Optimally controlled NMR in electrochemistry: Larmor and nutation frequency selective spin excitation for locally selective NMR experiments

Abstract. Spectroelectrochemical nuclear magnetic resonance (NMR) experiments are faced with numerous challenges originating from shielding effects and susceptibility gradients in samples, leading to inhomogeneous static magnetic fields B₀ and radio frequency (rf) fields B₁. Moreover, magnetic feedback caused by eddy currents in conductors can obstruct precise measurements. Previous works have shown that these eddy current induced magnetic field distortions can be accurately predicted by finite element method (FEM) simulations. In this work, we present a workflow combining FEM predictions with quantum optimal control (QOC) to tailor custom NMR pulses that exploit specific magnetic field distortions for selective excitation of affected sample regions. The desired selectivity was achieved using pattern pulses optimized for a particular B₁ or Larmor frequency ν₀. Experimental validation was performed on a heterogeneous phantom consisting of two cavities filled with two spectroscopically distinguishable liquids, one between copper disks to mimic an electrochemical cell, and one between polymer disks as reference. An over 30-fold suppression of the reference resonance in between polymer compared to the resonance in between copper disks was achieved, demonstrating how QOC-tailored pulses can selectively address FEM-predicted B₁ distortions to achieve spatial selectivity. It was also demonstrated how QOC-tailored pulses can selectively excite specific ν₀ despite of B₀ distortions, which implies that difficulties with conventional solvent suppression techniques in electrochemical setups can be mitigated using the adjustable robustness of QOC-tailored pulses. The presented approach sets the stage for gradient-free, localized in operando NMR in electrochemistry and material sciences, with the prospect of surface selectivity down to the detection limit of the setup.