A couple of days ago Jordan Giesige, who runs the informational youtube channel 'The limiting factor', released an ambitious video about Lithium-ion battery chemistry. The target audience: interested people with no background in chemistry. That video goes as far in depth as is possible within the length of that video.
My background is physics, I am active on physics.stackexchange, answering questions.
Eager to learn more I started looking for additional information. It appears there is little to no information at the level I am looking for. That is not surprising, of course, it is a rather specialized subject.
The following is an overview of how I currently understand the chemistry and electrochemistry of Lithium-ion batteries. My request is to correct me if you notice a misconception.
Rather than using the words 'anode' and 'cathode' I will simplify and I will use the names 'the graphite' and 'the cobalt' generically. That is, I'm aware there are other chemistries, such as iron phosphate chemistry, and that the cobalt is used in the form of a cobalt oxide; I'm using the name 'cobalt' generically to refer that aspect/side of the chemistry, whatever the actual implementation.
In the uncharged state there is a large population of lithium at the cobalt side, and the cobalt is in a particular oxidation state.
The electrolyte is an organic fluid, with an additive that readily forms a complex with lithium ions. That complex readily dissolves in the organic fluid. The manufacturing process introduces a population of lithium ions in the electrolyte.
(The first charging cycle (which happens at the factory), triggers an initial chemical process; that initial process is outside the scope of this question.)
When a standard charging cycle starts the following happens:
Electrons are being withdrawn from the cobalt side and are being delivered to the graphite side.
The electron depletion at the cobalt side facilitates a change in oxidation state of the Cobalt. This change in oxidation state drives release of lithium ions into the electrolyte. At the graphite side lithium ions enter the graphite structure, and obtain an electron from the graphite, from there on residing in the graphite in an intercalated state.
The electrolyte is designed to present a high energy barrier to dissolving of negative ions. Because of that energy barrier the probability of an electron migrating from the cobalt side to the graphite side is low.
In the charged state the graphite is slightly electron enriched, the cobalt side slightly electron depleted.
As current start flowing the available electrons are attracted by the cobalt, and the cobalt changes oxidation state. The now negatively charged cobalt oxide causes lithium ions to go out of solution, joining the cobalt.
At the graphite side electrons are withdrawn, and as a consequence the graphite is withdrawing electrons from the intercalated lithium atoms. Lithium ions go out of intercalation, and dissolve in the electrolyte.
What I don't know is whether it is the case that on both sides the process of electron transfer contributes to the overall voltage of the battery cell.
It could also be, I don't know, that the maintenance of the discharge current is all due to one side, with the other side actually presenting a bit of a negative contribution.
If it is the case that one side presents a negative contribution: I don't know which side that might be.
It could be, I don't know enough about electrochemistry to guess, that during discharge the chemical process of the graphite robbing the Lithium's outer electron releases the energy that is driving the overall process.
Hence the title of this question:
The overall chemistry is like a bucket brigade, on uneven terrain. I'm interested to know which stages in the process are driving force, and which stages are being driven.
This new edit is a comment, I write it here because comment space is (for good reasons) small. This is not a request to expand the answer further. This is feedback on how the answer has helped me.
Independent of the details of the chemistry at the graphite side and at the cobalt side: if at one side more Lithium ions would be entering the electrolyte than at the other end would be leaving the electrolyte the electrolyte would become positively charged. Becoming positively charged would come at an energy cost, so that is not going to happen; something else will happen, whatever it takes that keeps the net charge of the electrolyte close to neutral.
I am aware that the direction in which a chemical reaction proceeds is also sensitive to the concentration of the reactants, and the smaller the difference in electrochemical potential the larger the contribution of sensitivity to concentration of reactants.
To my understanding: when the net reaction consists of a cascade of sub-steps then it isn't necessarily meaningful to try and attribute a property of 'being the driver of the overall reaction'.
To my understanding: since the amount of electrolyte is quite limited the rates of Lithium ions entering/leaving the electrolyte are stronly coupled, and as a consequence the rates of the reactions at the graphite side and at the cobalt side are strongly coupled.