Larmor periods

The relationship between Ti and T2 was examined for a number of liquid alkanes and crude oils [15]. It was concluded that there is no difference for light oils, apparently because light oils satisfy the fast-motion condition (the correlation time is less than the Larmor period). However, viscous oils do not satisfy this condition as the departure between Tx and T2 correlates with an increasing viscosity and Larmor frequency. 

When the Zeeman interaction is much larger than the quadrupolar frequency (coo coq), the averaged quadmpolar Hamiltonian over a Larmor period,... 

Figures 1 and 3 show that although the modulations of the three-pulse, or stimulated echo are less intense than those of its two-pulse counterpart, the resolution is much higher and the spectrum is simplified because combination peaks only enter into the data through the presence of multiple ESEEM-active nuclei. Equation (8) shows that for an S = 1 /2, 7 = 1/2 spin system, judicious selection of the r-value can control the ESEEM amplitudes of the hyperfine frequencies from a and electron spin manifolds allowing them to be optimized or suppressed. For weakly coupled protons, where the modulation frequencies from both electron spin manifolds are centered at the proton Larmor frequency, x can be set at an integer multiple of the proton Earmor frequency to suppress the contributions of this family of coupled nuclei from the three-pulse ESEEM spectrum. It is common for three-pulse ESEEM data to be collected at several r-values, including integer multiples of the proton Larmor period, to accentuate the other low frequency modulations present in the data and to make sure that ESEEM components were not missed because of T-suppression.

Averaging over the Larmor period (Uo/27r is performed by taking the zero- and first-order terms in the Magnus expansion.They are notated here as and TtCq in order to stress their equivalence to the first- and second-order terms of standard perturbation theory 2... 

Upon substitution of these functions into the expressions (3.5.4) and (3.5.6) for Tj and T2, respectively, the dependence of the relaxation times on the correlation time depicted in Fig. 3.5.2 is obtained for a given Larmor frequency >l. Regimes of slow and fast motion are discriminated by the Ti minimum, where the correlation time is of the order of the Larmor period. In the regime where t/

molecular motion is fast on the NMR timescale, and the homogeneous linewidth is highly reduced. This situation is typical for small molecules at room temperature. It is called the extreme narrowing limit, where both Ti and T2 coincide. 

We assume a random walk, i.e., an incoherent motion, for the spin carrier. In practice this assumption is not restrictive. Coherence or incoherence of the motion is essentially a question of time scale. A motion appears coherent, i.e., ballistic, as long as it is not interrupted by any kind of collision. After a collision the memory is left and the motion appears incoherent. In spin dynamics studies the time scale to probe the motion corresponds to the Larmor periods in the applied magnetic fields, typically 10" and 10" s for the nuclear and electron spins, respectively. This is longer than the usual collision times of charge carriers in conducting materials. 



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