Thus far, the UHPC 101 series has focused on Coulombic Efficiency (CE); what CE measurements mean and how they can be used to quantify cell performance, how to fairly compare cells cycled at different rates or within different voltage intervals by normalizing for cycle time - giving the Coulombic Inefficiency per hour (CIE/hr), and the last post covered Capacity fade, the first of two components that constitute CE.
We’ve seen how CE and CIE/hr can be used to quantify cell degradation in significantly less time than traditional long-term cycling tests. But understanding why the CE of a cell is worse than another is crucial to the cell development cycle. Thus, the second part of the CE must be told; this is charge end-point capacity slippage.
Charge End-point Capacity Slippage
Charge end-point capacity slippage captures how much capacity is wasted on processes that do not necessarily cause capacity fade, but causes more capacity to be measured during charge compared to discharge. Almost always, cells will have a smaller discharge capacity than charge capacity in the same cycle (CE of less than 1.0). It isn’t obvious why the subsequent charge capacity of the cell is often greater than that previous discharge capacity. This arises due to charge end-point capacity slippage, and it is in a complex dance with capacity fade to make up the CE of a cell.
In contrast to capacity fade, where Li-ions from the positive electrode (the “Li inventory”) are consumed in irreversible reactions, charge end-point capacity slippage is due to other reactions in a Li-ion cell that don’t consume Li inventory, rather, they prevent electrons from being counted during discharge (decreasing the measured capacity) and cause extra electrons to be counted during charge (increasing the measured capacity). This may seem unclear at first, but it is important to keep in mind that Li-ion cells are intrinsically complex with many interacting components; there are many different mechanisms that can lead to charge end-point capacity slippage, but hopefully the examples given below will provide a basis for understanding.
Now, let’s reimagine our bucket analogy from our CE post:
We have a bucket with a small hole in it where the charging process is done by pouring water into the bucket and the discharge process is done by pouring the water out of the bucket (it doesn’t matter where the water goes). If we measure the charge capacity as the amount of water poured into the bucket, then we are counting the water that will leak before it is poured out.
Similarly, if we measure the discharge capacity as the amount of water that is poured out, then we are not counting the water that leaks while the water is being poured out.
In this scenario, the water that leaks between the time the bucket is filled and emptied is analogous to charge end-point capacity slippage because it causes the discharge capacity to be less that the charge capacity.
Interestingly, the total amount of water that has leaked out can be inferred without directly measuring it; simply knowing the amount of water in the bucket before and after it has been filled and emptied indicates how much water has leaked. It is the same with charge end-point capacity slippage; it indicates the amount of measured capacity owing to reactions or mechanism that don’t consume Li inventory.
To come full circle, now imagine this:
The water was replaced with maple syrup, just like in the analogy of the previous post (capacity fade), and there was a small amount of crystallization on the walls of the bucket every time it was filled, reducing the available bucket volume and consequently the amount of maple syrup that could be put in the bucket each “cycle”.
The relationship between the amount of syrup leaked and the amount of syrup crystallized is analogous to the relationship between charge end-point capacity slippage and capacity fade.
In order to understand how charge end-point capacity slippage arises, a slightly more technical discussion is needed compared to previous posts. The capacity of a cell during a particular cycle comes down to counting electrons that move through the cell circuit (measuring current). It is assumed that in a Li-ion cell, each electron that flows through the cell circuit corresponds to one Li-ion being inserted (or removed) and removed (or inserted) from each electrode – this is the “electrochemical” reaction through which energy is stored or released.
But there are other reactions in a Li-ion cell that skew the balance between electrons flowing through the cell circuit and Li-ions being inserted and removed from electrodes. An example of such a reaction is called electrolyte oxidation which, unlike electrolyte reduction, does not consume Li inventory, instead involves a Li-ion from the electrolyte. This type of reaction typically occurs at the positive electrode surface and manifests differently depending on whether the cell is being charged or discharged. During charge, an electrolyte species can lose an electron to the positive electrode material, becoming positively charged, causing an electron to flow through the cell circuit and a positively charged Li-ion from the electrolyte to insert into the negative electrode. The cell capacity is apparently increased because this reaction does not involve the removal of a Li-ion from the positive electrode, yet an electron passed through the cell circuit.
In contrast, during discharge, an electrolyte species can lose an electron to a positively charged Li-ion from the electrolyte as it is inserted into the positive electrode. This apparently decreases the discharge capacity because a corresponding electron does not pass through the cell circuit while the voltage of the positive electrode versus Li changes when a Li-ion is inserted. In each of the above cases, a Li-ion from the electrolyte is added to the lithium inventory. However, charge end-point capacity slippage can also arise due to reversible redox shuttle reactions between electrodes, mechanical self-discharge such as dendrite growth through the separator, or cell defects.
In this way, electrolyte oxidation (and other mechanisms) can lead to an apparent increase in charge capacity and an apparent decrease in discharge capacity. This asymmetric behavior between charge and discharge causes the voltage vs cumulative capacity curves to shift to the right each cycle. The leftmost panel in the figure above shows how the capacity at top of charge slips to the right with cycle number; this is the charge end-point capacity slippage.
The left-hand panels in the above figure show voltage vs capacity curves for two sets of pair cells with one set that experiences more charge end-point capacity slippage than the other. Similar to capacity fade (covered in the last post), charge end-point capacity slippage can be visualized in two ways:
I) the cumulative slippage, shown in the top right panel, picks out the capacity value at top of charge for each cycle relative to the first cycle (I.e., total slippage), and II) the relative slippage, or slippage per cycle, shown in the lower right panel, takes the difference between the capacity value at top of charge of cycle n and cycle n-1.
It is useful to look at charge end-point capacity slippage in both ways when comparing cells because some insight can be gained into both rates of oxidation reactions and the total number of reactions that have taken place, for example.
Together, capacity fade and charge end-point capacity slippage compose the CE of a cell. Since different reaction mechanisms give rise to each, it is important to look at the CE and its components when comparing cells – this information is invaluable to design and choose better cells using an understanding of degradation mechanisms. To compare cells cycled at different rates and/or within different voltage intervals, charge end-point capacity slippage and capacity fade can be normalized by the cycle time to give the CIE/hr.
We hope you are enjoying the UHPC 101 series so far! In the next post, we will show how the numerical value of CE for each cycle can be written in terms of capacity fade and charge end-point capacity slippage. This will bring the CE story together demonstrating how cycle-to-cycle cell degradation can be understood in terms of capacity fade and charge end-point capacity slippage and will wrap up the CE essentials. But there remains lots of space on the canvas to paint a holistic picture of cell health and performance; future posts will cover topics such as rate capability, delta V (also referred to as voltage hysteresis), differential voltage analysis, and differential capacity analysis.
Keep your eyes peeled as there is much more to come!
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