Phase Transition Kinetics of LiFePO₄ Biphasic Systems in Aqueous and Non-aqueous Electrolytes

Abstract

Power characteristics become one of the important performance measures of lithium-ion batteries as high-power applications such as electric vehicles are emerging. Among several electrochemical steps that limit the power characteristics, phase transition kinetics is known as the limiting step for two-phase coexisting (biphasic) materials. In this study, we used LiFePO₄ as a model biphasic material and investigated the intrinsic factor that limits the phase transition behavior. When the same LiFePO₄ electrodes were tested in non-aqueous and aqueous electrolytes, the activation energy for the aqueous system was lower. In addition, impedance measurements using 4-electrode cells show that the charge-transfer resistance at the electrode/electrolyte interface in the aqueous media is also lower than that in the non-aqueous media, suggesting more facile solvation/de-solvation process in the aqueous media. This indicates that the rearrangement of the phase transition boundary (LiFePO₄/FePO₄) is sufficiently fast and other factors such as charge-transfer at the electrode/electrolyte interface affects the whole reaction rate.

1. Introduction

Lithium-ion batteries (LIBs) are widely used with their advantage of high energy density, high charge-discharge efficiency and long lifetime. The demand for LIBs is rapidly rising to realize clean technology in our sustainable society such as electric vehicles and renewable energy storage. The power characteristics are regarded as one of the important performance measures of batteries, as represented in the Ragone diagram.^1–6 High power performance is required especially in the electric vehicle for quick vehicle acceleration to avoid accidents and for regenerative braking. The LIBs have inherently limited power characteristics due to the low ionic conductivity of organic electrolytes used in LIBs (typically 10⁻² cm⁻¹ at room temperature), compared to the values of the aqueous electrolyte (typically 10⁰ S cm⁻¹ at room temperature).⁷ To overcome this disadvantage, thin electrodes coated on the current collector foil are jelly-rolled or stacked to achieve certain power output.^8–10

Besides the ionic conductivity (or ion transfer speed) of the electrolyte, other factors can affect the power characteristics of the LIBs, such as phase transition behavior, ion/electron transfer in the electrode, and charge transfer at the electrode/electrolyte interface.¹¹ For example, when lithium iron phosphate, a representative two-phase coexistence (biphasic) material, is used as the electrode material, it has been reported that the phase transition behavior is often a limiting factor for high-power output, and migration of the phase boundaries is rate-determining.¹² Because lithium iron phosphate undergoes a volume change of about 7 % during the phase transition between LiFePO₄ and FePO₄, the lattice rearrangement at the phase transition border has been reported to determine the phase transition rate,¹³ even though the origin of the high transition rate and the resultant high-power characteristics of the LiFePO₄ electrodes are not fully understood. There are a few types of microscopic analysis to clarify the physical images of phase transition border.^14,15

The macroscopic dynamics of these reactions has been analyzed by operando measurement, where the behavior of the entire electrode is correlated to the electrochemical phase transition.¹⁶ For example, it has been shown that the amount of the electrochemical reaction product (LiFePO₄ or FePO₄) obtained from the operando X-ray absorption spectroscopy (XAS) measurements coincides with the amount of the passed current (integrated capacity).¹⁷ This behavior has been supported also by the optical measurements.¹⁸ Phase transitions are reported to be the rate-determining factor in some other biphasic systems.¹⁹

One of the common methods to evaluate the phase transition kinetics is chronoamperometry by the potential step measurement where the current response, associated with the fraction of the phase transition product, is measured as a function of time. It has been found for the lithium iron phosphate electrodes that the fraction of the phase transition product f follows the Avrami equation f = 1 − exp(−kt)ⁿ, where k, t and n are the reaction rate constant, time and Avrami exponent, respectively, and that the phase transition proceeds via the first-order reaction kinetics, namely n = 1.¹⁷ The first-order kinetics suggests that the rate of nucleation is slower than the rate of nuclear growth in the phase transition of the lithium iron phosphate.

Because the macroscopic reaction rate constant k is affected by many factors such as electrochemically active surface area and electrode morphology, the intrinsic reaction kinetics in different electrochemical systems can be well compared with the activation energy of the phase transition reaction.²⁰ The activation energy E_a can be obtained by the Arrhenius plots where the k values measured at various temperatures T are plotted versus T⁻¹. However, there is still discrepancy in the reported activation energy values for the identical phase transition behavior of the lithium iron phosphate electrodes (13 kJ mol⁻¹,²⁰ 40–42 kJ mol⁻¹,²¹ 34–41 kJ mol⁻¹²²), which suggests that there can be some other factors governing the phase transition rate. The phase transition process includes the rearrangement of the phase boundary, ion/electron transfer within the electrode, charge transfer at the electrode/electrolyte interface, and ion transfer in the electrolyte, as depicted in Fig. 1, and some of them can affect the entire rate even if the rearrangement of the phase boundary is the trigger of the phase transition. For example, the effect of the charge transfer at the electrode/electrolyte interface can be deduced by comparing the kinetics of the same electrode reactions in different electrolyte solutions, but no such research has been employed.

Figure 1.

Scheme of possible rate-determining factors in phase transition kinetics of biphasic material particle immersed in electrolytes during lithium extraction.

In this study, we use lithium iron phosphate (LiFePO₄) as a model electrode and examine the phase transition behavior. We changed the electrolyte solution to examine the effect of charge transfer at the electrode/electrolyte interface on the phase transition of LiFePO₄. We used non-aqueous and aqueous electrolytes with the LiFePO₄ electrode to change the charge transfer conditions at the electrode/electrolyte interface. The FePO₄ host is suitable to be examined in not only in non-aqueous but also aqueous electrolytes.^23–27 If the rearrangement of the phase boundary determines the whole process rate, such a change in the charge transfer conditions at the electrode/electrolyte interface does not affect the phase transition kinetics. Indeed, previous study has shown that the rate capability of the LiFePO₄ electrode in the aqueous systems is better than that in the organic electrolyte systems,²³ but this could be better wettability of the electrode in aqueous media. Therefore, in this study, the activation energy for the charge transfer process was comparatively evaluated by measuring the charge transfer impedance using four-electrode cells.²⁸ For the measurements in aqueous systems, we used newly developed water-stable lithium insertion electrodes made of chemically oxidized (delithiated) LiFePO₄ (O-LFP). By comparing the activation energy values of these experiments, the factor to determine the entire phase transition rate is discussed.

2. Experimental

The LiFePO₄ powder (Hosen, average particle size: several hundred nm, see Fig. S1) was mixed with carbon black (Denka), polyvinylidene fluoride (Kureha) and 1-methyl-2-pyrrolidone (Kanto Chemicals, 99 %) in a weight ratio of 85 : 10 : 5 : 64 to form electrode slurry. The slurry was coated onto metal foils. Aluminum foil was used as the current collector for the non-aqueous solution systems whereas titanium foil was used as the current collector for the aqueous solution systems to avoid possible aluminum corrosion in the aqueous electrolytes. The electrodes were dried in an oven at 80 °C in air. The thickness and loading amount of the LiFePO₄ electrode were ca. 25 mm and 0.28 mAh cm⁻², respectively. The charge-discharge experiments and the potential step measurements were employed using three-electrode cells. The non-aqueous type cell was constructed by using the prepared LiFePO₄ working electrode, a lithium foil counter electrode, a lithium foil reference electrode with a 1 mol dm⁻³ solution of LiPF₆ in ethylene carbonate (EC) and diethyl carbonate (DEC) (1 : 1 v/v) as the electrolyte. The aqueous cell was constructed by using the prepared LiFePO₄ working electrodes, a Ni wire counter electrode, an Ag/AgCl reference electrode (in saturated KCl) with a 0.5 mol dm⁻³ Li₂SO₄ aqueous solution as the electrolyte. This concentration was chosen to equalize the Li⁺ molarity in the non-aqueous and aqueous electrolytes. After the cell was assembled, the charging–discharging behavior was first measured to confirm the cell characteristics in both electrolyte systems, as shown in Fig. S2. Then, the potential step was employed by extracting lithium from LiFePO₄. Unless mentioned, the potential step was employed in the anodic (lithium extraction) direction and the width was kept 0.3 V from the open circuit state to control the effect of overvoltage on velocity for both aqueous and non-aqueous electrolyte systems.

To see whether the phase transition is rate-determining, the Avrami plot, showing the relationship between ln[ln(1 − f)⁻¹] and ln(t), was created using the integrated currents obtained from the results of the potential step measurements. When the phase transition is rate-determining, the slope of the Avrami plot is unity (n = 1) and the reaction apparently proceeds via the first-order reaction kinetics.²⁰ The Avrami plots based on the potential step results were used to obtain the reaction rate constant k. These electrochemical measurements were performed at several temperatures between 5 °C and 35 °C. Then the Arrhenius plot was made using the experimentally obtained rate constants k values at different temperatures, and the activation energy was evaluated.

To investigate the charge transfer resistance at the electrode/electrolyte interface, the four-electrode AC impedance measurements were performed using the cell shown in Fig. 2, consisting of a lithium conducting solid electrolyte (Li₂O–Al₂O₃–SiO₂–P₂O₅–TiO₂ sintered plate LiCGC, Ohara) sandwiched by two containers filled with lithium conducting liquid electrolytes. The thickness of LICGC and the volume of each electrolyte container were ca. 150 mm and ca. 15 cm³, respectively. The contacting area of the solid electrolyte to the liquid electrolyte was ca. 0.50 cm² (on one side), restricted by O-rings. The AC current was flown in between the two counter electrodes and the potential in between the two reference electrodes were measured. The resultant impedance spectra include three processes: lithium conduction in the solid electrolyte, lithium conduction in the liquid electrolyte and the charge transfer resistance at the electrode/electrolyte interface. The third term is generally considered as the process of solvation/de-solvation of ions.²⁸ In the non-aqueous system, metallic lithium was used for the counter and reference electrodes. In the aqueous systems, it is necessary to fabricate the electrode that can reversibly insert and extract lithium ions and is stable in the aqueous electrolytes. We employed partially chemically oxidized (delithiated) LiFePO₄ (O-LFP) electrodes for this purpose, which were obtained by partial chemical oxidation of LiFePO₄ by an oxidant of NO₂BF₄ adjusted to 0.1 mol dm⁻³ in the acetonitrile solvent. The successful partial oxidation (delithiation) was confirmed by X-ray diffraction as shown in Fig. S3 and the degree of delithiation was about 50 %, according to some peak intensity ratios. The O-LFP electrodes were used for both the counter and reference electrodes in the AC impedance measurement. The potential of the O-LFP electrode was +0.26 V vs. Ag/AgCl, which corresponds to ca. +0.46 V vs. SHE and ca. +3.50 V vs. Li/Li⁺, indicating an appropriate value as the FePO₄/LiFePO₄ redox couple written in the literature.²⁹ For examining the lithium conductivity of the solid electrolyte, gold was vapor-deposited onto both side of the solid electrolyte and the AC impedance was measured. The shape of the gold electrode deposited in each side of the solid electrolyte was a rectangle with its length of 13 mm and width of 12 mm. The AC amplitude and the frequency range were 50 mV and 7.0 MHz–0.1 Hz, respectively. In the similar way to the potential step measurements, the activation energy of the processes contained in the impedance spectra was evaluated.

Figure 2.

Schematic diagram of a four-electrode cell and possible resistance terms measured in impedance spectra. A. liquid electrolyte resistance, B. solid electrolyte resistance, C. charge-transfer resistance of reference electrode reactions, D. charge-transfer resistance at solid electrolyte/liquid electrolyte interface.

3. Results and Discussion

3.1 Potential step condition optimization

To appropriately obtain the rate constant, it is essential to ensure that the current response reflects the state of the entire electrode and that the fraction of the phase transition product f is correctly evaluated. That is, any reaction inhomogeneity in the electrode material that can mislead the results should be avoided. It is known that thick and dense electrodes often show reaction inhomogeneity due to limited ionic transportation within the electrode, and in particular, too high current density can result in considerable reaction inhomogeneity.³⁰ In addition, large current leads to the ohmic loss caused by electrolyte resistance, which gives uncertainty in the overpotential that clearly affects the reaction rate of the phase transition.²¹ Therefore, it is essential to use thin and porous electrodes and restrict the potential step width. On the other hand, too small potential step width can lead noisy current signals, especially sufficiently after the potential step.

We fabricated porous LiFePO₄ composite electrodes with a porosity of 50–60 % to ensure good ionic conductivity through the electrode to minimize the reaction inhomogeneity. Then, we tried to optimize the potential step width. The potential step measurements were anodically performed with the phase transition from LiFePO₄ to FePO₄ (the lithium extraction process). Figure 3a shows the current response in non-aqueous systems at 25 °C with the potential step widths of 0.2, 0.5 and 1.0 V, and Figs. 3b, 3c, and 3d shows the corresponding Avrami plots. The profiles with the 0.2 and 0.5 V steps were monotonous while that with the 1.0 V step was somewhat non-linear after 2500 s, suggesting the effect of reaction inhomogeneity. The Avrami plots with these steps showed nearly n = 1, (as in the previous study^17,20,21), and the obtained k value were close to each other at k ∼ 10⁻⁸ s⁻¹, suggesting that the modeled phase transition behavior is valid in these electrodes. This also means that the phase transition kinetics governs the current response and other processes such as ion/electron transportation in the composite electrodes¹¹ are fast enough to have little effect on the whole behavior at least in the beginning (−2000 s) of the chronoamperometry. After 2000 s, non-ideal behavior probably due to the reaction inhomogeneity and parasitic reactions was seen, and the corresponding data were not used in the following analysis. In the following experiments, we set the potential step width as 0.3 V, which is essential to minimize reaction inhomogeneity as well as possible water decomposition reaction in aqueous electrolyte experiments.

Figure 3.

(a) The current response during potential step measurement and (b), (c), (d) the corresponding Avrami plots in the non-aqueous electrolyte at 25 °C with potential step width of 0.2 (red), 0.5 (blue) and 1.0 (green) V. The electrolyte was 1 mol dm⁻³ LiPF₆ dissolved in EC : DEC = 1 : 1 vol/vol.

3.2 Comparison between non-aqueous and aqueous media

The slope of the Avrami plot of n = 1 for the non-aqueous system indicates that the phase transition of LiFePO₄ proceeds in the first-order reaction kinetics and that the phase transition itself is the rate-determining process. The potential step experiments were conducted also in the aqueous electrolytes, similarly to the non-aqueous electrolytes. Figures 4a and 4b show the time variation of the accumulated current value during the potential step measurement at 25 °C and the corresponding Avrami plot, respectively. Because the slope of the Avrami plot n is unity, it is shown, for the first time, that the phase transition governs the whole reaction kinetics, and the transition in the aqueous electrolytes is represented by a first-order reaction kinetics, as in the non-aqueous electrolytes.

Figure 4.

(a) The current response obtained during the potential step measurement at 25 °C and (b) the resultant Avrami plots. The electrolyte used was 0.5 mol dm⁻³ Li₂SO₄ dissolved in water.

The potential step measurements were made at several temperatures in both the non-aqueous and aqueous electrolytes. From the corresponding Avrami plots, the n values were calculated. All the slopes essentially indicate n = 1. The activation energy was obtained using the Arrhenius plot of the rate constant k at the tested temperatures, as shown in Fig. 5 and Table S1. The calculated activation energies for the aqueous and non-aqueous electrolytes were 2.2 ± 4 and 12 ± 8 kJ mol⁻¹, respectively, showing that the activation energy for the aqueous electrolytes is lower than that for the non-aqueous electrolytes. This suggested that, even if the phase transition governs the reaction kinetics, the rearrangement of the phase boundary (LiFePO₄/FePO₄) is not the main factor to determine the reaction rate but the charge transfer at the electrode/electrolyte interface also affects the whole rate. It should also be noted that the absolute values of the rate constant k are about 2 orders of magnitude greater in the aqueous electrolytes than in the non-aqueous electrolytes.

Figure 5.

Arrhenius plots of the rate constant k in aqueous (blue square) and non-aqueous (red circle) electrolytes.

3.3 Evaluation of the charge-transfer processes in aqueous and non-aqueous electrolytes

The lower activation energy (and also greater rate constants) for the aqueous electrolytes can be ascribed to the faster charge transfer at the electrode/electrolyte interface in aqueous systems than in non-aqueous systems. The activation energy of the charge transfer in non-aqueous systems have been evaluated with using the four-electrode cells containing the solid electrolyte²⁸ to show the significant effect of the solvation-de-solvation processes. Accordingly, we employed the similar four-electrode cell experiments in both the non-aqueous and aqueous systems to understand the effect of the electrolytes on the charge transfer. Although the charge transfer conditions in the LiFePO₄ electrodes and that in the solid electrolyte (lithium conducting glass-ceramics sintered plate) is not identical, we speculated that the charge transfer impedance obtained by four-electrode cells in the aqueous systems is lower than that in the non-aqueous systems, based on the phase transition behavior of the LiFePO₄ electrodes.

It has been shown that there are three impedance components in the four-electrode cell measurements, namely that of the liquid electrolyte (usually low values), that of the solid electrolyte, and that of the interface.²⁸ The second term was evaluated by the AC impedance measurements of the solid electrolyte using gold electrodes, and the activation energy was also obtained (see Figs. S4a and S4b). The frequency ranges and impedance of the solid electrolyte were ca. 500 kHz and 40 W cm² at 25 °C and the activation energy was ca. 20 kJ mol⁻¹. This value is somewhat lower than 31 kJ mol⁻¹, which has been reported in 1997,³¹ but is acceptable because the activation energy significantly depends on the fabrication process that can be modified since the first report was published.³¹

Next, we employed the four-electrode cell measurements with the same electrolyte we used in the potential step experiments. Figure 6a shows the Nyquist plot of the four-electrode cell measurement consisting of the non-aqueous electrolyte sandwiched by metallic lithium electrodes. The resultant impedance spectra include four terms as shown in Fig. 2: A. liquid electrolyte resistance, B. solid electrolyte resistance, C. charge-transfer resistance of reference electrode reactions, D. charge-transfer resistance at solid electrolyte/liquid electrolyte interface. The fourth term D is generally considered as the process of solvation/de-solvation of the transferred ions.²⁸ In the present system, the terms A, B and D can be measured because the charge transfer resistance of both lithium³² and O-LFP³³ electrodes is sufficiently low and because there is essentially little current passing through the reference electrode. The measurement was employed in the range of 10–35 °C to give the corresponding Arrhenius plot as shown in Fig. 6b. The main semicircles at around 1 kHz in Fig. 6a can be ascribed to the charge-transfer impedance at solid electrolyte/liquid electrolyte interface whereas the very small semicircles at around 1 MHz can be the components of the solid electrolyte and the electrolyte solution, considering the frequency ranges. Because the very high-frequency part was not appropriately analyzed due to the low data resolution, the spectra below 1 MHz were analyzed using the equivalent circuit shown in Fig. S5 and the fitted results are shown in Table S2. The charge transfer resistance at 25 °C and the activation energy were ca. 21 kW cm² and 45 ± 0.5 kJ mol⁻¹. The activation energy value is close to what has been reported in the literature,³⁴ but is higher than what we obtained in the phase-transition experiment, probably reflecting the charge-transfer kinetics depending on the kind of the solid material facing to the liquid electrolyte.

Figure 6.

(a) Nyquist plot of the impedance of the four-electrode cell consisting of Li|non-aqueous electrolyte|LICGC|non-aqueous electrolyte|Li and (b) the corresponding Arrhenius plots. The inset of (a) shows the partially enlarged Nyquist plot. The electrolyte was 1 mol dm⁻³ LiPF₆ dissolved in EC : DEC = 1 : 1 vol/vol.

Figure 7a shows the Nyquist plot of the four-electrode cell measurement consisting of the aqueous electrolyte sandwiched by water-stable lithium conducting O-LFP electrodes developed for this measurement. The measurement was employed in the range of 10–35 °C to give the corresponding Arrhenius plot as shown in Fig. 7b. There was only one single semicircle in the 1 MHz frequency range. The data analyzed by the equivalent circuit shown in Fig. S5 are shown in Table S2. The corresponding activation energy of ca. 41 ± 2.7 kJ mol⁻¹ is lower than the value in the non-aqueous electrolyte, being similar to the result obtained in the phase transition experiments. It is noted based on the frequency range consideration that the observed semicircles are mainly from the contribution from the charge-transfer between the solid electrolyte and aqueous electrolyte (process D), but also include small contribution from the solid electrolyte (process B). The low activation energy of the charge transfer in the aqueous systems has also been reported by Lee et al.³⁵ and Nakayama et al.³⁶ using LiMn₂O₄ film electrodes, who attribute the low activation energy to fast interfacial charge-transfer in the absence of the resistive surface film. On the other hand, the absolute resistance values in the aqueous electrolyte system (140 W cm² at 25 °C for example) are much lower than those in the non-aqueous electrolyte system (21 kW cm² at 25 °C), which can explain the greater rate constant found in the phase transition experiments and suggest the kinetically facile phase transition process in the aqueous systems. The low absolute resistance values could also be ascribed to the better wettability of the electrode.

Figure 7.

(a) Nyquist plot of the impedance of the four-electrode cell consisting of O-LFP|aqueous electrolyte|LICGC|aqueous electrolyte|O-LFP. The electrolyte was 0.5 mol dm⁻³ Li₂SO₄ dissolved in water, and (b) the corresponding Arrhenius plots.

Finally, the activation energy in the non-aqueous lithium electrolytes obtained in this study is compared with other reports. Our value was nearly the same as that reported by Allen et al.,²⁰ while it is much lower than those reported by Oyama et al.²¹ and Liao et al.,²² although the kind electrolyte used in the electrochemical measurements are all LiPF₆ dissolved in ethylene-carbonate-based solvents. This suggests that other factors such as material particle morphology or sizes and electronic conductivity of the electrode material can affect the phase transition behavior. Further study is needed to fully understand the factors affecting the phase transition rate.

4. Conclusion

The phase transition of LiFePO₄/FePO₄ proceeds according to the first-order reaction kinetics in both aqueous and nonaqueous electrolytes, showing that the phase transition governs the current response. The activation energy E_a for the aqueous system is lower than that for the nonaqueous system. The impedance measurement using the 4-electrode cell (containing O-LFP counter and reference electrodes in the aqueous system) indicates that the charge-transfer resistance in the aqueous media is also lower than that in the non-aqueous media, suggesting more facile solvation/de-solvation process in the aqueous media. This suggests that generally recognized high-power characteristics in the aqueous systems can be attributed to not only the high ionic conductivity of the electrolytes but also the fast charge-transfer kinetics at the electrode/electrolyte interface. A part of this fast kinetics can be attributed to the better wettability of the electrode in the aqueous electrolyte. This study shows the rearrangement of the phase transition boundary is considerably fast and other factors such as charge-transfer at the electrode/electrolyte interface affects the whole reaction rate. Further study in needed to fully understand the effect of these factors including the particle sizes as well as the morphology and to further enhance the power characteristics of the battery systems.

Acknowledgment

This work was supported by Japan Society for the Promotion of Science (JSPS), JST SPRING, Grant Number JPMJSP2106.

Data Availability Statement

The data that support the findings of this study are openly available under the terms of the designated Creative Commons License in J-STAGE Data at https://doi.org/10.50892/data.electrochemistry.24893175.

• 1) Power characteristics become one of the important performance measures of lithium-ion batteries as high-power applications such as electric vehicles are emerging. Among several electrochemical steps that limit the power characteristics, phase transition kinetics is known as the limiting step for two-phase coexisting (biphasic) materials. In this study, we used LiFePO₄ as a model biphasic material and investigated the intrinsic factor that limits the phase transition behavior. When the same LiFePO₄ electrodes were tested in non-aqueous and aqueous electrolytes, the activation energy for the aqueous system was lower. In addition, impedance measurements using 4-electrode cells show that the charge-transfer resistance at the electrode/electrolyte interface in the aqueous media is also lower than that in the non-aqueous media, suggesting more facile solvation/de-solvation process in the aqueous media. This indicates that the rearrangement of the phase transition boundary (LiFePO₄/FePO₄) is sufficiently fast and other factors such as charge-transfer at the electrode/electrolyte interface affects the whole reaction rate.

CRediT Authorship Contribution Statement

Chihiro Yamamoto: Conceptualization (Lead), Data curation (Lead), Methodology (Lead), Validation (Lead), Writing – original draft (Lead), Writing – review & editing (Lead)

Atsunori Ikezawa: Methodology (Supporting), Writing – review & editing (Supporting)

Takeyoshi Okajima: Writing – review & editing (Supporting)

Hajime Arai: Supervision (Equal), Writing – review & editing (Equal)

Conflict of Interest

The authors declare no conflict of interest in the manuscript.

Footnotes

C. Yamamoto: ECSJ Student Member

A. Ikezawa and T. Okajima: ECSJ Active Members

H. Arai: ECSJ Fellow

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