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

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, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mi>B</mml:mi> <mml:mn>0</mml:mn></mml:msub> </mml:mrow> </mml:math> , and the radio frequency field, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mi>B</mml:mi> <mml:mn>1</mml:mn></mml:msub> </mml:mrow> </mml:math> , 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mi>B</mml:mi> <mml:mn>0</mml:mn></mml:msub> </mml:mrow> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mi>B</mml:mi> <mml:mn>1</mml:mn></mml:msub> </mml:mrow> </mml:math> distortions is provided in this study. Three-dimensional finite element method (FEM) simulations of both <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mi>B</mml:mi> <mml:mn>0</mml:mn></mml:msub> </mml:mrow> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mi>B</mml:mi> <mml:mn>1</mml:mn></mml:msub> </mml:mrow> </mml:math> fields were employed to investigate cell structures with electrodes oriented perpendicular to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mi>B</mml:mi> <mml:mn>0</mml:mn></mml:msub> </mml:mrow> </mml:math> , 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, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mi>B</mml:mi> <mml:mn>1</mml:mn></mml:msub> </mml:mrow> </mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mi>NaHCO</mml:mi> <mml:mn>3</mml:mn></mml:msub> </mml:mrow> </mml:math> electrolyte. Finally, the theoretical and experimental results are distilled into design guidelines for EC-NMR cells.