Relaxation time measurements examples

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. 

Molecular Motions and Dynamic Structures. Molecular motions are of quite general occurrence in the solid state for molecules of high symmetry (22,23). If the motion does not introduce disorder into the crystal lattice (as, for example, the in-plane reorientation of benzene which occurs by 60° jumps between equivalent sites) it is not detected by diffraction measurements which will find a seemingly static lattice. Such molecular motions may be detected by wide-line proton NMR spectroscopy and quantified by relaxation-time measurements which yield activation barriers for the reorientation process. In addition, in some cases, the molecular reorientation may be coupled with a chemical exchange process as, for example, in the case of many fluxional organometallic molecules. ... 

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. 

The thyroid hormones, exemplified by thyroxine (5), provide an example of the use of both line-shape analysis and NMR relaxation time measurements, to give an insight into the internal flexibility, and perhaps the mode of action, of pharmaceutically important molecules (52,53,58). The thyroid hormones act by binding to a nuclear receptor and appear to control receptor function by inducing a conformational change that directs the alignment of functionally critical secondary-structure elements of the receptor (59). Synthetic thyrox-... 

NMR is unique in that it can provide detailed and specific information on molecular dynamics in addition to structural information. The use of relaxation time measurements allows the relative mobility of individual atomic positions within a macromolecule to be determined. The d3mamic information obtained includes not only the rates or frequencies of internal motions but also their amplitudes. Such amplitudes are often expressed by order parameters. Not surprisingly, it is observed in many cases that the termini of proteins are more flexible than internal regions. More interestingly, NMR has provided a number of examples where internal loops in proteins have been shown to have dynamics that may be associated with their function. A good example of this is HIV protease, where NMR studies have identified reduced-order parameters in the flap region of the molecule that may reflect flexibility to allow entry of substrates or inhibitors into the active site. 

The block diagram in the last section shows the spectrometer with the CAMAC modules identified. Several different experiments requiring different pulse sequences can be performed easily with such a system. A moderately complicated example is a spin-lattice relaxation time measurement in the time domain on a poly crystalline intermetallic sample containing 1=3/2 nuclei. Since a non-cubic 1=3/2 system has unequally spaced levels, special techniques must be used for relaxation time measurements (see III.C.3.) and we adopt the procedure of Avogadro and Rigamonti (1973) to initialize the populations before the magnetization recovery. 

NOEs are most useful in this area. For example, dithiazine 8 gives rise to NOE enhancements that are consistent with the orientation of the phenyl ring predicted from DFT calculations (Section 9.10.2) <2003SL1731>. Relaxation time measurements H-Ti confirmed the existence of interactions... 

The whole discussion of polymer adsorption so far makes the fundamental assumption that the layer is at thermodynamic equilibrium. The relaxation times measured experimentally for polymer adsorption are very long and this equilibrium hypothesis is in many cases not satisfied [29]. The most striking example is the study of desorption if an adsorbed polymer layer is placed in contact with pure solvent, even after very long times (days) only a small fraction of the chains desorb (roughly 10%) polymer adsorption is thus mostly irreversible. A kinetic theory of polymer adsorption would thus be necessary. A few attempts have been made in this direction but the existing models remain rather rough [30,31]. 

SSNMR spectroscopy is unparalleled with respect to the diversity of techniques designed specifically to probe structure and dynamics with site selectivity, not to mention examine phase/component miscibility. Beyond the first-pass analysis of ID spectra to differentiate potential salt and co-crystal forms from those of the individual components, both relaxometry and 2D correlation spectroscopy have been increasingly used to characterize salts and co-crystals. H Ti (or Tih) relaxation time measurements can provide direct evidence of phase heterogeneity (to confirm the presence of phase impurities and/or rule out salt/ co-crystal formation) based on the observation of multiple relaxation times characteristic of different component phases in a given material. rip(or Tipn) relaxation, which like Tih relaxation, is strongly affected by efficient spin diffusion over the entire proton reservoir, is also frequently applied to study mixtures, and in favorable cases, both Tih and TipH measurements can allow domain sizes (hundreds of angstroms in the case of Tih) to be calculated. In contrast to relaxometry, which provides direct evidence of component phase separation, dipolar correlation techniques, for example, CP-HETCOR... 

Creep Test. In a creep test, a constant shear stress is apphed to a sample for a certain period of time and the resulting deformation is monitored. This type of test is used to characterize viscoelastic properties of the paste. Creep tests can also be used to measure paste viscosity at very low shear rates (approximately 10 to 10" s ). In a strain test, a step shear rate is applied to the sample and the resulting stress relaxation is measured. Examples of creep tests for thick film pastes are shown in Fig. 8.82. 

Si MAS experiments have also been used to determine the effects of chemical modification of zeolites, for example by heat treatment, and quite substantial spectral changes can occur. In this connection relaxation time measurements can be... 

For example, if the molecular structure of one or both members of the RP is unknown, the hyperfine coupling constants and -factors can be measured from the spectrum and used to characterize them, in a fashion similar to steady-state EPR. Sometimes there is a marked difference in spin relaxation times between two radicals, and this can be measured by collecting the time dependence of the CIDEP signal and fitting it to a kinetic model using modified Bloch equations [64]. 

Figure B2.5.2. Schematic relaxation kinetics in a J-jump experiment, c measures the progress of the reaction, for example the concentration of a reaction product as a fiinction of time t (abscissa with a logaritlnnic time scale). The reaction starts at (q. (a) Simple relaxation kinetics with a single relaxation time, (b) Complex reaction mechanism with several relaxation times x.. The different relaxation times x. are given by the turning points of e as a fiinction of ln((). Adapted from [110].

Condensed phase vibrational or vibronic lineshapes (vibronic transitions create vibrational excitations of electronic excited states) rarely provide infonnation about VER (see example C3.5.6.4). Experimental measurements of VER need much more than just the vibrational spectmm. The earliest VER measurements in condensed phases were ultrasonic attenuation studies of liquids [15], which provided an overall relaxation time for slowly (>10 ns) relaxing small molecule liquids. 

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