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Materials Today d Volume 44 d April 2021 SHORT COMMUNICATION FIGURE 4 (a) Symmetrical Li||Li cells for PEO-based SPE with 20:1 (EO:Li) for varied current densities at 40 C. The Sand equation is only valid above the threshold (25 mA cm2) as the blocking-type polarization does not appear below this threshold value. (b) This threshold value can also be validated in NMC622||Li cells. The blocking-type polarization does not appear below 10 mA g1 for NMC622, which is 20 mA cm2 for Li. (The initial activation-like overvoltage for specific currents above 25 mA g1 is likely related with NMC-intrinsic wetting phenomena and disappears in second cycle, as shown in supplementary material). ization, is higher. In other words, below this threshold current density, the Li+ transport to the electrode is sufficient, thus the Li+ concentration in the electrolyte close to the electrode surface is not depleted and the Sand equation is not valid any more. This relation is also validated for varied SPE thicknesses, which is shown in supplementary material. The practical relevance of this finding is demonstrated for EO: Li (20:1) in Fig. 4(a). For current densities above the calculated threshold value of 25 mA cm2 (Table 1), the respective polariza- tions precisely appear as predicted by the Sand equation. Below this threshold value the Sand equation is not valid, as no polar- ization, thus Li+ depletion can be observed, even though a theo- retical transition time of 15 h should occur. This behavior is valid also in NMC622||Li cells, as shown Fig. 4(b). Given the NMC622 electrode-based mass loading of 2 mg cm2, the calculated threshold current is 12.5 mA g1. In other words, above this specific current (or C rate above % 0.1 C), a blocking-type polar- ization appears above the calculated threshold current and is absent below this value. This finally demonstrates the validity and relevance of the Sand equation and moreover, an ability to precisely predict an LMB cell behavior under practical conditions with respect to the threshold current. The initial charge process is methodically more beneficial to obtain the respective relations than the discharge. Theoretically, the Sand relation is also valid in the opposite direction of Li+ transport, i.e. during discharge in NMC622||Li cells, but the com- posite particle-based nature of NMC-based cathodes render the determination of active surface area and evaluation unnecessary challenging. In addition, the NMC characteristic voltage slope near end of discharge [43] render the attribution to Sand behav- ior more complex. Therefore, the investigation of Sand relation and related (transferrable) parameter is highly recommended in Li||Li symmetrical cells curing charge. (The respective discharge curves can be found in supplementary material) Conclusion The correlation between physicochemical aspects and cell perfor- mance for high voltage application is still pending for the bench- mark poly(ethylene oxide)-based solid polymer electrolyte (PEO- based SPE) in Li metal batteries. Given recent insights, a PEO- based SPE can be initially cycled and thus characterized even with high voltage electrodes, e.g. LiNi0.6Mn0.2Co0.2O2 (NMC622). It is shown, that the performance of NMC622||Li cells can be related with the salt concentration/ionic conductiv- ities of the SPE, which is particularly evident at lower tempera- ture, i.e. 40 C. However, below a certain salt concentration a sudden blocking-type polarization appears, which can be seen by an almost vertical voltage increase, also in Li||Li symmetrical cells. The assumed Li+ depletion on the electrode surface, thus the rela- tion with the Sand equation is confirmed by a good agreement between theoretical and experimental values of the transition time, i.e. the time when this polarization appears for the respec- tive current density. On this basis, DLi+ for varied salt concentra- tions can be calculated. In line with theory it is confirmed, that the Sand equation is practically only valid for conditions where Li+ depletion appears i.e. below a threshold salt concentration, above a threshold SPE thickness and/or above a threshold current density. The calcu- lated/predicted threshold current densities are experimentally verified in symmetric Li||Li and NMC622||Li full cells and demonstrate a simple way to precisely predict the practical max- imal (e.g. current) limits for SPEs. CRediT authorship contribution statement Lukas Stolz: Conceptualization, Writing-original draft, Inves- tigation, Methodology, Visualization. Gerrit Homann: Inves- tigation, Methodology, Software. Martin Winter: Funding acquisition, Project administration, Writing-review & editing. Johannes Kasnatscheew: Conceptualization, Writing- original draft, Supervision, Methodology, Visualization. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. 13 RESEARCH: Short CommunicationPDF Image | Sand equation and its enormous practical relevance
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