why do different electric cars (batteries really) have such different charging speed curves when going from low to high battery capacity?

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Audi E-tron seems to have more constant speed ~150 kW through the entire range 10% to 80%, whereas Tesla Model 3 has higher speed (close to 250 kW) between 10 and 20, and then gradually reduce to ~50 kW at 80% capacity. What determines this behaviour (I suppose from a electrochemical point of view)?

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Part of it is determined by the battery charging controller logic. Lithium ion batteries are typically charged at a constant current then it switches over to constant voltage. A battery cell has 2 sides, a positive side, the cathode and a negative side, the anode. It’s made by two different metals soaked in an electrolyte which is a liquid that has electrons floating in it typically in the form of salts. Salt is made of a negatively charged ion and a positively charged ion, e.g. table salt is sodium chloride the sodium is positively charged and the chloride is negatively charged. This is how electrons actually move inside the battery.

When metal rusts in water it is called a redox reaction; the iron loses an electron and is replaced by an oxygen atom from the water, it is oxidized, the water gains an electron lowering meaning it’s reduced. You start with Fe (iron) and H2O and end up with Fe2O3 (rust) and H2 (hydrogen gas). That chemical reaction required an electron to hitch a ride through the water into a water molecule and trade places with an oxygen atom.

We harness that reaction in a battery by finding 2 dissimilar metals (or carbon) or on opposite sides of the periodic table, one has an electron it’s wanting to give up and one has an electron it wants to gain. The electron is passed through the electrolyte but it causes an imbalance which is resolved by sending a flow of electrons from the negative terminal through the car’s electronics powering it, then to the positive terminal of the battery.

When an empty battery is being charged, all the electrons are on one side of the battery are forced to the other side by applying an electrical charge to the battery terminals. This can be done rapidly at first since it’s like filling an empty parking lot. The electrons flowing through the electrolyte have no problem finding an empty spot, as the battery’s charge starts to increase the spots fill up and charging gets slower and slower. The chemical reaction that takes place during charging and discharging of the battery causes it to heat up; this is the main limiting factor behind charging speed of a battery as heat is what kills it and battery charging controllers will limit the charge rate in order to keep the battery from overheating.

There are lots of battery technologies, lots of battery manufacturers, different battery wiring, different charge controller electronics, different cooling/warming strategy/technology, etc.

Even within the exact same battery technology, there can be slightly different electrolites between different manufacturers.

Due to different wiring and cell types some batteries are actually 360V, some are 450V, this is among those who claim 400V, as obviously some manufacturers use 800V batteries.

Tesla for example is warming the batteries when going to a super charger. It will pull 7kw for a while which doesn’t even go to the battery, but it it used to bring the battery at the optimal temperature for fast charging.