Spin-lattice relaxation glass

Fig. 19. Experimental spin alignment decay curves of chain deuterated PS-d3 at temperatures above and below the glass transition for various evolution times t,. Note the different timescales of t2 at the different temperatures. The straight lines indicate the decays of the plateau values on the timescale of the spin-lattice relaxation time T,. Sample characterization Mw = 141000, Mw/Mn = 1.13, atactic...

Fig. 1. Magnetic field dependences of the proton spin-lattice relaxation time of water in Bioran B30 and Vycor glasses at temperatures above 27°C and below the temperature where the non-surface water freezes ( —25°C and —35°C). The solid lines represent the power law in the Larmor frequency with an exponent of 0.67 (34).

Fig. 5. The spin-lattice relaxation rates of methylcyclohexane protons as a function of the pore radius reciprocal in porous sol-gel glasses at 300 K and a resonance frequency of 180 MHz (49).

Fig. 9. Magnetic field dependence of spin-lattice relaxation rates of acetone embedded in packed samples of calibrated porous glass beads with pore diameter of 75 A for several temperatures. The solid lines are best fits to the theory (66).

An interesting application in porous silica glass employs deuterium spin-lattice relaxation rates in selectively deuterated pyridine (50). The pore-size dependence shown in Fig. 20 is linear in the reciprocal of the pore radius for both the para and ortho positions, but the significant difference in the relaxation at these two positions precludes analysis by an isotropic... 

Fig. 21. Semi-logarithmic plots of the surface spin-lattice relaxation rates for ortho and para positions of pyridine as a function of the reciprocal temperature in porous sol-gel silica glasses. The surface rates are shown on the top and the rates in bulk pyridine are shown at the bottom 50).

The procedures for recording spectra of heteronuclei often differ considerably from those for H and (which would today be considered routine ) since it is necessary, even for routine measurements, to adjust the experimental conditions to suit the special properties of the nuclei to be observed. For example, the spin-lattice relaxation times for some nuclides, such as N, are very long, whereas for others (especially those with an electric quadrupole moment, such as N) they are very short. Also, the spectra observed for some nuclides contain interfering signals caused by other materials present, for example the glass of the sample tube ("B, Si), the spectrometer probe unit ( Al) or the transmitter/receiver coil. For many nuclides the sample temperature and its constancy are important factors for example, quadrupolar nuclides such as O give narrower signals when the temperature is increased. 

Figure 16-10. Spin-lattice relaxation rate (1/7, ) as a function of the reciprocal temperature for /7-spodumene (Li20 A1203 4Si02) and glass...

Because of the 100% isotopoic abundance of 27A1 and its very short spin-lattice relaxation time, even traces of aluminum are often detectable by MAS NMR. For example, Thomas et al. (156) were able to show that aluminum present as an impurity in soda glass is four-coordinated. However, quantitative determination of Al concentration in the sample is only possible when the quadrupolar effects are not so large as to affect significantly the apparent intensity of the 27A1 signal. 

Fyfe et al. (384) obtained quantitatively reliable 29Si NMR spectra of silica gel and high-surface area glass beads and of derivatized surfaces without resorting to cross-polarization. Spin-lattice relaxation times of these systems are of the order of 10-30 sec and spectra of adequate quality may be obtained at high fields. 

Key Words Dipolar glasses, Ferroelectric relaxors, Conducting polymers, NMR line shape, Disorder, Local polarization related to the line shape, Symmetric/asymmetric quadrupole-perturbed NMR, H-bonded systems, Spin-lattice relaxation, Edwards-Anderson order parameter, Dimensionality of conduction, Proton, Deuteron tunnelling. 

The dynamic window of a given NMR technique is in many cases rather narrow, but combining several techniques allows one to almost completely cover the glass transition time scale. Figure 6 shows time windows of the major NMR techniques, as applied to the study of molecular reorientation dynamics, in the most often utilized case of the 2H nucleus. Two important reference frequencies exist The Larmor frequency determines the sensitivity of spin-lattice relaxation experiments, while the coupling constant 8q determines the time window of line-shape experiments. 2H NMR, as well as 31P and 13C NMR, in most cases determines single-particle reorientational dynamics. This is an important difference from DS and LS, which access collective molecular properties. 

We first discuss the 2H NMR spin-lattice relaxation results of molecular glass formers at T< Tg. In Fig. 53, we present the mean relaxation time (7)), equal to the integral of the corresponding (nonexponential) relaxation function, for several glasses including a polymer (polybutadiene-d6). The temperature-... 

Figure 53. Mean 2H spin-lattice relaxation times for type A and type B glass formers as a function of reduced reciprocal temperature in a double logarithmic plot. (Compiled from Refs. 177, 178, 323, 422, and 423.)...

Various 2H, 13C and 31P NMR techniques were used to follow the slowing down of molecular dynamics during the glass transition.3 In particular, 2H NMR proved very powerful since solely molecular reorientation is probed and isotopic labeling is easily achieved. Fig. 7 shows the correlation time windows of the major 2H NMR techniques. Two reference frequencies exist The Larmor frequency col determining the sensitivity of the spin-lattice relaxation and the coupling constant 8q fixing the time window of line-shape experiments. 

Finally, we present the mean spin-lattice relaxation times (T ) of several glass formers as a function of the reduced reciprocal temperature TgjT in Fig. 13.100,101 Since the relaxation becomes non-exponential near Ts, the time constant (T ) as given by the integral over the normalized spin-lattice relaxation function is plotted. Well above Tg, a minimum associated with the a-process is observed for both type A and B glass formers. When approaching Tg, the relaxation of type A glass... 

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