Nuclear relaxation times, measurement

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. 

From nuclear relaxation time measurements, Alexandre and Rigny (3) were able to determine the chemical shift difference between the equatorial and the 2 axial fluorine atoms as 50 2 ppm. They also obtained a value of 195 Hz for the mean 01—F coupling constant and values for the exchange time between the fluorine atoms. 

Meiboom S and Gill D 1958 Modified spin-echo method for measuring nuclear relaxation times Rev. Sci. Instrum. 29 688-91... 

As the TieS lengthen and l/Tie (s ) approaches the size of the electron—nuclear interaction, considerable NMR line broadening can occur, and it may not be possible to acquire high-resolution NMR spectra under these conditions. The effect of Tie on the nuclear relaxation times is discussed in more detail in ref 22. Large hyperfine constants are observed (of many MHz) when the nuclear and electronic spins are on the same atom. For example, a hyperfine constant A/h of —324 MHz was measured by electron... 

When the CM complex is fully formed, [M] = 0 and [CM] = Cm, therefore, from Eq. (4.40), e = So- w thus defined as the enhancement factor measured in a solution where all the metal is complexed. Since usually q < p,eo should be smaller than unity if the intrinsic nuclear relaxation times are the same in the metal complex and in the aquaion. However, as often T cm < T m owing to a longer correlation time xc in the complex (Chapter 3), q can be larger than unity. This is particularly true when C is a macromolecule (e.g. a protein) and M is a metal ion with long electronic relaxation times. 

Selective T values are generally measured with the 180 r 90 pulse sequence using a soft 180° pulse. When the nuclear relaxation times are short, it may become impossible to invert the magnetization and at the same time maintain the required selectivity with the soft pulse. When such difficulties arise, a good compromise is to use a soft pulse that can at least saturate the signal. Then, the sequence becomes equivalent to a 90 r 90 pulse sequence. 

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. 

Relaxation time measurements have long been used to characterize molecular motions in solids. All nuclear spin relaxation processes are mediated by fluctuating nuclear spin interactions, with the fluctuations (generally) arising... 

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. 

B. D. Sykes, W. E. Hull, and G.H. Snyder, Biophys. /, 21, 137 (1978). Experimental Evidence for the Role of Cross-relaxation in Proton Nuclear Magnetic Resonance Spin Lattice Relaxation Time Measurements in Proteins. 

Let us finally also mention here the results of proton nuclear relaxation time 7 measurements on TEA(TCNQ)2 [53,54], From the frequency dependence of 7, it is deduced that the spin motion is a nearly one-dimensional diffusion. Moreover, the temperature dependence of the on-chain spin diffusion rate shows a quite remarkable feature while it is thermally activated below 220 K, it suddenly becomes temperature independent above 220 K. 

Meiboom S, Gill D. Modified spin-echo method for measuring nuclear relaxation times. Rev. Scient. Inst. 1958 29 688-691. Millet O, et al. The static magnetic field dependence of chemical exchange linebroadening defines the NMR chemical shift time scale. J. Am. Chem. Soc. 2000 122 2867-2877. 

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-... 

In the past, dipolar coupling has probably been the least used nuclear spin interaction as far as molecular motions studies are concerned, except in work involving relaxation time measurements (where dipolar coupling is frequently a major, if not dominant relaxation mechanism). However, in the last few years there have been a number of studies, which utilize dipolar coupling, particularly for studying motions in the fast limit. 

We first consider the A contribution. Equation 1, and an explanation in terms of a two-site model i.e., a model in which a water molecule exchanges between solution and sites (or class of sites) on or near a protein molecule such that at least one direction fixed in the water molecule is constrained to move rigidly with the protein molecule. In the simplest case, a water molecule attaches rigidly to the protein, moves with it for a while, and then leaves. In a somewhat more complex case, the attachment may be less rigid so that the water molecule is free to rotate about an axis fixed with respect to the protein. Additionally, a situation in which water molecules partially orient in the electric fields near the protein surface because of their electric dipole moments would also be a two-site model. Characteristic of a two site-model is that a time Tj, or a distribution of such times, can be defined that measures the mean lifetime of a water molecule in the protein-associated state. Moreover, such a time is in principle a measurable quantity, and its value must satisfy two criteria it must be at least comparable to if not longer than Tj, otherwise the nuclei of the bound water molecules could not sense the rotational motion of the protein molecules and it must be comparable to or shorter than the nuclear relaxation time of a bound water molecule, else it could not communi-... 

Pearson, H., Gust, D., Armitage, I. M., Huber, H., Roberts, J. D., Stark, R. E., Void, R. R., and Void, R. L. (1975). Proc. Nat. Acad. Sci. U.S.A. 72, 1599. Nuclear Magnetic Resonance Spectroscopy Reinvestigation of Carbon-13 Spin-Lattice Relaxation Time Measurements of Amino Acids. 

NMR spectroscopists are also interested in nuclear spin relaxation times. The relaxation time measures the time required for an excited nucleus to return to the ground state. Two types of relaxation times are involved spin-lattice relaxation time Ti, the time constant for thermal equilibrium between the nuclei and crystal lattice, and spin-spin relaxation time Tz, the time constant for thermal equilibrium between nuclei themselves. Information on molecular dynamics can be obtained from these relaxation times. Generally, T Tz for low-viscosity liquids and T Tz for solids. A combination of information in molecular dynamics (from relaxation times), molecular structure (from spin-spin interaction), molecular identification (from resonance frequency and chemical shift), and spin density (from signal intensity) make the NMR an extremely versatile tool. 

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