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What really changes is the oxidation state of the materials in the electrodes. During charging, lithium atoms lose electrons (oxidation) on one side and gain them on the other (reduction), creating an electric potential difference. The battery itself continues to have the same chemical elements, but in different electronic configurations - that's why discharging reverses the process and the battery returns to its previous state.

Basically, while you're charging, lithium ions (or another material, depending on the type) move from one electrode to the other inside the battery, storing chemical energy. The composition itself doesn't change drastically - it's more the charge state of the compounds that shifts, like a rebalancing of the molecules. This process repeats hundreds of times, which is why batteries degrade: the electrode materials slowly wear down over time. What's your phone model? There are battery types that degrade faster than others.

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