AggiE-Challenge: Final Report

Transcription

1 Faculty Advisors: P. P. Mukherjee, H. Liang Graduate Student Mentors: P. Barai, C. Chen, S. Cho, C. Lopez AggiE-Challenge: Final Report Analysis of Thermo-Mechano-Electrochemical Behavior in Lithium-Ion Batteries Dion Hubble, Benjamin Powell, Deepak Bhatia, Raul Calzada, Jordan Ellington, Wyatt Smitherman, Rhianne Compas, Nathan Kudlaty, Hung Nguyen Fall 13

2 Table of Contents BACKGROUND: INTRODUCTION TO LITHIUM-ION BATTERIES... 2 THERMAL EFFECTS... 3 ELECTROLYTE EFFECTS MECHANICAL EFFECTS METHOD METHOD CONCLUSIONS THERMAL ELECTROLYTE MECHANICAL ACKNOWLEDGEMENTS REFERENCES... 30

3 Background: Introduction to Lithium-Ion Batteries Batteries provide a way to chemically store energy, so that it can be utilized as electrical energy. A battery is essentially an electrochemical transducer: it converts chemical energy to electrical energy, and vice versa (for rechargeable batteries). It consists of two electrodes (an anode and a cathode), and a separator to prevent internal short circuiting. In the case of lithium-ion batteries, the separator allows for the diffusion of lithium ions across the cell through electrolyte, while electrons are forced to travel externally from one electrode to the other. The movement of electrons and lithium ions from one side to the other is the driving mechanism: without a closed circuit, the battery will not discharge lithium ions freely. While the composition of the electrodes determines best-case voltage and capacity characteristics, actual observed voltage and capacity depends on a number of limiting factors. Ambient temperature and electrolyte concentration are naturally coupled and, unless optimized, can form positive feedback loops which decrease battery performance. At high temperatures, this results in thermal runaway, whereas at low temperatures, this results in capacity loss. Additionally, battery degradation naturally occurs during discharge (and recharge) of lithium-ion batteries. All of these effects are accelerated by discharge at high rates. We hope to model and simulate all of these phenomena relating to low-temperature and high-rate discharge of lithium-ion batteries, in order to better understand their origin, and eventually decide how to best optimize a battery for their mitigation. Figure 1. Illustration of operation of a typical Li-ion battery.

4 Thermal Effects Almost all electric vehicles (EV) and hybrid electric vehicles (HEV) produced today incorporate the use of lithium ion batteries in order to store energy in an efficient and practical manner. Because of this, li-ion battery technology must adapt to accommodate a wide range of climates where these vehicles will operate. It has been determined that temperatures at or below 0 C significantly decrease the capacity and operating voltage of lithium ion batteries. High temperature thermal management is currently a key aspect of lithium ion battery research due to dangerous thermal runaway situations, which leaves remedies to poor low temperature performance relatively unexplored. The focus of this research is to understand the mechanisms that create poor low temperature performance and explore possible solutions. It has been observed that capacity can drop by as much as 30-40% or more when operating at 0 C at various C-rates [1]. Attempts to utilize nano-fiber electrode materials to mitigate poor transport effects at low temperatures also yields up to a 40% loss in capacity at 0 C (see Table 1). This kind of performance decrease precludes the use of lithium ion batteries for transportation, defense, and other commercial applications. Table 1. Specific capacity for 70 nm electrode at the indicated temperatures and discharge rates [1]. A study by Zhang, et. al. [2] performed electrochemical impedance spectroscopy (EIS) to study lithium ion battery cycling performance. At subzero temperatures, cell resistance is dominated almost entirely by charge transfer impedance. This concludes that the slow kinetics of the lithium ion cell reactions is the largest contributing factor to poor low temperature operation (see Figure 2).

5 Figure 2. Temperature dependence of the bulk resistance (R b ), solid-state interface resistance (R sei ), and charge transfer resistance (R ct ) as well as the R ct percentange at 3.87 V. [2] The group has chosen to explore the effect of changing electrode and electrolyte properties at various temperatures to observe the effect of battery performance. A one dimensional lithium ion battery modeling software called AutoLion was utilized for all simulations in this study. AutoLion utilizes what is known as a thermally-coupled battery model, which accounts for heat generated during battery discharge and couples the resulting temperature increase to relevant temperature-dependent parameters. This allows it to more accurately reproduce experimental results. The version of the software used here treats the battery as one-dimensional, which is a generally accurate assumption given that most cell sandwiches used in lithium-ion batteries have thicknesses much smaller (~3 orders of magnitude) than their lengths and widths. The first study completed using this software was determining the effect of temperature on the capacity of a standard lithium ion battery (Figure 3).

6 Figure 3. The effect of ambient temperature on the discharge voltage and capacity of a LiCoO2-Graphite cell. From Figure 3, it is seen that temperatures as low as -30 C can cause capacity losses of approximately 70%. These results validate the previous conclusion that low temperatures severely reduce battery performance. In order to determine the cause of such poor low temperature performance, various parameters were manipulated independently. It was first hypothesized that the freezing point of the electrode and electrolyte material were directly related to low temperature performance. Upon study of common cathode materials, it was observed that the freezing point of the individual material didn t have a statistically significant effect on the low temperature behavior of the cell. Varying cathode material as the parameter confounded too many experimental variables to exhibit any significant results. For this reason, we chose to narrow our search to a single cathode material and vary individual cell geometries. Lithium Nickel Cobalt Manganese Oxide (NCM) was chosen due to its stability and high specific power which makes it a common choice for electric vehicles. One parameter we chose to examine is the effect of cathode porosity on battery performance. The porosity was determined to have a significant effect on the self-heating on the battery, which will affect the battery s ability to quickly reach an operating temperature where high capacity and power can be achieved. Figure 4, Figure 5, and Figure 6 show the effect that cathode porosity has on the cell temperature and used capacity during discharge.

7 Temperature ( C) k = 0.50 k = 0.40 k = 0.30 k = 0.20 k = Capacity (mah) Figure 4. Effects of porosity on temperature distribution and capacity for constant Ambient Temperature, 298 K Temperature ( C) k = 0.50 k = 0.40 k = 0.30 k = 0.20 k = Capacity (mah) Figure 5. Effects of porosity on temperature distribution and capacity for constant Ambient Temperature, 273 K.

8 Temperature ( C) k = 0.50 k = 0.40 k = 0.30 k = 0.20 k = Capacity (mah) Figure 6. Effects of porosity on temperature distribution and capacity for constant Ambient Temperature, 323 K. Convective heat transfer experienced in Figures 4-6 was 20 W/m 2 K, to capture typical cell heat transfer in an electric vehicle. Based on the results, decreasing the cathode porosity increased the operating temperature of the cell. These hotter cells displayed maximum capacity at porosities of However, the highest rate of temperature increase was experienced in cells with porosities lower than High heating rates in these low porosity cells (k=0.15) can be utilized to increase performance of nearby cells with the optimal porosity. This free heat generation cell array may increase the low temperature performance of an entire battery pack by utilizing the self-heating aspects of a battery in an efficient manner. Figure 7 shows the temperature difference at any point in time during a discharge cycle for a high porosity cell adjacent to a cell with a porosity of k=0.15. The temperature difference corresponds to the heat flux between the cells.

9 25 20 k = 0.50 k = 0.40 k = 0.30 T ( C) k = time (s) Figure 7. Temperature difference between two adjacent cells at an ambient temperature of 273K with a convective heat transfer coefficient of 20 W/m 2 K. There is a large change in temperature difference between the cells of porosity k=0.2 and k=0.3, even though Figures 4-6 suggest that these porosities allow for the same discharge capacity. Therefore, improved battery performance would result in selecting a battery with a porosity of k=0.3 if considering the use of a free heat generation cell array. Active cooling mechanisms in battery cell arrays could potentially diminish the effects of cell to cell heating. Therefore, it is important to study the effect of convective heat transfer on these phenomena. Figure 8, Figure 9, and Figure 10 show the effect of convective heat transfer coefficient on battery performance with different porosities.

10 Temperature ( C) k = 0.50 k = 0.40 k = 0.30 k = 0.20 k = Capacity (mah) Figure 8. Effects of porosity on temperature distribution and capacity subject to convective heat transfer, 0[W/m 2 -K], adiabatic case Temperature ( C) k = 0.50 k = 0.40 k = 0.30 k = 0.20 k = Capacity (mah) Figure 9. Effects of porosity on temperature distribution and capacity subject to convective heat transfer, 50[W/m 2 -K].

11 Temperature ( C) k = 0.50 k = 0.40 k = 0.30 k = 0.20 k = Capacity (mah) Figure 10. Effects of porosity on temperature distribution and capacity subject to convective heat transfer, 100[W/m 2 -K]. As previously estimated, the adiabatic case (h=0) maximizes cell discharge capacity. This is the best case scenario to maximize heat flux in our free heat generation cell array. Figure 11 shows the temperature difference between a cell with a cathode porosity of k=0.15 compared to cells of various porosities in an adiabatic, room temperature environment. Temperature differences observed are increased with porosity.

12 T ( C) k = 0.50 k = 0.40 k = 0.30 k = time (s) Figure 11 Temperature difference between two adjacent cells at an ambient temperature of 298K with a convective heat transfer coefficient of 0 W/m 2 K. Similar to Figure 7, trade-offs between cell capacity and temperature difference yield that a porosity of k=0.3 would most likely yield the greatest battery performance. Comparing Figure 7 and Figure 11 with Figures 4-6 the ideal porosity value would be 0.30 in order to keep capacity at an optimal level. Selection of an ideal porosity is not recommended without further developments in the free heat generation cell array model. An optimal porosity value may be lower than 0.20 due to increased temperatures (Figures 4-6), thus an adequate thermal model should be developed in order to estimate the heat flux between two adjacent cells. This heat flux should then be used to determine the cell temperature distribution to compare between different porosities. It is likely that a high contact resistance between adjacent cells. This modeling should include varying convective heat transfer coefficient.

13 Electrolyte Effects While the active materials themselves provide a basic framework for energy storage in a lithiumion battery (LIB), charge and discharge would not be possible without a medium for lithium transfer between electrodes in other words, an electrolyte. While the properties of the active materials determine basic parameters such as maximum voltage and maximum capacity of the battery, the properties of the electrolyte have a strong influence on the actual, measured battery performance. Deficiencies in electrolyte properties may lead to loss of capacity, lower observed cell voltage, and poor cycling performance. Conversely, if electrolyte properties are improved, whether through introduction of additives or by changing to a new electrolyte system, overall battery performance will correspondingly improve. Electrolytes used in LIBs consist of a lithium salt, traditionally LiPF 6, dissolved in a mixture of polar, aprotic solvents. Aqueous solvents cannot be used with this salt due to the PF 6 - ion s tendency to react in protic media to form HF. Typical solvents are carbonates, either linear (such as DMC, dimethylcarbonate) or cyclic (such as EC, ethylene carbonate, and PC, propylene carbonate). Cyclic carbonates tend to dissolve lithium more readily, but they also have high viscosities, necessitating the addition of linear carbonates to ensure thorough wetting of all active material. [3] During discharge of a typical LIB, lithium moves out of the porous anode (i.e. graphite) and into the electrolyte, while on the opposite end of the cell, existing lithium ions are pulled from the electrolyte and into the porous cathode (i.e. NCM). This gives rise to two separate driving forces for lithium transfer across the cell: concentration gradient of lithium and electrostatic force. The ions respond to these driving forces through two, electrolyte-dependent parameters: diffusivity and ionic conductivity. Both parameters are strongly dependent on temperature, as well as local concentration. Diffusivity describes the response (flux) of lithium due to a concentration gradient. All chemical species, including ions, tend to move randomly due to thermal energy. If there are more of a particular species in one place relative to another, then more of that species will on average move towards the deficient area than away from it. As each ion moves, it bumps into other particles which change its course and, on average, slow the group s movement. Diffusivity is a measure of how quickly the species, in this case lithium ions, can move to fill a deficient area; therefore, it will depend on both the speed of the ion (temperature) and each ion s immediate surroundings (concentration). Since lithium ions can collide with both solvent molecules, themselves, and counter-ions, diffusivity can be changed for a system by altering either the solvent or the salt composition, as well as overall lithium concentration. In general, lower concentrations lead to higher diffusivities. Conductivity describes the response (current) of lithium due to an electrostatic field. As the positively-charged lithium ions move in response to the potential difference between cathode and anode, they bump into, and lose energy to, their surroundings. Because of this, the ions arrive with less energy than they started with; this energy loss is measured as an Ohmic potential drop. Conductivity is a measure of how much (or rather, how little) energy is lost in transit. If too few ions are present (low concentration), conductivity drops due to a lack of charge carriers: a smaller number of ions must move more quickly to carry the same current, and will lose more energy to collisions. If too many ions are present (high concentration), conductivity decreases because repulsion between ions becomes significant, and the potential experienced by each ion correspondingly decreases. This leads to a sweet spot for

14 conductivity, typically seen just above 1 mol/l for the typical solvent-salt system. In reality, conductivity tends to influence discharge characteristics much more than diffusivity. Charge conservation dictates that all current flowing out of the anode (electrons into a circuit) must be matched by current flowing out of the cathode (lithium ions into the electrolyte). Since it is precisely this movement of ions that produces a concentration gradient in the cell, discharging at higher currents will lead to higher concentration polarization, and therefore a drop in concentration-dependent ionic conductivity. Likewise, operating at lower temperatures will also decrease ionic conductivity through its temperature-dependence. Herein lies the primary difficulty of operating LIBs at high discharge rates and/or low temperatures: electrolyte conductivity is reduced by concentration polarization, causing lower observed voltages, and therefore less capacity available above the cutoff voltage of the system. To illustrate these effects, simulations were performed using AutoLion 1-D. A prismatic cell was set up, with a total capacity of 8.05 Ah. This cell measured 72mm 65.2mm 12mm. Graphite was used as the anode, NCM the cathode, and each had a porosity of Electrode length was 80 µm each. A Celgard porous separator, with a porosity of 0.4 and length of 20 µm, was used. Nominal electrolyte concentration was set at 1.2 mol/l. Bruggeman exponents, which account for tortuosity in porous media, were set at 1.5 for all regions. For some simulations, self-heating was taken into consideration. For these cases, heat transfer coefficient at the surface of the cell was taken to be 20 W/m 2 K, and cell specific heat was assumed to be 1000 J/kg K. All of these parameters are the default settings for an AutoLion Prismatic RED cell. This simulation setup is hereafter referred to as the default cell. A series of simulations were performed in order to demonstrate the overall detrimental effects of high current and/or low temperature. The first study scanned a range of discharge currents, with ambient temperature set to 25 and self-heating allowed. Current was expressed in C-rate; 1C equals the amount of current needed to discharge the entire battery in one hour, 2C is twice that amount, etc. The results are shown below in Figure 12. Expectedly, operating voltage decreases at higher discharge rates, leading to lower capacity at the cutoff voltage of 2.5 V. Interestingly, the 4C discharge run showed a slightly higher total capacity than the 2C discharge; this is because self-heating increased temperature so much that the improvement in transport properties outweighed the unfavorable concentration gradient.

15 Figure 12. Simulation results for default cell at different C-rates and 25 C ambient temperature Next, a similar scan was run over a range of temperatures, from 40 C to -20 C, again with selfheating. A similar drop in operating voltage was observed at lower temperatures, due to the same increase in concentration gradient. Figure 13 below shows the results. Notice the loss of almost 25% capacity at - 20 C, as compared to room temperature. Also notice the voltage recovery effect at low temperature, where operating voltage rapidly drops and then stabilizes back to a higher value. This effect is often seen in experimental data [4] and is due to the rapid self-heating, which improves electrolyte properties enough to recover performance. This effect will be demonstrated later in this report.

16 Figure 13. Simulation results for default cell at different ambient temperatures and 1C discharge rate Then, to demonstrate both low temperature and high-rate discharge effects together, another C- rate scan was run, this time at -10 C, with self-heating. The results are shown in Figure 14 below. Discharge at 4C produces a huge self-heating effect; by the endpoint of discharge, cell temperature has risen by almost 65 C. Correspondingly, the voltage recovery effect is dramatic, leading to a much higher endpoint capacity for the 4C discharge than for either 1C or 2C.

17 Figure 14. Simulation results for default cell at different C-rates and -10 C ambient temperature AutoLion automatically saves electrolyte data, such as concentration and potential, for each separate discharge. To demonstrate the direct role that concentration plays in the above results, two isothermal simulations were performed: one at 25 C and 1C discharge, and one at -10 C and 1C discharge. Electrolyte data was then plotted as a function of position in the cell sandwich for two separate times in each case: 50 seconds into discharge, and at the endpoint when cell voltage reaches the cutoff of 2.5V. Then, the -10 C run was repeated with self-heating, to show the dramatic difference in performance. The isothermal, room temperature run displayed a total capacity of 7246 mah at cutoff voltage. Electrolyte data at 50 seconds is displayed in Figure 15a below. Concentration has not changed much from its initial value of 1.2 mol/l, and ionic conductivity is relatively constant at 1.34 S/m. Electrolyte potential, which lithium ions experience at each individual point, is also relatively constant, indicating almost non-existent polarization due to concentration effects.

18 Figure 15a. Electrolyte concentration, ionic conductivity, and potential for default cell after 50 seconds of 25 C, isothermal, 1C discharge At the endpoint of this discharge, as shown in Figure 15b, concentration has polarized noticeably, but still not much at a maximum deviation of a little over 0.4 mol/l from nominal. Conductivity has dipped slightly as a result, but is still relatively constant at around 1.25 S/m in the anode and 1.35 S/m in the cathode. Electrolyte potential has dropped in value due to the drop in active material potential and the need to maintain a constant driving force for ion transport, but still displays relatively low slope from one end to the other, again indicating very little polarization, even by the endpoint of discharge. Figure 15b. Electrolyte concentration, ionic conductivity, and potential for default cell at endpoint (3329 seconds) of 25 C, isothermal, 1C discharge The isothermal run at -10 C, however, performs much poorer, reaching cutoff voltage after only 2806 mah (35% of rated capacity). Even at only 50 seconds in, as seen in Figure 16a below,

19 concentration has already shifted noticeably from its nominal value, reaching a little over 1.6 mol/l in the anode and a little over 0.7 mol/l in the cathode. Conductivity does not vary too widely yet, though the temperature difference has had an immediate negative effect, dropping average conductivity to 0.56 S/m. As a result, electrolyte potential is already slightly polarized, varying by about 0.2 V across the cell. Figure 16a. Electrolyte concentration, ionic conductivity, and potential for default cell at 50 seconds of -10 C, isothermal, 1C discharge By the end of discharge, the cell has polarized considerably, as Figure 16b shows. Concentration varies from 3.5 mol/l, nearly triple its nominal value, at the far end of the anode to only mol/l at the far end of the cathode. Conductivity drops considerably as a result, reaching a minimum in the anode of only S/m. This lack of conductivity prevents electrolyte potential from adjusting normally, and as a result there is a 1.2 V electrolyte polarization between anode and cathode. This additional polarization manifests as a drop in observed voltage, and results in cutoff voltage being reached at only 35% discharge. This illustrates the positive feedback loop between conductivity and concentration that results in loss of performance at low temperature: initially low conductivity causes large concentration gradients, which results in even lower conductivity, etc.

20 Figure 16b. Electrolyte concentration, ionic conductivity, and potential for default cell at endpoint (1289 seconds) of - 10 C, isothermal, 1C discharge When self-heating is allowed to occur, however, performance improves significantly. This is a direct result of electrolyte effects. To illustrate the voltage recovery effect from temperature increase during discharge, the -10 C run was repeated with self-heating allowed. The new endpoint results can be seen in Figure 16c. This time, the cell reaches 6099 mah of discharge before cutoff voltage is reached, and cell temperature increases from -10 C to 4.4 C. Concentration still varies more than it did at room temperature endpoint, but only reaches 2.23 mol/l in the anode and 0.51 mol/l in the cathode. Conductivity now only varies from 0.38 S/m to 0.90 S/m; in fact, it some regions is has actually increased from its starting value due to self-heating! As a result, electrolyte polarization at the endpoint is only a little over 0.3 V, and the cell has had the chance to discharge much more before the combination of solid phase voltage change and electrolyte polarization drops overall voltage to the cutoff.

21 Figure 16c Electrolyte concentration, ionic conductivity, and potential for default cell at endpoint (2802 seconds) of -10 C, with self-heating, 1C discharge

22 Mechanical Effects In a lithium-ion battery, the movement of electrons and lithium is the source of providing electrical power. The process of lithium ions entering and leaving the electrodes is known as lithiation and delithiation. [5] These high concentration gradients can cause significant mechanical stress in the electrodes and can potentially create cracks in the active material. Cracks in active material can cause the growth of Solid Electrolyte Interface (SEI) in those crevices. SEI forms spontaneously at the electrodeelectrolyte interface and places a very critical role in the performance and safety of a Li-ion battery. This formation is both useful and harmful to battery system. During initial cycles, SEI serves as a medium for exchange of li-ions but has a negative effects once the SEI layer begins to become thick. In this research, our group investigated the formation of cracks and developed code to identify any possible cracks that may lead to pieces of the active material to break off from the main electrode. Since these pieces will be covered with SEI, they will also have some trapped Li-ions in them. These ions cannot be released back into the electrolyte and will have negative effects on battery functionality. Method 1 In this research we were interested in quantitatively describing how this loss of active material and the lithium ions trapped in the surrounding SEI affect the capacity and charge rates of these types of batteries. In order to identify any possible particle isolations, our team investigated the following- Step 1 1. Identify broken bonds in the active material through previously developed MATLAB code. 2. Identify cracks that start from the exterior boundary of the active material and traverse towards the interior. 3. Identify cracks that may intersect, resulting in the enclosed area to break off and lead to particle isolation. Several matrices with information on the node locations, broken bond location and the identifiers for the broken bond is stored and processed. These nodes are then plotted for creating a visual aid for the user in the function known as Disp_Orientation. Step 2 The next crucial step involves identifying boundaries of the active material. This is an automated process and will work for any set of data given that the provided data follows the same output format as the one used for testing. This is performed in function idboundary.

23 Figure 17. MATLAB output showing the detected external boundary and all the broken bonds (black lines) connecting different nodes Step 3 Once the external boundaries have been isolated, every nodes neighbours and bonds are automatically mapped in the two functions called- neighbour_elements and neighbor_nodes. Step 4 Figure 18. Output of the data given which would be recreated in Figure 3

24 The final step is to automatically recreate the traces for the given data to show proof of concept. This is automatically performed in the function called Algorithm2. This consists of a series of statements that try to take into account various possible traces that may exist in the active material. Figure 19. Final output of the code to show automatic routing Method 2 A second approach was also utilized to solve the problem of mapping the fractures and cracks in a lithium active material. This approach started out the same as the earlier-described, and operated off the same initial data sets: Coordinates of the nodes used in the FEA The match-up between the node #s and element #s The broken element #s The center and radius of each active material in the FEA However, this approach utilized a radial walk algorithm to find the location and length of each crack or fracture in the active material. The approach of this code is as follows: Step 1 The location of each element midpoint was determined through the use of the External code function. External: A MatLab function which takes in two of the initial data sets (the node coordinates and the match-up between node #s and element #s) and returns a matrix of element locations Because it is the broken elements which create cracks and fragment, this method thus focused on the element locations (rather than the nodes) as the primary means of obtaining its results. Figure 20 demonstrates the graph of nodes in a single material, while Figure 21 shows the graph of the corresponding elements.

25 Figure 20. Nodes in Active Material Figure 21. Elements in Active Material

26 Step 2 The nodes and elements were separated into their materials through the use of the Materialistic code function. Materialistic: A Matlab function which takes in the matrix of elements put out from Elementary, as well as the initial data set of the centers/radii of active materials, and splits up the former into a number of matrices. Each corresponds to its own material. In this way, each material could be analyzed separately in the remaining stages of the process, without different materials polluting the results of each. Figure 22 below demonstrates the output of this function, once plotted on a scatter graph. Figure 22. Material Plot

27 Step 3 Because it is the exterior fractures and cracks (those which extend to the outside of an active material) whose lengths are desired, it was necessary to determine the identity of the exterior elements. This was done through the use of the External code function, which assigned a value of 1 to exterior elements on a certain material and a value of 0 to all others. External: A MatLab function which takes a single material s matrix of element locations (from the outputs of Materialistic) and, element-by-element, determines if each is an exterior element based on the number of elements surrounding it. It outputs this information as 1 or 0. Step 4 The final stage of this process involved the code function Fragmented, which had the task of actually determining two things. 1. Whether or not a broken exterior element actually formed a fragment 2. The length of the crack (or fragment) that was formed In order to perform these two vital tasks, the code had to assume that each and every broken exterior element formed EITHER a crack OR a fragment. Fragmented: A MatLab function that determines crack and fragment locations, as well as the length of each. It does this by starting at a broken exterior elements and walking along any adjacent broken elements. This code served as the most important stage of the whole process. It worked by starting at a single exterior broken element, then searching in a radial pattern for adjacent broken elements. If one is found, it jumps to this element and then repeats the search. This process of searching and jumping (known as walking ) repeats itself continuously, incrementing each time to keep track of the length, until the code jumps to another exterior broken element. When it does, the code realizes that a fragment has been created and it ends itself. A plot of this is shown below in Figure 23, where the broken exterior elements are shown in red and the broken interior elements are shown in blue.

28 Figure 23. Broken Elements in an Active Material By looking at Figure 23 it can be seen that several cracks are apparent in the active material. However, the purpose of this program is to provide this information without any sort of visual information. Therefore, the accompanying information must be produced by the code, the matrix of which is shown below in Table 2.

29 Table 2. Columns 6 and 7 of Final Matrix Each row corresponds to a single broken exterior element, from the material displayed in Figure 5 (moving from bottom-left to top-right). The earlier columns in the final output matrix contain information such as X-position, Y-position, Element No., and other such identifiers. However, these final two columns are the most important. The first tells whether or not the exterior element forms a fragment (1 if true, 0 if false), and the second tells the length of the crack or fragment formed. By looking at Table 1, it can be noticed that no fragments are formed in the displayed material, but that the longest crack formed is somewhere near the bottom of the matrix and has a length of 2.75 units. Both pieces of information can be verified by examining Figure 5, indicating that this code does in fact produce the required deliverables.

30 Conclusions Thermal Extreme low temperatures below 0 C in the harsh winter months cause a significant drop in operating voltage and capacity, resulting in a loss of power and range. Self-heating during cell discharge can increase cell temperature and improve charge and ion transport capabilities, but can create dangerous thermal runaway situations. Cathode porosity was explored as a parameter that affects cell heating. It was found that lower porosity increases the heating rate of the battery during discharge. A porosity of 0.2 to 0.3 has the highest capacity. However, higher porosity cells are more stable in avoiding the possibility of thermal runaway. It is hypothesized that the high heating rate of a low porosity cell in a battery array can offer free heat generation to nearby high porosity cells, resulting in a more efficient battery pack for low temperature operation. The heat flux and convective heat transfer effects need to be modeled in order to confirm the most effective cell porosity and arrangement. Electrolyte Obviously, electrolyte effects play a huge role in observed discharge characteristics. In fact, much of the difference in battery performance between high and low temperatures, and between high and low discharge rates, can be attributed to ion conductivity in the electrolyte and its change with temperature/concentration. Therefore, if one wishes to improve low temperature or high discharge battery performance, it is necessary to optimize the electrolyte conductivity. Several articles in scientific literature have begun to explore this topic [3]. Additionally, effects other than ion transport influence low temperature performance; Zhang et al. have reported that cells with LiBF 4 discharge more fully at low temperature than those with LiPF 6, due to decreased charge-transfer resistance (resistance to intercalation) at the electrodes [6]. These interfacial effects dominate at extremely low discharge rates, although bulk electrolyte properties still have a greater influence at 1C and above [4]. Mechanical Cracks can be induced by many factors, both external and internal to the battery. In this group we investigated the occurrence of diffusion-induced cracks in the active material (ref. Pallabs Paper) and based on that phenomenon, our group developed code to automatically detect any form of particle isolation. There is loss of active lithium ions when isolated in broken chunks of active material, which further reduces the capacity of the battery. Our codes takes in the necessary data and automatically detects areas where two cracks converge and lead to particle isolation. This information would be useful in the future for observing the effects of SEI formation on the area exposed due to cracks, as well as predicting capacity loss over multiple cycles. Two very different approaches for tracing were used and they both show promising results. More test runs are needed in order to prove the robustness of the program.

31 Acknowledgements Thanks to Texas A&M and the Dwight Look College of Engineering for providing the funding necessary to make this AggiE-Challenge project possible. Special thanks to the following people for all of their help: Dr. Mukherjee and Dr. Liang (Faculty Mentors) Pallab Barai, Seongkoo Cho, Chien-Fan Chen, and Carlos Lopez (Graduate Student Mentors) References [1] C. R. Sides, C. R. Martin, Nanostructured electrodes and the Low-Temperature Performance of Li-ion Batteries, Adv. Mater. (2005), 17, 125. [2] S.S. Zhang, K. Xu, T.R. Jow, Electrochemical impedance study on the low temperature of Li-ion batteries, Electrochimica Acta, (2004), 49, [3] Alexandra Lex-Balducci, Wesley Henderson, and Stefano Passerini. "Electrolytes for Lithium-Ion Batteries," in Lithium-Ion Batteries: Advanced Materials and Technologies. CRC Press, [4] Y. Ji, Y. Zhang, C.Y. Wang, Li-Ion Cell Operation at Low Temperatures, J. Electrochem. Soc. (2013), 160, A636. [5] P. Barai and P.P. Mukherjee, Stochastic Analysis of Diffusion Induced Damage in Lithium-Ion Battery Electrodes, J Electrochem. Soc. (2013) 160, A955. [6] S.S. Zhang, K. Xu, T.R. Jow, A new approach toward improved low temperature performance of Liion battery, Electrochem. Comm. (2002), 4, 928.