline-(i7, the subspectrum of the methyl group was removed. (From Ref. 306.)...

Figure 55. 2H NMR spectra for type B glasses at 777), ss 0.85. Results for the neat systems lolucncw/,. polybinadiene-7,. and decaline-7,s are shown together with those for the binary mixtures 45% chlorobenzene-<7 in decaline and 55% decalincw/, s in chlorobenzene. Solid-echo delays...

Figure 56. (a) Results from random walk simulations for different solid-echo delay times 7, the... 

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