Kinetics of Electrochemical Insertion and Extraction of Lithium Ion at SiO

Figure 1 shows cyclic voltammograms of SiO in an electrolyte consisting of dissolved in EC:DMC (1:1 by volume). Cathodic and anodic peaks were observed in a potential range of 0–0.6 V. These peaks were attributed to the insertion and extraction of lithium ion at the SiO electrode. The anodic peak was small at the first cycle, and it gradually increased at the following cycles. These behaviors implied that the electrochemical reaction at SiO was complicated and that there were side reactions at the early cycles. To investigate the kinetics of the charge transfer at SiO, we need to know the mechanism of the electrochemical reaction at SiO.

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SiO consists of two phases: amorphous Si domains and amorphous domains (random mixture model).^{28, 29} Both of these two domains electrochemically react with lithium. One of the most plausible reaction mechanisms is as follows:

• (1)  
  Amorphous Si domains: .
• (2)  
  Amorphous domains: .

Nagao et al. reported the formation of Li–Si alloys and after the electrochemical insertion of lithium ion by neutron elastic scattering measurements.⁸ Miyachi et al. used X-ray photoelectron spectroscopy to elucidate that Li–Si alloys, , and lithium silicates were formed after the first charge.^{10, 11} Kim et al. verified the above reaction mechanism by a solid-state and nuclear magnetic resonance technique, electrochemical dilatometry, and charge–discharge measurement.¹² A reaction at amorphous Si domains is an alloying reaction that occurs reversibly to give the charge–discharge capacity. The cathodic and anodic peaks in a potential range of 0–0.6 V in the cyclic voltammogram were attributed to the alloying/dealloying reaction of amorphous Si domains. However, a reaction at amorphous domains is almost irreversible, which might be included in the cathodic peak at the early cycles of the cyclic voltammogram.

An SEM image of an as-prepared SiO electrode is shown in Fig. 2a and 2c. The surface of a SiO electrode was a particle- or needlelike structure with a size of . To confirm that the morphology remained unchanged during ac impedance spectroscopy, we obtained SEM images of SiO that was held at 0.2 V for 24 h (Fig. 2b and 2d). There was no crack on the SiO electrode after being held at 0.2 V, and the surface morphology was almost the same as that of an as-prepared SiO electrode. As shown in Fig. 2d, there existed some precipitates on the SiO electrode after being held at 0.2 V. They were formed from the decomposition of electrolytes and were a kind of solid electrolyte interphase (SEI).

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Figures 3 and 4 show Nyquist plots of a SiO electrode in an electrolyte consisting of dissolved in EC:DMC (1:1 by volume) at 303 K. The measurement was conducted after 10 cycles of cyclic voltammetry to make sure that the irreversible reactions (i.e., the reaction at amorphous domains and the decomposition of electrolytes) were terminated. Therefore, the kinetics of the alloying/dealloying reaction of the amorphous Si domains could be investigated by ac impedance spectroscopy. In the Nyquist plot at 1.7 V, one semicircle appeared at a characteristic frequency of 1 kHz. When the electrode potential was lowered to below 1.0 V, another semicircle was observed at a characteristic frequency of 1–0.1 Hz. Two semicircles and Warburg impedance were clearly observed in the Nyquist plot at 0.3 V. Because a three-electrode cell was used, the resistance from the counter electrode (lithium metal) could be neglected. Hence, this system should give the following components of resistance: (i) lithium-ion transport in an electrolyte , (ii) lithium-ion transport in an SEI film , (iii) alloying reaction resistance at amorphous Si domains (charge-transfer resistance ), (iv) lithium diffusion in an electrode, and (v) electron transport in an electrode and at an electrode/current collector interface . Among these components of resistance, the electron transport (v) and lithium-ion transport in the electrolyte solution (i) usually give no semicircle in the present frequency range due to their high characteristic frequencies. These components of resistance appeared as a intercept in the Nyquist plot. The lithium diffusion in an electrode (iv) gave the Warburg impedance , which was observed as a straight line with an angle of 45° from the axis. The remaining two processes [(ii) and (iii)] give their own semicircles at each characteristic frequency. The semicircle with a characteristic frequency of 1 kHz was observed at 1.7 V, at which the charge-transfer reaction could not occur. Therefore, we assigned this semicircle to the lithium-ion transport in the SEI film (ii). The other semicircle with a characteristic frequency of 1–0.1 Hz appeared only below 1.0 V. Hence, this semicircle was attributed to the charge-transfer resistance at amorphous Si domains (iii).

We configured an equivalent circuit (Fig. 3c) to evaluate the charge-transfer resistance and the ion-transport resistance in the SEI. A resistance, two resistance–capacitance parallel circuits, and a Warburg impedance were connected in series. and denote a capacitance element in an SEI and a double-layer capacitance, respectively. Depending on the shape of the semicircle, a constant phase element was properly used as an alternative for . The best fit of the parameters in the equivalent circuit to experimental Nyquist plots gave the values of the charge-transfer resistance and the ion-transport resistance in the SEI.

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The Nyquist plots showed a drastic change in a potential range of 0.30–0.20 V (Fig. 4). Figure 5 shows the potential dependence of the charge-transfer resistance , the ion-transport resistance in the SEI , and the sum of the electron-transport resistance and the lithium-ion transport resistance in the electrolyte . The value significantly decreased in a potential range of 0.27–0.24 V and then disappeared below 0.24 V. This variation in was attributed to the change in the activity of lithium in the Li–Si alloy. The and values also varied with decreasing potentials in a range of 0.26–0.22 V, and these changes were reversible. The change in was derived from the increasing electronic conductivity of amorphous Si domains due to the alloying with lithium. The reversible change in was caused by the volume changes of SiO. This hypothesis is supported by the report of Kim et al.¹² They observed a significant expansion of the SiO electrode below 0.25 V. In our study, the value also changed significantly below 0.26 V, as shown in Fig. 4 and 5. Therefore, the volume change in SiO was a major cause of the change in , although the detailed mechanism was not clear in this work. An important result here is that was smaller than below 0.24 V. These results imply that the charge-transfer reaction at a SiO electrode is relatively fast.

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The interfacial conductivity obeys the Arrhenius equation

where the symbols , , , and denote frequency factor, activation energy, gas constant, and absolute temperature, respectively. Hence, the charge-transfer resistance depends on two factors, the activation energy and the frequency factor. We used the activation energy to discuss the kinetics of the charge-transfer reaction at SiO. A study on activation energies is useful for a clear discussion because the activation energy values indicate the essential kinetics of the reaction without the influences of effective surface area, activity of reactants, and temperature.

Figure 6 shows the Arrhenius plots of the interfacial conductivities at SiO at 0.4 V in various electrolytes. The activation energies of the charge-transfer reaction were evaluated from the slopes of the Arrhenius plots according to the Arrhenius equation (Eq. 1). The activation energies were around in the four electrolytes. These values are small compared to those at other electrodes. When a graphite electrode was used, the activation energy of the charge-transfer process was reported to be in EC-based electrolytes.^{14, 15} In positive electrode materials such as and , the activation energies were evaluated to be around in PC-based electrolytes.^{16, 17} Therefore, the small activation energies at SiO suggest that the charge-transfer reaction at SiO is much faster than those at other insertion electrodes.

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One of the important points of the present paper is the effect of the desolvation of lithium ion during the insertion of lithium ion into the SiO electrode. Our group studied the kinetics of charge (lithium ion) transfer at various interfaces and reported that the desolvation of lithium ion was the rate-determining step of charge-transfer reactions, resulting in large activation energies (around or more).^{14, 15, 18, 19} In the SiO electrode, however, the extremely small activation energies (around ) of the charge-transfer reaction suggest that the desolvation of lithium ion does not influence the charge transfer at SiO.

A comparison of activation energies in various electrolytes supports this hypothesis about the effect of the desolvation of lithium ion. Table I shows activation energies of charge (lithium ion) transfer at interfaces consisting of various solid and liquid phases. The activation energies greatly varied at a graphite/liquid electrolyte interface¹⁵ and ideal interfaces^{17, 18} consisting of a solid electrolyte [ (LLT) or Li–Al–Ti-phosphate-based glass] and a liquid electrolyte. The activation energies of charge transfer at these interfaces depended on the enthalpy changes of the reaction calculated with the density functional theory by Gaussian 98.²⁷ Because the enthalpy changes indicate the solvation abilities of solvents, the correlation between the activation energies and the enthalpy changes suggests that the activation energies reflect the energy for desolvation of lithium ion from the solvent. In the SiO electrode, however, the activation energies of charge transfer remained unchanged at around in the four electrolytes. Based on these results, the kinetics of the charge transfer at SiO is not influenced by the compositions of electrolytes and that the desolvation of lithium ion is not the rate-determining step of the charge transfer at SiO.

Table I. Activation energies of charge (lithium ion) transfer at the interfaces consisting of various solid and liquid phases.

Solvent	Enthalpy change a
		Solid electrolyte18, 19	Graphite14, 15	SiO
DMSO	−235.5	70b	Cointercalation	29
PC	−217.1	57b	Exfoliation	30
EC:DMC (1:1)	−210.3 (EC)	51c	58	32
DMC	−190.3	32c	40	31
Fluoroethylene carbonate	−185.5	32b	—	—

^aReaction enthalpy of the reaction . ^bSolid glass electrolyte (OHARA glass). ^cSolid .

The results in the present study indicate that the kinetics of the electrochemical reaction at SiO is quite different from those at other insertion electrodes. As discussed above, the electrochemical reaction at SiO is the alloying/dealloying reaction at the amorphous Si domains. We consider that the absence of the effect of the desolvation is inherent in the alloying/dealloying reaction. Although the detailed mechanism is not yet clear, the small activation energies at SiO suggest that the SiO electrode has a kinetic advantage over other insertion electrodes such as graphite.