Effects Of Additional Subcircuit
Figure 2a shows the dependence of the Li collection rate and faradaic efficiency on the secondary-power-supply voltage in the new electrochemical pumping system. In our previous study42, which was also conducted using the LLTO electrolyte diaphragm and Pt electrodes used in the present study, no electronic conduction occurred in the LLTO, and the Li-ion transference number was 1 when the main-power-supply voltage was below 2.0 V. The distance between the second and third electrodes and concentration of the cathode-side LiOH solution were 57 mm and 0.001 mol/L, respectively. The values for a conventional electrochemical pumping system without the secondary power supply and third electrode were plotted using a secondary-power-supply voltage of 0 V. When the main-power-supply voltage was 2.0 V, the faradaic efficiency remained constant regardless of the secondary-power-supply voltage, and the Li collection rate increased with increasing secondary-power-supply voltage. Increasing the secondary-power-supply voltage led to hydrogen gas generation owing to the remarkably rapid reduction of protons at the third electrode, which was confirmed by naked-eye observation, although this was not evident on the surface of the cathode in the conventional system (secondary-power-supply voltage = 0 V).
The increase in the Li recovery rate can be explained using the subcircuit constituent factors Esecond, R2, RLiOH, and R3 in the simplified equivalent circuit (Fig. 1b). Equations (5) and (6) describe the relationship between the power supply voltages, impedance of the elementary reaction process, and currents.
E main = R1I1 + RLLTOI1 − R2(I3 − I1) = (R1 + RLLTO + R2)I1 − R2I3, (5)
E main + Esecond = R1I1 + RLLTOI1 + RLiOHI3 + R3I3 = (R1 + RLLTO)I1 + (RLiOH + R3)I3, (6)
where Emain, Esecond, R1, RLLTO, R2, RLiOH, R3, I1, I3 − I1, and I3 are the main-power-supply voltage; secondary-power-supply voltage; impedance of the anodic reaction on the first electrode; impedance of Li-ion conduction via LLTO; impedance of the reaction on the second electrode, which was caused by the cathodic (H2 generation and elution of Li+ into the solution) or anodic reactions (O2 generation and elution of Li+ into the solution); resistance of the solution in the cathode-side tank; impedance of the hydrogen-gas-generating reaction at the third electrode; and currents monitored using ammeters I, II, and III, respectively. R1I1, RLLTOI1, R2(I3 − I1), RLiOHI, and R3I3 represent the overpotential of the anodic reaction, difference between the Fermi potentials of the two electrolyte surfaces (electrolyte overpotential), overpotential of the cathodic reaction, potential difference between the second and third electrodes in the LiOH solution in the cathode-side tank, and overpotential of the hydrogen-gas-generating reaction at the third electrode, respectively. The direction of the current, as depicted in Fig. 1b, was opposite to the direction of the electron flow, as shown in Fig. 1a. All impedances were considered to be constant and independent of the voltage. Because R and all I had positive values, I1 and I3 increased with increasing Esecond, as indicated by the third term in Eq. (6). Because Emain was constant in the experiments that yielded the Fig. 2 results, I1 also increased with increasing I3, as indicated in Eq. (5). In other words, both I1 and I3 increased with increasing Esecond. The Li-ion transference number was 1 under the experimental conditions that led to the Fig. 2 results; thus, according to Faraday’s law, I1 was equivalent to the Li collection rate ν. Therefore, the increase in the Li collection rate (Fig. 2a) was due to the construction of the subcircuit (Mechanism I) comprising a secondary power supply and additional electrode. Phenomenologically, this was caused by two factors: an increase in the anodic reaction rate caused by the overpotential of the anodic reaction R1I1 at the first electrode, and an increase in the cathodic reaction rate caused by the overpotential of the cathodic reaction R3I3 at the third electrode, which result from the increase in I1. This effect was clarified by analyzing the dependence of the Li collection rate on the distance between the second and third electrodes and the concentration of the cathode-side LiOH solution (Supplementary Figs. 1a and 1b, respectively). In both experiments, the main- and secondary-power-supply voltages were 2.0 and 5.0 V, respectively. A cathode-side LiOH solution concentration of 1.0 mol/L and a distance between the second and third electrodes of 57 mm were used to obtain the data shown in Supplementary Figs. 1a and 1b, respectively. The Li collection rate monotonically increased with decreasing distance between the second and third electrodes (Supplementary Fig. 1a) and increasing concentration of the cathode-side LiOH solution (Supplementary Fig. 1b). The decreasing distance between the electrodes as well as the increasing conductive carrier density due to the increase in LiOH solution concentration diminished the resistance of the cathode-side solution between the second and third electrodes (RLiOH). Consequently, I1 and I3 increased even when Emain and Esecond were fixed, as indicated by the second term in Eq. (6). These phenomena can be explained by the fact that the aforementioned increases in current were due to enhanced rates of elementary reactions and ion diffusion, which were caused by the decrease in the potential of the elementary reactions owing to the reduction in the potential difference between the second and third electrodes. The results shown in Supplementary Fig. 1b indicate that the Li collection rate in the new system did not decrease significantly, even if the chemical potential difference decreased owing to the increase in Li-ion concentration of the cathode-side solution as the Li migration proceeded. This feature is another advantage of the new system, considering that the Li concentration of the cathode-side solution must be high to permit industrial production of lithium carbonate or LiOH powders.
Limitations Of New System In Terms Of Li Collection Rate
In this section, the dependence of I1, I2, and I3 on the secondary-power-supply voltage (Fig. 2b) is examined and the limitations involved in balancing the main- and secondary-power-supply voltages are discussed. As inferred from the simplified equivalent circuit (Fig. 1b), the sum of I1 and I2 is I3, regardless of the direction of voltage or current. When Emain was equal to or higher than the theoretical electrolysis voltage of H2O, I1 and I3 were always positive, and oxygen and hydrogen gases were always generated at the first and third electrodes, respectively, regardless of the power-supply voltage. However, the direction of I2 was reversed by the secondary-power-supply voltage. When the main-power-supply voltage was fixed at 2.0 V, I2 was always positive if the secondary-power-supply voltage was equal to or greater than 6.0 V. That is, a sufficiently high secondary-power-supply voltage above a certain threshold ensured that the potential of the second electrode was always higher than the oxygen-gas-generating potential, thereby preventing the reduction of the LLTO electrolyte. However, I2 was always negative at secondary-power-supply voltages below 5.0 V, and hydrogen gas was generated at the second electrode. Moreover, although the main-power-supply voltage was constant, all gas generation speeds varied with the secondary-power-supply voltage so clearly that they could be ascertained visually. Considering that the gas-generating-reaction rate varied with the reaction overpotential (that is, the potential of the reaction field), the cathode-side surface potential of the electrolyte diaphragm changed with the secondary-power-supply voltage. Overall, the results indicate that a high secondary-power-supply voltage increased the upper limit of the main-power-supply voltage at which a positive cathode-side surface potential could be maintained for the electrolyte diaphragm.
The changes in faradaic efficiency, Li collection rate (Fig. 3a), and currents (Fig. 3b) when the main-power-supply voltage was varied and the secondary-power-supply voltage was fixed at a high value of 10.0 V were subsequently analyzed. The currents shown in Fig. 3b are approximately two orders of magnitude larger than those in Fig. 2b. As shown in Fig. 3b, I1 and I3 were always positive and increased with increasing main-power-supply voltage. In contrast, I2 gradually decreased with increasing main-power-supply voltage. Notably, even when the main-power-supply voltage was 5.0 V, I2 was positive and oxygen gas was generated at the second electrode. The main-power-supply voltage at which I2 became negative, which was estimated by extrapolating the plot in Fig. 3b, was approximately 7 V or higher. The use of a higher secondary-power-supply voltage will increase the upper limit of the main-power-supply voltage.
Overall, these results suggest that by increasing the secondary-power-supply voltage to an appropriate value, the main-power-supply voltage can be increased indefinitely while preventing electronic conduction in the electrolyte diaphragm. Essentially, this new electrochemical pumping system can achieve an arbitrarily high Li-extraction/recovery without the abrupt drop in energy efficiency due to the reduction in faradaic efficiency. In practice, this was confirmed by analyzing the dependence of the faradaic efficiency and Li migration rate on the main-power-supply voltage (Fig. 3a). In conventional systems, electronic conduction is known to occur in the LLTO electrolyte at main-power-supply voltages above 2.5 V, which lead to an abrupt decrease in the faradaic efficiency42. However, in the new system operated a secondary-power-supply voltage as high as 10.0 V, a faradaic efficiency of 1 was maintained even when the main-power-supply voltage was 5.0 V. The Li collection rate in this scenario was 1.40 kg/m2/h, which was 464 times higher than the maximum value (3.01 g/m2/h) obtained using a conventional system operated at a main-power-supply voltage of 2.0 V; the value obtained by establishing contact between the first and second electrodes and the LLTO electrolytic diaphragm is greater than that [2.40 g/m2/h] reported by Zhen et al43). Because these voltages can be further increased by maintaining the balance between the main- and secondary-power-supply voltages, as described above, the Li collection rate is theoretically not limited to the values reported herein and can be extremely high.
Enhancement Of The Reaction Field Area For Rate-limiting Processes
Nyquist (Fig. 4a) and Bode plots (Figs. 4a and 4b, respectively) were acquired by performing two-pole complex impedance measurements between the first and second electrodes using a LiOH solution (1.0 mol/L) in both the anode- and cathode-side tanks. The main-power-supply voltage was 2.0 V. The open and closed symbols in Fig. 4 correspond to the conventional (no secondary power supply) and new systems (secondary power supply voltage = 2.0 V), respectively. Three arcs with peak frequencies of approximately 10− 1, 101.5, and 102.5 Hz were observed in the spectrum of the conventional system. Our previous study40 revealed that the arc with a peak frequency of approximately 102.5 Hz corresponds to the grain-boundary impedance of the LLTO electrolyte, and that the other two arcs in the low-frequency region represent electrode reactions accompanied by gas generation. The arc with a peak frequency of approximately 101.5 Hz became negligibly small after the secondary-power-supply voltage was applied. This is because the hydrogen-gas-generating reaction occurred at the third electrode, which had a large surface area and reaction field. Consequently, the hydrogen-gas-generating reaction presumably exhibited an increased rate and no longer dominated the Li collection rate. Therefore, the total impedance was also considerably reduced and the new system containing the third electrode with a large surface area was presumed to dramatically increase the Li collection rate (Mechanism III). Moreover, the intensity of the arc with a peak frequency of ~ 10− 1 Hz decreased slightly because the reaction field for oxygen gas generation increased, as oxygen gas was generated at the first as well as the second electrodes.