I know that the maximum charging voltage for lithium ion batteries is 4.2v. I also know that charging a lithium ion battery involves a constant current and constant voltage phase.
But what will happen if I continuously charge a lithium ion battery with a maximum of 4.0v at 100mA? Will it destroy the battery?
You will prolong the battery life. As per https://batteryuniversity.com/article/bu-808-how-to-prolong-lithium-based-batteries :
Most Li-ions charge to 4.20V/cell, and every reduction in peak charge voltage of 0.10V/cell is said to double the cycle life. For example, a lithium-ion cell charged to 4.20V/cell typically delivers 300–500 cycles. If charged to only 4.10V/cell, the life can be prolonged to 600–1,000 cycles; 4.0V/cell should deliver 1,200–2,000 and 3.90V/cell should provide 2,400–4,000 cycles.
Most EVs with LiIon batteries have less than 4.2V maximum charge voltage and recommend charging up to 80-90% of available capacity when possible. (Source: my ID.4 owners manual)
I also know that charging a lithium ion battery involves a constant current and constant voltage phase.
It usually does, but it's not necessary. That's the way commercial chargers work, to get the fastest charge while staying within the no-damage parameters.
One common regime that chargers use is to charge to 4.2v, then turn off until the voltage has fallen to 4.1v, then recharge to 4.2v.
For my money, 'providing enough charge over time' to keep the cell at 4.1v would be kinder if that charge was delivered steadily and the cell never exceeded 4.1v, than if it was provided in bursts and the cell cycled between 4.1v and the higher more damaging 4.2v. The first option is of course a continuous trickle charge.
However, I'm not a battery manufacturer, and I've yet to find data from any of them that discusses longevity under sub-maximum voltage trickle charge conditions. An immense amount of effort has been put into characterising rechargeable cells to get fastest charge rates and largest usable capacity (which, let's face it, is where the volume and the money is), and rather less into using them more gently.
To your specific charging conditions of 4v 100mA. If 100mA is less than the battery's max charge current, then your CI phase will be OK. Once the cell gets to 4v, the charging current will fall. I expect it would fall to essentially nothing.
I would risk keeping it on CV at 4v indefinitely, taking appropriate precautions to mitigate fire risk. You might be tempted to do the same. You will not find any reputable sources that will tell you this is OK. I will not be responsible for your cells if you do this, and find they degrade more quickly than you hoped.
It would be interesting for someone, perhaps you, to test a few cells with differing lower voltage trickle charge regimes and report the results, perhaps quarterly over a five or 10 year period. I've considered it, but am unlikely to get around to it.
Yes, charging a Li-Ion cell at constant voltage without ever terminating the charge will likely destroy the cell.
What will happen is that your battery will get (maybe slowly) to 4.0 V, and, if the voltage stays, the charging current will gradually decrease, and will decrease to zero. This will put the cell into overcharged state, even if the voltage was not at maximum for the cell's capacity.
Most common rationalization of overcharging process is that “the lithium builds up faster than it can dissipate. The result is that metallic lithium plates up on the anode. At the same time, the cathode becomes an oxidizing agent and loses stability”.
In other words, if the cell is subjected to CV and the current stops over time as it normally goes, ions of Lithium started to build up without the current forcing them to move. That's why the charging process must be stopped at some point. So it is not the voltage level (although overvoltage causes other bad effects), but the fact that current eventially stops, and Lithium build-up starts.
As result of electrolyte decomposition some gassing might occur resulting in bulged/bloated/swollen cell, and the cell typically looses 50-70% nominal capacity due to some irreversible changes in microstucture of electrode materials.
Bottom line - don't charge Li-Ion cells continuously.
For more scientific explanation, see this article in "Frontiers in Energy Research"
While CC and CV modes have their specific negative effects *) and one need to be careful, the OP asked specifically for charging in CC+CV mode, meaning, with a both CurrentLimit and a VoltageLimit. This is a different thing. It means watching both limits at the same time. This means that such a charger would reduce voltage or reduce current as the other value approaches the limit. This means, never exceeding the current limit, and never exceeding the voltage limit.
If voltage is measured properly at the cell **), there is no way the cell can reach overvoltage condition of >4.2V, even if trickle-charge is allowed near the end for a prolonged time.
If the battery is designed to be charged up to 4.2V, then trickle-charging it with diminishing current up to 4.0V means that the battery will be kept in an under-charged state.
According to https://batteryuniversity.com/learn/article/charging_lithium_ion_batteries charging up to 4.0V instead of 4.2V means storing 70-80% of the maximum charge a li-ion could hold if charged to its maximum.
Further trickle (i.e. 0.05C) charging (with cut off condition of 4.0V) would not hurt the battery, if voltage is not allowed to exceed 4.0V, because if it would hurt the battery, than it would mean that, by design, the battery is either not allowed to be charged above 4.0V, or is not allowed to be charged with charging current lower than some value, or both, and we precisely know both those sentences are false: max V is 4.2 and those batteries only have max-charging-current and no min-charging-current.
Be sure to also read "Overcharging Lithium-ion" & "Charging Non-cobalt-blended Li-ion" paragraphs from the above-mentioned article. Especially "non-cobalt" batteries mentioning li-ions with lower target voltage rating.
You may also find Charging li-ion cell using constant-voltage only helpful.
**) All traces, wires, connectors, etc have resitance. If you measure the voltage not directly at the cell, your measurement may read "4.19V" while it's "4.22V" few wires further at the battery. Be sure what exactly are you measuring and with what uncertainties.
*)
However, keep in mind that in both cases, "may" means it doesn't need to happen. Every voltage source has some finite max output current capability, every current source has some finite max voltage capability. If your CV voltage source has low max current output, trying to draw more than it can supply will simply overload the voltage source in some way and causing it to drop out of the CV mode and provide voltage lower than set. And similar for CC current source.
Of course if those sources are not designed for working in such conditions, it may damage them to some extent, but not the battery.
Of course a damaged voltage/current source may start misbehaving and may in turn damage the battery.
Of course you're doing it at your own risk. I did not advise you to do this.
I had to write this warnings in case some evil lawyers are reading this :)
