Free transverse relaxation time

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. 

A short introduction in the application of MT techniques has been given in Section 3.3. Mechanisms of MT are described by interactions between two separated pools of protons, one of them consisting of free protons with long transverse relaxation time (pool A, 7 2 > 10 ms) and the other of protons bound to macromolecules with an inherent short transverse relaxation time (pool B, T2< 10 ps). By selective saturation of the magnetization of the protons in pool B it is possible to reduce signal intensity of pool A and therefore to draw conclusions about the amount of protons present in pool B. 

If the spectrum involves only one resonance (or if linewidths do not allow for the separation of several resonances), a single experiment can be run with acquisition of the amplitude of each echo along the pulse train (for sensitivity enhancement, accumulations can be carried out). This experiment is especially valuable for determining the relative proportions of two species which differ by their transverse relaxation time, for instance the two types of water (free and bound), if exchange between these two states is sufficiently slow. For this type of measurement, a low resolution spectrometer (without any shim system) proves to be quite sufficient. 

Nuclear Magnetic Resonance (NMR) Spectroscopy. Longitudinal and transverse relaxation times (Ti and T2) of 1H and 23Na in the water-polyelectrolytes systems were measured using a Nicolet FT-NMR, model NT-200WB. T2 was measured by the Meiboom-Gill variant of the Carr-Purcell method (5). However, in the case of very rapid relaxation, the free induction decay (FID) method was applied. The sample temperature was changed from 30 to —70°C with the assistance of the 1180 system. The accuracy of the temperature control was 0.5°C. 

Here T2 is transverse relaxation time of an electron spin. The EPR absorption lineshape is related to free induction decay G(t) through the Fourier transformation [16]. After averaging over all angles between the surface and the external magnetic field H the following equation was obtained for D = 2 systems [138] ... 

From equations (7.98) and (7.99), the kinetic parameters can be obtained using the observed NMR line-width and chemical shift of the free solvent signal. In equations (7.98) and (7.99), Pm is the mole fraction of the bound solvent, T2a, T2, T2m and Tos are transverse relaxation times of pure, free, bound and outer sphere solvent, Aa>s, Acom and Achemical shifts relative to pure solvent of free, bound and outer sphere solvent,... 

The principle of Fourier transform (FT) NMR spectroscopy is the observation of the so-called free induction decay (FID) after the application of radio frequency (rf) pulses to the resonating nuclei. The carrier frequency of the rf-pulses is the Larmor frequency. In many cases, the FID is observed after single-pulse (SP) excitation, e.g., after application of a so-called 7r/2-pulse which rotates the magnetization by 90° from the direction of the external magnetic field (z-direction) into the x,y-plane. The characteristic time constant for the free induction decay is the transverse relaxation time, T2, which is given by T2=(2/M2) =0.53 (A Vi/2)" for Gaussian lines. Fourier transformation of the FID yields the common absorption spectrum. 

The shape of NMR lines in a homogeneous magnet is dictated by the decay of the transverse magnetization, which is detected as the free induction decay (FID) following a radiofrequency pulse. If the observed nucleus remains in the same environment (associated to the same characteristic resonance frequency), the NMR lines will have a Lorentzian shape with a width at half height given by the effective transverse relaxation time T2). The faster the transverse relaxation, the broader will be the line (1) ... 

Spin-lattice relaxation times (Tx) were obtained by the saturation-recovery method. Transverse relaxation times (T2) for the narrow central component of the line shapes were measured directly from the Lorentzian line shapes. The line shapes are Fourier transforms (FT) of quadrupole echo (QE) or free induction decay (FID) transients. Complete line shapes and long Tx measurements were obtained with a composite pulse QE sequence with a 3.5 psec tt/2 pulse length. Long Tx and weak signal strength made data accumulation tedious A single Tx measurement or spectral line shape often required over 12 hours of data acquisition. 

T,f = longitudinal relaxation time of free state T e = electron spin relaxation time Ti = transverse relaxation time Lb = transverse relaxation time in paramagnetic complex (bound state)... 

Ti[ = transverse relaxation time of free state 13 = Bohr magneton Vn = nuclear magnetogyric ratio 5 = induced shift... 

Fig. 17a-c. Effective proton transverse relaxation time T2=(l/T2,j) (see Eq. 160) in different linear polymers of different molecular masses measured at 90 MHz as a function of the reciprocal temperature [33]. A characteristic temperature Tchar shows up for MyJ>Mc in the form of a relatively sharp bend in the temperature dependence. This bend disappears when approaching the critical molecular weight from above. For M additional molecular weight dependence reveals itself as a consequence of the chain length dependent free-volume effects, a Polyisobutylene. Symbols for the data points have been plotted for three different molecular weights only, while the data for all other molecular weights are represented by polygonal lines for the sake of clearness. From the top to the bottom, the lines refer to data for M = 1,600 5,800 15,800 34,000 55,000 80,600 122,000 182,000 393,000 610,000 830,000 1,100,000. The critical molecular... 

Experimental data of the effective transverse relaxation time are plotted in Fig. 17 as a function of the reciprocal temperature for different polymers. The molecular weight dependence for M free-volume effects. We will come back to this sort of molecular weight effect later in the review. 

Fig. 26. Decay times Tpu) to 1/e of the initial value of the free-induction signals in melts of linear polyethylene at 150 "C as a fimction of molecular mass. The horizontal broken line (a) indicates the instrumental homogeneity limitation determined with a water sample at 30 °C (see Fig. 25). The motional averaging region (b) is characterized by a strong molecular mass dependence equivalent to that of the proper (effective) transverse relaxation time (see Fig. 19d). It is therefore attributed to the combined influence of components B and C. The plateau (c) reached at high molecular masses reflects the unaveraged effect of internal field inhomogeneities corresponding to a full width at half maximum of the resonance line of about 7 ppm. This value can be estimated on the basis of the magnetic susceptibility of polyethylene relative to that of empty voids [152]...

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