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1. SEIs form on both the anode and cathode, but usually are more of a research concern for the anode (lithium-intercalated graphite is highly reactive). They form an interphase between the graphite / silicon of the anode and the liquid electrolyte, and have both beneficial and adverse consequences. On the downside, they slow down ion diffusion into and out of the anode, and get thicker over time (quickly early on, increasingly slowly later on). But the upside is quite a fortunate coincidence (since the formation of SEIs was not intended in early li-ion work): they protect the electrode from further decomposition. Hence forming an SEI is important, and its durability and how effectively it resists further degradation is critical. The work here is to form an SEI with as desirable properties as possible in as cost-effective of a manner as possible.
2. Voltage directly corresponds to capacity, by P = I * V. The other part of the equation is amp hours, which corresponds directly to how many lithium ions are mobile between the anode and cathode (voltage is the change in electric potential between the anode and cathode).
3. Li-ion batteries work by moving lithium ions intercalated (inserted into) the cathode across a membrane to intercalate into the anode when charging, and the reverse when discharging. Intercalation is a diffusion problem, both in terms of how much you can ultimately insert / extract, and the rate at which you can do so. And temperature strongly influences diffusion rates. The hotter you can run your cells, the faster you can diffuse ions in / out (current Teslas usually supercharge in the 50s celsius, and discharge in the 30s, under ideal conditions, according to ScanMyTesla data). Lithium ions can only intercalate into cold cells slowly, or not at all (which one may experience as a lack of regen or slow supercharger speeds when the battery is cold). If Tesla can run cells hotter when charging without adversely affecting battery life, they'll be able to charge (significantly) faster, and to (slightly) higher capacities.
So deliberate rust?
