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I know that the potentials on the supercapacitor electrodes will attract opposite charges in the electrolyte thereby forming a double layer. This double layer acts as an insulator to prevent current flow. However, usually when an electrolyte connects two electrodes current can flow. Imagine a battery terminal connected to an iron nail connected to salt water connected to a copper wire connected to the other battery terminal. The iron nail and copper wire have potentials due to the battery, but current still flows through them. No insulating double layer was formed. So what special thing about supercapacitors causes the insulating double layer to form?

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in (EDLCs) energy storage is dominated by electrostatic charge diffusion and accumulation at the interface of the electrode and electrolyte which would could be seen as smaller capacitors forming on the edge of electrolyte and electrode surface, and the accumulation of those capacitors gives rise to what we call double layer

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