Workflow for systematic design of electrochemical in operando NMR cells by matching B 0 and B 1 field simulations with experiments

Abstract

Combining electrochemistry (EC) and nuclear magnetic resonance (NMR) techniques has evolved from a challenging concept to an adaptable and versatile method for battery and electrolysis research. Continuous advancements in NMR hardware have fostered improved homogeneity of the static magnetic field, $B_0$ , and the radio frequency field, $B_1$ , yet fundamental challenges caused by introducing essential conductive components into the NMR sensitive volume remain. Cell designs in EC-NMR have largely been improved empirically, at times supported by magnetic field simulations. To propel systematic improvements of cell concepts, a workflow for a qualitative and semi-quantitative description of both $B_0$ and $B_1$ distortions is provided in this study. Three-dimensional finite element method (FEM) simulations of both $B_0$ and $B_1$ fields were employed to investigate cell structures with electrodes oriented perpendicular to $B_0$ , which allow realistic EC-NMR measurements for battery and electrolysis applications. Particular attention is paid to field distributions in the immediate vicinity of electrodes, which is of prime interest for electrochemical processes. Using a cell with a small void outside the electrochemical active region, the relevance of design details and bubble formation is demonstrated. Moreover, $B_1$ amplifications in coin cells provide an explanation for unexpectedly high sensitivity in previous EC-NMR studies, implying the potential for selective excitation of spins close to electrode surfaces. The correlation of this amplification effect with coin geometry is described by empirical expressions. The simulations were validated experimentally utilising frequency-encoded ¹H profile imaging and chemical shift imaging of ¹H, ¹³C, and ²³Na resonances of ${\mathrm{NaHCO}}_3$ electrolyte. Finally, the theoretical and experimental results are distilled into design guidelines for EC-NMR cells.

Figure 1

(a–b) Sectional side view of experimental setup for investigations of changes in the $B_{\mathrm{0}}$ field without and with electrolyte in the notch underneath the Cu WE, respectively. (c) Technical drawing with exact dimensions given.

Figure 2

(a–b) Sectional view of the experimental coin cell setup for investigations of changes in the $B_{\mathrm{1}}$ field with PEEK and Cu discs, respectively. (c) Technical drawing of the sectional view with exact dimensions given. (d) Setup in FEM simulations using EMpro showing the RF coils and the resulting $B_{\mathrm{1}}$ field direction parallel to the discs.

Figure 3

Spatially resolved NMR spectra of CSI measurements of experimental setups (a–c) without Cu foil, (e–g) with Cu foil and air underneath, and (i–k) with Cu foil and electrolyte underneath, depicted between $z=[\mathrm{0},\mathrm{2}]$ mm. Spectra are shown for ¹H, ¹³C, and ²³Na, respectively. Simulated $B_{\mathrm{0}}$ distortions, represented by histograms over the same $z$ interval, for the case of (d) no Cu foil and water filled notch, (h) air, and (l) water underneath the Cu foil, respectively. The histograms were corrected under the assumption of perfect shimming of the sample without Cu foil.

Figure 4

(a–b)  $B_{\mathrm{1}}$ field intensities in layers exactly on top of the Cu disc and 50 $\mathrm{\mu }$ m above it, respectively. (c)  $B_{\mathrm{1}}$ field intensities in the sectional side view through the Cu disc. The magnitude of $B_{\mathrm{1}}$ field was calculated considering all components of the three-dimensional vector. (d) Frequency-encoded ¹H density profile of the experimental setup with horizontally placed Cu foil. For the imaging experiment, a pulse length of 16.5 $\mathrm{\mu }$ s was used, while the 90° pulse duration was 18.5 $\mathrm{\mu }$ s. Thus, increased intensities close to the electrode at $z=\mathrm{0}$ mm can be correlated to local enhancement of $B_{\mathrm{1}}$ field.

Figure 5

Spatial distribution of calculated $B_{\mathrm{1}}$ field in a central sectional plane perpendicular to the coin surface with coins of (a) 1 mm distance and 1 mm thickness, (b) 0.1 mm distance and 1 mm thickness, (c) 1 mm distance and 5 mm thickness, and (d) 0.1 mm distance and 5 mm thickness. The origin of the $z$ axis is centred between the two coins, whose edges are marked by white, dashed lines. (e) Histogram of $B_{\mathrm{1}}$ field intensities between the coins for the four presented calculations. A simulation without conductive coins (see “empty”) serves as a reference case to quantify $B_{\mathrm{1}}$ field enhancement. All histograms were normalised; therefore all integrals are equal.

Figure 6

(a) Calculated $B_{\mathrm{1}}$ field from simulations in a line along the $x$ axis, parallel to and central between the coin surfaces. The calculated $B_{\mathrm{1}}$ field in an empty volume without conductive coins is plotted as a reference. (b) RF amplification in comparison to $B_{\mathrm{1}}$ field in an empty volume for two extreme conditions: For a coin distance of 0.05 mm, thickness was varied between [0.05, 0.1, 0.5, 1, 2, 3, 4, 5] mm. For a coin thickness of 5 mm, distance was varied between [0.05, 0.1, 0.5, 1, 2, 3, 4, 5] mm. Dashed lines represent exponential fits to the data.

Figure A1

Simulated $B_{\mathrm{0}}$ distortions, represented by histograms over the $z$ axis, for the case of (a) no Cu foil and electrolyte-filled notch, (b) air, and (c) electrolyte underneath the Cu foil, respectively. The histograms were not corrected in terms of shimming.

Figure B1

(a, c, e, g) Nutation curves and (b, d, f, h) nutation spectra of the ¹H water resonance in nutation experiments with coin cell setups with 1 mm electrode distance, respectively. (a–b) PEEK discs with 1 mm thickness. (c–d) Cu discs with 1 mm thickness. (e–f) PEEK discs with 5 mm thickness. (g–h) Cu discs with 5 mm thickness. The point with highest intensity in nutation spectra is selected as the nutation frequency. Numerically exactly matching values are due to the limited number of 80 discrete points of the nutation curve.

Figure B2

(a, c, e, g) Nutation curves and (b, d, f, h) nutation spectra of the ¹H water resonance in nutation experiments with coin cell setups with 0.1 mm electrode distance, respectively. (a–b) PEEK discs with 1 mm thickness. (c–d) Cu discs with 1 mm thickness. (e–f) PEEK discs with 5 mm thickness. (g–h) Cu discs with 5 mm thickness. The point with highest intensity in nutation spectra is selected as the nutation frequency. Numerically exactly matching values are due to the limited number of 80 discrete points of the nutation curve.

Figure B3

Calculated $B_{\mathrm{1}}$ field from simulations in a central line along the $x$ axis, parallel to the coin surface. (a) For a coin distance of 0.05 mm, thickness was increased in the order [0.05, 0.1, 0.5, 1, 2, 3, 4, 5] mm, indicated with changing colour from green to blue. (b) For a coin thickness of 5 mm, distance was decreased in the order [5, 4, 3, 2, 1, 0.5, 0.1, 0.05] mm, indicated with changing colour from green to blue.

Figure D1

Calculated $B_{\mathrm{1}}$ field from simulations using the electrodes of coin cells as the RF coil. The magnitude of $B_{\mathrm{1}}$ field in the $xz$ plane between coins with 1 mm distance is depicted for electrode thickness of (a) 1 mm and (b) 0.1 mm. (c) Mean field averaged over the $z$ axis plotted over the $x$ axis for electrode thickness of 1 mm and 0.1 mm.