Supporting Information for. Impedance Spectroscopy Characterization of Porous Electrodes. under Different Electrode Thickness Using a Symmetric Cell

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1 Supporting Information for Impedance Spectroscopy Characterization of Porous Electrodes under Different Electrode Thickness Using a Symmetric Cell for High-Performance Lithium-Ion Batteries Nobuhiro Ogihara,* Yuichi Ito, Tsuyoshi Sasaki and Yoji Takeuchi Toyota Central R&D Labs., Inc., Nagakute, Aichi , Japan. * ogihara@mosk.tytlabs.co.jp Figure S1 Dependence of Nyquist plots for symmetric cells using two identical positive electrodes at a state of charge (SOC) of %. Figure S2 Dependence of Nyquist plots for symmetric cells using two identical positive electrodes at SOC of 5%. Figure S3 Nyquist plots for symmetric cells using two identical positive electrodes at SOC of and 5%, and the best-fitting results. Figure S4 Activation energies for R sol, R ion, and R ct as a function of electrode thickness. Table S1 Selected fitting results of Nyqusit plot at SOC %. Table S2 Selected fitting results of Nyqusit plot at SOC 5%. S1

2 Temperature dependence of ionic resistance in pores for various electrode thicknesses -2 (a) 4-2 (b) 4-2 (c) (d) Z' / Ωcm 2 Figure S1 Nyquist plots for symmetric cells using two identical positive electrodes at a state of charge (SOC) of % in 1. M LiPF 6 in EC/DMC/EMC (3/4/3) at temperatures of, 1, 2, 3 and 4 C. The electrode thickness is (a) 17, (b) 23.5, (c) 33 and (d) 48.5 µm. S2

3 Temperature dependence of ionic resistance in pores for various electrode thicknesses Z'' / Ω cm 2 :16.5 µm :23.5 µm :33.5 µm :48.5 µm :63.5 µm 1 Hz 1 Hz Z' / Ω cm 2 Figure S2 Dependence of Nyquist plots for symmetric cells using two identical positive electrodes at SOC of 5% in the high-frequency region at temperatures of C. The length of the straight line with a slope of 45 in the high-frequency region increases with increasing electrode thickness. S3

4 Relationships between Nyquist plots and respective internal resistance components -3 (a) -2 Z'' / Ω cm 2 1 Hz 2 Hz (b) R sol R ct Z' / Ω cm 2 Figure S3 Nyquist plots for symmetric cells using two positive electrodes in 1. M LiPF 6 in EC/DMC/EMC (3/4/3) at C. The electrode thickness is 64 µm. Electrodes prepared at SOC of (a) % (squares) and (b) 5% (circles), and solid lines are the best-fitting results with the equivalent circuits using generalized finite length Warburg element open circuit terminus (Wo) and short circuit terminus (Ws) for descriptive purposes, respectively. 1-3 The equivalent circuit provides an excellent fit ( 1% error) to the experimental data as summarized in Table S1 and S2. S4

5 Table S1. Selected fitting results of Nyqusit plot at SOC % using generalized finite length Warburg element open circuit terminus (Wo). R Wo corresponds to R ion /3, τ Wo is resistance-capacitance time constant, and α Wo is a fractional exponent between and 1. 3 Parameter Value Error Error% R Wo (Ω) τ Wo (s) α Wo Goodness of Fit: Chi-Squared (χ 2 ):.498 Weighted Sum of Squares: Table S2. Selected fitting results of Nyqusit plot at SOC 5% using generalized finite length Warburg element short circuit terminus (Ws). R Ws corresponds to R ion /3 + R ct, τ Ws is resistance-capacitance time constant, and α Ws is a fractional exponent between and 1. Parameter Value Error Error% R Ws (Ω) τ Ws (s) α Ws Goodness of Fit: Chi-Squared (χ 2 ):.379 Weighted Sum of Squares:.5166 S5

6 Kinetic interpretation of individual internal resistance components as a function of electrode thickness From the temperature dependence of each internal resistance component, all internal resistances display Arrhenius behavior. To determine the kinetic parameters of interfacial phenomena at porous electrodes as a function of electrode thickness, the activation energies of each resistance (R x ) were evaluated using the Arrhenius equation, 1 a R x E = A exp RT where A, E a, R, and T are the frequency factor, activation energy, gas constant, and absolute temperature, respectively. Figure S4 Activation energies for R sol, R ion, and R ct as a function of electrode thickness. S6

7 REFERENCES 1. Johson, D., Zview: Version 3.2. Scribner Associates, Inc., Southern Pines Jang, J. H.; Oh, S. M., Complex Capacitance Analysis of Porous Carbon Electrodes for Electric Double-Layer Capacitors. J. Electrochem. Soc. 24, 151, A571-A Sugimoto, W.; Iwata, H.; Yokoshima, K.; Murakami, Y.; Takasu, Y., Proton and Electron Conductivity in Hydrous Ruthenium Oxides Evaluated by Electrochemical Impedance Spectroscopy: The Origin of Large Capacitance. J. Phys. Chem. B 25, 19, S7