Relaxation parameters

The three relaxation parameters Tj, Tj and NOE all depend on the same distances -e.g., between nuclei or nuclei and electrons - and on the same time constants of 

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Linear response theory is an example of a microscopic approach to the foundations of non-equilibrium thennodynamics. It requires knowledge of tire Hamiltonian for the underlying microscopic description. In principle, it produces explicit fomuilae for the relaxation parameters that make up the Onsager coefficients. In reality, these expressions are extremely difficult to evaluate and approximation methods are necessary. Nevertheless, they provide a deeper insight into the physics. 

Small molecules in low viscosity solutions have, typically, rotational correlation times of a few tens of picoseconds, which means that the extreme narrowing conditions usually prevail. As a consequence, the interpretation of certain relaxation parameters, such as carbon-13 and NOE for proton-bearing carbons, is very simple. Basically, tlie DCC for a directly bonded CH pair can be assumed to be known and the experiments yield a value of the correlation time, t. One interesting application of the measurement of is to follow its variation with the site in the molecule (motional anisotropy), with temperature (the correlation... 

The following diseussion of the time dependenee of the EPR response in a TREPR experiment is based on the assumption that the transient paramagnetie speeies is long lived with respeet to the spin relaxation parameters. 

Wang wa used. The total energies were converged to 0.1 mRy/atom. The number of k points was chosen so as to correspond to 120 points in the irreducible wedge of the Brillouin zone of the fee structure, the energy cut-off was 16 Ry. We have tested various values of these parameters and it turned out that the present choice is sufficient to achieve desired uniform accuracy for all structures. For each structure the total energy was minimized with respect to the lattice constant. These interaction parameters correspond to the locally relaxed parameters and are denoted by superscript CW. 

Since NMR relaxation in proteins is determined by dynamics on the picosecond to nanosecond time scale, experimental NMR relaxation parameters can provide important information concerning picosecond motions. Time correlation func-... 

Interproton distances of 0-ceIIobiose (see Ref. 49) error 0.01 A. Interproton distances of 1,6-anhydro- -D-glucopyranose (see Ref. 49) error 0.01 A. Interproton distances of -cellobiose octaacetate (see Ref. 49) error 0.05 A. Interproton distances of 2,3,4-tri-0-acetyl-l,6-anhydro- -D-glucopyranose (see Ref. 49) error 0.05 A. Error calculations based on the errors of the measured quantities in Eqs. 18 and 21. Interproton distances calculated from the relaxation parameters of the methylene protons. 

R. L. Kleinberg 1996, (Utility of NMR T2 distributions, connections with capillary pressure, day effect, and determination of the surface relaxivity parameter n >). Magn. Reson. Imaging 14 (7/8), 761—767. 

An advantage of NMR spectroscopy is the analysis of protein dynamics. Measurement and analysis of the relaxation parameters R1 R2, and the 15N NOE of 15N-labeled proteins leads to an order parameter (S2) that can describe the relative mobility of the backbone of the protein. Both collagenase-1 and stromelysin-1 have been studied either as inhibited complexes or the free protein [19, 52], Stromleysin-1 was studied with inhibitors binding to prime or nonprime subsites. Presence or absence of inhibitors in the nonprime sites had minor effects on the highly ordered structure of residues in these subsites, which are in contact with the... 

Isochronal temperature scans reflect or contain information about the relaxation parameters. It is apparent (Figure 1) that the relaxed and unrelaxed moduli, Ep E(j are approximated by the high and low... 

Figure 3 Time scale of motions detected by a variety of NMR measurements including relaxation parameters, and analyses of line shape, SLF and exchanges.

Nevertheless, the T1 and NOE values are found to be unchanged from the solution to the gel of water content 75% and 53%. As discussed already in Section 2.1, it is very difficult to analyse such relaxation parameters in terms of a single correlation time. The calculated correlation times are found to give consistent values among those obtained from the Ti, T2, and NOE values with the width parameter of p = 18 (PVP solution) and p = 16 (PVP gel) and b = 1000. As the degree of cross-linking is increased, a discrepancy in the correlation times still occurs (a factor of 3 at 75%) but is much improved by this treatment. 

The coupling term, traditionally denoted by cr B (which has however nothing to do with the screening coefficient of Section 2.2), is the so-called cross-relaxation rate and is a relaxation parameters which depends exclusively on the dipolar interaction between nuclei A and B, contrary to auto-relaxation rates which are compounds of several contributions. For instance, if A is a carbon-13, the auto-relaxation rate can always be written as... 

As seen from the above theoretical developments, accessing geometrical (and stereochemical) information implies at least an estimation of the dynamical part of the various relaxation parameters. The latter is represented by spectral densities which rest on the calculation of the Fourier transform of auto- or cross-correlation functions. These calculations require necessarily a model for describing molecular reorientation... 

It can be noticed that at least two independent relaxation parameters in the symmetric top case, and three in the case of fully anisotropic diffusion rotation are necessary for deriving the rotation-diffusion coefficients, provided that the relevant structural parameters are known and that the orientation of the rotational diffusion tensor has been deduced from symmetry considerations or from the inertial tensor. 

The 13C NMR sensitivity can sometimes be a problem, but for the kind of samples studied here the effective concentration of monomer units is several molar which does not place excessive demands on present Fourier transform NMR spectrometers. In addition to the sensitivity of the chemical shift to structure (9), the relaxation of protonated carbons is dominated by dipole-dipole interaction with the attached proton (9). The dependence of the relaxation parameters T, or spin-lattice, and Tor spin-spin, on isotropic motional correlation time for a C-H unit is shown schematically in Figure 1. The T1 can be determined by standard pulse techniques (9), while the linewidth at half-height is often related to the T2. Another parameter which is related to the correlation time is the nuclear Overhauser enhancement factor, q. The value of this factor for 13C coupled to protons, varies from about 2 at short correlation times to 0.1 at long correlation... 

Electronic relaxation is a crucial and difficult issue in the analysis of proton relaxivity data. The difficulty resides, on the one hand, in the lack of a theory valid in all real conditions, and on the other hand in the technical problems of independent and direct determination of electronic relaxation parameters. Proton relaxivity is essentially influenced by the longitudinal electron spin relaxation time, Tle, of Gd111. This decay is too fast to be assessed by commonly available techniques, though very recently Tlc values have been directly measured.74 Nevertheless,... 

As shown in Section IV.D, it is possible, within the adiabatic approximation, to account for the general situation where the relaxation parameters of the fast mode y0 and of the bending mode y are not supposed to be equal. 

Study Relaxation parameter Method for determination of WHC Na Correlation coefficient... 

Finally, NMR relaxometry has also been used in the determination of composition of meat and meat products. Correlations between relaxation parameters and fat content in minced meat and meat emulsions,115 117 protein content in fresh meat115,118 and moisture content in sausages119 have been demonstrated results from fat determinations are summarised in Table 3. 

Table 1. The relaxation parameters a, and A for the first eight glitches of the Vela pulsar, AQC is the jump value, tg is an interglitch time [16].

It is found that the relaxation parameter T p as a function of temperature does not follow an increase with chain length, as the square of the number of methylene carbons. Nor is it linear with N, the number of methylene carbons, which should be true if relaxation to the lattice were rate controlling. Rather, it shows a temperature-induced increase of the minimum value of Tjp with about the 1.6 of N. So, both spin diffusion and spin lattice coupling are reflected. For a spin diffusion coefficient D of approximately 2 x 10 12 cm.2/sec., the mean square distance for diffusion of spin energy in a time t is the ft1 = 200/T A, or about 15A on a Tjp time scale. 

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