Effects of Diffusion on Free Precession in Nuclear Magnetic Resonance Experiments

TLDR

Free‑precession nuclear resonance techniques, including a convenient variation of Hahn’s spin‑echo method, are studied, noting that transverse‑relaxation measurements in fluids are often compromised by diffusion but that the technique can also directly measure molecular self‑diffusion. The authors employ a 90°/180° pulse sequence, reformulate Hahn’s diffusion analysis to extend T2 measurement while largely circumventing diffusion, analyze convection effects, and introduce a null method using unequal pulses to measure T1. The extended scheme successfully mitigates diffusion effects in T2 measurement, and the self‑diffusion constant of water at 25 °C was measured as 2.5 ± 0.3 × 10⁻⁵ cm²/s, agreeing with prior values.

Abstract

Nuclear resonance techniques involving free precession are examined, and, in particular, a convenient variation of Hahn's spin-echo method is described. This variation employs a combination of pulses of different intensity or duration ("90-degree" and "180-degree" pulses). Measurements of the transverse relaxation time ${T}_{2}$ in fluids are often severely compromised by molecular diffusion. Hahn's analysis of the effect of diffusion is reformulated and extended, and a new scheme for measuring ${T}_{2}$ is described which, as predicted by the extended theory, largely circumvents the diffusion effect. On the other hand, the free precession technique, applied in a different way, permits a direct measurement of the molecular self-diffusion constant in suitable fluids. A measurement of the self-diffusion constant of water at 25\ifmmode^\circ\else\textdegree\fi{}C is described which yields $D=2.5(\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ ${\mathrm{cm}}^{2}$/sec, in good agreement with previous determinations. An analysis of the effect of convection on free precession is also given. A null method for measuring the longitudinal relaxation time ${T}_{1}$, based on the unequal-pulse technique, is described.