ENMR-derived Transference Numbers in Different Reference Frames

Abstract

With the powerful measurement technique of electrophoretic NMR (eNMR) direct insight into ion movements in liquid electrolytes is possible. This direct access to ion mobilities allows for the calculation of important transport parameters like the transference number of ionic species.[1] The transference number is a valuable performance indicator for batteries and a necessary input parameter for physics-based battery simulations. However, their reference frame dependence has to be carefully considered. With our transport theory for highly concentrated electrolytes we can describe transport processes in different reference frames. It was originally developed in the center-of-mass representation.[2] How-ever, we recently showed how eNMR measurements on ionic liquid mixtures can be better described via the volume-based frame of reference assuming local molar volume conservation and a vanishing volume flux as boundary condition (Fig. 1).[3,4] We derived rules to transform between different reference frames. We apply these transformation rules to transference numbers of ionic liquid mixtures and assess them quantitatively in different repre-sentations, like the center-of-mass-, volume- or species-fixed reference frames (Fig. 2). This rationalizes the role of transference numbers in highly concentrated electrolytes and adds to recent discussions about their frame-dependence. [1] Gouverneur, M. et al. Phys. Chem. Chem. Phys. 2018, 20(11), 7470-7478. DOI: 10.1039/c7cp08580j [2] Schammer, M. et al. J. Electrochem. Soc. 2021, 168(2), 026511. DOI: 10.1149/1945-7111/abdddf [3] Lorenz, M. et al. J. Phys. Chem. Lett. 2022, 13(37), 8761-8767. DOI: 10.1021/acs.jpclett.2c02398 [4] Kilchert, F. et al. 2022 arxiv.org/abs/2209.05769