Local Heat Generation in a Single Stack Lithium Ion Battery Cell

Local Heat Generation in a Single Stack Lithium Ion Battery Cell

Electrochimica Acta 186 (2015) 404–412 Contents lists available at ScienceDirect Electrochimica Acta journal homepage: www.elsevier.com/locate/elect...

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Electrochimica Acta 186 (2015) 404–412

Contents lists available at ScienceDirect

Electrochimica Acta journal homepage: www.elsevier.com/locate/electacta

Local Heat Generation in a Single Stack Lithium Ion Battery Cell C. Heubnera,b,* , M. Schneidera , C. Lämmela , A. Michaelisa,b a b

Fraunhofer IKTS Dresden, Winterbergstr. 28, 01277 Dresden, Germany TU Dresden, Institute for Materials Science, Helmholtzstr.7, 01069 Dresden, Germany

A R T I C L E I N F O

A B S T R A C T

Article history: Received 4 June 2015 Received in revised form 18 September 2015 Accepted 29 October 2015 Available online 1 November 2015

The local heat generation in a single stack lithium ion battery cell was investigated as a function of the Crate and state of charge (SoC). For that purpose, a custom build electrochemical cell design developed for local in-operando temperature measurements is used. The local temperature evolution in both electrodes and the separator is compared with local heat generation rates calculated from galvanostatic intermittent titration technique (GITT) measurements. The impact of reversible and irreversible heats is evaluated as a function of the C-rate and the SoC. The results reveal substantial differences in the local heat generation rates of the individual components of the battery cell related to their kinetic and thermodynamic properties. Significant SoC dependencies of the local reversible and irreversible heat generation are reflected by both the local temperature measurements and the heat generation rates calculated from GITT. A distinct asymmetry between charging and discharging is revealed which results from the intrinsic asymmetry of the reversible heat as well as differences in the kinetic limitations of the lithiation and delithiation of active materials. This study indicates, that the heat generation rates of the individual cell components should be considered accurately in order to build up basics for targeted material-, design- and thermal management optimization to handle thermal issues in large battery packs. ã 2015 Elsevier Ltd. All rights reserved.

Keywords: Battery lithium ion local heat generation heat sources

1. Introduction Performance, safety and lifetime of lithium ion batteries are strongly affected by temperature [1]. The degradation is enhanced at elevated temperatures [2] and the performance is drastically reduced at low temperatures [3]. The self-discharge is usually expected to be negligible at room temperature but becomes significant at temperatures above 50  C [4]. Furthermore, elevated temperatures can trigger exothermic reactions and decomposition of the SEI or the separator resulting in a thermal runaway [5,6]. The optimization of lithium ion batteries, regarding these problems, requires a fundamental understanding of the heat generation. Many researchers studied heat generation, temperature evolution and heat dissipation theoretically using 1D models assuming uniform heat generation as well as detailed thermal-electrochemical 3D models [1]. However, associated simulations require a detailed knowledge of material properties, thermodynamic and kinetic parameters as well as an accurate validation. Some researchers investigated the heat generation experimentally by using commercial and custom calorimeters or simply measuring

* Corresponding author. Tel.: +4935125537324; fax.: +493512554176. E-mail address: [email protected] (C. Heubner). http://dx.doi.org/10.1016/j.electacta.2015.10.182 0013-4686/ ã 2015 Elsevier Ltd. All rights reserved.

the temperature of the battery. Accelerated rate calorimetry [7,8] and isothermal heat conduction calorimetry [9–14] are primary applied to measure the heat that is dissipated from the battery. Temperature measurements are commonly done by placing a thermocouple on the surface of the battery(system) [15–20]. All these measurements suffer from the fact that the measured temperatures are integral values of the investigated setup consisting of the actual electrochemical cell and periphery (housing, current collector tabs, etc.). Actually, the heat generation within the individual components of the battery cell, which are the negative electrode, the separator and the positive electrode, distinctly differs due to different material properties as well as electrochemical kinetics and thermodynamics [21,22]. Consequently, a detailed understanding of the temperature evolution in the battery cell requires the knowledge of local heat generation rates. Recently, spatially resolved temperature measurements have been published [17,20,23–25]. However, the achieved resolution is much lower than required to resolve the spatial dimensions of the individual battery cell components which are in the submillimeter range. The presented techniques are well suited for the investigation of design effects but did not include any information about the local heat generation rates of the positive and the negative electrode or the separator.

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In this study a custom build electrochemical cell developed for local in-operando temperature measurements is used to investigate the local temperature evolution in a single stack lithium ion battery cell. In a previous paper the proper functioning of this setup has been demonstrated [21]. In the present paper, this setup is used to investigate the influence of the C-rate on the local heat generation as a function of state of charge (SoC) and the lithium concentration in the active materials, respectively. The local temperature measurements were compared to local heat generation rates calculated from galvanostatic intermittent titration technique (GITT) measurements. 2. Experimental and Methods The investigation of local heat generation rates is carried out on the example of a well-established reference system for high energy density applications. Commercially available composite electrodes (MTI Corp.) were investigated. The active materials of the positive and the negative electrode were LiCoO2 (LCO) and graphite (C), respectively. The separator was a borosilicate glass-microfiber filter (Whatman). Commercially available high purity 1 M LiPF6 in ethylene carbonate (EC): diethyl carbonate (DEC) in a 1:1 weight ratio (BASF, SelectilyteTM) was used as electrolyte. The geometrical properties of the electrodes and the separator were estimated by scanning electron microscopy. Geometrical and physical properties of the battery components are displayed in Table 1. The assembly of electrochemical cells was carried out in an argon filled glove box (MBraun). For the electrochemical experiments a multi-channel potentiostat / galvanostat with integrated frequency response analyzer (VMP3, Biologic) was used. First, the cells were subjected to a CCCV procedure as formation and to determine the capacity of the cell (3.55 mAh), which was close to the theoretical capacity (3.85 mAh) based on the mass of LCO in the positive electrode. Hereinafter, local in-operando temperature measurements were carried out in parallel to a rate capability test including C–rates from 0.2 C to 1.0 C. Fig. 1 displays an overview of the experimental details. For local in-operando temperature measurements a custom build electrochemical cell is used, which was introduced in a previous paper [21]. Within this cell the local temperature measurements are realized by a specific arrangement of three thermocouples schematically shown in Fig. 1. The type K thermocouples with a diameter of 0.25 mm are covered with a heat conducting but electrical insulating epoxy resin. The small volume results in small heat capacity and a very fast response characteristic. The electrical isolation reduces noise from the surroundings. The finally utilized thermocouples were carefully selected after preliminary investigations concerning the offset in thermal equilibrium and the thermoelectric voltage response in dynamic temperature tests ranging from 15  C to 30  C. Thermocouples that exhibit a

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thermoelectric voltage in a range of 39.1  0.4 mV K1 were selected for the experiments. Offsets between the three thermocouples were corrected as a part of the calibration. Two of the thermocouples are pressed against the backside of the electrodes. A third one penetrates the anode and is pressed against the separator. The thermocouples are spring mounted to realize a reproducible positioning and thermal contact. The electrode stack itself is spring mounted within the cell body to guarantee a reproducible contact pressure between the components. The electrodes were connected from the backside by electrical contacts implemented into the cell body. The cell body consists of polyetheretherketone (PEEK). All connections were sealed twice with gaskets. The cell and the device for data acquisition and analog to digital conversion (DT9874 MEASURpoint, Data Translation) were placed in a climate chamber (20  C) with forced convection resulting in a stable surface temperature (0.1  C) of the cell body and the cold junction. Measurements were conducted after a relaxation period of 24 h to ensure thermal equilibrium. The raw data were smoothed using a simple moving average algorithm in order to reduce the noise and to improve the discriminability between the local temperatures. In addition to the temperature measurements identical electrodes were investigated by GITT. GITT is well established for the investigation of insertion kinetics [27]. Starting from an insertion electrode of known stoichiometric composition and in electrochemical equilibrium, a constant current is applied to the cell and the potential response is measured. After a certain time interval, the current is interrupted and concentration gradients within the electrode and the electrolyte relax by diffusion of the mobile species accompanied by a drift of the electrode potential towards a new steady state value. This procedure is repeated until a defined cut-off potential is reached. In this study GITT was used to determine the overpotential of the electrode reactions as a function of the applied C – rate and the SoC. For that purpose 3electrode Swagelok1 cells were prepared with LCO and graphite being the working electrode, respectively. A sheet of lithium metal was used as counter electrode. As reference electrode the tip of a flattened lithium metal wire (<0.5 mm in diameter) was embedded in a double-layer separator peripherally at the electrodes. GITT studies were performed using the identical pretreatment and Crates as for the temperature measurements. Local heat generation rates were calculated from the GITT results and compared to the local in-operando temperature measurements. 3. Results and discussion 3.1. Local in-operando temperature measurements Fig. 2 presents an overview of the experiment including voltage profiles and local in-operando temperature measurements for

Table 1 Geometrical and physical properties of the investigated battery components.

Positive electrode Negative electrode Separator Electrolyte a b c d e

(Active) material

Thickness d/mm

Mean particle radius r/mm

Porosity F/%

Heat capacity cp/J g1 K1

Density r/g cm3

Volume V/cm3

LiCoO2 (LCO) Graphite (C) Borosilicate glass LiPF6 in EC/DEC

120a

3a

33a

1.27b

2.33b

0.014

a

a

a

a

b

0.013

e

0.019 –

110

150 –

a

5 – –

35 83 –

d

Estimated from SEM micrographs (see supplementary material). Taken from Ref. [26]. Taken from SelectilyteTM datasheet. Estimated from the ratio of the mass density compared to bulk borosilicate glass. Estimated from the values for bulk borosilicate glass and electrolyte, weighted with respect to the porosity.

1.43

a

1.93 2.06b

1.35

1.33 1.22c

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Fig. 1. Overview of experimental details. Left: experimental arrangement (PC – personal computer, VMP3–potentiostat/galvanostat, DT9874–device for data acquisition and analog to digital conversion, EC – electrochemical cell). Centered: electrochemical cell design, PEEK housing with sample chamber (1) and spring mounted stamp (2). Right: schematic drawing of the electrode arrangement and the positioning of the thermocouples within sample chamber (TLCO – thermocouple at the LCO electrode, TSep – thermocouple close to the separator, TC – thermocouple at the graphite electrode).

Fig. 2. Overview of the voltage profiles and local in-operando temperature measurements for different C-rates (TLCO – temperature at the positive electrode, TSep – Temperature close to the separator, TC – temperature at the negative electrode).

different C-rates. During charging and discharging the temperatures of the negative electrode, the separator and the positive electrode deviate from the ambient temperature given by the climate chamber. The temperature evolution varies with the applied C-rate and is different for charging and discharging. The observed temperature changes are small compared to investigations on multi-stacked battery systems as e.g. a cylindrical 18650 cell, e.g. Ref. [16]. This is due to highly non-adiabatic conditions which are related to the geometric properties of the electrode stack. Actually, the stack is well isolated using a PEEK housing. However, it has to be emphasized that it is a very thin cylinder (height 0.35 mm, diameter 12.7 mm). Consequently, the ratio between the surface area for heat dissipation and the absolute heat capacity is very small resulting in highly nonadiabatic conditions. Accordingly, steady state conditions are

rapidly established for a given heat generation rate and the temperature difference between a battery component and its surroundings is directly proportional to its heat generation rate. In the case of adiabatic conditions the heat generated within the cell would be accumulated over the charging/discharging process and the temperature would increase monotonously. In contrast, using the developed setup, alterations of the heat generation rates with the C-rate or the SoC are directly identified as changes in temperature. Furthermore, the local temperature measurements indicate the component of the battery stack which dominates the heat evolution in the cell. Thereby, the authors assume that the component which shows the highest temperature dominates the heat evolution if the overall temperature change is positive and vice versa. However, the temperature changes with respect to the ambient temperature as well as the differences between the local temperatures are small due to the highly non-adiabatic conditions and need to be discussed regarding accuracy and precision. Actually, the accuracy of measuring absolute temperatures utilizing thermocouples is commonly stated to be inferior to 1  C. As we are interested in changes and differences in temperature, associated with the local heat generation rates, the accuracy of the absolute temperature is of minor, but the precision of very high importance in this study. The inaccuracy of 1  C is caused by variations of the materials properties. The thermoelectric voltage is formed because the temperature gradient between the hot junction and the cold junction causes charge carriers in the material to diffuse from the hot side to the cold side. Thus, the thermoelectric voltage depends on the material itself as well as its transport properties. As a consequence, structural defects and impurities significantly influence the thermoelectric voltage [28]. Owing to this fact, the authors carefully selected the finally utilized thermocouples after preliminary investigations concerning their thermoelectric voltages as described in Section 2 (39.1  0.4 mV K1). Since the temperature is calculated from the average thermoelectric voltage of 39.1 mV K1, the maximum error between two thermocouples is approximately 1% K1 or 10 mK K1, respectively. In particular, if the temperature changes 100 mK in the course of the experiment, the error is less than 1 mK. Therefore, this typically huge source of error is reduced to a minimum and the precision of measuring changes in temperature is increased to a maximum in the present study. The device used for data acquisition and analog to digital conversion of the thermoelectric voltages is made for ultra-precise temperature and voltage measurements. The voltage range is 75 mV with a resolution of 24-bit (<10 nV). As the thermoelectric voltage of the

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Fig. 3. a) Comparison between local temperatures during OCP period and discharging with 0.6 C, raw data are given for the OCP period to illustrate the effect of smoothing; b) histogram of the raw data in Fig. 3a and normal distribution (Eq. (1)) calculated with the indicated parameter.

thermocouples is 39.1  0.4 mV K1, a noise level of 10 nV adds less than 0.3 mK error. Further noise is produced by the cold junction compensation and the surroundings. Fig. 3a shows raw data and smoothed data during an OCP period of 1.5 h as well as the smoothed local temperatures during the subsequent discharge cycle with a C-rate of 0.6 C. Fig. 3b displays a histogram of the raw data presented in Fig. 3a. Obviously, the noise is normally distributed and the probability density can be described by the Gaussian: ! 1 ðT  mT Þ2 f ðTjmT ; s T Þ ¼ pffiffiffiffiffiffiffiexp  ð1Þ 2s 2T s T 2p where mT is the mean and s T is the standard deviation. Respective fits to Eq. (1) are also given in Fig. 3b with the indicated parameter. During the OCP period, the standard deviation is less than 3 mK for all thermocouples and the difference between the mean values is less than 1 mK. In comparison, when the cell is discharged with 0.6 C, the temperatures increase approximately 100 mK in 1.5 h and the difference between the temperatures at the LCO and the graphite electrode is larger than 10 mK at e.g. 0.75 h. This is more than 30 and 3 times the standard deviation, respectively. As the noise is normally distributed, a difference of the smoothed data of more than 3 s T means that less than 10% of the raw data points overlap. Regarding this precision of the measurements, the temperature changes as well as the difference between the local temperatures appear to be truly related to the local heat generation rather than being purely statistical. Fig. 4 compares the local temperature evolution for charging and discharging at different C-rates. Generally, the overall heat evolution is smaller for charging than for discharging and increases

with increasing C-rate. The temperature evolution is nonmonotonic. This indicates variations of the heat generation rates depending on the SoC. At the beginning of charging and C-rates <0.6 C the temperatures drop below the ambient temperature provided by the climate chamber. This must be attributed to an endothermic effect. At higher SoC the temperatures exceed the ambient temperature. Consequently, the heat generation is exothermic in this case. In contrast to this behavior, the temperature evolution for C–rates 0.6 C is always positive during charging and no cooling effect can be observed. In comparison to the charging process, the temperature evolution during the discharging process is positive for all C-rates and SoC. The temperature rises quickly at the beginning of discharge, passes a plateau region and increases again at high SoC. The local temperatures become more distinct with increasing C-rate, which is reasonable because of reduced time for thermal relaxation. However, the discriminability is much more pronounced during the discharging process. This indicates that the differences in temperature did not merely depend on thermal relaxation but rather on differences in the local heat generation rates of the individual battery components. A detailed discussion of the local heat regeneration rates and a comparison to the measured local temperature evolution is part of the following sections. 3.2. Heat generation rates from GITT GITT measurements were performed additionally to the temperature measurements in order to determine electrode specific heat generation rates. Assuming negligible heat of mixing [29], the local heat generation rate is the sum of irreversible and

Fig. 4. Temperature profiles for different a) charging rates b) discharging rates.

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reversible heats [30]: q_ ¼ q_ irr þ q_ rev ¼

Ih IT DR S  zFV V

ð2Þ

where I, h and DR S are the absolute applied current in the GITT experiment, the overpotential and the entropy change of the halfcell reaction. T,z and F are the absolute temperature, the valence and Faraday’s constant. Equilibrium potentials Eeq ðxÞ (OCP after 3 h of relaxation) and non-equilibrium potentials EðxÞ (at the end of each current impulse) were extracted from the measurements as a function of the lithium concentration x in the active materials. The overpotential is calculated to:

hðxÞ ¼ EðxÞ  Eeq ðxÞ

ð3Þ

Using the determined overpotentials and the entropy data reported by Reynier et al. [31,32], the local heat generation rates of the LCO based positive electrode and the graphite based negative electrode were calculated according to Eq. (2). The results are presented in the form of color-coded contour plots (Figs. 5 and 6). Please note that Figs. 5 and 6 have different scaling in order to improve the resolution. The C-rate is positive and negative for charging and discharging, respectively. Fig. 5 shows the reversible and the irreversible volumetric heat generation rate as well as the total heat generation of the LCO electrode. The total heat generation significantly depends on the C-rate and the lithium concentration x in LixCoO2. Furthermore, a distinct asymmetry between lithiation (discharging) and delithiation (charging) is revealed. The magnitudes of the volumetric heat generation rate are consistent with previously measured values for full cells. For example, at a discharge rate of 1.0 C, the volumetric heat generation rate of the LCO electrode ranges from 25 WL1 to 150 WL1, with respect to the total cell volume approximately 9 WL1 to 50 WL1. By comparison, the volumetric heat generation rate ranged from 13.3 WL1 to 84.5 WL1 for commercial 18650 cells with carbon-based negative electrodes and LiCoO2 based positive electrodes tested by Onda et al. using the 0.92 C rate [12]. This indicates that the heat generation in the cell is significantly induced by the positive electrode. According to the results in Fig. 5, the total heat generation is slightly endothermic for delithiation (charging) at C-rates <0.6 C and x > 0.55. This effect is caused by the reversible heat of the electrode reaction. Except for the order – disorder phase transition around x = 0.5, the entropy of delithiation is positive, which is mainly caused by the increase of configurational entropy due to the formation of vacancies in the crystal lattice [31]. This process consumes an amount energy which will be removed from the thermal energy of the system. Consequently, a cooling effect can be

observed. During lithiation (discharging) the configurational entropy is reduced resulting in an exothermic reversible heat effect. Additionally to this intrinsic asymmetry between discharging and charging, the kinetic limitations which are represented by the overpotential h, are not similar for lithiation and delithiation, particularly the charge transfer resistance (asymmetric charge transfer coefficient a 6¼ 0:5 [33]) and mass transport limitations (e.g. core shell model [34]), resulting in different irreversible heat generation rates, Ih, for charging and discharging. The reversible heat generation rate is directly proportional to the applied C-rate q_ rev  I, whereas the irreversible heat generation rate shows a complex, disproportional current dependence q_ irr  Ia , with a > 1 [35]. Consequently, the ratio between reversible and irreversible heat is a function of the C-rate. The reversible heat dominates at small currents and the irreversible heat at higher C-rates. During delithiation the absolute values of the endothermic reversible heat and the exothermic irreversible heat are almost identical and extinguish each other for approximately 0.6 C and x > 0.6. In this case, the total heat generation rate is close to zero. The entropy of the half-cell reaction DR S as well as the kinetic parameters (exchange current density j0, ohmic resistance R, diffusion coefficient D) change with the lithium concentration x in LixCoO2. Thereby, j0 increases with decreasing x [36,37], resulting in a reduction of the activation overpotential to realize a certain current. The electrical resistance of LixCoO2 decreases with decreasing x [38], and the ohmic contribution to the total overpotential is reduced. The lithium diffusion in the active material is enhanced with increasing number of vacancies and decreasing lithium concentration, respectively [36,39]. Consequently, the heat generation caused by the diffusion overpotential is reduced with increasing SoC. In total, the kinetic limitations significantly decrease with increasing SoC and the irreversible heat generation rate is largest at low SOC. Additionally, the reversible heat is largest and exothermic for lithiation and 0.95 > x > 0.7. It can be concluded, that the total heat generation of the LCO electrode is largest for discharging and mid to low SoC. Fig. 6 shows the reversible and the irreversible volumetric heat generation rate as well as the total heat generation of the graphite electrode. As for the LCO electrode the total heat generation significantly depends on the C-rate and the lithium concentration x in LixC6. Generally, the total heat generation is lower compared to the LCO electrode. For example, at a discharge rate of 1.0 C, the volumetric heat generation rate of the graphite electrode ranges from 5 WL1 to 30 WL1 and is averagely 15 WL1. By comparison, the volumetric heat generation rate of the LCO electrode ranges from 25 WL1 to 150 WL1 and is averagely 110 WL1.

Fig. 5. Reversible, irreversible and total heat generation rate of the LCO electrode as a function of the C-rate and the SoC.

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Fig. 6. Reversible, irreversible and total heat generation rate of the graphite electrode as a function of the C-rate and the SoC.

In contrast to the electrodes the heat generation rate of the separator is exclusively determined by the irreversible heats due to ohmic losses and mass transport limitations: I q_ Sep ¼ ðhV þ hD Þ V

ð4Þ

where hV is given by Ohms law corrected by the porosity: d

hV ¼ j sF and hD can be estimated to [40]:

ð5Þ

hD ¼

ð6Þ

  RT jd ln 1  zF zFDF

with j, s and D being the current density, the conductivity and the diffusion coefficient of the electrolyte, d and F are the thickness and the porosity of the separator. Eqs. (4)–(6) were used to calculate the heat generation rate of the separator as a function of the C-rate. In order to compare the impact of anode, separator and cathode on the heat generation in the cell, the dissipated heat, Q, during a complete charge/discharge cycle was calculated by numerical integration of the determined heat generation rates: Z V Qk ¼ k ð7Þ q_ k dt V cell where V k is the volume of the component k. The dissipated heat for the cell, Q cell , is then given by the sum of all components. Fig. 7

shows Q cell and the contributions of the graphite electrode, the separator and the LCO electrode for different C-rates. The dissipated heat increases with increasing C-rate. The LCO electrode clearly dominates the heat generation during discharge. The separator as well as the graphite electrode have a minor impact. The behavior during charging is more complex as the impact of the battery components is a strong function of the C-rate. As expected from Figs. 5 and 6, the endothermic reversible heat of the LCO electrode dominates the heat evolution at small C-rates and heat is removed from the surroundings. For medium C-rates endothermic reversible and exothermic irreversible heats of the LCO electrode compensate each other resulting in a small total heat generation. As a consequence, the graphite electrode clearly dominates the heat evolution in the cell within this range of C-rates. As the C-rate increases further, the irreversible heat generation rate of the LCO electrode rises quickly compared to the graphite electrode. Accordingly, the impact of the LCO electrode increases with increasing C-rate and dominates the heat evolution at the 1.0 C rate. These differences in the C-rate dependence of the local heat generation rates are related to the thermodynamic and kinetic properties of the battery components. Table 2 compares the magnitudes of kinetic and thermodynamic parameters which are related to the heat generation rates. Average values are given for parameters that exhibit a significant SoC dependence. Diffusion coefficients of the active materials were taken from single particle studies. First of all, the entropy change in graphite is much lower than in LCO resulting in less reversible heat. Furthermore, the electric conductivities of graphite and the electrolyte are orders of magnitude higher than for LCO resulting in less ohmic overpotential and corresponding Joule heating. Additionally, the exchange current density and the lithium diffusion coefficient in the active materials are higher for graphite resulting in reduced irreversible heat generation in comparison to LCO. The heat generation within the separator is the lowest of all components because of high electrolytic conductivity as well as the absence of charge transfer losses and reversible heats.

Table 2 Comparison of kinetic and thermodynamic parameters of the battery components.

Fig. 7. Dissipated heat for a complete charge (discharge) cycle. The broad bars correspond to the cell, the inner bars represent the contributions of the components.

Parameter

Graphite

Electrolyte

LCO

|DRS|/J mol1 K1 s /S cm1 D/cm2 s1 j0/mA cm2

5 [32] 103 [41] 108 [43] 2 [45]

– 101 [42] 106 [42] –

35 [31] 104 [41] 1010 [44] 0.03 [46]

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3.3. Comparison between GITT results and local temperatures The following section deals with the comparison between the measured local temperature evolution and the local heat generation rates calculated from the GITT results. As shown in the previous section, the separator hardly influences the overall heat generation in the cell. Furthermore, q_ Sep did not show any SoC dependence. For the sake of improved clarity the values for the separator are not shown in this section. Fig. 8 compares the measured local temperature evolution and the local heat generation rates calculated from GITT for charging and discharging using the example of the 0.4 C rate. At the beginning of the charging process, the temperatures of electrodes drop below the ambient temperature up to approximately SoC = 0.3. The decrease in temperature is clearly dominated by the positive electrode. In this SoC range, the local heat generation rates reveal a significantly endothermic effect at the positive electrode. The heat generation at the negative electrode is endothermic for SoC < 0.1 and exothermic for SoC > 0.1. When q_ C becomes exothermic the decrease in temperature is more and more reduced. At SoC = 0.4 the endothermic effect at the positive electrode and the exothermic effect at the negative electrode are approximately identical and the temperatures are close to the ambient temperature. In the SoC range 0.4 to 0.8 the endothermic effect at the positive electrode tends to zero. Consequently, the overall heat evolution is dominated by the negative electrode and the temperatures rise above the ambient temperature. For SoC > 0.8 a significant increase in temperature is observed. However, in this region the distinction between the temperatures of the electrodes is difficult. The GITT results suggest an increase of the heat generation rate at the positive electrode. This exothermic

effect is associated with a peak in the reversible heat generation rate which is caused by an order/disorder transition in LCO [31]. During discharge the temperature change is positive and clearly dominated by the positive electrode for any SoC. Furthermore, the difference between the temperatures of the positive and the negative electrode is more pronounced than for charging. This is in accordance with the local heat generation rates. The discharge process starts at approximately SoC = 0.9. At this point the local heat generation rates are close to zero. During further discharging q_ LCO increases continuously whereas q_ C stays close to zero up to approximately SoC = 0.5. In this SoC range the temperature rise in the cell is clearly dominated by the positive electrode. For 0.5 > SoC > 0.3, q_ C is slightly negative whereas q_ LCO is positive and increases further. The predicted cooling effect at the negative electrode weakens the temperature rise in the cell and the difference between TLCO and TC is slightly enlarged. When q_ C becomes positive the temperature rise in the cell is enhanced again. Fig. 9 compares the measured local temperature evolution and the local heat generation rates calculated from GITT for charging and discharging using the example of the 0.8 C rate. In contrast to the charging process for the 0.4 C rate, the local temperatures are close together and the overall temperature change is positive for any SoC. This is in good accordance with the local heat generation rates. In contrast to 0.4 C, q_ LCO is slightly positive in the 0.1 < SoC < 0.3 range. At the 0.4 C rate, the reversible heat of the positive electrode dominates the heat evolution in the cell. Due to the different current dependencies the ratio of irreversible to reversible heat increases with increasing C-rate. At the 0.8 C rate, the endothermic reversible heat is overcompensated by the exothermic irreversible heat and the total heat generation rate

Fig. 8. Comparison between the local temperature development and the local heat generation rates calculated from GITT for charging and discharging (0.4 C).

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Fig. 9. Comparison between the local temperature development and the local heat generation rates calculated from GITT for charging and discharging (0.8 C).

q_ LCO is slightly exothermic in this region. The heat generation rates of the positive and the negative electrode are close together and just a small difference in the local temperatures is observed. For SoC > 0.5, q_ LCO increases whereas q_ C decreases. In this region, the local rates of heat generation are almost identical and no difference can be observed in the local temperatures. During the respective discharging process the temperature evolution is comparable to the 0.4 C rate except for the absolute value of the temperature change. Similar to charging, the ratio of irreversible to reversible heat increases with increasing C-rate. Consequently, endothermic effects have a minor impact compared to the 0.4 C rate. The comparison between the local heat generation rates based on GITT and the local in-operando temperature measurements shows a good coincidence. The highest temperatures are observed for discharging at high C-rates and mid to low SoC. The local temperature measurements reveal, that this effect is mainly caused by the LCO electrode. The separator as well as the graphite electrode show a minor impact on the heat generation in the cell. 4. Conclusion The C-rate dependence of the local heat generation rates of the electrodes was estimated from GITT measurements as a function of the SoC. The results are compared with local in-operando temperature measurements, showing a good agreement. Both, local temperature measurements and GITT results reveal significant differences of the local heat generation which can be related to the thermodynamic and kinetic properties of the individual battery components. For the investigated system the following conclusions can be drawn:

 The heat generation in the separator is small compared to the electrodes for all investigated C-rates because of the high electrolytic conductivity and the absence of charge transfer losses and reversible heats.  The heat generation of the LCO electrode is dominated by the reversible heat for C-rates < 0.6 C and irreversible heat dominates for C-rates > 0.6 C.  The heat generation of the graphite electrode is dominated by the reversible heat for C-rates < 0.9 C and irreversible heat dominates for C-rates > 0.9 C.  The overall heat generation in the cell is dominated by the LCO electrode for almost all C-rates due to large entropy changes as well as large kinetic limitations compared to the graphite electrode. The local reversible as well as irreversible heat generation rates strongly depend on the SoC which is reflected by both the local temperature measurements and the heat generation rates calculated from GITT. Most notably, the increase of kinetic limitation of the LCO electrode with decreasing SOC remarkably influences the heat generation in the cell. Furthermore, a significant asymmetry between charging and discharging is revealed which is caused by the intrinsic asymmetry of the reversible heat as well as differences in the kinetic limitations of the lithiation and delithiation of LCO. This study indicates, that the heat generation rates of the individual battery cell components should be considered accurately in order to generate a fundamental knowledge of the heat generation in battery cells and corresponding basics for a targeted material-, design- and thermal management optimization to handle thermal issues in large battery packs.

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