Relaxation time measurements and

Maryott A. A., Farrar T. C., Malmberg M. S. 35C1 and 19F NMR spin-lattice relaxation time measurements and rotational diffusion in liquid CIO3F. J. Chem. Phys. 54, 64-71 (1971). 

The solvent mobility in atactic polystyrene-toluene solutions has been studied as a function of temperature using NMR. The local reorientation of the solvent was studied using deuterium NMR relaxation times on the deuterated solvent. Longer range motions were also probed using the pulsed-gradient spin-echo NMR method for the measurement of diffusion coefficients on the protonated solvent. The measurements were taken above and below the gel transition temperatures reported by Tan et al. (Macromolecules, 1983. 16, 28). It was found that both the relaxation time measurements and the diffusion coefficients of the solvent varied smoothly through the reported transition temperature. Consequently, it appears that in this system, the solvent dynamics are unaffected by gel formation. This result is similar to that found in other chemically crossed-linked systems. 

Th4Hi5. Three kinds of information are obtained from the samples of Th4H15 information on rigid lattice structure from free induction decays, on proton motion from relaxation time measurements, and on internal fields from peak locations that were found using the multiple pulse techniques. Figure 1... 

In a study combining 2H relaxation-time measurements and use of paramagnetic lanthanide shift reagents, the ratio of the relaxation times of axial and equatorial deuterons in 2,2,6,6-tetradeuterio-4-t-butylcyclohexanone [20]... 

Elastomer-filler interactions were the subject of many intensive investigations. Kaufmann and co-workers [17] investigated carbon-black-filled EPDM by nuclear spin relaxation time measurements and found three distinct regions in the material. These regions are characterised by different mobility of the elastomer chains a mobile region in which the polymer chains have no interaction with the filler particles, loosely bound rubber in an outer shell around the carbon black particles and an inner shell of tightly bound elastomer chain with limited mobility. 

However, the NMR properties of solid-phase methane are very complex, due to subtle effects associated with the permutation symmetry of the nuclear spin set and molecular rotational tunnelling.55 Nuclear spin states ltotai = 0 (irred. repr. E), 1 (T) and 2 (A) are observed. The situation is made more complicated since, as the solids are cooled and the individual molecules go from rotation to oscillation, several crystal phases become available, and slow transitions between them take place. Much work has been done in the last century on this problem, including use of deuterated versions of methane for example see Refs. 56-59. Much detail has emerged from NMR lineshape analysis and relaxation time measurements, and kinetic studies. For example, the second moment of the 13C resonance is found to be caused by intermolecular proton-carbon spin-spin interaction.60 Thus proton inequivalence within the methane molecules is created. 

Muller and coworkers have recently reported the molecular behavior of 1,3,5-trioxane in a cyclophosphazene inclusion compound using H-2 NMR [68]. The experimental data were obtained by variable-temperature line shape analysis, spin-spin and spin-lattice relaxation time measurements and by 2D exchange between 30 and 370 K. At room temperature, highly mobile trioxane guests were observed. They undergo various overall and conformational motions which give rise to substantial orientational disorder within the hexagonal cyclophosphazene channels. 

We have utilized in the last two sections the fact that the bulk diffusion coefficient D is related to NMR relaxation times through the magnetic field gradient. The precision in the determination of D is directly related to the precision of the relaxation time measurement and of the gradient G. Therefore, it is important to determine G as accurately as possible. Very often, this is the weak link in the experiment, a fact which is not always recognized. 

Jayakody et al. investigated the dynamical processes and mass transport of phosphoric acid-doped meto-polybenzimidazole (m-PBl) by spin—lattice Tj and spin—spin T2 relaxation time measurements and by PFG NMR measurement. It was concluded that the high proton conductivity is correlated with rapid proton self-diffusion. The P NMR study not only revealed the presence of both phosphoric acid and dimeric pyrophosphoric acid but also indicated strong interaction between the phosphate groups and the m-PBI... 

Relaxation and spectral studies involving water and other substances sorbed on carbon materials Studies of sorption of deuterated water and other H-containing substances on porous carbons, including relaxation time measurements and recording of H NMR spectra... 

In a further study [63], inversion recovery spin-relaxation time measurements and computer fitting of overlapping spectra regions were used to identify additional peaks in vulcanized natural rubber cured with 1, 3, and 5% sulfur for different time intervals. Those overlapping crosslinked carbons with different T times showed different peak intensities which could be determined by computer fitting of the peaks. Two new peaks at 37.8 ppm and 25.5 were identified. 

Other properties of association colloids that have been studied include calorimetric measurements of the heat of micelle formation (about 6 kcal/mol for a nonionic species, see Ref. 188) and the effect of high pressure (which decreases the aggregation number [189], but may raise the CMC [190]). Fast relaxation methods (rapid flow mixing, pressure-jump, temperature-jump) tend to reveal two relaxation times t and f2, the interpretation of which has been subject to much disagreement—see Ref. 191. A fast process of fi - 1 msec may represent the rate of addition to or dissociation from a micelle of individual monomer units, and a slow process of ti < 100 msec may represent the rate of total dissociation of a micelle (192 see also Refs. 193-195). 

Sohaublin S, FIdhener A and Ernst R R 1974 Fourier speotrosoopy of non-equilibrium states. Applioation to CIDNP, Overhauser experiments and relaxation time measurements J. Magn. Reson. 13 196-216... 

The Fourier transform of a pure Lorentzian line shape, such as the function equation (4-60b), is a simple exponential function of time, the rate constant being l/Tj. This is the basis of relaxation time measurements by pulse NMR. There is one more critical piece of information, which is that in the NMR spectrometer only magnetization in the xy plane is detected. Experimental design for both Ti and T2 measurements must accommodate to this requirement. 

Turning from chemical exchange to nuclear relaxation time measurements, the field of NMR offers many good examples of chemical information from T, measurements. Recall from Fig. 4-7 that Ti is reciprocally related to Tc, the correlation time, for high-frequency relaxation modes. For small- to medium-size molecules in the liquid phase, T, lies to the left side of the minimum in Fig. 4-7. A larger value of T, is, therefore, associated with a smaller Tc, hence, with a more rapid rate of molecular motion. It is possible to measure Ti for individual carbon atoms in a molecule, and such results provide detailed information on the local motion of atoms or groups of atoms. Levy and Nelson " have reviewed these observations. A few examples are shown here. T, values (in seconds) are noted for individual carbon atoms. 

Fig. 7. A C-13 relaxation time measurement of solid state wetted cellulose acetate (6% by weight water) using the inversion recovery (IR) method at 50.1 MHz and spinning at 3.2 kHz at the magic angle (54.7 deg) with strong proton decoupling during the aquisition time (136.3 ms), (upper part of the Figure). Tau represents the intervals between the 180 deg (12.2 us) inverting and 90 deg (6.1 us) measuring pulse. 2200 scans were collected and the pulse delay time was 10 s, Cf. Table 3 and Ref.281...

Here p is the solution density, v the sound velocity, ctp the coefficient of thermal expansion, Cp the specific heat, and F the concentration dependence of the equilibrium, r = [LS] -f- [HS] . The measurement of ultrasonic relaxation thus enables the determination of both the relaxation time x and the... 

NMR signals are highly sensitive to the unusual behavior of pore fluids because of the characteristic effect of pore confinement on surface adsorption and molecular motion. Increased surface adsorption leads to modifications of the spin-lattice (T,) and spin-spin (T2) relaxation times, enhances NMR signal intensities and produces distinct chemical shifts for gaseous versus adsorbed phases [17-22]. Changes in molecular motions due to molecular collision frequencies and altered adsorbate residence times again modify the relaxation times [26], and also result in a time-dependence of the NMR measured molecular diffusion coefficient [26-27]. 

The measured NMR signal amplitude is directly proportional to the mass of adsorbate present, and the NMR signal versus pressure (measured at a fixed temperature) is then equivalent to the adsorption isotherm (mass of adsorbate versus pressure) [24-25]. As in conventional BET measurements, this assumes that the proportion of fluid in the adsorbed phase is significantly higher than the gaseous phase. It is therefore possible to correlate each relaxation time measurement with the calculated number of molecular layers of adsorbate, N (where N = 1 is monolayer coverage), also known as fractional surface coverage. 

The response from the water and hydrocarbon can be distinguished by measuring the distributions of the diffusion coefficients simultaneously with the distributions of the relaxation times. The resulting distributions are displayed on a two-dimensional diffusion coefficient-relaxation time map and the distributions for... 

The measurement of viscosity is important for many food products as the flow properties of the material relate directly to how the product will perform or be perceived by the consumer. Measurements of fluid viscosity were based on a correlation between relaxation times and fluid viscosity. The dependence of relaxation times on fluid viscosity was predicted and demonstrated in the late 1940 s [29]. This type of correlation has been found to hold for a large number of simple fluid foods including molten hard candies, concentrated coffee and concentrated milk. Shown in Figure 4.7.6 are the relaxation times measured at 10 MHz for solutions of rehydrated instant coffee compared with measured Newtonian viscosities of the solution. The correlations and the measurement provide an accurate estimate of viscosity at a specific shear rate. 

Several commercial companies now offer process compatible NMR systems. These systems are either low resolution based on relaxation time measurements or high resolution Fourier Transform spectral measurements. The low resolution systems are manufactured by Process Control Technologies (www.pctnmr.com) and Progression, Inc. (www.progression-systems.com). Progression s systems... 

Chemical engineers should be aware of the existence of relaxation techniques for studies of very fast reactions. However, since relaxation time measurements call for sophisticated experimental equipment and techniques, they are seldom made outside of basic research laboratories. 

A more complex but faster and more sensitive approach is polarization modulation (PM) IRLD. For such experiments, a photoelastic modulator is used to modulate the polarization state of the incident radiation at about 100 kHz. The detected signal is the sum of the low-frequency intensity modulation with a high-frequency modulation that depends on the orientation of the sample. After appropriate signal filtering, demodulation, and calibration [41], a dichroic difference spectrum can be directly obtained in a single scan. This improves the time resolution to 400 ms, prevents artifacts due to relaxation between measurements, and improves sensitivity for weakly oriented samples. However, structural information can be lost since individual polarized spectra are not recorded. Pezolet and coworkers have used this approach to study the deformation and relaxation in various homopolymers, copolymers, and polymer blends [15,42,43]. For instance, Figure 7 shows the relaxation curves determined in situ for miscible blends of PS and PVME [42]. The (P2) values were determined... 

The aim of this work was to find out how to get more information about stereochemistry and molecular motion of polymer methyl- and methyl-phenyl-siloxanes by measuring longitudinal relaxation times, Tj, and nuclear Overhauser effects, NOE, of the individual building blocks. 

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