RESUMEN
In NMR, the repetition of pulse sequences with a recycle time that does not allow the spin system to completely relax back to equilibrium is a well known and often used method to increase the signal to noise ratio at given total measuring time. For isolated spins I=1/2, the steady-state of a train of strictly identical pulse sequences separated by free evolution periods of same duration is described by the well known Ernst-Anderson model, and the optimum pulse angle is given by the Ernst angle. We showed recently that equivalent formula, but with super-operators in the Liouville space, can be obtained for general spins I. In this article, this formalism is generalized to pure NQR of spins I=3/2, and applied to calculate the signal resulting from single and solid-echo sequences, in the limit when the recycle time T>5T2q, where T2q is the transverse (coherence) quadrupolar relaxation time. In particular, we show that powder samples have a behaviour that is very close to NMR of spins I=1/2. For instance, the generalized Ernst angle ßM that maximizes the signal amplitude for a single pulse train is well described by the simple formula cos(1.52ßM)≈exp(-T/T1q), whatever the quadrupolar asymmetry parameter η, T1q being the longitudinal (population) quadrupolar relaxation time. Moreover, a simplified NMR-like formula that describes the overall behaviour of nutation curves is proposed, and it is shown that the signal to noise ratio (SNR) at given experimental time is exactly the same as in NMR of spins I=1/2 as a function of recycle time, when properly normalized. Some theoretical predictions for the single pulse and solid-echo sequence were compared to experiments, and validated, by performing 35Cl pure NQR experiment on chloranil (C6Cl4O2 tetrachloro-1,4-benzoquinone) powder.
RESUMEN
The aim of this work is to generalize the Ernst-Anderson model developed to account of the steady-state regime of isolated spins I=1/2 subject to a train of strictly identical pulse sequences separated by free evolution periods of same duration. We generalize this model to the general case of spins I≥1 and general pulse sequence within the framework of the Liouville space. In particular, it is proved that under reasonable assumptions, a well defined steady-state regime is reached which is independent of the initial conditions. The general formal expressions obeyed by the steady-state density operator are given as a function of pulse propagators and relaxation operator for single and two-pulse sequences. In solid-state NMR where recycle time can be made, at the same time, much longer than typical coherence relaxation times and smaller than typical population relaxation times, further simplification leads to more tractable formula. As an example, the formalism is applied to I=1 spins with hard and soft single pulse sequence, or to the solid echo sequence. In particular, we were able to generalize the Ernst-Anderson formula to spins I=1. The pertinence of the theory is verified by comparing the theoretical and numerical simulations outputs to 2H single crystal experiments performed on nonadecane/urea C19D40/urea-H4 compound.
RESUMEN
Cross relaxation, and mI-dependence of the intrinsic electron spin-lattice relaxation rate We, are incorporated explicitly into the rate equations for the electron-spin population differences that govern the saturation behaviour of 14N- and 15N-nitroxide spin labels. Both prove important in spin-label EPR and ELDOR, particularly for saturation recovery studies. Neither for saturation recovery, nor for CW-saturation EPR and CW-ELDOR, can cross relaxation be described simply by increasing the value of We, the intrinsic spin-lattice relaxation rate. Independence of the saturation recovery rates from the hyperfine line pumped or observed follows directly from solution of the rate equations including cross relaxation, even when the intrinsic spin-lattice relaxation rate We is mI-dependent.