Attenuation of the NMR signal due to hydrodynamic Brownian motion

• Published in: Journal of molecular liquids 2017-05, Vol.234, p.182-186
• Main Authors: Lisý, Vladimír, Tóthová, Jana
• Format: Article
• Language: English
• Subjects: Brownian motion; Generalized Langevin equation; Hydrodynamic theory; Induction signal; NMR; Spin echo
• ISSN: 0167-7322; 1873-3166
• DOI: 10.1016/j.molliq.2017.03.085

Nuclear magnetic resonance (NMR) is a widely used nondestructive method to study random motion of spin-bearing particles in different systems. In the long-time limit the theoretical description of the NMR experiments is well developed and allows proper interpretation of measurements of normal and anomalous diffusion. The traditional description becomes, however, insufficient for the shorter-time dynamics of the particles. In the present paper, the all-time attenuation function of the NMR signal in a magnetic-field gradient due to the Brownian motion (BM) of particles in incompressible liquids is calculated by using the method of accumulation of phases by a precessing magnetic moment, without reference to a concrete model of the stochastic dynamics. The obtained expressions are then used to evaluate the attenuation within the hydrodynamic theory of the BM. It is shown that the well-known time behavior of the formulas corresponding to the Einstein theory of diffusion in the case of steady gradient and Hahn's echo experiments is reached at times much larger than the characteristic time of the loss of memory in the particle dynamics. At shorter times the attenuation function significantly differs from the classical formulas used to interpret these experiments. Spin-echo attenuation function A(δ, Δ) within the hydrodynamic theory of Brownian motion (green) approaches very slowly the classical result (blue) based on the Einstein theory of diffusion. Red line corresponds to the standard (memoryless) Langevin theory. [Display omitted] •The attenuation of the NMR signal from spins moving in a field gradient is calculated.•The steady-gradient and Hahn spin-echo experiments are considered.•The particle motion is described within the hydrodynamic theory of Brownian motion.•The theory is applicable for incompressible fluids at any times of observation.•The classical results are approached very slowly with increasing time.