Question

According to the Arrhenius-based aging model, what is the direct mathematical relationship between an increase in operating temperature and the rate of capacity fade in a battery?

Accepted Answer

The Arrhenius-based aging model describes the rate of battery capacity fade as an exponential function of temperature. The mathematical relationship is expressed by the equation k equals A times e raised to the power of negative Ea divided by RT, where k is the reaction rate of capacity fade, A is the pre-exponential factor representing the frequency of molecular collisions, Ea is the activation energy, R is the universal gas constant, and T is the absolute temperature in Kelvin. Activation energy is the minimum amount of energy required for a chemical degradation reaction to occur within the battery. The term e raised to the power of negative Ea divided by RT indicates that as the absolute temperature T increases, the exponential term grows significantly larger, leading to a non-linear, exponential increase in the rate of capacity fade. Because the relationship is exponential, even a small increase in operating temperature results in a disproportionately large increase in the speed of chemical degradation processes, such as solid electrolyte interphase layer growth, which reduces the total capacity of the battery over time.

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According to the Arrhenius-based aging model, what is the direct mathematical relationship between an increase in operating temperature and the rate of capacity fade in a battery?