Transverse relaxation function

Figure 8.7A Semi-logarithmic plot of the proton transverse relaxation functions recorded from 1,2 polybutadiene, at 348 K. Vinyl contents are %12 = 0.82 (curve a), 0.66 (curve b), 0.58 (curve c), 0.40 (curve d) and 0.22 (curve e)...

The appropriate differential-recurrence equation for the transverse relaxation functions... 

The total transverse relaxation function M(t) for inter-crosslinked chains and dangling chain ends follows an exponential correlation function [58], as shown in Equation 9.10 ... 

Even for this simplest case, there is considerable variety due to the flexibility of the transverse relaxation function Gx(t), whose... 

Brereton MG, Ward IM, Boden N, Wright P. Nature of the proton NMR transverse relaxation function of polyethylene melts. 1. Monodispersed polyethylenes. Macromolecules 1991 24 2068. 

The transverse relaxation functions can be analyzed for two components related to the central and chain-end blocks according to... 

K = 63 M 1, Kb = 1.4M-1)47 lithium-7 (K = 14 M 1 K" = 0.5 M 1) 49) and for cesium-133 (K, st 50 M-1, K = 4M 1)S0). In the case of sodium-23, transverse relaxation times could also be utilized to determine off-rate constants k ff = 3 x 105/sec k"ff = 2x 107/sec47,51). Therefore for sodium ion four of the five rate constants have been independently determined. What has not been obtained for sodium ion is the rate constant for the central barrier, kcb. By means of dielectric relaxation studies a rate constant considered to be for passage over the central barrier, i.e. for jumping between sites, has been determined for Tl+ to be approximately 4 x 106/sec 52). If we make the assumption that the binding process functions as a normalization of free energies, recognize that the contribution of the lipid to the central barrier is independent of the ion and note that the channel is quite uniform, then it is reasonable to utilize the value of 4x 106/sec for the sodium ion. 

The exchange of the coordinated aqua ligand of the W(IV) aqua oxo species was qualitatively studied by NMR line-broadening as a function of temperature based on Eq. (26), where the transverse relaxation time of the bound oxygen-17 nucleus is given by 1/T2b. The l/T2Qb represents the quadrupolar relaxation rate and kmi the chemical exchange rate constant... 

When l l, the above gives the so-called cross-correlation functions and the associated cross-correlation rates (longitudinal and transverse). Crosscorrelation functions arise from the interference between two relaxation mechanisms (e.g., between the dipole-dipole and the chemical shielding anisotropy interactions, or between the anisotropies of chemical shieldings of two nuclei, etc.).40 When l = 1=2, one has the autocorrelation functions G2m(r) or simply... 

Fig. 5. Transverse relaxation times of carbonyl carbon as a function of rotational correlation time, rc (a), at four polarizing magnetic field strengths, and as a function of field strength, B0, against four different correlation times (b), according to Eq. (1).

The measured spin relaxation parameters (longitudinal and transverse relaxation rates, Ri and P2> and heteronuclear steady-state NOE) are directly related to power spectral densities (SD). These spectral densities, J(w), are related via Fourier transformation with the corresponding correlation functions of reorientional motion. In the case of the backbone amide 15N nucleus, where the major sources of relaxation are dipolar interaction with directly bonded H and 15N CSA, the standard equations read [21] ... 

In the limit of zero gradient, the sequence reduces to the Hahn echo, and it is conventional to expand the echo amplitude as a multiple exponential function of T, and define, the usual transverse relaxation times, T,... 

Fig. 8. Evolution of the longitudinal and transverse relaxation times (Ti and T2, respectively) as a function of (for a fixed measurement frequency Vo = 400 MHz) assuming that the considered spin is subjected to random fields whose correlation function is proportional to being the correlation time. Notice the continuous...

The functional form of the nuclear longitudinal relaxation immediately suggests that the contact contribution can provide the values of the contact coupling constant and of 72e = Tso, provided that the lifetime, xm, is longer than T e- No information on the field dependence of electron relaxation can be achieved. On the contrary the functional form of transverse nuclear relaxation contains a non-dispersive term, Tig. The latter, as we have seen for the dipolar contribution, increases with increasing the field (Fig. 3), and therefore the nuclear contact transverse relaxation also increases with increasing the field. Its measurement is thus informative on the t value. 

Figure 3.11 Catalytic efficiency, (fcca,/K ,)app ( ), of salt-activated subtilisin Carlsberg in hexane, THF, and acetone in comparison with T2 (transverse relaxation constant) (O) of mobile deuterons as a function of dielectric constant of solvent [103].

Fig. 5.3. Water proton longitudinal relaxivity as a function of proton Larmor frequency ( H NMRD profiles) for solutions of Fe(OH2) + at ( ) 278 K, ( ) 288 K, (A) 298 K, ( ) 308 K. High field transverse relaxivity data at 308 K >) are also shown. The lines represent the best fit curves using the Solomon-Bloembergen-Morgan equations (Eqs. (3.11), (3.12), (3.16), (3.17), (3.26) and (3.27)) [4],...

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