doi: 10.1149/2.057207jes2012, Volume 159, Issue 7, Pages A1034-A1039.J. Electrochem. Soc.

and Yoshio UkyoNobuhiro Ogihara, Shigehiro Kawauchi, Chikaaki Okuda, Yuichi Itou, Yoji Takeuchi

Impedance Spectroscopy Using a Symmetric CellElectrodes for Lithium-Ion Batteries by Electrochemical Theoretical and Experimental Analysis of Porous

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2012 The Electrochemical Society

A1034 Journal of The Electrochemical Society, 159 (7) A1034-A1039 (2012)0013-4651/2012/159(7)/A1034/6/$28.00 The Electrochemical Society

Theoretical and Experimental Analysis of Porous Electrodes forLithium-Ion Batteries by Electrochemical Impedance SpectroscopyUsing a Symmetric CellNobuhiro Ogihara,,z Shigehiro Kawauchi, Chikaaki Okuda, Yuichi Itou, Yoji Takeuchi,and Yoshio Ukyo

Toyota Central R&D Labs., Inc., Nagakute, Aichi 480-1192, Japan

The purpose of this study was to understand the electrochemical behavior of the interface between porous electrodes and electrolytesof lithium-ion batteries. We propose a new analytical approach that is a combination of the transmission line model theory for cylin-drical pores and electrochemical impedance spectroscopy using symmetric cells. Mathematical model and experimental impedancebehavior results agree with each other. By mathematically fitting the experimental impedance plots, the individual internal resistancecomponents of the actual porous electrode/electrolyte interface could be described as the following four parameters: electric resis-tance (Re), electrolyte bulk resistance, (Rsol), ionic resistance in pores (Rion), and charge-transfer resistance for lithium intercalation(Rct). In actual electrodes, the Rion obtained in this study is a characteristic parameter of the porous electrode/electrolyte interfacethat is important to consider for thick electrodes. 2012 The Electrochemical Society. [DOI: 10.1149/2.057207jes] All rights reserved.

Manuscript submitted March 12, 2012; revised manuscript received March 12, 2012. Published July 17, 2012.

The development of rechargeable lithium-ion batteries has had asubstantial impact on society. The development of large-size lithium-ion batteries is important in automotive applications, such as hy-brid electric, plug-in hybrid, and electric vehicles. Input-output powercapabilities are an important concern in these applications. Internalresistance of the lithium-ion cell is a key factor for device powercapability. Here, the purpose of this study was to obtain a detailedunderstanding of the internal resistance specific to the porous elec-trode/electrolyte interface for lithium-ion batteries. Electrochemicalimpedance spectroscopy (EIS) is a useful technique for analysis ofthe internal resistance.1 As a preliminary step, a suitable EIS methodis developed to interrogate the true electrode/electrolyte interface. Asshown in Fig. 1, the internal resistances at the porous electrodes couldbe expressed by four parameters: electric resistance (Re), electrolytebulk resistance (Rsol), ionic resistance in pores (Rion), and charge-transfer resistance for lithium intercalation (Rct). To obtain these in-ternal resistances, we propose a new analytical approach, which is acombination of a theory based on the transmission line model (TLM)for cylindrical pores and an EIS analysis technique using symmetriccells (EIS-SC).

In previous experimental EIS analyzes of lithium-ion batteries,little consideration has been given to the geometry of porous elec-trode structures although a relatively large number of simulationand modeling studies of lithium-ion batteries,24 electric doublelayer capacitors,5,6 or hydrogen evolution reaction using porous Nielectrodes7,8 have been reported. EIS impedance results were mainlyexpressed as Nyquist plots (real part: Z, imaginary part: Z), whichgive no detailed information on the porous-electrode structure. Un-doubtedly, the actual electrodes of lithium-ion cells have severaltypes of porous structures consisting of a mixture of active material,carbon-conducting agent, and binder. This mixture involves severalinternal resistances caused by various factors including geometric ef-fects. Especially, the authors believe that lithium ion movement in theelectrolyte-filled pores influences the internal resistance in the thickelectrodes. When charge transfer reaction occurs, the charge-transferresistance has been often interpreted to include the ionic resistancein pores. In order to consider the internal resistance essentially, thosetwo resistances should be distinguished. TLM has been widely used todescribe such porous electrodes as a cylindrical pore for both faradaic(ideally non-polarized electrode) and non-faradaic (ideally polarizedelectrode) processes.5,6,911 TLM for cylindrical pores is applied ei-ther to estimate Nyquist plot profiles or to find individual internalresistances by experimental data fitting.

Electrochemical Society Active Member.zE-mail: ogihara@mosk.tytlabs.co.jp

Figure 1. Schematic illustration of respective internal resistances at porouselectrodes for lithium-ion batteries.

In the EIS-SC technique, two identical electrodes are prepared atthe same potential before measurement and used as both electrodes inthe symmetric cell.12,13 In conventional EIS measurements for positiveor negative electrodes, lithium metal is often used as a counter elec-trode. The resulting impedance spectrum includes the impedance be-havior of the lithium-metal electrode and consequently gives a mixedimpedance profile (Z() = Z+() + ZLi(), as shown in Fig. 2a).Therefore, these EIS measurements are not suitable for expressing theaccurate internal resistance of the actual porous electrode. In contrastto the conventional EIS, EIS-SC provides the impedance spectra of thetrue electrode/electrolyte interface without interference from counterelectrodes (Z() = 2Z+(), illustrated in Fig. 2b, 2c).

From the temperature dependence of the respective internal resis-tances obtained by experimental, a kinetics interpretation for faradaicprocesses is discussed, and comparisons between the charge-transferreaction at the interface and the lithium ion conduction in the bulkelectrolyte and in the electrolyte-filled pores are made.

Mathematical BackgroundImpedance theory for cylindrical pores by use of the transmis-

sion line model. In the case of a non-faradaic process, the overallimpedance is expressed as Equation (1).

Z =

Rion,LjCdl,A2r coth

Rion,L jCdl,A2r L (1)

Figure 3a shows the Nyquist plot for a cylindrical pore calculatedusing Eq. (1) when numerical values are given for each parameter. Inthe high frequency region, the plot is linear with a 45-degree slopefrom the real axis, and transitions to a constant Z value at low

Journal of The Electrochemical Society, 159 (7) A1034-A1039 (2012) A1035

Figure 2. Schematic cell configurations: (a) asymmetric cell for conventional and classical impedance measurements, (b) symmetric cell without separatorincluding electrolyte for electric resistance (Re) measurements, and (c) symmetric cell with separator including electrolyte for ionic resistance in pores (Rion) andcharge-transfer resistance of lithium intercalation reaction (Rct) measurements.

frequencies. As shown in Fig. 3a, the limiting values of the real (Z)and imaginary parts (Z) as 0 are shown as follows,11

Z 0 =Rion

3(2)

Z 0 =1

Cdl(3)

where Rion is a characteristic parameter that expresses the mobility oflithium ions inside the porous electrodes.

In the case of a faradaic process, The overall impedance is thencalculated by Eq. (4).

Z =

Rion,L Rct,A(1 + jRct,ACdl,A) 2r

coth

Rion,L (1 + jRct,ACdl,A)2r

Rct,AL (4)

The Nyquist plots calculated with Eq. (4) are shown in Fig. 3band 3c for Rct, A values of 300 cm2 and 3000 cm2, respectively.At high frequencies, the plots display linear behavior with a 45-degreeslope, and show semi-circle behavior in the low frequency region. Theresults in Fig. 3 show that if the same Rion, L value is used, Eq. (1) and(4) give the same result in the high frequency region. The limitingvalues of the Z and Z components of Eq. (4) as 0 are writtenas follows,11

Z 0 =Rion

3+ Rct (5)

Z 0 = 0 (6)The internal resistances shown in Fig. 3a and 3b are related through

equations (2) and (5). Therefore, the meaning of Rion and Rct can beeasily understood from the profile of the Nyquist plots. If the valueof Rion, L is the same in both cases, when Rct, A is increased to large

A1036 Journal of The Electrochemical Society, 159 (7) A1034-A1039 (2012)

Figure 3. Simulated Nyquist plots for a cylindrical pore, L = 1 cm,r = 0.5 cm, Cdl = 0.1 mF cm2, as predicted by: (a) Eq. (1), Rion,L= 100 cm1, (b) Eq. (4), Rion,L = 100 cm1, Rct,A = 300 cm2,(c) Eq. (4), Rion,L = 100 cm1, Rct,A = 3000 cm2, Frequency range:100 kHz100 mHz.

values (as shown in Fig. 3c), the Nyquist plot calculated using Eq. (4)becomes similar to that calculated with Eq. (1).

Experimental MethodsLiNiO2-based positive electrodes were prepared by coating a dis-

persion composed of LiNi0.75Co0.15Al0.05Mg0.05O2, carbon black (as aconducting agent), and polyvinylidene fluoride (PVDF) (as a binder,Kureha Corp. Japan) (85:10:5 weight ratio) in N-methyl-2-pyrrolidone(NMP) on aluminum foil. LiNi0.75Co0.15Al0.05Mg0.05O2 was preparedby a coprecipitation method.1 The surface morphology of the posi-tive electrode was examined by scanning electron microscope (SEM,Hitachi, S-4300). Figure 4 shows the SEM images of the positive elec-trode. The SEM images of the electrode indicate that heterogeneousporous structures are formed by mainly active material (Fig. 4a) orcarbon black (Fig. 4b) particles. Graphite-based negative electrodeswere prepared using the same procedure as for the positive electrodes.The mixture of graphite and PVDF (90:10 weight ratio) was coatedon a copper foil. Both electrodes were dried at 120C under vacuumfor at least 10 hrs before construction of the electrochemical cell.Typical loadings for the positive and negative active materials were7.0 and 5.0 mg cm2, respectively. The electrolyte used in the experi-ments was 1.0 M LiPF6 dissolved in a solution of ethylene carbonate(EC), dimethyl carbonate (DMC), and ethyl methyl carbonate (EMC)(30/40/30 volume ratio, respectively). A microporous polypropylenefilm was used as a separator.

All electrochemical measurements were performed usinglaminate-type pouch cells assembled in an argon-filled drybox. ForEIS measurements of Re (Fig. 2b), two identical electrodes were as-sembled in direct contact (e.g., positive-positive electrodes) withoutthe separator (electrically non-blocking condition). For EIS measure-ments of non-faradaic processes to determine Rion, identical electrodeswere assembled with the polypropylene separator (electrically block-ing condition). Prior to EIS measurements of faradaic processes todetermine Rct (Fig. 2c), cells with positive and negative electrodeswere prepared with the separator, cycled between 4.1 and 3.0 V atleast once at a low current density of 0.05 mA cm2, and maintainedat 3.685 V for an additional 2 hrs for setting the state of charge (SOC)at 50%. The symmetric cells were then prepared with electrodes takenfrom this cell.

Figure 4. SEM images of the LiNiO2-based positive electrode surface.

AC impedance measurements (Solatron 1260/1286) were per-formed at open circuit potential. The frequency was varied from100 kHz to 100 mHz with a perturbation amplitude of 10 mV (peakto peak), while the measurements were performed between 30 and60C.

Results and DiscussionImpedance of porous electrodes of the symmetric cell. The

impedance behavior of the porous positive electrodes was investigatedin detail. Because the formation of an SEI film leads to a complex inter-face on the graphite negative electrodes, the positive electrodes wereselected for use in preliminary impedance experiments. The symmet-ric cell results for positive electrodes with SOC = 0 and 50% werecharacterized as being due to non-faradaic and faradaic processes,respectively. Figure 5 shows a comparison of the Nyquist plots ob-tained by experiment and calculation. The experimental data are inagreement with theory and indicate that the EIS-SC method is notonly able to isolate positive and negative electrode effects, as reportedpreviously,12,13 but is also able to produce an ideal impedance spec-trum that can be expressed by the TLM for cylindrical pores, whichdescribes the true porous electrode/electrolyte interface.

At SOC = 0% (Fig. 5a), a linear plot with a 45-degree slopefrom the real axis was observed in the high frequency region. Theimaginary part of the impedance increases at low frequencies andthe plot approaches a vertical line, which indicates typical electricalblocking behavior. This behavior suggests that only the formation ofan electrical double layer occurs. No charge-transfer reactions (i.e.lithium intercalation) occur at the interface despite using the charge-transfer-active LiNiO2 electrode. This also means that the electrode isin an electrochemical equilibrium state without charge-transfer. Thisresult reflects the lithium ion conduction in the bulk electrolyte and inthe electrolyte-filled pores, which are expressed as the electrolyte bulkresistance (Rsol) and the ionic resistance in pores (Rion), respectively.At low frequencies, the Nyquist plot does not behave as a perfectly

Journal of The Electrochemical Society, 159 (7) A1034-A1039 (2012) A1037

Figure 5. Nyquist plots for symmetric cells using two positive electrodes in1.0 M LiPF6 in EC/DMC/EMC (30/40/30) at 20C. Electrodes prepared at:(a) SOC = 0% (squares) and (b) SOC = 50% (circles). The solid lines are thebest-fitted results with the equivalent circuits using Eq. (1) and (4), for (a) and(b), respectively.

vertical line. This may be due to a small leakage current. Previouswork has shown that the leakage current influence appears in the lowfrequency region of the electrical double layer formation and is dueto the non-uniform current distributions caused by pore geometry orside reactions.6,8 If the leakage current effect is large, the slope at lowfrequencies decreases. From this point of view, the leakage currenteffect seems to be negligible for the Nyquist plot obtained in thisstudy.

While the Nyquist plot at SOC = 50% (Fig. 5b) is almost the sameas that seen for SOC = 0% (Fig. 5a) in the frequency region greaterthan 20 Hz, the plot appears as a semi-circle at low frequencies. Basedon the consideration of theoretical modeling in Fig. 4, the Nyquist plotcontains information on Rsol and Rion in the high frequency region aswell as the charge-transfer resistance for the lithium-intercalation re-action (Rct) (a faradaic process) in the low frequency region. Theoverlap of the Nyquist plots in the high frequency region for SOC= 0 and 50% is an interesting and important experimental result. Thisresult suggests that Rion exists independently and can be separatedusing the results from Rct in the porous electrodes for faradaic pro-cesses. Hence, Rsol and Rion can be treated independently using theproposed analytical method in this study. Consequently, the electro-chemical behavior of faradaic processes for the porous electrode canbe examined in detail. Furthermore, the potential dependence of Rctcan be accurately determined by controlling the electrode potentialbefore EIS-SC.

Temperature dependence of individual internal resistances ofporous electrodes. In this section, the temperature dependence ofNyquist plots is used to build a kinetics interpretation of the individ-ual internal resistances. Figure 6 shows the temperature dependenceof Nyquist plots between 20 and 60C at SOC = 0%. As seen inFig. 5a, at all temperatures, straight lines with 45-degree slopes areobserved at high frequencies, and near-vertical lines are observed atlow frequencies. The temperature-dependent profiles show the typicalelectric blocking behavior and can be described by the TLM model forcylindrical pores for non-faradaic processes. With decreasing temper-ature, the real impedance component at 100 kHz, which determinesthe value of Rsol, shifts toward more positive values and the length ofthe 45-degree-slope line, which reflects Rion, increases. This indicatesthat these two internal resistances gradually increase with decreas-ing temperature. The frequency where the slope changes from 45 to

Figure 6. Nyquist plots for symmetric cells using two positive electrodes atSOC = 0% in 1.0 M LiPF6 in EC/DMC/EMC (30/40/30) at varioustemperatures.

90 degrees is nearly equal (around 20 Hz) for all temperatures. Thismeans that the time constant for lithium ion conduction in the bulkelectrolyte and inside pores does not vary with changes in temperature.

Figure 7 shows the temperature dependence of Nyquist plots mea-sured at SOC = 50%. Similar behaviors seen in Fig. 5b are alsoobserved at all temperatures. The plots in Fig. 7 can be describedby TLM for cylindrical pores for faradaic processes at all tempera-tures. The 45-degree-slope lines in Fig. 7 show similar behavior tothose in Fig. 6. This means that Rion in faradaic processes exists in-dependently from Rct at all temperatures. The semi-circle in the lowfrequency region, which corresponds to Rct, becomes larger with de-creasing temperature. It seems that the temperature dependence of Rctis larger than that of Rsol or Rion. In addition, at temperatures higherthan 30C, a 45-degree-slope, straight line appears at low frequenciesranging from 100 mHz to 1 Hz. This straight line at very low fre-quencies corresponds to typical semi-infinite diffusion for long-rangeionic diffusion in the bulk of active-electrode materials.14,15

Figure 7. Nyquist plots for symmetric cells using two positive electrodes atSOC = 50% in 1.0 M LiPF6 in EC/DMC/EMC (30/40/30) at varioustemperatures.

A1038 Journal of The Electrochemical Society, 159 (7) A1034-A1039 (2012)

Figure 8. Temperature dependences of each internal resistance: (a) electricresistance (Re), (b) electrolyte bulk resistance (Rsol), (c) ionic resistance inpores (Rion), and (d) charge-transfer resistance of lithium intercalation reaction(Rct). The data were obtained by fitting with Eq. (1) and (4). Rct is calculatedusing Eq. (5).

Equivalent circuits from the TLM for cylindrical pores model wereused to obtain the quantitative internal resistance parameters fromthe experimentally recorded Nyquist plots. As shown in Fig. 5, theimpedance profiles could fit well with the equivalent circuits usingEq. (1) and (4). Rsol, Rion, and Rct can be obtained separately fromthe Nyquist plots using Eq. (5). The inverse of the internal resistancesobtained by fitting is plotted as a function of temperature in Fig. 8. Reis obtained from measurements performed under the same conditionsusing the cell configuration shown in Fig. 2b. Re is smaller by 2-4 or-ders of magnitude when compared with other internal resistances, andcan therefore be ignored. Rion is larger than Rsol, but the temperaturedependency of Rsol and Rion is similar. The relationship between Rsoland Rion is expressed in Eq. (7).

RionRsol

= Snr 2

Ll

(7)

This relationship strongly depends on the ratio of the distance oflithium ion movement to the contact area. Rct is the largest of thesefour internal resistances for temperatures between room temperatureand 30C. However, Rct shows a strong temperature dependence,and becomes smaller than Rsol and Rion above room temperature.

Kinetics interpretation of individual internal resistances of porouselectrodes. To determine the kinetic parameters of interfacial phe-nomena at porous electrodes for faradaic processes, the activationenergies of each resistance (Rx) were evaluated using the Arrheniusequation,

1Rx

= A exp( Ea

RT

)(8)

where A, Ea, R, and T are the frequency factor, activation energy, gasconstant, and absolute temperature, respectively. All internal resis-tances display Arrhenius behavior as shown in Fig. 8. The activationenergies for the individual internal resistances are calculated fromEq. (8) and are listed in Table I. The activation energies for Rsol(14.9 kJ mol1) and Rion (16.3 kJ mol1) are similar. Although theindividual resistances are different, the concordance of the activationenergies for these resistances implies analogous kinetic processes. Theactivation energies for Rsol and Rion are reflective of lithium ion conduc-

Table I. Summary of Activation Energies for the InternalResistance at Porous Electrodes.

Internal resistance Activation energy (kJmol1)Re 0.84Rsol 14.9Rion 16.3Rct 57.6

tion (or transport) in the bulk electrolyte and in the electrolyte-filledpores, respectively. This assignment is based on our experimentallydetermined activation energy of 16 kJ mol1 for the ionic conductivityin the bulk electrolyte. Previous studies reported that the activationenergies for lithium-ion conduction in a crystalline solid electrolyte,La0.55Li0.35TiO3, and in a Li-Al-Ti-phosphate-based glass electrolytewere 2836 kJ mol1.16 Additionally, the lithium ion migration pro-cesses associated with diffusion of naked lithium ions through anSEI film layer on graphite negative electrodes was shown to have anactivation energy of 2025 kJ mol1.17 Therefore, the values of theactivation energies for Rsol and Rion obtained in this experiment are at-tributable to lithium ion conduction in the liquid phase. Furthermore,the agreement of the Rsol and Rion activation energies indicates a nearlyenergy-free kinetic barrier for transport of lithium ions at the interfacebetween the bulk electrolyte and inside the electrolyte-filled pores.

The activation energy for Rct (57.6 kJ mol1) is higher than those ofother resistances. This large value is consistent with previous reportsthat lithium ion transfer at several solid/liquid interfaces is affectedby lithium ion desolvation.18,19 Thus, a higher kinetic barrier exists atthe solid/liquid interface than exists for moving from the electrolytebulk to electrolyte inside the pore. Simple comparison of the internalresistance components at porous positive electrodes reveals that theordering of the activation energies is as follows:

Ea,ct > Ea,ion Ea,sol >> Ea,e.

Importance of Rion on electrochemical behavior in porouselectrodes. Based on the above results, Rct is the dominant com-ponent of the total internal resistance. However, Rion is one of thecharacteristic parameters of porous electrodes that is expected to bedependent on the electrode geometry. Here, we consider thick porouselectrodes based on the TLM theory for cylindrical pores. If the re-sistance per unit area (Rion, L and Rct, A) remains constant and L isincreased, Rion increases while Rct decreases (see list of symbols).Furthermore, from Eq. (7), Rion becomes greater than Rsol if the elec-trode thickness (L) becomes larger than the characteristic lithium ionmovement distance in the bulk electrolyte (l). This prediction suggeststhat Rion will be expected to become the largest resistance componentof the examined internal resistances, and is expected to have a largeeffect on the total internal resistance in thicker electrodes. We stronglybelieve that Rion should be a significant factor for porous electrodesthicker than those examined in the current study. Such effects on thethick electrode will be discussed in detail in subsequent reports.

ConclusionsIn this paper, the individual internal resistance components of

the porous electrode/electrolyte interface have been investigated indetail by combining the transmission line model (TLM) theory forcylindrical pores with electrochemical impedance spectroscopy usingsymmetric cells (EIS-SC). With this approach, we have succeededin separating four internal resistances at the porous electrode as thefollowing parameters: Re, Rsol, Rion, and Rct. From the temperaturedependence of these resistances, a kinetics interpretation is given tothe comparison between the charge-transfer reaction at the interfaceand the lithium ion conduction inside pores for faradaic processes.The Rion obtained is a characteristic parameter of the actual porouselectrode/electrolyte interface that is important to consider for thickelectrodes. The results show that despite its simplicity, our approach

Journal of The Electrochemical Society, 159 (7) A1034-A1039 (2012) A1039

will give reasonably accurate results and is sufficient for analysisof the electrochemical characteristics of actual porous electrodes forlithium-ion batteries.

List of SymbolsL unit pore length, cmL characteristic distance of lithium ion movement in the bulk

electrolyte, cmr pore radius, cm electrolyte resistance, cmS electrode surface area, cm2n number of pores per unit electrode surface areaZi, L interfacial impedance per unit pore length, cmZi, A interfacial impedance per unit surface area, cm2Re electric bulk resistance, Rsol electrolyte resistance (Rsol = l / S ), Rion, L ionic resistance per unit pore length (Rion, L = /r2), cm1Rion ionic resistance in pores (Rion = Rion, L L / n), Rct, A charge-transfer resistance per unit surface area, cm2Rct total charge-transfer resistance (Rct = Rct, A / 2rL), Cdl, A electric double layer capacitance per unit surface area, Fcm2Cdl total electric double layer capacitance (Cdl = Cdl, A 2rL), F

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