Factors Limiting Li⁺ Charge Transfer Kinetics in Li-Ion Batteries

The Li⁺ charge transfer process is defined as the process of turning a solvated Li⁺ in the electrolyte into Li in the electrode by accepting an electron from the electrode. At the graphite anode, during charge, as shown in Fig. 1a, the Li⁺ charge transfer process is made of the following three steps ignoring the transport of the solvated Li⁺ in the electrolyte before reaching at the SEI and electrolyte interface. This is reasonable as the electrolytic conduction of 1 M LiPF₆ in EC: EMC (30:70 vol.%) varied from 1.1 mS cm⁻¹ at −40°C to 9.6 mS cm⁻¹ at 25°C with an activation energy of Li⁺ conduction of only 22 kJ mol⁻¹ or less.^11,12

• (1)  
  Li⁺⋅(solv.)_n → Li⁺, (De-solvation of Li⁺ at the SEI/electrolyte interface)
• (2)  
  Li⁺ → Li⁺, (Li⁺ transport through anode SEI towards anode)
• (3)  
  x Li⁺ + x e⁻ + C₆ → Li_xC₆. (Li⁺ charge transfer: Li⁺ reaching the anode and accepting an electron at the anode-SEI interface or at the anode-electronic conductor/SEI interface. The electron is supplied through the external circuit during charge.)

The kinetics of the Li⁺ transport in the SEI is determined by the nature of SEI, which is made of mixtures of inorganic and organic Li⁺ conductors.¹³

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At the cathode, there is a Li de-intercalation process resulting in a solvated Li⁺ in the electrolyte, which is described in the following steps.

• (1)  
  LiCoO₂ → x Li⁺ + x e⁻ + Li_1-xCoO₂, (Li de-intercalation, dissolution, from LiCoO₂ to become Li⁺ and e⁻)
• (2)  
  Li⁺ → Li⁺, (Li⁺ transport through cathode/electrolyte interphases, CEI)
• (3)  
  Li⁺ → Li⁺⋅(solv.)_n (Li⁺ solvation in electrolyte)

During discharge as shown in Fig. 1b, the Li⁺ charge transfer process that involves the Li⁺ de-solvation step from the solvated Li⁺ in the electrolyte is occurring at the cathode and the Li de-intercalation step, Li_xC₆ → x Li⁺ + x e⁻ + C₆, is occurring at the anode.

Step 3, in which the Li⁺ accepts an electron and becomes Li intercalated graphite, is considered a fast step. Step 4, the de-intercalation kinetics at the electrode and electrolyte interface, is also considered fast. The subsequent diffusion of Li in the electrode bulk active material is often the slower and rate limiting step in the battery charge discharge processes at normal ambient temperatures. Although the diffusion of Li within the active cathode or anode material is not our main focus, it is worth of our understanding as it links to the Li⁺ charge transfer kinetics at the electrode and electrolyte interface closely. The relative facility of each of these steps changes as a function of temperature, so the rate limiting step may change at different temperatures. For example, studies by Wang et al.,¹⁴ involving the low temperature characterization of graphite and MCMB coke anodes, have shown that the stage transformation resistance, or diffusion in the bulk electrode, is rate determining at 25°C, whereas the SEI resistance is rate limiting at −30°C. As described, the researchers reported over a 27-fold increase in the SEI resistance from 25°C to −30°C, which was the primary cause for the high polarization observed at low temperature. Smart et al.¹⁵ have previously reported that cells consisting of MCMB anodes and LiNiCoO₂ cathodes with various electrolytes display poorer cathode kinetics compared to the anode. However, at temperatures below −30°C the lithium intercalation kinetics at the MCMB appear to become performance limiting, illustrating that the kinetics change at different temperatures for the different electrodes. Others have also reported MCMB anodes to be performance limiting at temperatures < −20°C compared to the LiCoO₂ cathodes.¹⁶ These studies illustrate that broad conclusions of which electrode is rate determining over a wide range of temperatures may not be valid. Nonetheless, the diffusion of Li in the electrode changes with temperature and can be dominating in certain systems depending on temperature.

Therefore, the investigation on whether the de-solvation step, step 1, and the diffusion of Li⁺ across the SEI and CEI, steps 2 and 5, respectively, occurring at the electrode/electrolyte interfaces are possible rate limiting steps will be our main focus. How do we characterize the charge transfer kinetics? How do we determine which step is rate limiting?

The resistance resulting from the charge transfer process is denoted as R_ct, which results from contributions from both the de-solvation step and the diffusion in the SEI step. The R_ct follows the relationship based on the thermally activated process,¹⁷

where A_o, E_a, R and T are a frequency factor, the activation energy, the gas constant and the temperature in Kelvin, respectively. The E_a of the Li⁺ charge transfer process, or the lithium-ion kinetics, represents the barrier that the Li⁺ needs to overcome to cross the interface between the electrolyte and the electrode. The value of E_a can be obtained from the slope of a log(1/R_ct) versus the inverse of temperature (1/T) plot.

Electrochemical impedance spectroscopy (EIS) measurements¹⁸ can be used to characterize the resistance of different processes occurring in an electrochemical cell through the fitting of the impedance spectra, Nyquist plots, to an equivalent circuit.

Which step is rate limiting appears to depend on the cell components that are used in the formation of interfaces or interphases, including the electrode and electrolyte type selections. The cell interfaces that can potentially lead to the de-solvation process being a rate limiting step is to be considered first, and then the conditions under which the Li transport in SEI as a rate limiting step will be discussed.

Abe et al.⁴ reported the study of the activation energy of the Li⁺ charge transfer process across the HOPG electrode and electrolyte interface. When the HOPG electrode is held at 0.4 V or lower vs. Li/Li⁺ in 1 M LiClO₄ in EC:DEC electrolyte, there is a SEI formed on HOPG and the solvated Li⁺ needs to de-solvate to diffuse through SEI and reach the electrode before accepting an electron. When the HOPG is held at 1.1 V in 1 M LiCF₃SO₃ in 1,2-dimethoxyethane (DME) electrolyte, there is no SEI formed on HOPG, and the solvated Li⁺ can intercalate into graphite directly. The E_a for this process, which involves no de-solvation, is only 25 kJ mol⁻¹. This is much lower than an E_a of 53 to 59 kJ mol⁻¹ for the prior process, which involves de-solvation because of the existence of the SEI. It is therefore concluded that the rate limiting step is de-solvation. Further studies support this conclusion. Two of them are briefly reviewed below.

Li⁺ charge transfer at the interface between solid-state ceramic electrolyte and liquid electrolyte

The study of the solid-state (SS) electrolyte and liquid electrolyte interface was first reported by Abe et al.⁶ This study uses a four-Li electrode cell as shown in Fig. 2,⁶ in which the SS electrolyte disk is in the center and in contact with the liquid electrolyte only. Two Li electrodes on each side of the SS electrolyte with one being the reference electrode and other one being the counter electrode are designed. This design allows the measurement of Li⁺ de-solvation and solvation into and out of the SS electrolyte without encountering other complications. The SS electrolytes used in this study are crystalline lithium lanthanum titanate, Li_0.35La_0.55TiO₃ (LLT),^19,20 and Li-Al-Ti-phosphate (Li_1+xAl_xTi_2-x(PO₄)₃) based glass electrolyte (Ohara glass).²¹ The activation energy of Li⁺ charge transfer at the interfaces of the Ohara glass and the liquid electrolytes including 1 M LiCF₃SO₃ in dimethyl sulfoxide (DMSO), propylene carbonate (PC), and mono-fluoroethylene carbonate (FEC) are 69.9, 57.3 and 31.5 kJ mol⁻¹, respectively, based on the charge transfer resistance obtained from the EIS measurements, which are consistent with the DFT calculated reaction enthalpy, ΔH, values of −235.5, −217.1, and −190.3 kJ mol⁻¹, respectively. The ΔH is defined as H (Li⁺ - solvent) – [H(solvent) + H (Li⁺)]. The de-solvation step as a rate limiting step is clearly demonstrated in this interface. These results suggest that the higher reaction enthalpy energy of solvent or the higher solvation ability of the solvent with Li⁺ leads to higher activation energy for de-solvation.

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Li⁺ charge transfer at the interface between Li₄Ti₅O₁₂ (LTO) and liquid electrolyte

In Li-ion batteries, the SEI formed between the graphite anode and the electrolyte allows the repeated charge/discharge operation of the batteries achieving long cycle life with little loss of capacity. The charge and discharge rates achievable are increasingly limited with decreasing temperature. A study of low temperature impedance of Li-ion batteries indicates that the impedance of the cell is dominated by the charge transfer resistance, R_ct.²² The R_ct includes mainly the resistance for the de-solvation step and the diffusion of Li⁺ in SEI. The de-solvation (and solvation) step should occur at both the anode and the cathode before a Li⁺ can intercalate into the electrodes. If the de-solvation process was the rate limiting step, it should be reasonable to expect the E_a at both the anode and cathode should be similar. If they are different, the roles of the SEI and CEI need to be considered. Three studies that are used as examples to clarify which step is the rate limiting step in Li-ion batteries are presented below.

Differentiating Li⁺ charge transfer at graphite/electrolyte and LiFePO₄/electrolyte interfaces in a full cell

Impact of additives on Li⁺ charge transfer kinetics on both anode and cathode

Jones et al.⁹ investigated the impact of electrolyte compositions on the charge discharge behavior of Li-ion cells consisting of LiNi_0.80Co_0.15Al_0.05O₂ (NCA) cathodes and graphite anodes with Tonen separator (polyethylene) in a baseline electrolyte of 1.0 M LiPF₆ in EC:EMC:MP (20:20:60 vol. ratio), where MP is methyl propionate. The test cells are in a spiral wound configuration with a capacity of about 105 mAh incorporating a Li reference electrode allowing the monitoring the charge transfer resistance at the anode and the cathode at the same time. The schematics of the cell construction are shown in Fig. 3. By introducing different additives, it is reasonable to expect that the nature of the SEI and CEI formed during formation resulting from the reduction on the anode and oxidation on the cathode with the electrolyte would vary from one additive to the other. However, the bulk electrolyte in the cells should remain relatively constant, since the additives are introduced in low concentration. The additives with their concentrations selected for this study include lithium bis(oxalato)borate (LiBOB) in 0.1 M concentration, vinylene carbonate (VC) in 2 wt %, 1,3-propanesultone (PS) in 2%, lithium difluoro(oxalato)borate (LiDFOB) in 0.1 M, and lithium bis(fluorosulfonyl)imide (LiFSI) in 0.1 M. The structures of these additives are shown in Fig. 4.

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The impedance of the cells at the temperatures of 23, −20, −30, −40°C are measured at the cell voltage set at 4.07 V, at which the potential of the graphite anode is of about 0.090 to 0.105 V vs. Li/Li⁺ and the potential of the NCA cathode is about 4.179 V vs. Li/Li⁺. The impedance, including that at the anode and that at the cathode, for the baseline electrolyte with and without these additives have been measured. The impedance of both the graphite anode and the NCA cathode at 23°C are shown as Nyquist plots in Figures 5a and 5b, respectively. The R_cts at this temperature judging from the diameter of the semicircle are quite small at both the anode and cathode, with the values at the anode being about three times larger than that at the cathode. The straight lines after the semicircle shown Fig. 5 suggest that a diffusion limited process most likely occurring in the electrodes is limiting the rate performance of the cell.

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The impedance of both the graphite anode and the NCA cathode at −30°C are shown as Nyquist plots in Figures 6a and 6b, respectively. At this temperature, the cell resistance is dominated by the resistance at the graphite anode. Fig. 6a shows that the electrolytes with LiDFOB and LiFSI produce the SEI layers with resistance similar to the baseline electrolyte, while the other additives, VC, LiBOB, and PS, produce more resistive SEIs on the graphite anode. Fig. 6b shows that the electrolytes with VC, LiBOB, LiDFOB, and PS additives produce less resistive CEIs than the baseline electrolyte on the NCA cathode.

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The equivalent circuit as shown in Fig. 7 is used to analyze the charge transfer resistance, R_ct, which is equivalent to R2 as shown in the figure. The activation energy, E_a, of the Li⁺ charge transfer process at the anode and at the cathode, can be determined from the slopes of the log (1/R_ct) vs. 1000/T plots as shown in Figs. 8a and 8b. These plots all display a good linear relationship. The room temperature R_ct values at the cathode in the electrolytes with VC and LiDFOB are not shown, as the numbers are too small to be accurate. However, the estimated values would fall within the linear relationship with the values at lower temperatures. These E_a values at both graphite anode and NCA cathode are summarized in Table I.

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Table I. Activation energy of Li⁺ charge transfer at the graphite anode/electrolyte interface and the NCA cathode/electrolyte interface.

	Ea, kJ mol−1
Electrolyte	At Graphite Anode	At NCA Cathode
Baseline	57.7	71.8
+ 2% VC	66.1	100.0
+ 0.1 M LiBOB	69.1	61.2
+ 0.1 M LiDFOB	61.9	85.9
+ 2% PS	58.7	65.7
+ 0.1 M LiFSI	58.7	66.4

Baseline electrolyte: 1 M LiPF₆ in EC:EMC:MP (20:20:60 v/o).

The effects of LiFSI and LiBOB additives on R_ct and E_a are especially noteworthy. The addition of LiFSI in the baseline electrolyte results in lower R_ct at the graphite anode than that in the baseline electrolyte and an E_a similar to that of the baseline electrolyte. It also results in lower R_ct at the cathode than that in electrolyte without FSI and, at the same time, slightly lower E_a for Li⁺ charge transfer at the cathode. The addition of LiBOB results in a lower R_ct and E_a on the NCA cathode than that in the baseline electrolyte. However, the presence of LiBOB results in higher R_ct and E_a on the graphite anode compared to the baseline electrolyte. Different additives lead to different reduction and oxidation reactions at the anode and the cathode and, therefore, different SEI and CEI, respectively.¹⁰ The bulk electrolyte compositions remain about the same. Therefore, we conclude that the SEI is the rate limiting step in the Li-ion batteries.

Li⁺ charge transfer between HOPG and 1 M LiClO₄ in DMC electrolyte

At the interfaces between SS ceramic electrolyte, LLT or Ohara glass, and liquid electrolyte and between the LTO and liquid electrolyte interface, the E_a for Li⁺ charge transfer correlates well with the ability of these solvents binding the Li⁺.^6,5 At the SS electrolyte and the liquid electrolyte interface, we can consider that the SS electrolyte is equivalent to a SEI as in Li-ion batteries. In this case, LLT or Ohara glass is not a rate limiting factor. Considering both LLT and Ohara glass are fast Li⁺ conductors, with high Li⁺ conductivity of around 1.0 × 10⁻³ S cm⁻¹ and an activation energy of around 33 kJ mol⁻¹,^19–21 it is reasonable that the rate limiting step is dominated by de-solvation in these systems. At the interface between the LTO and liquid electrolyte at 1.5 V vs. Li/Li⁺, there is no electrolyte reduction reaction and therefore no SEI is formed on LTO at 1.5 V vs. Li/Li⁺ in LiClO₄ in EC:EMC electrolyte.⁵ Furthermore, LTO is a good Li⁺ conductor near 1.5 V vs. Li/Li⁺, where LTO shows the highest Li⁺ redox reactions. Li⁺ conduction in LTO has been studied and shown an E_a of around 27 kJ mol⁻¹ using electrochemical methods²⁸ or varying between 0.30–0.48 eV for the spinel phase Li₄Ti₅O₁₂ and between 0.20–0.51 eV in the lithiated rock salt phase Li₇Ti₅O₁₂ using first principle calculations.²⁹ With no SEI and fast Li⁺ conduction in LTO, the Li⁺ de-solvation process is a rate limiting step at the LTO and electrolyte interface.

The studies of Li⁺ charge transfer at Gr/electrolyte interface and at the LFP/electrolyte interface in a Gr / electrolyte / LFP full cell in the same electrolyte shows a large difference in E_a between the two interfaces.⁷ This large difference is attributed to the difference in the nature of the SEI and CEI on the graphite anode and LFP cathode, respectively. It is worth noting that the E_a for Li⁺ charge transfer across the LFP/electrolyte interface is 33 kJ mol⁻¹, which is very similar to that for the electrochemical FePO₄ to LiFePO₄ phase transformation, which is found to be about 30 kJ mol⁻¹.^30–32 This number is derived from using the Avrami-Johnson-Mehl-Eroofev equation.^30–32 A recent study by Johannes et al.³³ on hole polaron formation and migration in olivine phosphate materials using DFT method is also worth noting as a reference. It is found that the polaron migration barrier in LFP, which is closely linked to the Li⁺ conduction kinetics, is 0.20 eV or 19.3 kJ mol⁻¹. This number is lower than the activation energy for the electrochemical FePO₄ to LiFePO₄ transformation. It could suggest that there is a CEI on LFP at the voltage less than 3.6 V, even if it is insignificant, that can affect the charge transfer kinetics.

The additives in the electrolyte impact not only anode, but also cathode, Li⁺ charge transfer kinetics in Li-ion cells, such as Gr / electrolyte / NCA cell studies,⁹ where the reduction and oxidation reactions of the electrolytes varied with the selection of additives. This agrees with the Li⁺ charge transfer kinetics studies of HOPG in 1 M LiClO₄ in DMC electrolyte, in which HOPG has a different preformed SEI. In summary, all components in the electrolyte such as salt, e.g. LiClO₄ vs. LiPF₆, solvent, e.g. carbonate vs. ester, additive, e.g. LiFSI vs. VC, can change the nature of SEI and CEI, and therefore influence the Li⁺ charge transfer kinetics.^10,34 Table III summarizes the impact of salt, solvent and additive on the activation energy of Li⁺ charge transfer at the graphite anode using limited examples for illustration only.

Recent computational studies of the de-solvation kinetics and the transport properties of the SEI are worth mentioning as references for the above experimental studies.^36,37 Molecular Dynamics simulations were performed to evaluate the de-solvation energy of an electrolyte consisting of 1 M LiPF₆ / EC:DMC (3:7 mole ratio) in contact with a SEI made of Li₂EDC, (CH₂OCO₂⁻/Li⁺)₂, or Li₂BDC, key SEI components.³⁶ The many-body polarizable APPLE&P force field was used in the simulations. E_a, the activation energies, for the Li⁺ solvation−de-solvation reactions are 0.42−0.46 eV (40–44 kJ mol⁻¹) for the SEI−electrolyte system. E_a for the Li⁺ diffusion in bulk Li₂EDC is 0.64 eV (62 kJ mol⁻¹).³⁷ The activation energy for the lithium diffusion in the other common SEI compound Li₂CO₃ for the combined process of the formation the Li⁺ defect and Li⁺ hopping was estimated to be around 0.7 eV (67.5 kJ mol⁻¹) at low voltages close to lithium metal potential, indicating that many common SEI components have similar activation energy.³⁸ However, it should be noted that the SEI in Li-ion batteries is more complicated than that assumed in the simulation. The computational results in general agree with what have been observed.

As mentioned previously in the section of Li⁺ Charge Transfer Process^14–16 and a recent study on LiNi_1/3Co_1/3Mn_1/3O₂ by Kasnatscheew et al.,³⁹ the lithium migration through the solid bulk active electrode materials may be rate limiting in some systems under certain conditions, especially at warmer temperatures. In the context of the above results and discussion, Li⁺ charge transfer kinetics is mostly dominated by the SEI in Li-ion batteries. In the case when the SEI is very conductive and of low activation energy for Li⁺ conduction, such as LLT and Ohara glass, the Li⁺ charge transfer kinetics is dominated by the de-solvation process. In the case when there is no SEI or CEI, or insignificant SEI/CEI, such as with the LTO/electrolyte interface or LFP/electrolyte interface, the Li⁺ charge transfer kinetics is dominated by de-solvation or by the Li transport in the electrode.

When the additive is introduced in the electrolyte, the redox chemistries on the electrodes are modified resulting in different SEI and CEI from the original. Using full cells, such as Gr / 1 M LiPF₆ in EC:EMC:MP / NCA with a Li reference electrode, allows one to examine the full impact of additives on the Li⁺ charge transfer kinetics at both the anode and the cathode at the same time. In this work, we found that the LiBOB additive leads to a reduced R_ct and E_a at the NCA cathode, but results in much increased R_ct and E_a at the graphite anode. The LiFSI additive amongst those studied in this work provides the best overall benefits in terms of Li⁺ charge transfer kinetic improvement.

Some work described here was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration (NASA) and supported by the NASA Planetary Sciences Division (PSD). The authors also wish to thank Oleg Borodin of the U.S. Army Research Laboratory for helpful discussion.

T. Richard Jow 0000-0003-1615-8593