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Technology
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Electrolytic capacitors use the chemistry to make a very high dielectric allowing the plates to get very close and increase the capacitance and decrease the size.
A cell in a battery is a capacitor then converts the charge on the plates into chemical energy and vice versa allowing much more energy storage and a flat operating range as the plates charge is replenished by the chemical reaction.
This article doesn't go into details but it sounds like the breakthrough is a much better dialectic then storing energy in a chemical reaction.
Good comment, but check your uses of "then".
Yeah should have that. Mornings are hard.