Collection of Czechoslovak Chemical Communications - digital archive 

Abstract

The spin-echo experiment on a spin system with only partial motional narrowing and an exponential field autocorrelation function is considered. The pattern of the intensity decrease in the echo spectra depends on the ratio τ/τ_c of the time delay τ in the echo experiment to the correlation time τ_c of the narrowing motion. With the large ratios (fast motion), the decrease is the same as in the case of extreme narrowing; to obtain undistorted T₂ values, the ratio should be at least several units in the single-echo experiment and at least few decades in the multiple-echo experiment. With the small ratios (slow motion), the logarithmic decrease depends non-linearly on τ, and the T₂ value found by the linear least-squares adjustment is much longer than that obtained from the extreme narrowing approximation. At very small ratios, the multiple echo yields about 3τ_c/(ω_pτ)² for T₂ as compared with 1/(ω_p²r_c) obtained from the extreme narrowing approximation; ω_p² is the second moment of the Gaussian line being narrowed. The expression for T₂ in the multiple spin echo is similar to that previously found for T_2e in the solid multiple spin echo. The echo experiment changes the line shape, which at large τ/τ_c approaches the Lorentzian one. The case of a multiexponential field autocorrelation function is also briefly considered.

Keywords: Nuclear magnetic resonance spectroscopy; Partial motional narrowing; Spin-echo experiment; Line shape analysis; Autocorrelation function.

References: 10 live references.