Measuring Temperature Dependence of Entropy Via Temperature Ramps Using Float Current Analysis
Authors: Lewerenz Meinert , Azzam Mohamed , Ehrensberger Moritz , Scheuer Reinhard , Endisch Christian 
Published: February 2024

Float current analysis is a long-term self-discharge experiment keeping the voltage (float voltage) constant and measuring the resulting current with high precision. After a transient phase lasting around 30 days, the current reaches a steady state, named float current (10.3390/en16093889).
The float current reflects the self-discharge of a cell, after effects due to the oversized anode to the cathode (anode overhang effect) are concluded (10.1016/j.est.2018.04.029). In some publications, the float currents show strong correlation with the capacity loss rate (10.1016/j.jpowsour.2017.03.136, 10.3390/batteries7020022).
To characterize the cells, the float current is measured while keeping the cell voltage constant and varying the temperature in steps or as a ramp. Changing the temperature leads, due to the entropy effect, to an increase or decrease of the cell voltage depending on the sign and magnitude of the entropy coefficient (10.1149/1945-7111/ac3938). As the voltage in our experiment is kept constant, one observes an additional positive or negative current resulting from changes in temperature. In a stepwise temperature approach, a waiting time of about 1 day must be considered until currents resulting from the steps temperature transient have subsided. To understand more about entropy, we used this dependence as will be rolled out in the following.
For our experiment we investigated three different cell types of the format 18650 with varying cathode active materials (LFP, NMC, NCA) with up to five different float voltages. The cells were kept at constant voltage using a precision Keysight test bench in a Binder temperature chamber. The temperature was varied from 5 to 50°C using temperature ramps with rates of 0.56 K/h to 2.25 K/h. The results are compared to a stepwise temperature increase with 5 K increments.
During ramp phases, we measure the float currents superimposed on the positive or negative influence of the entropy. By calculating the average of a temperature upwards ramp and a temperature downwards ramp, the entropy share is eliminated and only the pure temperature-dependence of the float current is obtained. The shape of the float current over temperature is an exponential increase, indicating an Arrhenius relation. As a homogeneous temperature change must be established, faster temperature ramps reveal strongly distorted transient-parts at the begin and end of the ramp, while a lower velocity shows only a very small transient-part. Comparing the low temperature velocities with stepwise approach, we observed a high agreement of both strategies demonstrating the validation of the temperature ramp approach.
To obtain the entropy share during temperature ramps, the float current results are subtracted from the respective upwards and downwards ramps. Contradicting the general opinion of entropy for batteries, we did not observe a constant entropy coefficient over temperature but an entropy coefficient increasing linearly with temperature for all cell types and cell voltages. This finding is of high importance for high-precision measurement of lithium-ion batteries.

Figure 1