Fast spinning limit

For the normally observed central transition then, this frequency in the fast spinning limit is... 

This represents the speed that must be exceeded for MAS to cause even partial averaging of the second-order quadrupolar interaction, but fulfilling this condition does not mean that the fast spinning limit has been achieved. 

In the fast spinning limit, the time-dependent terms of Eq. (21) are av-... 

The key to obtaining pore size information from the NMR response is to have the response dominated by the surface relaxation rate [19-26]. Two steps are involved in surface relaxation. The first is the relaxation of the spin while in the proximity of the pore wall and the other is the diffusional exchange of molecules between the pore wall and the interior of the pore. These two processes are in series and when the latter dominates, the kinetics of the relaxation process is analogous to that of a stirred-tank reactor with first-order surface and bulk reactions. This condition is called the fast-diffusion limit [19] and the kinetics of relaxation are described by Eq. (3.6.3) ... 

Abernathy and Sharp (130,145) treated the intermediate regime, when the reorientation of the paramagnetic species is in-between the slow- and fast-rotations limits. They applied the spin-dynamics method, described in Section VI, to the case of outer-sphere relaxation and interpreted NMRD profiles for non-aqueous solvents in the presence of complexes of Ni(II) (S = 1) and Mn(III) (S = 2). 

Expressions for determining rate constants from exchange contributions to observed linewidth for unequally populated systems in the fast exchange limit have been derived from the formal solutions to the Bloch equations modified for chemical exchange [3, 127-129]. These equations relate each rate constant to the site populations, chemical shift difference between sites, and spin relaxation times T and T2. For example, the forward rate A i 2 is given by [3, 127] ... 

Boltzmann factor) of finding the atom in the respective state. In the fast relaxation limit, the nucleus senses the average spin (actually the average Bint), obtained by thermally averaging the expectation values of the individual level, in the present case (Sz)th = SZ) +1/2 + + e AEIkT), where AE = g/ B is the Zeeman... 

In the opposite limit of infinitely fast spin conversion the recombination through the singlet channel is 4 times slower because of the full equilibration of the spin state populations of RIPs. 

A similar result was expected in Ref. 221 for cps(c>) = 1 — cp(cr), but the obtained difference between the recombination rates in the opposite limits was half as much kc for the slowest conversion and kj2 for the fastest one. This is because the isotropic Ag mechanism determining the spin conversion in Ref. 221 mixes the singlet with the 7b) sublevel only. In the rate approximation one can easily get the same, assuming that the spin transitions between the singlet and triplet RIPs occurs with equal rates in the forward and backward directions as in Eq. (3.585b). However, the transition from the slow to the fast conversion limit resulting from the rate approximation differs somehow from that obtained with the Hamiltonian approach in Ref. 221. 

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