Calendar aging in batteries refers to the gradual degradation of performance and capacity over time, even when the battery is not in use. This phenomenon is primarily driven by parasitic chemical reactions within the cell, influenced by storage conditions such as temperature, state of charge (SOC), and humidity. Understanding and modeling calendar aging is critical for predicting battery lifespan, optimizing storage protocols, and improving battery management systems (BMS).

### **Factors Influencing Calendar Aging**
The rate of calendar aging is highly sensitive to environmental and operational conditions. The key factors include:

1. **Temperature**: Elevated temperatures accelerate chemical reactions, including those that degrade battery materials. The Arrhenius equation is often used to quantify the temperature dependence of degradation rates. For example, a lithium-ion battery stored at 40°C may degrade twice as fast as one stored at 25°C due to increased parasitic reactions.

2. **State of Charge (SOC)**: High SOC levels increase the thermodynamic driving force for side reactions, such as electrolyte decomposition and solid-electrolyte interphase (SEI) growth. Storing a battery at 100% SOC can lead to faster capacity fade compared to storage at 50% SOC.

3. **Humidity**: While sealed batteries are less affected by external humidity, internal moisture can catalyze unwanted reactions. In some chemistries, trace water can react with electrolyte components, generating acidic species that corrode electrodes.

### **Modeling Approaches for Calendar Aging**
Two primary modeling approaches are used to predict calendar aging: empirical models and physics-based models.

#### **Empirical Models**
Empirical models rely on experimental data to establish correlations between storage conditions and degradation. A common method involves accelerated aging tests at elevated temperatures and SOC levels, followed by extrapolation to real-world conditions.

- **Arrhenius-Based Models**: The Arrhenius equation describes the temperature dependence of reaction rates:
\[ k = A \cdot e^{(-E_a / RT)} \]
where \( k \) is the degradation rate, \( A \) is a pre-exponential factor, \( E_a \) is the activation energy, \( R \) is the gas constant, and \( T \) is temperature. By fitting degradation data at multiple temperatures, the model can predict aging under different thermal conditions.

- **SOC-Dependent Fade Models**: Empirical studies often show that capacity loss follows a power-law relationship with time:
\[ \Delta Q = k \cdot t^n \]
where \( \Delta Q \) is capacity loss, \( t \) is time, and \( k \) and \( n \) are fitting parameters dependent on SOC and temperature.

#### **Physics-Based Models**
Physics-based models aim to capture the underlying mechanisms of degradation, such as SEI growth, lithium plating, and electrolyte oxidation.

- **SEI Growth Models**: The solid-electrolyte interphase (SEI) forms on the anode surface and slowly thickens over time, consuming active lithium. Physics-based models describe SEI growth as a diffusion-limited process, where the SEI thickness increases with the square root of time.

- **Open-Circuit Voltage (OCV) Decay Analysis**: OCV drift during storage can indicate side reactions. For example, a gradual voltage drop in lithium-ion cells may reflect self-discharge due to parasitic reactions. Physics-based models correlate OCV changes with specific degradation mechanisms.

### **Parasitic Reactions and Material Stability**
Calendar aging is driven by several parasitic reactions:

1. **Electrolyte Decomposition**: Organic electrolytes can break down at high voltages, forming gas products and resistive layers on electrodes.
2. **Transition Metal Dissolution**: In layered oxide cathodes, transition metals may dissolve into the electrolyte, especially at high SOC and temperature.
3. **Lithium Plating**: Metallic lithium can deposit on the anode during high-SOC storage, leading to irreversible capacity loss.

Material stability plays a crucial role. For instance, high-nickel cathodes degrade faster than lithium iron phosphate (LFP) due to their reactivity with electrolytes. Similarly, silicon anodes experience more severe aging than graphite due to volume changes and SEI instability.

### **Industry Standards for Calendar Aging Testing**
Standardized testing protocols ensure consistent evaluation of calendar aging. Key standards include:

- **IEC 61960**: Specifies test conditions for lithium-ion cells, including storage at fixed SOC and temperature.
- **UL 1974**: Provides guidelines for assessing degradation in stationary storage systems.
- **SAE J2929**: Focuses on safety and performance of automotive batteries under storage conditions.

Tests typically involve storing cells at controlled temperatures (e.g., 25°C, 40°C, 60°C) and SOC levels (e.g., 30%, 50%, 80%, 100%) while periodically measuring capacity and impedance.

### **Implications for Battery Management Systems**
Calendar aging models inform BMS strategies to prolong battery life:

- **Optimal Storage SOC Recommendations**: BMS may advise storing batteries at 40-60% SOC to minimize degradation.
- **Temperature Management**: Thermal control systems mitigate aging by maintaining moderate storage temperatures.
- **State of Health (SOH) Estimation**: Calendar aging models help BMS track capacity fade and predict remaining useful life.

### **Conclusion**
Calendar aging models are essential for understanding battery degradation during storage. Empirical approaches, such as Arrhenius-based models, provide practical predictions, while physics-based models offer deeper insights into degradation mechanisms. Industry standards ensure reliable testing, and BMS leverage these models to optimize storage conditions. By accounting for temperature, SOC, and material stability, stakeholders can enhance battery longevity and performance in real-world applications.