Heat of Mixing During Fast Charge/Discharge of a Li-Ion Cell: A Study on NMC523 Cathode

Abstract

Predicting temperature rise accurately during fast charge/discharge of a Li-ion cell is essential to avoid thermal runaway and extend battery life. While modeling the temperature rise, it is necessary to model the heat generation correctly. Heat of mixing, one of the four main sources of heat generation in a Li-ion battery, has often been considered insignificant and therefore excluded from modeling. When included, it is modeled using the expression from a Taylor expansion approximation. In this work, we have shown the conditions when including the heat of mixing becomes important and quantified the error associated with using the Taylor expansion, especially under high charge/discharge conditions. Consequently, we carry out the calculation of the rate of enthalpy change and the heat generation rate from the most fundamental equation for the rate of the total enthalpy change without simplifying assumptions or approximations. The heat generation rate calculated doing so naturally includes irreversible, reversible and mixing heat. We then exclusively separate out the heat of mixing by subtracting the rate of enthalpy change by reaction from the rate of the total enthalpy change. Results show that the contribution of heat of mixing in the total heat generated increases with the charge/discharge rate and is as large as 23% for a 6 C discharge. This result suggests that while modeling heat generation for fast charge/discharge, it is necessary to include the heat of mixing and avoid calculating it using the Taylor expansion approximation.

A review of thermal physics and management inside lithium-ion batteries for high energy density and fast charging

“…In this section, the different sources of heat generation inside the battery are reviewed in detail. The contribution by various sources can vary with the energy density and charge rate, e.g., the heat of mixing, assumed to be negligible in prior works, contributes ~23% to the total heat generation at a charge rate of 6C [146]. We also review and evaluate existing models to calculate battery heat generation.…”

“…For the entire porous electrode with a local current density ( ), the entropic heat per unit cross sectional area is (11) However, the reaction is not the only source for the entropy change. Entropy of the electrochemical system can also change due to diffusion within electrode particles to form uniform concentration, and in such a case, the heat released or absorbed due to entropy change contributes to the total heat of mixing [146]. The entropic coefficient ' ( can generally be measured by two methods.…”

“…One is by measuring the open circuit potential ( ) as a function of temperature for different SOC's [164]. The other, much quicker, method is using isothermal calorimetry [146,154,155]. At lower charge/discharge rates, the entropic heat can be comparable in magnitude to the irreversible heat [156,157].…”

“…7a, when lithium diffuses inside an electrode particle in the presence of a concentration gradient of lithium within the particle, the local composition and hence the energy of the active material experienced by the particle changes with time. This change in the energy is manifested as heat and is known as the heat of mixing in the particles [146]. At low charge/discharge rates, the rate of diffusion is comparable to the lithium flux in or out of the particle and strong concentration gradients do not develop within the particle.…”

“…As a result, the surface concentration of lithium ions differs significantly from the concentration inside the particle, and a strong concentration gradient develops within the particle. When lithium diffuses through this strong concentration gradient the local composition and therefore energy changes rapidly and is manifested as heat [146]. Therefore, at high charge/discharge rates, heat of mixing cannot be neglected.…”