Electrochemical Impedance Analysis for Li-ion Batteries (& economy a bit).

I. Main Issue

(1) Equivalent circuit elements

(a) Anode (e.g., graphite)

1. A solvation/desolvation resistance at high frequencies (*4), and a diffusion resistance in the liquid electrolyte that fills the void space in the electrode at low frequencies (Warburg impedance) in series.
2. A capacitance of the Solid-Electrolyte Interphase (SEI) film in parallel with the above-mentioned resistance components (*5).
3. The rate determining step is the lithium-ion diffusion in the liquid electrolyte that fills the void space in the electrode. Note that the Warburg impedance is represented as the distributed constant circuit (*2).

• Lithium ion diffusion in the intercalation materials: With the enough amount of lithium ions near the graphite active-material particles, a graphite particle can respond in a faradaic manner at, e.g., the C-rate of 600C (*1), thus the lithium ion diffusion in the intercalation materials is fast enough.

(b) Cathode (e.g., lithium transition-metal complex oxides)

1. A solvation/desolvation resistance at high frequencies (*4) and the Warburg impedance at low frequencies in series.
2. A capacitance of an Cathode-Electrolyte Interphase (CEI) film in parallel with the solvation/desolvation resistance (*5).
3. The rate determining step is the lithium-ion diffusion in the liquid electrolyte that fills the void space in the electrode. Note that the Warburg impedance is represented as the distributed constant circuit (*2).

• Lithium ion diffusion in the intercalation materials: With the enough amount of lithium ions near the cathode active-material particles, and with the enough electron paths, e.g., a LiCoO2 particle can respond in a faradaic manner, e.g., at 360C, a LiFePO4 particle or a LiMn2O4, particle e.g., at 36,000C etc. (*1), thus the lithium ion diffusion in the intercalation materials is fast enough.
• The impedance of the cathode component is highly dependent on its state of charge (SOC); this can help the analysis. The high-frequency cathode component usually lies at lower frequencies than the anode high-frequency component. The high-frequency cathode impedance often becomes a bit larger than the anode counterpart, needless to say, depending on the conductive material weight ratio. The CEI component overlaps with the anode SEI component.

(c) Electrolyte

An electrolyte resistance, which fills the void space in the separator, in the highest frequencies (*3).

(2) Connect the above components as the simplest model.

(3) Electrode/material degradation

(a) Review—Post-Mortem Analysis of Aged Lithium-Ion Batteries: Disassembly Methodology and Physico-Chemical Analysis Techniques.

(b) Liイオン二次電池における充放電Li輸送と劣化現象のモデル解析

1. Cell aging is simulated that the linear one in the early stage of cycling is due to the SEI growth at the anode but the highly nonlinear one in the end accompanying the rapid capacity drop and resistance rise is resulted from the surface phase transition at the cathode.
2. The intergranular fracture between the cathode material particles becomes sluggish in the end.

(c) Modeling of lithium plating induced aging of lithium-ion batteries: Transition from linear to nonlinear aging

1. "Cell aging is found to be linear in the early stage of cycling but highly nonlinear in the end with rapid capacity drop and resistance rise."
2. "The linear aging stage is found to be dominated by SEI growth, while the transition from linear to nonlinear aging is attributed to the sharp rise of lithium plating rate."
3. "Lithium plating starts to occur in a narrow portion of the anode near the separator after a certain number of cycles. The onset of lithium plating is attributed to the drop of anode porosity associated with SEI growth, which aggravates the local electrolyte potential gradient in the anode. The presence of lithium metal accelerates the porosity reduction, further promoting lithium plating. This positive feedback leads to exponential increase of lithium plating rate in the late stage of cycling, as well as local pore clogging near the anode/separator interface which in turn leads to a sharp resistance rise."

(cf. 1) SEI

1. E. Peled, J. Electrochem. Soc., 126 (1979) 2047-2051.
2. D. Aurbach et al., J. Electroanalyticalchemistry and Interfacial Electrochemistry, 297 (1991) 225-244.
3. M. Fujimoto et al. (Sanyo Electric), US Patent 5,352,548, 1994 (Vinylene carbonate, VC).
4. A. Chu et al., J. Electrochem. Soc., 144 (1997) 4164-4169.
5. K. Xu, Chem. Rev., 104 (2004) 4302-4417.
6. H. Ota et al., J. Electrochem. Soc., 151 (2004) A1778-A1788 (highly pure VC).
7. Y. Naruse et al. (SONY), JP Patent 3,546,566, 1997 (Ethylene sulfite, ES).
8. S. Mio et al. (Mitsubishi Chemical), WO2011/136189, 2011 (1,3-propene sultone, PES).
9. P. G. Balakrishnan et al., J. Power Sources, 155 (2005) 401-414 (lithium bioxalateborate, LiBOB).

(cf. 2) CEI

1. M. G. S. R. Thomas, P. G. Bruce, J. B. Goodenough, J. Electrochem. Soc., 132 (1985) 1521-1528.
2. D. Aurbach et al., Electrochim. Acta, 47 (2002) 4291-4306 (VC).
3. M. Xu et al., J. Power Sources, 193 (2009) 804-809 (PS).
4. B. Li et al., Electrochem. Commun., 17 (2012) 92-95 (PES).
5. K. Amine et al., Electrochem. Commun., 7 (2005) 669-673 (LiBOB).

https://www.linkedin.com/pulse/electrochemical-impedance-analysis-lithium-ion-batteries-toru-hara/