N.M.R. solid echoes in systems of dipolar-coupled inequivalent spins-1 or dipolar-coupled inequivalent pairs of spins-1/2 |
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Authors: | P.K. Kahol N. Boden |
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Affiliation: | 1. Physics Department and Institute of Aviation Research, The Wichita State University , Wichita, Kansas, 67208, U.S.A.;2. Chemistry Department , The University of Leeds , Leeds, LS2 9JT, England |
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Abstract: | Proton solid-echo transverse relaxation functions for many thermotropic and lyotropic mesophases, mapped by measurement of the echo amplitude Syx (t′ = τ) as a function of τ using a Py (90°)-τ-Px (90°)-t′ sequence, yield gaussian behaviour of the form exp [-½M E 2τ2] for decays up to 20–30 per cent of the value at τ = 0. M E 2, the second moment for the dipolar interactions between the spin-½ pairs, is related to the van Vleck second moment M VV 2 through a factor f. Whilst experiments suggested a value of 0·70–0·72 for f = M E 2/M VV 2, simple models that ignored the non-equivalence of the dipolar-coupled spin-pairs had predicted f = 0·65. In this paper we derive an exact analytic expression for the spin response of a model of two dipolar-coupled inequivalent spins-1 to the pulse sequence Py (90°)-τ-P α(β)-t′, and show that the present model, with the quenching of the spin-flip terms of the dipolar hamiltonian, resolves the afore-mentioned discrepancy. We also reconcile the differences between the experimental and the earlier predicted values of f for deuteron N.M.R. spin echoes in perdeuterated solids. |
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