Extreme narrowing condition limit

The assumption of a single electron spin and a single T2 holds usually for S = 1/2 and for S > 1 in certain limits. Let us assume that the instantaneous distortions of the solvation sphere of the ion result in a transient ZFS and that the time-dependence of the transient ZFS can be described by the pseudorotation model, with the magnitude of the transient ZFS equal to At and the correlation time t . The simple picture of electron relaxation for S = 1 is valid if the Redfield condition (Att <5c 1) applies. Under the extreme narrowing conditions ((Os v 1), the longitudinal and transverse electron spin relaxation rates are equal to each other and to the low-field limit rate Tgo, occurring in Eqs. (14) and (15). The low field-limit rate is then given by (27,86) ... 

At the other limit of correlation times, Eqs. 8.6 and 8.9 show that for small tc, the denominators approach unity, and T2 = T,.The region of Tc< 1 /(o0 is often called the extreme narrowing condition. Note that we are considering here only dipolar interactions. Other relaxation mechanisms discussed subsequently may cause T2 to be smaller than 7), even under the extreme narrowing condition. 

The simple exponential relaxation behavior dictated by Eq. (2) for molecules in the "extreme narrowing" conditions cannot be applied to molecules of limited mobility. Outside the region of extreme narrowing the behavior is reminiscent of that of spin 1/2 dipole-dipole relaxation (Fig. 2), but it is complicated bj the fact that several nuclear transitions are possible. Thus for a nucleus like with 7 = 5/2 there are five transitions, 3/2 -o-5/2, 1/2 <->3/2, 1/2-o-—1/2,... 

Derivation of the time dependence of the longitudinal and transverse magnetization for an ensemble of I = 3/2 nuclei in the presence of chemical exchange processes and under non-extreme narrowing conditions is by no means trivial. The general solution has been given by Bull [409], Here we will limit ourselves to a discussion of his results for a system of two sites. 

We have applied the discrete-exchange model to these data. An exchange between Na ion under a particular slow-motion condition and in the extreme narrowing limit is assumed. Transverse relaxation time and diffusion coefficient are written as follows ... 

In this section, the reader will be confronted with and introduced to some comparatively elemental facts on the theory underlying interpretation of the shielding parameter accessible for normal molecules in isotropic solutions, where normal refers to molecules which are not oversized (such as vanadium bound to proteins), and were we therefore are in the so-called extreme narrowing limit , characterised by the condition 2TruQT << 1, where vq is the measuring frequency and the molecular correlation time, a measure of the mobility of a solute molecule in a solvent. Extreme narrowing simply means that the molecule is freely mobile and the frequency applied to obtain NMR information does not influence the respective parameters. Although the term contains the component extreme , we are well in the domain of normal conditions. 

This condition is referred to as the extreme narrowing limit since all broadening effects attributable to dipolar interactions are fully averaged to zero under these conditions. This regime typically applies only to small molecules in low viscosity solvents, and the point at which this condition breaks down depends on the correlation time of the molecule as well as the field strength of the spectrometer (through co). 

The maximum possible negative NOE in a homonuclear system is —100%. Between the extreme narrowing and spin diffusion limits, lies the difficult region in which NOEs can become zero (when cooTc 1) or at least rather weak, often demanding a change in experimental conditions or the use of rotating-frame NOE measurements. 

Are these multiple steady states possible in practical situations From an inspection of Figs. 11.8.1-3 and 11.8.1-4 it is clear that the conditions chosen for the reaction are rather drastic. It would be interesting to determine the limits on the operating conditions and reaction parameters within which multiple steady states could be experienced. These limits will probably be extremely narrow, so that the phenomena discussed here would be limited to very special reactions or to very localized situations in a reactor, which would probably have little effect on its overall behavior. Indeed, in industrial fixed bed reactors, the flow velocity is generally so high that the temperature and concentration drop over the film surrounding the particle is small, at least in the steady state. 

Another point regarding the isotope studies is that if the extreme narrowing limit may be safely assumed the isotope effect may equally well be studied at fixed frequency or fixed magnetic field. However, when nonextreme narrowing conditions apply the study has to be made at fixed frequency. 

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