I took apart a dead electronic cigarette and found the internal 140mAh lithium cell was completely flat so I decided to open it to see if it would explode in flames or do something else that was equally exciting.
Inside the outer aluminium tube was a tight scroll with four layers. A copper tape with a grey coating on both sides, a shiny silvery tape (aluminium?) with a similar coating and two plastic dielectric films to separate them. The electrical connection points were taken from the mid point of the metal tapes and passed through a chunky rubber grommet.
Although there was a strong aromatic smell the inside was completely dry. I tore a bit off the end of each metal tape and submerged them in water, hoping for a violent chemical reaction, but the lithium must be bound into a stable form in the grey coating as nothing happened.
The inside of the cell is actually surprisingly simple. Just the two bits of coated metal tape and the insulators rolled into a tight scroll secured with a bit of Sellotape!. The tapes were about 100mm (4") long and very thin. I'm sure the science is quite complex though.
Perhaps the lack of reactivity was down to the cell being completely discharged.