Measurement of the Entropy of Reaction By Frequency Separation Method
Authors: Abbasalinejad Armin , Besli Muenir Mustafa , Chung Seung Hyun , Christensen Jake , Kim Sun Ung 
Published: May 2020

Lithium-ion batteries are the most preferred candidate power sources for electric vehicles (EVs) and hybrid electric vehicles (HEVs) [1]. In these applications, thermal management of battery systems is critical in preventing catastrophic thermal runaway. Therefore, the study of thermodynamic quantities such as entropy change (ΔS/nF) during battery operation over the lifespan is important as it is directly related to accurate temperature prediction of the system. Thermodynamically, the reversible entropy heat (including the derivative of open-circuit potential (OCP), U with respect to temperature, T) is related to the reaction entropy, and its values have been measured potentiometrically or calorimetrically [2]. The traditional methods require measuring the change in voltage after changing the temperature of the battery, and measuring the change in temperature or heat flux after applying the change in voltage. However, both of these methods are difficult to apply to the batteries in EVs or HEVs because it is hard to control the temperature, or to measure the heat flux of the batteries in the pack.
In this presentation, we will demonstrate a new approach to evaluate the derivative, dU/dT using a frequency separation method. In theory, when a current of a sinusoidal current of frequency ω is applied to a battery, the Joule heat has a 2ω frequency and the reaction heat has a 1ω frequency. By analyzing the temperature data with a thermoelectrochemical model, dU/dT can theoretically be evaluated. To see if this method could be applied to batteries, we applied the technique to a commercial pouch battery. First, the pouch battery was disassembled and an ICP-OES measurements revealed that the active materials were graphite and LiCoO2 (LCO). Second, a thermoelectrochemical model was developed and parameterized for the battery that can predict thermal and electrochemical behaviors simultaneously (See Figure 1(a) and 1(b)). The model includes an energy equation that consists of heat accumulation, conduction, convection, and heat generation from the Joule heat and the reaction heat. Previously reported dU/dT values of graphite and LCO [2,3] were implemented. Third, an experiment was conducted to observe the temperature fluctuations. Figure 1(b) shows that the magnitudes of the temperature fluctuation at the 1ω frequency and the 2ω frequency are clearly different experimentally. Finally, the thermoelectrochemical model was fitted with the experimental data. The fitting parameters were only the convective heat transfer coefficient h and the heat capacity cp
. Figure 1(b) demonstrates that the model and the experimental results were well matched.
Using this thermoelectrochemical model, it is predicted that the change in dU/dT values can be easily tracked while operating the battery. For example, an algorithm can be developed to find dU/dT values that minimize the difference between experiment and model temperatures, so that we can track the change in dU/dT values over time. This method provides a new option for measuring the reversible entropy heat by controlling current and measuring temperature, which may be advantageous for state estimation in some EV/HEV battery pack designs.
References
[1] A. Barré, B. Deguilhem, S. Grolleau, M. Gérard, F. Suard, and D. Riu, “A review on lithium-ion battery ageing mechanisms and estimations for automotive applications,” J. Power Sources, vol. 241, pp. 680–689, 2013.
[2] K. E. Thomas, C. Bogatu, and J. Newman, “Measurement of the entropy of reaction as a function of state of charge in doped and undoped lithium manganese oxide,” J. Electrochem. Soc., vol. 148, no. 6, pp. A570–A575, 2001.
[3] N. S. Hudak, L. E. Davis, and G. Nagasubramanian, “Cycling-induced changes in the entropy profiles of lithium cobalt oxide electrodes,” J. Electrochem. Soc., vol. 162, no. 3, pp. A315–A321, 2015.
Figure 1. Demonstration of (a) electrical and (b) thermal behaviors by applying a sinusoidal current of frequency 1ω to a battery under natural convection condition.

Figure 1