Electrochemical Impedance Analysis of Lithium Cobalt Oxide Batteries

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Electrochemical Impedance Analysis of Lithium Cobalt Oxide Batteries
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english
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Erol,Salim
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Master's ( M.S.)
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University of Florida
Degree Disciplines:
Chemical Engineering
Committee Chair:
Orazem, Mark E
Committee Members:
Chauhan, Anuj
Jones, Kevin S

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Subjects / Keywords:
battery -- impedance -- lithium -- overcharge -- overdischarge -- selfcharge -- selfdischarge
Chemical Engineering -- Dissertations, Academic -- UF
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Chemical Engineering thesis, M.S.
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Abstract:
Impedance measurements on commercial LiCoO2 secondary 2032 button cells are shown to be extremely sensitive to state-of-charge, overcharge, overdischarge, and elapsed time. The LiCoO2 cells were initially charged under galvanostatic control to 3.80 V. Each cell was potentiostatically held at constant cell potential. After the constant-potential rest period, the impedance was measured using a 10 mV perturbation and 100 kHz ? 0.02 Hz frequency range. Lissajous plots were used to ensure linearity during the impedance measurement. Following each impedance measurement, the cell potential was potentiostatically modified for the charge and discharge profiles in 0.20 V steps. In the same manner, the discharge profile analysis was executed immediately following the charge schedule. To study the influence of overcharge, the cell was initially charged under constant current to 4.20 V. Impedance measurements were performed at each 80 mV step up to and including 5.00 V. A similar protocol was followed for the overdischarge. Impedance measurements were performed at each 80 mV step down to and including 2.20 V. After overcharging to a potential of 5 V, the battery was allowed to relax for four days at the open-circuit condition. When held at open-circuit, the overcharged battery rapidly reached a cell potential within the nominal operating range. After overdischarging to a potential of 2.20 V, the battery was allowed to relax for four days at the open-circuit condition. When held at open-circuit, the overdischarged battery also reached a cell potential within the nominal operating range, but this process was slower. The impedance response showed a persistent change to the electrochemical characteristics of a coin cell subjected to overcharge and returned to normal cell potentials; whereas, the electrochemical characteristics returned quickly to normal for a coin cell subject to overdischarge and returned to normal cell potentials. Measurement model analysis was used to show that the change in the impedance response with elapsed time was due to a change in the Ohmic resistance.
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by Salim Erol.
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Thesis (M.S.)--University of Florida, 2011.
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1 ELECTROCHEMICAL IMPEDANCE ANAL YSIS OF LITHIUM COBALT OXIDE BATTERIES By SALIM EROL A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORID A IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2011

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2 2011 Salim Erol

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3 To my parents and friends

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4 ACKNOWLEDGMENTS First of all, I would like to thank Dr. Mark Orazem for gu iding me in my thesis with his large knowledge and experiences in elec trochemical engineerin g field. He always has been positive and patient with me. Second, I thank to my research group members, who helped and supported me whenever I need. Last but not least, I want to thank Turkish Educational Ministry for the financ ial support throughout my master’s program.

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5 TABLE OF CONTENTS page ACKNOWLEDG MENTS .................................................................................................. 4LIST OF FI GURES .......................................................................................................... 6ABSTRACT ..................................................................................................................... 8INTRODUCT ION ........................................................................................................... 10ELECROCHEMICAL IMPEDAN CE SPECTRO SCOPY ................................................ 12EXPERIMENTAL METHOD .......................................................................................... 153.1 Coin Cells ......................................................................................................... 153.2 Instrum entation ................................................................................................. 153.3 Protocol ............................................................................................................. 15RESULTS AND DISCUSSION S OF EXPERIM ENTS ................................................... 174.1 Normal O perati on.............................................................................................. 174.2 Overch arge ....................................................................................................... 174.3 Overdi scharge .................................................................................................. 234.4 Influence of Elapsed Ti me ................................................................................ 25MEASUREMENT MODE L ANALYSI S .......................................................................... 285.1 Measurement Model ......................................................................................... 285.2 Measurement Mo del Resu lts ............................................................................ 30CONCLUSION S ............................................................................................................ 33LIST OF RE FERENCES ............................................................................................... 34BIOLOGICAL SKETCH ................................................................................................. 36

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6 LIST OF FIGURES Figure page 1-1 The indication of movements of Li+ ions when a LiCoO2 battery is charged and dischar ged ................................................................................................... 102-1 A simple electrochemical circuit repr esentati on .................................................. 122-2 Perturbation of an electrochemical syst em with a small sinusoidal signal at steady state, where and represent the potential and current oscillating at the same frequency and the phase difference between potential and current is ......................................................................................................... 132-3 Impedance representation for t he system in Figure 2-1 where , and Here is representing the characteristic frequen cy ...................................................................................... 134-1 Impedance response in Nyqui st format for two LiCoO2 coin cells under normal operating conditions with cell pot ential as a parameter: a) included whole frequency and b) with zoom ing into high frequencies .............................. 174-2 Impedance response in Nyquist format for a LiCoO2 coin cell under overcharge conditions with cell potential as a param eter: a) potential ranging from 4.20 to 4.44 V; and b) potentia l ranging from 4. 44 to 4. 60 V ...................... 184-3 Impedance response in Nyquist format for a LiCoO2 coin cell under overcharge conditions with cell potential as a param eter: a) potential ranging from 4.60 to 4.76 V; and b) wit h zooming into high frequenc ies ......................... 194-4 Impedance response in Nyquist format for a LiCoO2 coin cell under overcharge conditions with cell potential as a param eter: a) potential ranging from 4.76 to 5.00 V; and b) wit h zooming into high frequenc ies ......................... 204-5 Open-circuit potential as a function of time for an overcharged cell: a) in normal scale and b) in se mi-logarithmic scale .................................................... 214-6 Impedance response in Nyquist format for a LiCoO2 coin cell during selfdischarge under overcharge conditions with elapsed time as a parameter: a) included whole frequencies and b) with zooming into high frequencies ............. 214-7 Impedance response of a button cell at a potential of 4 V before and after the cell was over charged .......................................................................................... 22

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7 4-9 Impedance response in Nyquist format for a LiCoO2 coin cell under overdischarge conditions with cell potent ial as a parameter: a) potential ranging from 2.84 to 2.60 V; and b) pot ential ranging from 2.60 to 2.36 V ......... 234-10 Impedance response in Nyquist format for a LiCoO2 coin cell under overdischarge conditions with potentia l ranging from 2. 36 to 2. 20 V .................. 244-11 Open-circuit potential as a function of time for an overdischarged cell: a) in normal scale and b) in se mi-logarithmic scale .................................................... 254-12 Impedance response in Nyquist format for a LiCoO2 coin cell during selfcharge under overdischarge c onditions with elapsed ti me as a parameter: a) included whole frequencies and b) with zooming in great er frequencies ............ 264-13 Impedance response of a button cell at a potential of 4 V before and after the cell was overdi scharg ed ..................................................................................... 264-14 Impedance response of a button cell at a potential of 4 V with elapsed time as a param eter ................................................................................................... 275-1 Measurement model analysis for the impedance response of a button cell at a potential of 4 V with elapsed time as a parameter ........................................... 305-2 Ohmic and charge transfer resistance obtained from the measurement model analysis of the data presented in Figure 4-14 as a function of elapsed time ...... 315-3 Scaled impedance response of a button cell at a potential of 4 V with elapsed time as a pa rameter ............................................................................................ 32

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8 Abstract of Thesis Pres ented to the Graduate School of the University of Florida in Partial Fulf illment of the Requirements for t he Degree of Master of Science ELECTROCHEMICAL IMPEDANCE ANAL YSIS OF LITHIUM COBALT OXIDE BATTERIES By Salim Erol August 2011 Chair: Mark E. Orazem Major: Chemical Engineering Impedance measurements on commercial LiCoO2 secondary 2032 button cells are shown to be extremely sensitive to stat e-of-charge, overchar ge, overdischarge, and elapsed time. The LiCoO2 cells were initially charged under galvanostatic control to 3.80 V. Each cell was potentiostatically held at constant cell potential. After the constantpotential rest period, the impedance was measured using a 10 mV perturbation and 100 kHz – 0.02 Hz frequency range. Lissajous plots were used to ensure linearity during the impedance measurement. Following each im pedance measurement, the cell potential was potentiostatically modified for the charge and discharge profiles in 0.20 V steps. In the same manner, the discharge profile an alysis was executed immediately following the charge schedule. To study th e influence of overcharge, t he cell was initially charged under constant current to 4.20 V. Impedance measurements were performed at each 80 mV step up to and including 5.00 V. A si milar protocol was followed for the overdischarge. Impedance measur ements were performed at each 80 mV step down to and including 2.20 V. After overcharging to a potential of 5 V, t he battery was allowed to relax for four days at the open-circuit condition. When hel d at open-circuit, the overcharged battery

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9 rapidly reached a cell potential within the nominal operating range. After overdischarging to a potential of 2.20 V, the battery was allow ed to relax for four days at the open-circuit condition. When held at open-c ircuit, the overdischarged battery also reached a cell potential within t he nominal operating range, but this process was slower. The impedance response showed a persi stent change to t he electrochemical characteristics of a coin cell subject ed to overcharge and returned to normal cell potentials; whereas, the electrochemical char acteristics returned quickly to normal for a coin cell subject to overdischarge and retu rned to normal cell potentials. Measurement model analysis was used to show that the change in the impedance response with elapsed time was due to a change in the Ohmic resistance.

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10 CHAPTER 1 INTRODUCTION Lithium-ion (Li-ion) batteries are rechar geable batteries that are used in a broad range of electronic devices. They have a higher power density as compared to other batteries such as nickel-cadmium and lead-acid.1 When they are charged Li+ ions leave cathode and move to anode, wh en they are discharged vice versa. The most common lithium-ion batteries use a LiCoO2 cathode, a graphite anode, and a LiPF6 electrolyte. The structure of a LiCoO2 battery and movements of Li+ ions are presented in Figure1-1. Figure 1-1. The indica tion of movements of Li+ ions when a LiCoO2 battery is charged and discharged It is recognized that the cycle life of a Li-i on battery is reduced if it is overcharged or overdischarged. Urqui di-Macdonald and Bomberger2 discussed use of artificial neural networks to predict the cycle life of Li-ion batteries. Peterson et al.3 studied the effects of combined driving and vehicle-to-grid (V2G) usage on the lifetime performance of

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11 relevant commercial Li-ion cells. Maleki and Howard4 reported that ov erdischarging of Li-ion cells below 1.5 V may cause capac ity losses and/or thermal stability changes which could impact tolerance to abuse c onditions. They reported impedance diagrams which showed increased in high and low fr equency asymptotes with cycle life. Belov and Yang5 used electrical impedance spectrosc opy and scanning electron microscopy to characterize electrode materials at di fferent state-of-ove rcharge and overcharge conditions. A dramatic increas e in resistance for the 4.6 a nd 5.0 V test was reported, but the interpretation was only qualitative.

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12 CHAPTER 2 ELECROCHEMICAL IMPEDANCE SPECTROSCOPY Impedance spectroscopy is an exper imental method for analyzing and characterizing electrochemical systems. An electrochemica l system, as shown in Figure 2-1, can be represented by an equivalent circ uit which consists of resistances and capacitances. Here C is capacitance, Re is ohmic resistance, and Rt is charge transfer resistance. Figure 2-1. A simple electroc hemical circuit representation The impedance can basically be described as the complex ratio of oscillating potential, and current. 6 Here is impedance, is a complex number equal to is the phase difference between the potential and current, and and are the real and imaginary components of the impedance, respec tively. Based on the equation the electrochemical system should be perturbed by oscillating potential or current with a significantly small values which is indicated in Figure 2-2. 7

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13 Figure 2-2. Perturbation of an electrochemical system with a small sinusoidal signal at steady state, where and represent the potential and current oscillating at the same frequency and the phase difference between potential and current is Figure 2-3. Impedance representation for the system in Figure 2-1 where , and Here is representing the char acteristic frequency

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14 Impedance data, which are obtained from va rious oscillating frequencies, are represented on a complex plane, which is known as the Nyquist plot. Figure 2-3 shows a typical impedance response plot corresponding to the circuit in Figure 2-1.6

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15 CHAPTER 3 EXPERIMENTAL METHOD Electrochemical experiments were performed on commercial LiCoO2 coin cells. Impedance spectroscopy was used to monitor changes associated with different statesof-charge, imposition of overcharge and imposition of overdischarge. 3.1 Coin Cells Commercial secondary 2032 button (or co in) cells were purchased from AA Portable Power Corp. (Richmond, CA, http://www.batteryspace.com). The 2032 specification means that the batteries were 20 mm in diameter and 3.2 mm in height. The cathode was LiCoO2, the separator was Celgard 8 m and the anode was carbon. The normal potential range of the ce lls is between 3.00 and 4.20 volts. 3.2 Instrumentation Electrochemical and impedance experim ents were performed using a Gamry PCI4/750 Potentiostat connected to a deskt op computer. Gamrys Virtual Front Panel (VFP600) and Electrochemical Impedance S pectroscopy (EIS300) software packages were employed. The primary purpose of the potentiostat in these experiments was to maintain a constant cell potentia l while measuring the impedance. 3.3 Protocol The impedance response was analyzed ov ercharge and overdischarge profiles. The LiCoO2 cells were initially charged under galv anostatic control to 3.80 V. Each cell was potentiostatically held at constant cell potential. After the constant-potential rest period, the impedance was measured using a 10 mV perturbation and 100 kHz 0.02 Hz frequency range. Lissajous plots were us ed to ensure linearity during the impedance measurement.8 Following each impedance measur ement, the cell potential was

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16 potentiostatically modified for the charge and dischar ge pro files in 0.20 V steps. In the same manner, the discharge profile analysi s was executed immediately following the charge schedule. The software incorporated in the Gamry system enabled consistent and precise procedures to be performed whic h served to reduce errors among the repetitive experiments. In addition, t he effect of overcharging a LiCoO2 cell was analyzed. The cell was initiall y charged under constant current to 4.20 V. As before, a 10 mV ac perturbation and 100 kHz 0.02 Hz frequency range were implemented. Impedance measurements were performed at eac h 80 mV step up to and including 5.00 V. A similar protocol was followed for the overdischarge. Im pedance measurements were performed at each 80 mV st ep down to and including 2.20 V. All experiments were performed at room temperat ure (around 20 oC), and they were repeated a few times with same type of battery cells to ensure that the results were both consistent and reproducible.

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17 CHAPTER 4 RESULTS AND DISCUSS IONS OF EXPERIMENTS The impedance responses of the LiCoO2 coin cells are presented for normal operation, overcharge, and ov erdischarge conditions. To el ucidate the sources of changes seen in impedance re sults, impedance measurement s were also made as a function of elapsed time. 4.1 Normal Operation The impedance response for two commercial LiCoO2 coin cells is presented in Figure 4-1 with cell potential fr om 3.0 to 4.2 V as a paramet er. These results represent the impedance response under normal operating conditions. Figure 4-1. Impedance response in Nyquist format for two LiCoO2 coin cells under normal operating conditions with cell pot ential as a parameter: a) included whole frequency and b) with z ooming into high frequencies 4.2 Overcharge To explore the sensitivity of impedance s pectroscopy to overcharging the battery, the coin cell potential was increased in 80 mV increments and the impedance was measured after the cell current approached zero The impedance is a strong function of

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18 cell potential. To make the features visibl e, the impedance response is presented in a sequence of plots. The impedance response is presented in Figure 4-2 for cell potential ranging from 4.20 to 4.44 V (Figure 4-2(a) ) and potential ranging from 4.44 to 4.60 V (Figure 4-2(b)). Figure 4-2. Impedance response in Nyquist format for a LiCoO2 coin cell under overcharge conditions with cell potential as a paramet er: a) potential ranging from 4.20 to 4.44 V; and b) potent ial ranging from 4.44 to 4.60 V

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19 The impedance response is presented in Fi gure 4-3 for cell potential ranging from 4.60 to 4.76 V (for whole frequency range Figure 4-3(a) and for zooming into high frequencies Figure 4-3(b)). Figure 4-3. Impedance response in Nyquist format for a LiCoO2 coin cell under overcharge conditions with cell potential as a paramet er: a) potential ranging from 4.60 to 4.76 V; and b) with zooming into high frequencies The impedance response is presented in Fi gure 4-4 potential rang ing from 4.76 to 5.00 V (for whole frequency r ange Figure 4-4(a) and for zooming into high frequencies Figure 4-4(b)). The results indicate that, for potenti als above 4.6 V, the low-frequency impedance increases very sharply.

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20 Figure 4-4. Impedance response in Nyquist format for a LiCoO2 coin cell under overcharge conditions with cell potential as a paramet er: a) potential ranging from 4.76 to 5.00 V; and b) with zooming into high frequencies After overcharging to a potential of 5 V, the battery was allowed to relax for two days at the open-circuit condition. When hel d at open-circuit, the overcharged battery rapidly reached a cell potential within the nom inal operating range, as shown in Figure 4-5. During self-discharge, randomly taken impedance measurements were shown in Figure 4-6 whose response remains extensive and has very small differences with time (for whole frequency range Figure 4-6(a) an d for zooming into high frequencies Figure 4-6(b)). While the resulting potential was well within the nominal operating range, the impedance response measured before and after t he cell was overcharged, presented in Figure 4-7, shows dramatic differences.

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21 Figure 4-5. Open-circuit potential as a func tion of time for an overcharged cell: a) in normal scale and b) in semi-logarithmic scale Figure 4-6. Impedance response in Nyquist format for a LiCoO2 coin cell during selfdischarge under overcharge conditions with elapsed time as a parameter: a) included whole frequencies and b) wit h zooming into high frequencies

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22 Figure 4-7. Impedance response of a button cell at a potential of 4 V before and after the cell was overcharged Figure 4-8. Impedance response in Nyquist format for a LiCoO2 coin cell under overdischarge conditions with cell potential as a parameter : a) potential ranging from 3.00 to 2.84 V; and b) with zooming into high frequencies

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23 4.3 Overdischarge To explore the sensitivity of impedance s pectroscopy to over discharging the battery, the coin cell potential was decr eased in 80 mV increments and the impedance was measured after the cell current approac hed zero. The impedance is again a strong function of cell potential. To make the features visible, the impedance response is presented in a sequence of pl ots. The impedance response is presented in Figure 4-8 for cell potential ranging from 3.00 to 2.84 V (for whole frequency range Figure 4-8(a) and for zooming into high fr equencies Figure 4-8(b)). The impedance response is presented in Fi gure 4-9 for cell potential ranging from 2.84 to 2.60 V (Figure 4-9(a) ) and potential ranging from 2.60 to 2.36 V (Figure 4-9(b)). Figure 4-9. Impedance response in Nyquist format for a LiCoO2 coin cell under overdischarge conditions with cell potent ial as a parameter: a) potential ranging from 2.84 to 2.60 V; and b) potential ranging from 2.60 to 2.36 V

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24 Finally, the impedance response is presented in Figure 4-10 for cell potential ranging from 2.36 to 2.20 V. After overdischarging to a potential of 2.20 V, the battery was allowed to relax for two days at the open-circuit condition. When held at open-circuit, the overdischarged battery slowly reached a cell potential within the nominal operating range, as shown in Figure 4-11. Figure 4-10. Impedance response in Nyquist format for a LiCoO2 coin cell under overdischarge conditions with potentia l ranging from 2.36 to 2.20 V

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25 Figure 4-11. Open-circui t potential as a function of time for an overdischarged cell: a) in normal scale and b) in semi-logarithmic scale During self-charge, randomly taken im pedance measurements were shown in Figure 4-12. The response remains extensive until a certain time, and then it recovers itself by getting the smaller impedance valu es with reaching the nominal range (for whole frequency range Figure 4-12(a) and for zooming into high frequencies Figure 412(b)). In contrast to the results seen for t he overcharged battery (Figure 4-7), the impedance response measured before and after the cell was overdischarged, presented in Figure 4-13, showed only minor di fferences in the Ohmic resistance. 4.4 Influence of Elapsed Time To explore whether the differences in the impedance response shown in Figure 413 for the cell before and after over-disc harge could be attributed to elapsed time, a sequence of impedance measurem ents were made at a potentia l of 4 V. The resulting impedance spectra are shown in Figure 414 with elapsed time as a parameter.

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26 Figure 4-12. Impedance response in Nyquist format for a LiCoO2 coin cell during selfcharge under overdischarge c onditions with elapsed ti me as a parameter: a) included whole frequencies and b) wit h zooming in greater frequencies Figure 4-13. Impedance response of a button ce ll at a potential of 4 V before and after the cell was overdischarged

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27 Figure 4-14. Impedance response of a button ce ll at a potential of 4 V with elapsed time as a parameter

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28 CHAPTER 5 MEASUREMENT MODEL ANALYSIS A measurement model analysis was employ ed to extract physically meaningful parameters. A graphical analysis was used to show that the change in the impedance response with elapsed time was due to a change in the Ohmic resistance. 5.1 Measurement Model As described by Orazem,9 the measurement model wa s introduced as a means to resolve recurring issues in regression of impedance data, e.g.,10,11,12 1. identification of the most appropriate weighting strategy for regression, 2. assessment of the noise level in the measurement, and 3. identification of the fr equency range unaffected by inst rumental artifacts or nonstationary behavior. A distinction is drawn, following Agarwal et al.,10,11,12 between stochastic errors that are randomly dist ributed about a mean value of zero, e rrors caused by the lack of fit of a model, and experimental bias errors that are propagated thr ough the model. The experimental bias errors, a ssumed to be those that cause lack of consistency with the Kramers-Kronig relations,13,14,15 may be caused by non-stationar ity or by instrumental artifacts. The problem of interpretation of impedance data is therefore defined to consist of two parts: one of identificat ion of experimental errors, wh ich includes assessment of consistency with the KramersKronig relations, and one of fi tting, which entails model identification, selection of weighting strategies, and exami nation of residual errors. The error analysis provides information that can be incorporated into regression of process models. The measurement model method for dist inguishing between bias and stochastic errors is based on using a gener alized model as a filter fo r non-replicacy of impedance

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29 data. The measurement model is composed of a superposition of line-shapes which can be arbitrarily chosen subject to the constrai nt that the model satisfies the KramersKronig relations. The model composed of Voigt elements in series with a solution resistance has been shown to be a useful measur ement model. With a sufficient number of parameters, t he Voigt model was able to provide a statistically significant fit to a broad variety of impedance spectra.10 The measurement model is used first to filter lack of replication of repeated impedance scans. The statistics of the resid ual errors yields an estimate for the variance (or standard deviation) of stochastic measurement errors. Th is experimentallydetermined variance is then used to weight subsequent regression of the measurement model to determine consistency with the Kram ers-Kronig relations. If the data can be represented by a model that is itself consistent with the Kramers-Kronig relations, the data can be considered to be consisten t. The concept of using a generalized measurement model to assess consistency wit h the Kramers-Kronig relations, first introduced by Agarwal et al.,10, 12,16 was also employed by Boukamp and Macdonald17 and by Boukamp18 using weighting strategies based on an assumed error structure. The experimental determination of the stochasti c error structure as used here, however, allows formal quantification of the ext ent of agreement with the Kramers-Kronig relations. Other transfer-function models can be used as a measurement model so long as they are consistent with the Kramers-Kronig relation s. Shukla and Orazem have demonstrated that the stochastic error stru cture determined from replicated impedance measurements is independent of the type of measurement model used.19 While the regressed parameters may not be associated unequivocally with a set of deterministic

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30 or theoretical parameters for a given system, the meas urement model approach has been shown to represent adequate ly the impedance spectra obtained for a large variety of electrochemical systems.10 Regardless of their interp retation, the measurement model representation can be used to filter and thus identify the non-stationary (drift) and high-frequency (noise) components contained in an impedance spectrum. The measurement model has been applied in previous works to assess the error structure of a variety of systems in cluding electrohydrodynamic impedance,20 electrochemical impedance data for reducti on of ferricyanide on a Pt rotating disk,21 for corrosion of cast iron in Evian water,22 for corrosion of aluminum in orange juice,9 for charging of electroactive polymers,23 and for analysis of PEM fuel cells.24, 25 Here the error analysis approach is applied to electr ochemical impedance data collected for lithium-ion batteries. 5.2 Measurement Model Results The measurement model was used to assess the high-frequency asymptote for the real part of the impedance. This term is the Ohmic resist ance for the cell. A truncated data set was used to estimate t he charge-transfer resistance for the highfrequency capacitive loop. A sample of the fi tting results is shown in Figure 5-1. Figure 5-1. Measurement model analysis fo r the impedance response of a button cell at a potential of 4 V with elaps ed time as a parameter

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31 The resulting values for Ohmic and char ge-transfer resistance are shown in Figure 5-2 as a function of elapsed time. The chargetransfer resistance is independent of time, but the Ohmic resistance increases with time. The effect can be demonstrated by plotting a scaled impedance in which -Zj/Rt is plotted as a function of (Zr-Re)/Rt. The results, presented in Figure 5-3, show that the shape of the capacitive loop is unaffected by the passage of time. The superposition of impedance curves shows that there were no mechanistic changes in the electrochemical reactions, and that the c hange in the impedance response with elapsed time can be attributed solely to a change in the Ohmic resistance. Figure 5-2. Ohmic and charge transfer resistance obtained from the measurement model analysis of the data presented in Figure 4-14 as a function of elapsed time

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32 Figure 5-3. Scaled impedance response of a button cell at a potential of 4 V with elapsed time as a parameter

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33 CHAPTER 6 CONCLUSIONS The impedance response was demonstrated to be very sensitive to the history of a lithium-ion button cell. The imped ance increases dramatically when the battery is either overcharged or overdischarged. When the batte ry is held at open circuit, the cell returns to a potential within the nom inal normal operating range. When the battery had been overcharged, the impedance remains much la rger than it was originally. When the battery had been overdischarged, the impedance is essentially the same as it was originally. Any differences in impedance response were attributed to passage of time.

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34 LIST OF REFERENCES [1] M. Winter and R. J. Br odd, “What Are Batteries, Fuel Cells, and Supercapacitors?” Chemical Reviews, 104 (2004) 4245–4270. [2] M. Urquidi-Macdonald and N. A. Bomber ger, “Predicting Failure of Secondary Batteries,” Journal of Po wer Sources, 74 (1998) 87–98. [3] S. B. Peterson, J. Apt, and J. Whitac re, “Lithium-Ion Battery Cell Degradation Resulting from, Realistic Vehicle and Vehi cle-To-Grid Utilization,” Journal of Power Sources, 195 (2010) 2385–2392. [4] H. Maleki and J. N. Howard, “Effe cts of Overdischarge on Performance and Thermal Stability of a Li-Ion Cell,” Jour nal of Power Sources, 160 (2006) 1395– 1402. [5] D. Belov and M.-H. Yang, “Failure Me chanism of Li-Ion Battery at Overcharge Conditions,” Journal of Solid Stat e Electrochemistry, 12 (2008) 885–894. [6] M. E. Orazem and B. Tribollet, “Elect rochemical Impedance Spectroscopy,” John Wiley & Sons Inc.,(2008) 310-313. [7] S. Wu, “Influence of Electrode Geometry on Local and Global Impedance Response,” University of Florida PhD thesis, (2010), 27-29. [8] B. Hirschorn, B. Tribo llet, and M. E. Orazem, “On Se lection of the Perturbation Amplitude Required to Avoid Nonlinear Effects in Impe dance Measurements,” Israel Journal of Chemis try, 48 (2008) 133–142. [9] M. E. Orazem, “A Systematic Approach toward Error Structure Identification for Impedance Spectroscopy,” Journal of Elec troanalytical Chemis try, 572 (2004) 317– 327. [10] P. Agarwal, O. D. Crisalle, M. E. Orazem, and L. H. Garc a-Rubio, “Measurement Models for Electrochemical Impedance Sp ectroscopy: I. Demonstration of Applicability,” Journal of the Electr ochemical Society, 139 (1992) 1917–1927. [11] P. Agarwal, O. D. Crisalle, M. E. Orazem, and L. H. Garc a-Rubio, “Measurement Models for Electrochemical Impedance Spec troscopy: II. Determination of the Stochastic Contribution to the Error Stru cture,” Journal of the Electrochemical Society, 142 (1995) 4149–4158. [12] P. Agarwal, O. D. Crisalle, M. E. Orazem, and L. H. Garc a-Rubio, “Measurement Models for Electrochemical Impedance Spectro scopy: III. Evaluation of Consistency with the Kramers-Kronig Relations,” Journal of the Electrochemical Society, 142 (1995) 4159–4168.

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35 [13] R. de L. Kronig, On the Theory of Dis persion of X-Rays,” Journal of the Optical Society of America and Review of Scient ific Instruments, 12 (1926) 547–557. [14] R. de L. Kronig, “Dispersionstheori e im Rntgengebeit,” Phys. Zs., 30 (1929) 521– 522. [15] H. A. Kramers, “Die Dispersion und Adsorption von Rntgenstrahlen,” Phys. Zs., 30 (1929) 522–523. [16] P. Agarwal, M. E. Or azem, and L. H. Garca-Rubio, “Application of the KramersKronig Relations to Electrochemical Impedanc e Spectroscopy,” in Electrochemical Impedance : Analysis and Interpretation, J. Scully,D. Silverman, and M. Kendig, editors, volume ASTM STP 1188 (Philadelphi a, PA: American Society for Testing and Materials, 1993) 115–139. [17] B. A. Boukamp and J. R. Macdonal d, “Alternatives to Kronig-Kramers Transformation and Testing, and Estimation of Distributions,” Solid State Ionics, 74 (1994) 85–101. [18] B. A. Boukamp, “A Linear Kronig-Kr amers Transform Test for Immittance Data Validation,” Journal of the Electrochemical Society, 142 (1995) 1885–1894. [19] P. K. Shukla, M.E. Orazem, and O. D. Crisalle, “Validation of the Measurement Model Concept for Error Structure Identif ication,” Electrchimica Acta, 49 (2004) 2881–2889. [20] M.E. Orazem, P. Agar wal, C. Deslouis, and B. Tribollet, “Application of Measurement Models to Electrohydrodynam ic Impedance Spectroscopy,” Journal of the Electrochemical Society, 143 (1996) 948–960. [21] M. E. Orazem, M. Durbha, C. Deslouis, H. Takenouti, and B. Tr ibollet, “Influence of Surface Phenomena on the Impedance Res ponse of a Rotating Disk Electrode,” Electrochimica Acta, 44 (1999) 4403–4412. [22] I. Frateur, C. De slouis, M. E. Orazem, and B. Tr ibollet, “Modeling of the Cast Iron/Drinking Water System by Elec trochemical Impedance Spectroscopy,” Electrochimica Acta, 44 (1999) 2087–2093. [23] C. Deslouis, T. E. Mo ustafid, M. M. Musiani, M. E. Orazem, V. Provost, and B. Tribollet, “Effect of Cations on the Diffusivi ty of the Charge Carriers in Polyaniline Membranes,” Electrochimica Acta, 44 (1999) 2087–2093. [24] S. K. Roy and M. E. Orazem, “Erro r Analysis for the Impedance Pesponse of PEM Fuel Cells,” Journal of the Electrochemical Societ y, 154 (2007) B883–B891. [25] S. K. Roy and M. E. Orazem, “Analysi s of Flooding as a Stochastic Process in Polymer Electrolyte Membrane (PEM) F uel Cells by Impedance Techniques,” Journal of Power Sources, 184 (2008) 212–219.

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36 BIOLOGICAL SKETCH Salim Erol received his Bachelor of Sci ence degree in chemical engineering from Eskisehir Osmangazi University in June of 2006. Then he began a master’s program at Marmara University in Turkey. While he wa s preparing his master’s thesis, he applied for a government scholarship, and he was chosen as a scholar for his master’s and his Ph.D. Consequently, he had to leave his program in Turkey, in order to make a new start toward a master’s degree and Ph.D. fr om an American univers ity. To reach a sufficient level in English, he studied at an English-language school, the English Programs for Internationals at the University of South Carolina, and finished the school in April of2009. After, he enter ed the University of Florida as a master’s student in the chemical engineering depar tment in August of 2009. He has been in the electrochemical impedance re search group, under the dire ction of Professor Mark Orazem, since January of 2010.