The authors of [1] demonstrate that under some assumptions, the "knee" in the typical Cell capacity fade curve (when after some number of cycles the cell enters a different mode with a higher capacity fade rate per each cycle) can be solely explained by the increase in Cell internal resistance.

You can see the knee on the lower-right chart, the black line which models the cell capacity:

In the figure above, $R_1$ models the increase of the cell internal resistance (but not diffusion resistance) relative to the baseline level which is assumed to be 0.15 Ohm. Blue squares and red triangles designate the points on the open-circuit voltage curve where the cell charging ($OCV_{BOD}$ = "beginning of discharge" = end of charge) and discharging ($OCV_{EOD}$ = "end of discharge") should stop, respectively, assuming the CCCV charging protocol with cutoff C/10 rate in the constant voltage phase, and 1C constant-current discharging protocol.

The model shows that if cell internal resistance raises by 100% from 0.15 Ohm to 0.15+0.15 = 0.3 Ohm (see the top row of charts) then this change can only explain a slight decrease of cell capacity. But if cell internal resistance increases by 233% to 0.15+0.35=0.5 Ohm (see the bottom row of charts) then this change can explain accelerated capacity fade. Cell discharge stops when the open-circuit voltage is still on the plateau.

Here is a real cycling experiment:

The meaning of blue squares and red triangles is the same as in the figure above. The rightmost chart demonstrates the results of the experiment: $Q_{Exp}$ means "experimental", i. e. the measured capacity, and $Q_R$ is the predicted capacity assuming the increase of cell resistance is the only reason for the capacity fade.

It's important to note that this cell was cycled at 45 °C, probably to induce severe SEI growth to make the cell resistance increase as much as the model above "requires" (hundreds of percent). I think that under normal conditions, cell internal resistance should not increase by more than 20-30% (e. g., demonstrated in this study).

Also, the authors characterised the cell discharge capacity at 1C rate, which is not typical in experiments but was needed to demonstrate the knee effect on a real cell.

One thing that seems questionable to me in explaining this experimental result by the model proposed above is that the gap between the measured capacity and the predicted capacity increases until about the 600th cycle (which would be expected, meaning that there are some other factors contributing to the capacity fade other than the rise in cell resistance, e. g., Loss of lithium inventory) and decreases after the 600th cycle meaning that some of the capacity fade mechanisms are reversed, which is impossible in this experiment.


This model is at odds with the theory that Cell capacity fade accelerates when Lithium deposition becomes irreversible. However, I'm inclined to think that both theories are right under some circumstances. The internal resistance can play a significant role only in energy cells, that the authors themselves point out:

This contribution is likely to be highly significant in energy cells compared with power cells where initial diffusional resistances are low.

Albeit the authors didn't consider diffusion resistance in the model, it's more likely that in reality, diffusion resistance plays an even bigger role in limiting the cell's 1C discharge capacity when the SEI layer grows.

Even in energy cells, to be able to explain the knee on the capacity fade curve, the internal resistance should increase by hundreds of percent which is only possible when cells are cycled at a very high temperature. However, in different experiments in literature, we see that the capacity fade curve can have a knee even when the cell is cycled at the standard temperature.

Positive feedback loops of cell degradation can also explain why capacity fade accelerates when the cell degrades.

In general, the fact that the rise in cell internal resistance can contribute to the observed cell capacity fade reminds me that Cell data mining, analysis, and modelling are greatly complicated by factors that are not essential to cell electrochemistry.


[1] Analysis of the effect of resistance increase on the capacity fade of Li-ion batteries