Coulombic efficiency, CE, is the ratio of discharge capacity over charge capacity of a specific electrode in a cell, as shown in the following equation[1].
CE equals 100% if no side reactions on the electrodes in an ideal cell, indicating no Li loss in charging and discharging process. In reality, parasitic side reactions do exist, including either chemical or electrochemical. In the former case, electrons generated from the parasitic reactions may or may not be collected by the current collectors, depending on the reaction pathways. In the latter case, electron loss and acceptance still take place on the current collectors but are irreversible.
Possible side reactions include:
- Electrolyte decomposition
- Electrolyte polymerization
- Solid electrolyte interphase (SEI) formation
- Reorganization of the cathode lattice
- Lithium metal cell, the presence of Lithium reservoir may later CE measurement result
- Irreversible electrochemical reactions
Coulombic efficiency can be precisely measured by Novonix HPC instrument[2]. It has two contributions: charge end-point capacity slippage and capacity fade as shown in the following picture.
Discharge and charge end-point capacity slippages
Discharge and charge end-point capacity slippages[3] are the differences between the end-points of cycle n and cycle n−1:
Δqnc=qnc−qn−1c
and Δqnd=qnd−qn−1d,
respectively.
The capacity fade
The capacity fade[4], Qf, for cycle n is the difference between the discharge capacity of cycle n−1 and cycle n:
Qf=Qn−1d−Qnd.
Qf can also be written as the difference between the discharge and charge end-point capacity slippages:
Qf=Δqnd−Δqnc
To see this, imagine sliding the discharge curve of cycle n to the left by an amount Δqnc such that the charge end-points of cycle n and cycle n−1 lie on top of each other. The difference in discharge end-points then gives the capacity fade, Qf, and is the same as the difference between the discharge and charge end-point capacity slippages.
The CE for cycle n, which is the discharge to charge capacity ratio, can now be written in terms of the capacity fade, Qnf, and the charge end-point capacity slippage, Δqnc, by noting that the cycle n discharge capacity is the cycle n charge capacity minus the discharge capacity slippage, Qnd=Qnc−Δqnd:
Since the discharge end-point capacity slippage can be expressed in terms of the capacity fade and charge end-point capacity slippage, the above equation can be rewritten as the following:
Coulombic Inefficiency per hour (CIE/hr)
To allow the comparison between cells that were cycled at different rates and/or to different states of charge causing the cycle time to be different, the time factor is considered and a new expression, Coulombic Inefficiency per hour (CIE/hr) can be defined as the following:
Differentiating capacity fade and charge end-point capacity slippage in CE measurement into Qf and Δqncshed more light into the understanding the degradation mechanisms of a battery cell. As shown in the following example, two cells have exactly same CE; however further analysis, the same CE comes from two different sources: black has higher capacity fade, while red has higher charge end-point capacity slippage.
Combination with other measurements, the cell with larger charge end-point capacity slippage (red) might be due to a comparably increased impedance; it is possible that salt from the electrolyte was being consumed during electrolyte oxidation, which would likely lead to worse performance over time compared to the cell with larger capacity fade (black)[5].
Capacity retention
Capacity retention, or the remaining capacity in the cell after certain cycling, can be effectively calculated by the following equation.
Where CE refers to coulombic efficiency and n is the cycle number. If 800 stable cycles with more than 80% capacity retention is desired, the averaged CE would have to be at least 99.97%.
[1] https://doi.org/10.1038/s41560-020-0648-z
[2] https://www.novonixgroup.com/bts-ultra-high-precision-coulometry/
[3] https://www.novonixgroup.com/blogs/uhpc-101-part-4-charge-end-point-capacity-slippage/
[4] https://www.novonixgroup.com/blogs/uhpc-101-part-3-capacity-fade/
[5] https://www.novonixgroup.com/blogs/uhpc-101-part-5-coulombic-efficiency-the-breakdown/