There’s no denying the usefulness and importance of Coulombic Efficiency. However, when comparing cells cycled under different conditions, to have a direct comparison, there’s a few things that must be considered since cell degradation depends on both time and cycle number. Things like reactions of electrolyte components will occur even if a cell is sitting on a shelf not being cycled.
The time dependence of reactions within a lithium-ion cell are challenging for meaningful comparisons of CE – which measures these reactions – where cycles take a different amount of time to complete; cells with cycles that take more time will experience more reactions per cycles. In this way, CE is understood to be a function of both cycle number and time.
What is Coulombic Inefficiency Per Hour (CIE/hr)?
In this section we’ll explore how to compare the CE of cells cycled differently, whether it’s at different rates (currents) or to different states of charge (voltages).
As mentioned above, it’s important to understand the time dependence of CE because time-dependent degradation reactions in the cell will lead to higher CE values for a cell that’s cycled faster, compared to the same cell that’s cycled slower.
To make CE more useful and relevant for a given product or technology application, CE may need to be normalized for time, broadening its scope of applicability. This is Coulombic Inefficiency per hour (CIE/hr).
Here’s a practical example: consider two identical cells cycling under the same current but to different upper cut-off voltages: 4.1 V and 4.3 V. The cell cycling to 4.1 V will complete a cycle in less time than the cell cycling to 4.3 V. The CE must be normalized for time to fairly compare these two cells.
Envision a glass of water that leaks every time a drink is taken from it. Of course, the faster the drink cycle (pick up glass, drink, put the glass down), the less water will be lost. The leaking rate, however, doesn’t change because drinking is occurring faster – it’s just that less time is being allowed for the leak.
The CE of a Li-ion cell is always less than 1.000000, partly due to unwanted reactions that consume lithium and lead to capacity loss over time. Each of these reactions occur at some rate. With more time elapsed in a cycle, there’s more time for these unwanted reactions to occur. If the CE of two cells is measured under different cycling rates, the cell under the higher rate may experience fewer lithium-consuming reactions per cycle because less time elapses per cycle. Coulombic Inefficiency per hour (CIE/hr) normalizes the CE by the time per cycle. The Coulombic Inefficiency (CIE) is defined as 1 – CE, so conversely to CE, better cells will minimize CIE. Measurements at higher rates, which take less time, have smaller CIE (larger CE), thus when dividing by the time per cycle, the CIE is reduced by a smaller factor.
Similarly, measurements at lower rate take more time per cycle and have larger CIE, so dividing by the time per cycle reduces the CIE by a larger factor. This way, the CIE/hr allows comparison of CE measurements of cells cycled under different rates provided the electrochemical reaction mechanisms do not depend on current.
Returning to the example of the two identical cells cycled to 4.1 V and 4.3 V under the same current, if the CIE/hr of each cell was the same, it would be an indication that the unwanted reactions in the cell are not worsened by cycling to a higher voltage. These kinds of inferences can be very useful for determining cell operability windows given a set of application constraints. In some chemistries, such as Silicon-containing anodes for example, degradation mechanisms depend on both time and the number of cycles; a greater number of cycles in the same amount of time can increase the CIE/hr. Having a solid grasp of CIE/hr measurements can help gain insight into the degree of cycle-based versus time-based degradation mechanisms.
To illustrate CIE/hr in action look at the image below. It shows two sets of cells cycled at the same temperatures and voltage limits at low rates of C/32 (black) and C/16 (red). The cells running at the slower rate have a higher CIE when plotted vs. Cycle or time. However, when CIE/hr is plotted vs. the total time the cell is being tested for the unwanted mechanisms appear to be identical between the cells, regardless of cycle number.
The Usefulness of UHPC
This all goes to show that careful analysis of CE and CIE/hr from UHPC data can be used to determine the effects of various operating conditions on unwanted mechanisms occurring in cells. UHPC provides accuracy and precision that allows these metrics to give insight into how cells respond to environmental conditions, voltage windows, and different applied rates* with respect to both time and cycle number. Using UHPC, these precise tests investigating the electrochemical stability of cells can be done in only 2-3 weeks, allowing better decisions to be made more quickly compared with traditional cycling.
Disclaimer: UHPC measurements to probe different failure mechanisms at various operational conditions require careful consideration of the rate being applied to the cell due to the effects of kinetics. Kinetically limited cells are subject to additional failure mechanisms that influence CE, such as lithium plating and self heating, as well as lithium concentration gradients within the electrodes. Any CE measurement to specifically probe the electrochemical stability of materials within the cell must be performed with sufficiently low rate so that there are no apparent capacity losses due to kinetics.
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