Stray Field NMR: a powerful method to measure dynamics at the millisecond scale

TL;DR

STRAY Field NMR (STRAFI) enables diffusion NMR measurements across a multiscale time window by exploiting a permanent stray-field gradient, overcoming the diffusion-time limitations of conventional PFG-NMR. The authors present a robust STRAFI methodology with a dedicated experimental setup, gradient calibration, and SE/STE pulse sequences that enable accurate diffusion measurements for a broad range of nuclei, including those with short $T_{2}$. They demonstrate the approach on exotic nuclei in concentrated electrolytes, multimodal diffusion in bimodal systems, and diffusion in micrometre-scale confinement, highlighting access to dynamics inaccessible to standard methods. By linking diffusion timescales to microstructural features such as porosity and surface interactions, STRAFI-NMR offers a versatile, non-destructive tool for materials science, energy storage, and soft matter research.

Abstract

Transport properties in fluids and confined systems play a central role across a wide range of natural and technological contexts, from geology and environmental sciences to biology, energy storage, and membrane-based separation processes. Nuclear Magnetic Resonance (NMR) provides a unique, non-destructive means to probe these properties through species-selective measurements of self-diffusion coefficients. While pulsed field gradient NMR (PFG-NMR) is routinely used, its access to diffusion times is typically limited to values no shorter than about 10 ms, restricting its applicability to systems with fast dynamics and long relaxation times. Diffusion NMR in a permanent magnetic field gradient (STRAFI) offers a complementary, multiscale approach, enabling diffusion measurements over an extended temporal window, from a few hundred microseconds to several tens of seconds. Despite its strong potential, this technique remains rarely implemented due to experimental and methodological challenges. In this work, we present a robust and versatile STRAFI-based methodology, including a specifically designed experimental setup, optimized pulse sequences, and rigorous data analysis, allowing accurate extraction of self-diffusion coefficients for a broad range of nuclei. The capabilities of the approach are illustrated through diverse applications, including the study of concentrated electrolytes using "NMR-exotic" nuclei ($^{35}$Cl, $^{79}$Br/$^{81}$Br, $^{127}$I, $^{17}$O) and the characterization of micrometre-scale porosity in membranes.

Figures (8)

• Figure 1: Schematic drawing of the set-up. The sample is placed in the leaking field of the coil. The position $z$ determines the magnetic field $B$ and the magnetic gradient $|G|$ experienced by the sample. A pulse sequence generated by an horizontal coil around the sample excites spins in a region of thickness $\Delta z$ of the order of $10$ µm up to $1$ mm.
• Figure 2: Calibration of the STRAFI magnetic gradient $G$ at a given position $z$ directly in the sample of interest CsCl/H$_{2}$O, using $^{133}$Cs as the probe. Diffusion of $^{133}$Cs is measured over long times $\Delta t$ using PFG-NMR experiments. This value is used to fit the magnetic gradient $G$ from STRAFI experiments. With this calibrated value, the diffusion coefficient of $^{35}$Cl in the same sample is obtained using STRAFI-NMR. $^{1}$H could also be used as a probe.
• Figure 3: Single Echo (SE) (top) and Stimulated Echo (STE) (bottom) sequences. For each of them, an example of the echo intensity decrease when varying $\tau$ (top, SE on $^{17}$O in water at $298$ K) or $\tau_{1}$ and $\tau_{2}$ (bottom, STE on $^{23}$Na in a 2-methoxyethyl ether with NaTFSI salts at $333$ K) are shown on the right. The decrease of the echo intensity as a function of $\tau$ is shown for the SE sequence on the top middle figure, where colours correspond to $\tau$ values shown in the top right graph.
• Figure 4: Fit of echo intensity decrease for SE sequences on CsX/H$_{2}$O salts at saturation concentration, $n$ being the number of water molecules per CsX at this concentration. Experimental data (blue diamonds) are fitted with Eq. \ref{['eq:intensitySE']}, with $T_{2}$ and $D$ as fitting parameters. The obtained values are used to compute $\tau_{D}^{SE}$ and $\tau_{T_{2}}$, which are shown (d) for the three studied nuclei $^{35}$Cl, $^{81}$Br and $^{127}$I.
• Figure 5: Simultaneous fit of STE sequences $I(\tau_{1})$ for various fixed $\tau_{2}$ values, for $^{133}$Cs in CsBr/H$_{2}$O, using a genetic algorithm. Each colour corresponds to $I(\tau_{1})$ for a given fixed $\tau_{2}$ value.