Relaxation rate total

The most popular, and also a very accurate, experimental method for measuring nonselective spin-lattice relaxation-rates is the inversion recovery (180°-r-90°-AT-PD)NT pulse sequence. Here, t is the variable parameter, the little t between pulses, AT is the acquisition time, PD is the pulse delay, set such that AT-I- PD s 5 x T, and NT is the total number of transients required for an acceptable signal-to-noise ratio. Sequential application of a series of two-pulse sequences, each using a different pulsespacing, t, gives a series of partially relaxed spectra. Values of Rj can... 

Finally, it is worth while to consider the applicability of these relaxation methods to molecules having flexible conformations. Examples given in the previous Section demonstrated that relaxation rates are able to define either the most probable conformation of a flexible molecular segment, or to specify a range of allowed conformations from the total number of confor-... 

The first comparison is based on the T values of gaseous, liquid and adsorbed molecules. Unfortunately, no measurements are available for butenes in the gas or liquid phase. Nevertheless a reasonable parallel can be drawn with propylene where the three different phases were investigated (35) at 295 K for the gas (1 atm) Tj of C2 is 0.095 s in the liquid state (2.6. M in CDCI3) 59.9, 58.7 and 65.2 s for Cj, C2 and C3 respectively adsorbed on NaY zeolite 0.81, 1.6 and 0.81 s. The shortest relaxation times characterize the gas phase where the spin-rotation mechanism (NOE factor n = 0) is very effective (30,35). In the liquid, dipole-dipole and spin-rotation mechanisms both play a role and the total relaxation rate is about three orders of magnitude lower than in the gas phase. The adsorbed molecules show therefore an intermediate behaviour between gas and liquid, as it was also suggested by chemical shift data. 

Molecular hydration in solution is described not only by the inner-sphere water molecules (first and second coordination spheres, see Section II.A.l) but also by solvent water molecules freely diffusing up to a distance of closest approach to the metal ion, d. The latter molecules are responsible for the so-called outer-sphere relaxation (83,84), which must be added to the paramagnetic enhancement of the solvent relaxation rates due to inner-sphere protons to obtain the total relaxation rate enhancement,... 

An electron spin can relax by coupling with a neighboring electron spin. Therefore, when a paramagnetic metal ion interacts with a second paramagnetic metal ion, the electron relaxation rates of the two metal ions may be dramatically affected. If Si and S2 are the two spins coupled by a scalar interaction, new spin levels will be established due to the interaction, with total S varying in unitary steps from Si — S2I to Si + S2. The energies of these spin levels are given by )... 

Fig. 25. Determination of the confidence interval. Qi(r) is the total quadratic deviation assuming a relaxation rate value r and fitting all other parameters in Eq.(24). Its absolute minimum at r2 defines the most probable relaxation rate R. Q2 is the minimum of Qi(r) and Q i equals Q2 plus the least significant increment determined by statistical methods. This defines the confidence interval C.I. comprised between the two vertical lines. For more details, see the text.

Thus, if Pi is known, then the measurement of 77 provides the extreme narrowing conditions, the heteronuclear NOE reaches a maximum value (minimum for 71 < 0) and can be used to determine the dipole-dipole contribution to the total relaxation rate ... 

From the functional form of Eq. (4.30) it is easy to predict the behavior of saturation transfer as a function of the exchange rate. When the rate constant for the B - A transformation (k i) is much smaller than the longitudinal relaxation rate of the nucleus in the B site (Rf), the saturation transfer tends to zero. When the rate constant is much higher, the saturation transfer tends to —1, i.e. there is a total transfer of magnetization to the B site when the A site is kept saturated. Note that these conditions are referred to as fast exchange, even if the exchange is still slow with respect to the chemical shift separation. Fast exchange conditions on the... 

For the homonuclear case, generalized by substituting pi(j) with the total relaxation rate pi in Eq. (VII. 13) and the following, we obtain... 

The total paramagnetic relaxation rate enhancement due to the paramagnetic agent is given as in Eq. (3), or expressed in relaxivities as in Eq. (4) ... 

Figure 3. Plot for determining the association constant K for the interaction of a-MDG with Mn-Con A. F the fraction of Ca2 -Mn2 -Con A molecules with saccharide, is determined from observation of the solvent-proton relaxation rate at 0.04 MHz, as discussed in the text. PT is the total Ca2 -Mn2 -Con A concentration, mM (monomer), and ST the total saccharide concentration, mM. The slope of the line through the data give a K of 1.1 X 10s M"1. Measurements were made at 25° in pH 5.6,0.1 M potassium acetate buffer, n = 1.0 in KCl.

The total relaxation rates (in the absence of spin diffusion) can be written as... 

Laser-induced fluorescence is a sensitive, spatially resolved technique for the detection and measurement of a variety of flame radicals. In order to obtain accurate number densities from such measurements, the observed excited state population must be related to total species population therefore the population distribution produced by the exciting laser radiation must be accurately predicted. At high laser intensities, the fluorescence signal saturates (1, 2, 3 ) and the population distribution in molecules becomes independent of laser intensity and much less dependent on the quenching atmosphere (4). Even at saturation, however, the steady state distribution is dependent on the ratio of the electronic quenching to rotational relaxation rates (4, 5, 6, 7). When steady state is not established, the distribution is a complicated function of state-to-state transfer rates. 

All the spectroscopic approaches applied for structural characterization of mixtures derive from methods originally developed for screening libraries for their biological activities. They include diffusion-ordered spectroscopy [15-18], relaxation-edited spectroscopy [19], isotope-filtered affinity NMR [20] and SAR-by-NMR [21]. These applications will be discussed in the last part of this chapter. As usually most of the components show very similar molecular weight, their spectroscopic parameters, such as relaxation rates or selfdiffusion coefficients, are not very different and application of these methodologies for chemical characterization is not straightforward. An exception is diffusion-edited spectroscopy, which can be a feasible way to analyze the structure of compounds within a mixture without the need of prior separation. This was the case for the analysis of a mixture of five esters (propyl acetate, butyl acetate, ethyl butyrate, isopropyl butyrate and butyl levulinate) [18]. By the combined use of diffusion-edited NMR and 2-D NMR methods such as Total Correlation Spectroscopy (TOCSY), it was possible to elucidate the structure of the components of this mixture. This strategy was called diffusion encoded spectroscopy DECODES. Another example of combination between diffusion-edited spectroscopy and traditional 2-D NMR experiment is the DOSY-NOESY experiment [22]. The use of these experiments have proven to be useful in the identification of compounds from small split and mix synthetic pools. 

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