NMR diffusion in restricted environment approached by a fractional Langevin model

TL;DR

This paper models NMR diffusion in confined environments using a fractional Langevin approach, revealing anomalous diffusion effects and fractional decay behaviors in the NMR signal.

Contribution

It introduces a fractional Langevin model within the Gaussian phase approximation to describe restricted diffusion in NMR, capturing anomalous diffusion phenomena.

Findings

Fractional exponential decay in NMR signal due to anomalous diffusion

Recovery of classical results in the limit of normal diffusion

Modeling of confined diffusion effects in NMR experiments

Abstract

The diffusion motion of spin-bearing molecules is considerably affected in confined environments. In Nuclear Magnetic Resonance (NMR) experiments, under the presence of magnetic field gradients, this movement can be encoded in spin phase and the NMR signal attenuation due to diffusion can be evaluated. This paper considered this effect in both normal and anomalous diffusion by means of the Langevin stochastic model within the Gaussian phase approximation (GPA) for a constant gradient temporal profile. The phenomenological approach illustrates the emergence of fractional order exponential decay in the NMR signal and retrieves the classical result from Hanh echo.