Lithium-ion (Li-ion) batteries are the most commonly used rechargeable batteries in consumer and automotive applications due to their high energy density, proper power density, relatively high battery voltage and low weight to volume ratio.
The term lithium ion battery refers to the entire battery chemistry group. A common characteristic of these chemicals is that the negative electrode and the positive electrode material are used as a host of lithium ions, and the battery contains a nonaqueous electrolyte.
Increased demand and pressure to improve battery performance exacerbate the need for mathematical modeling. Modeling and simulation allows analysis of an almost unlimited number of design parameters and operating conditions at a relatively small cost. Experimental testing is used to provide the necessary validation of the model.
Figure 1: The 2D version of the Newman model predicts the edge effect of the spiral cell geometry where the electrodes at both ends of the roll have no counter electrode on one side.
The Newman Model
Mathematical models can describe and predict battery voltage and current density during discharge, recharge, transient studies, and mechanisms including aging and failure. Under these conditions, the effects of different material properties and design parameters can be studied.
The main force of high-fidelity modeling of lithium-ion batteries is the so-called Newman model. This model has been proven by many scientists for many years. For example, it has been further developed and expanded by others to explain designs with multiple electrode materials, solid electrolyte interface formation and alternative electrode dynamics. The original 1D model was also developed by COMSOL for 2D, 2D axisymmetric and 3D models.
Performance Models
A typical experiment that can be accurately described by a physics-based battery model is a discharge-recharge cycle, as shown in Figure 2, in which a high energy battery for mobile applications is simulated.
In Figure 2, the green line indicates the current density. The current density is defined as positive during the initial discharge of 2000 seconds and then for a period of time (0 current) for 300 seconds. Then recharge the battery (negative current) for 2,000 seconds and then let it rest.
The response of the battery voltage to this period is shown by the blue curve and is very accurately predicted by the model. The voltage decays with discharge time due to mass transfer resistance, concentration and activation overpotentials, and thermodynamic losses. The battery voltage increases as the battery is charged, again due to the same loss, but now the opposite sign. When the battery stops working, the voltage slowly reaches a stable open circuit voltage.
Figure 2: Using the current density (green) as input and the battery voltage (blue) predicted by the model to simulate a discharge-recharge cycle with a stationary period in between.
The advantage of performance models is that they can be used to find and analyze processes that cause battery performance limitations and the loss of these limitations. These models can also be used to evaluate how energy and power densities are changed when changing electrode designs and how electrode materials are used in battery design.
Thermal management and safety
Most of the losses in the battery, such as ohmic losses and activated overvoltages, generate heat. In addition, the battery system may require heating to work during cold weather and startup. Cooling and heating of the battery system requires thermal management.
Using a physics-based model, you can get different heat sources directly from the model. The advantage of using a thermal model is that the temperature inside the battery can be estimated from the measurement of the surface. This allows for the study of undesirable effects such as internal shorts, which may be the cause of thermal runaway.
Temperature variations are dominant in large cells because uneven current distribution results in uneven heat generation. The normal operation and conventional start-up heating and cooling designs focus on minimizing weight and power consumption.
Figure 3: Battery temperature in cooling channels and battery packs for automotive applications.
The design of the thermal management system in a battery system is essentially complicated because it must be able to handle faulty batteries. Since the metal deposit on the cathode grows on the electrolyte and is in contact with the anode electrons, it is usually caused by a short circuit of the electrode.
Figure 4: Local charge state of the electrode particle surface in a lithium ion battery after 0.01 second self-discharge. Due to the internal short circuit, the negative electrode (bottom) is depleted and the positive electrode (top) accumulates.
Mechanical damage is another cause of battery shorts. If a foreign metal object penetrates the battery pack or if the battery pack is crushed and damaged, an internal conduction path may be provided, resulting in a short circuit. One standard safety test for lithium ion batteries is the "nail test," in which the nail is driven into the battery to create a short circuit. The nail conducts current as an external circuit with a very small load, while the area around the nail appears as a discharge period.
Characterization and health
Lithium-ion batteries lose capacity and internal resistance increases over time. After a while, the battery does not provide the required energy or power. The reaction that causes this aging can be included in the performance model.
There are many factors that affect performance, and it is often difficult to separate the effects of different design and operating parameters from performance. The key to separating the effects of different phenomena involved is that they usually have different time constants. For example, electrochemical reactions are generally fast compared to molecular diffusion.
An increasingly common method for analyzing the health of batteries is Electrochemical Impedance Spectroscopy (EIS). The method is based on measuring impedances at different frequencies to separate processes with different time constants.
The physics-based performance model of EIS can be combined with experimental measurements to investigate the effects of battery material aging and attenuation at the battery level.
Beyond the Newman model
Understanding the latest developments in electrodes in batteries is the use of heterogeneous models to process the geometry of the material in detail compared to a uniform model. This is done by constructing the geometry from the photomicrograph.
Figure 5: Neck stress concentration between particles in a negative electrode in a lithium battery model having a hypothetical structure composed of ellipsoidal particles.
The above example shows a hypothetical heterostructure in which graphite particles are described as ellipsoids and the pore electrolyte fills the voids between the skeletons formed by the ellipsoids. The structural analysis combined with detailed electrochemistry, the volume expansion caused by lithium intercalation, reveals that the neck of the skeleton structure is subjected to the highest stress and strain. Therefore, cracks may be formed in the repeated cycle and ohmic loss is increased, which contributes to deterioration of battery performance.
Multiphysics model and partial differential equation
The most accurate way to describe a lithium-ion battery is through a physics-based model developed using partial differential equations. Further development of these batteries requires new models and new formulations, such as the heterogeneous models exemplified above. Models must be able to describe the basic processes that determine battery performance to gain a deeper understanding of the knowledge needed to develop new materials and new designs. There is no way to solve this problem: models and simulations are shortcuts.
The term lithium ion battery refers to the entire battery chemistry group. A common characteristic of these chemicals is that the negative electrode and the positive electrode material are used as a host of lithium ions, and the battery contains a nonaqueous electrolyte.
Increased demand and pressure to improve battery performance exacerbate the need for mathematical modeling. Modeling and simulation allows analysis of an almost unlimited number of design parameters and operating conditions at a relatively small cost. Experimental testing is used to provide the necessary validation of the model.
Figure 1: The 2D version of the Newman model predicts the edge effect of the spiral cell geometry where the electrodes at both ends of the roll have no counter electrode on one side.
The Newman Model
Mathematical models can describe and predict battery voltage and current density during discharge, recharge, transient studies, and mechanisms including aging and failure. Under these conditions, the effects of different material properties and design parameters can be studied.
The main force of high-fidelity modeling of lithium-ion batteries is the so-called Newman model. This model has been proven by many scientists for many years. For example, it has been further developed and expanded by others to explain designs with multiple electrode materials, solid electrolyte interface formation and alternative electrode dynamics. The original 1D model was also developed by COMSOL for 2D, 2D axisymmetric and 3D models.
Performance Models
A typical experiment that can be accurately described by a physics-based battery model is a discharge-recharge cycle, as shown in Figure 2, in which a high energy battery for mobile applications is simulated.
In Figure 2, the green line indicates the current density. The current density is defined as positive during the initial discharge of 2000 seconds and then for a period of time (0 current) for 300 seconds. Then recharge the battery (negative current) for 2,000 seconds and then let it rest.
The response of the battery voltage to this period is shown by the blue curve and is very accurately predicted by the model. The voltage decays with discharge time due to mass transfer resistance, concentration and activation overpotentials, and thermodynamic losses. The battery voltage increases as the battery is charged, again due to the same loss, but now the opposite sign. When the battery stops working, the voltage slowly reaches a stable open circuit voltage.
Figure 2: Using the current density (green) as input and the battery voltage (blue) predicted by the model to simulate a discharge-recharge cycle with a stationary period in between.
The advantage of performance models is that they can be used to find and analyze processes that cause battery performance limitations and the loss of these limitations. These models can also be used to evaluate how energy and power densities are changed when changing electrode designs and how electrode materials are used in battery design.
Thermal management and safety
Most of the losses in the battery, such as ohmic losses and activated overvoltages, generate heat. In addition, the battery system may require heating to work during cold weather and startup. Cooling and heating of the battery system requires thermal management.
Using a physics-based model, you can get different heat sources directly from the model. The advantage of using a thermal model is that the temperature inside the battery can be estimated from the measurement of the surface. This allows for the study of undesirable effects such as internal shorts, which may be the cause of thermal runaway.
Temperature variations are dominant in large cells because uneven current distribution results in uneven heat generation. The normal operation and conventional start-up heating and cooling designs focus on minimizing weight and power consumption.
Figure 3: Battery temperature in cooling channels and battery packs for automotive applications.
The design of the thermal management system in a battery system is essentially complicated because it must be able to handle faulty batteries. Since the metal deposit on the cathode grows on the electrolyte and is in contact with the anode electrons, it is usually caused by a short circuit of the electrode.
Figure 4: Local charge state of the electrode particle surface in a lithium ion battery after 0.01 second self-discharge. Due to the internal short circuit, the negative electrode (bottom) is depleted and the positive electrode (top) accumulates.
Mechanical damage is another cause of battery shorts. If a foreign metal object penetrates the battery pack or if the battery pack is crushed and damaged, an internal conduction path may be provided, resulting in a short circuit. One standard safety test for lithium ion batteries is the "nail test," in which the nail is driven into the battery to create a short circuit. The nail conducts current as an external circuit with a very small load, while the area around the nail appears as a discharge period.
Characterization and health
Lithium-ion batteries lose capacity and internal resistance increases over time. After a while, the battery does not provide the required energy or power. The reaction that causes this aging can be included in the performance model.
There are many factors that affect performance, and it is often difficult to separate the effects of different design and operating parameters from performance. The key to separating the effects of different phenomena involved is that they usually have different time constants. For example, electrochemical reactions are generally fast compared to molecular diffusion.
An increasingly common method for analyzing the health of batteries is Electrochemical Impedance Spectroscopy (EIS). The method is based on measuring impedances at different frequencies to separate processes with different time constants.
The physics-based performance model of EIS can be combined with experimental measurements to investigate the effects of battery material aging and attenuation at the battery level.
Beyond the Newman model
Understanding the latest developments in electrodes in batteries is the use of heterogeneous models to process the geometry of the material in detail compared to a uniform model. This is done by constructing the geometry from the photomicrograph.
Figure 5: Neck stress concentration between particles in a negative electrode in a lithium battery model having a hypothetical structure composed of ellipsoidal particles.
The above example shows a hypothetical heterostructure in which graphite particles are described as ellipsoids and the pore electrolyte fills the voids between the skeletons formed by the ellipsoids. The structural analysis combined with detailed electrochemistry, the volume expansion caused by lithium intercalation, reveals that the neck of the skeleton structure is subjected to the highest stress and strain. Therefore, cracks may be formed in the repeated cycle and ohmic loss is increased, which contributes to deterioration of battery performance.
Multiphysics model and partial differential equation
The most accurate way to describe a lithium-ion battery is through a physics-based model developed using partial differential equations. Further development of these batteries requires new models and new formulations, such as the heterogeneous models exemplified above. Models must be able to describe the basic processes that determine battery performance to gain a deeper understanding of the knowledge needed to develop new materials and new designs. There is no way to solve this problem: models and simulations are shortcuts.
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