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SHORT COMMUNICATION Materials Today d Volume 44 d April 2021 FIGURE 3 (a) Voltage curves as a function of time for an exemplary Li salt concentration of 20:1 (EO:Li), in symmetrical Li|SPE|Li cells for varied current densities. The higher the current density, the lower s. (b) The relation of the current density and the respective s allows determination of DLi +. The values from (a), i.e. (i), (ii) and (iii), fit well with mathematically derived curve from the Sand equation. the charge process. Beginning with a slight overvoltage, this sud- den polarization appears at %75 mAh g1, which can be indi- cated by an almost vertical voltage profile. This points to a sudden appearance of an additional kinetic issue and can be proved in symmetric Li||Li cells for equal Li current densities as shown in Fig. 2(b). The ratio of 20:1 (EO:Li) shows partially both, a reasonable charge but also a blocking-type polarization. This phenomenon is obviously independent of the cathode and rather related with the electrolyte properties, i.e. ionic conductiv- ity. To be more precise, this phenomenon can be attributed to the Li+ depletion at the electrode/electrolyte interface during Li plating (Fig. 2c) as the parameter fit with the theoretical Sand equation (I) [32,41], with j (current density), s (transition time), ze (electron number per unit), F (Faraday constant), c (salt concentration) and DLi+(Diffusion constant). The period when the Li+ concentration in the electrolyte approaches zero at the electrode surface is The current density is inversely proportional to the transition time according Eq. (1). This is verified for varied current densities in Li||Li cells, which is shown in Fig. 3(a) for 20:1 (EO:Li) ratio, thus a Li salt concentration of 1 mol L1. According to the Sand equation, DLi+ can be accurately determined for each measure- ment and is in average 3.0 ∙10-9 cm2 s1 [34]. The transition times for the respective current densities (i), (ii) and (iii) are marked in Fig. 3(b). All three points fit to the curve derived from the Sand equation, which gives mathematical evidence for the proposed relation of Li+ depletion in the electrolyte close to the electrode surface as source of blocking-type polarization and is valid for other Li salt concentrations (supplementary material). In a similar way, DLi+ can be determined for the other salt con- centrations at 40 C and are summarized in Table 1. As expected, DLi+ gets higher with increasing salt concentration because the quantity of Li+-conducting amorphous phases in the PEO-based SPE, thus Li+ mobility, increases with the amount of plasticizing Li salt [22]. It is worth noting that the Sand equation is only valid for con- ditions when Li+ depletion occurs, thus for scenarios where the rate of Li+ transport within the SPE to the electrode surface is not sufficient to counteract Li+ depletion [39]. Hence, for a given salt concentration, the Li+ depletion appears for a sufficiently pffiffiffipffiffiffiffiffiffiffiffiffiffiffi þ high current density and/or high SPE thickness as the diffusion 1 jðsÞ1⁄4zeFc p DLi pffiffi ð1Þ pffiffiffiffiffiffiffi length L 1⁄4 Ds at the time s must be lower than the SPE thick- 2s ness [34,42]. The respective threshold current density (j*) and/or threshold thickness (L) can be calculated according Eq. (2) via incorporation of Eq. (3) into Sand equation (1): pffiffiffi j 1⁄4zeFc pDLiþ ð2Þ 2L s 1⁄4 pffiffiffiffiffiffiffiffiffiffiffi ð3Þ defined as transition time (s). The blocking-type polarization sub- + pffiffi L DLiþ sequently appears when Li is fully depleted at the surface, thus when the reaction causing depletion is faster than the Li+ trans- port through the SPE, as shown in Fig. 2(d). As confirmed on Cu substrate and in a three-electrode cell setup with the use of a reference electrode (supplementary material), this polarization appears at the electrode, where Li+ gets depleted, i.e. during Li plating process. For a defined SPE thickness of 100 mm, the threshold current densities are calculated and summarized in Table 1 for varied salt concentrations. For higher salt concentrations, thus higher D+ , Li the threshold current for the Sand equation, i.e. for the appear- ance of Li+ depletion in the electrolyte and blocking-type polar- TABLE 1 + DLi and threshold currents (j*) for varied salt concentrations calculated on the basis of the Sand equation. EO:Li ratio 10:1 12:1 15:1 20:1 50:1 DLiþ /109 cm2 s1 7.8 1.4 3.6 0.4 3.2 0.3 3.0 0.3 1.1 0.3 j*/lA cm2 106 20 43 4 33 3 25 2 5 2 12 RESEARCH: Short CommunicationPDF Image | Sand equation and its enormous practical relevance
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