The Sand equation and its enormous practical relevance for solid-state lithium metal batteries

In this work, different Li salt concentrations and ionic conductivities of poly(ethylene oxide)-based solid polymer electrolytes (PEO-based SPEs) are correlated with the performance of LiNi 0.6 Mn 0.2 Co 0.2 O 2 (NMC622)||Li full cells. While the SPEs with different salt concentrations behave similarly in NMC622||Li cells at 60 °C, their influence on the specific capacities is significant at 40 °C. Below a distinct salt concentration, i.e.  > 20:1 (EO:Li), a sudden blocking-type polarization appears, indicatable by an almost vertical voltage profile, both in full and in Li||Li symmetric cells. The corresponding time and current density for this polarization-type is shown to mathematically fit with the Sand equation, which subsequently allows calculation of D Li +. According this relation, lack of Li + in the electrolyte close to the electrode surface can be concluded to be the origin of this polarization, but is shown to appear only for “kinetically limiting” conditions e.g. above a threshold current density, above a threshold SPE thickness and/or below a threshold salt concentration (ionic conductivity), i.e. at mass transfer limiting conditions. With the support of this relation, maximal applicable current densities and/or SPE thicknesses can be calculated and predicted for SPEs.