Optimally controlled nuclear magnetic resonance (NMR) in electrochemistry: Larmor versus 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 inhomogeneities in the static magnetic fields $B_0$ and the radio frequency (rf) fields $B_1$ . 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 either a particular $B_1$ or Larmor frequency ${\nu }_0$ . 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 a 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 $B_1$ distortions in the vicinity of electrical conductors to achieve spatial selectivity with simultaneous ${\nu }_0$ robustness. It was also demonstrated how QOC-tailored pulses can selectively excite specific ${\nu }_0$ despite $B_0$ 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.