When I was a young student (in a third world country, mind you), around Y2K, we learned about capacitors in pF, nF and uF ranges, that's pico-, nano- and micro- Farads, i.e. 0.000000000001 F, 0.000000001 F and 0.000001 F. All these are useful and used in practically all existing electronics. They are also very small amounts of Farads. Consequently, one whole Farad was considered ginormous, an almost mythically high capacity. I remember one student bragging that he actually saw a 1 F capacitor, and it was huge - larger than a brick. It was something of a Holy Grail to have one (though they would be useless for all "normal" things we did with electronics).
About a decade and a half later, advances in material science have made "supercapacitors" (those larger than 1F) extremely common and cheap. Still, because of what I was taught, I consider supercapacitors like the 9th world wonder.
I won't go into their construction, you can read about supercapacitor details on Wikipedia, I'll just make a small note on the difference between capacitors and batteries: though both store energy, batteries do it through chemistry: a reaction has to happen both to absorb and to release energy, so typically, battery capacity depends on the volume of the chemicals inside; capacitors store energy in their geometry: typically the larger the surface area of the capacitor's innards, the larger the capacity. Modern supercapacitors achieve huge surface areas within reasonable volumes by using a very fine powder, usually graphite or its more exotic cousins like carbon nanotubes. There are other significant differences, like in energy density (even supercapacitors have very small energy densities compared to the low-end batteries), charge / discharge curves (capacitors can be both charged and discharged much faster, almost instantaneously) and in charge cycles and durability (the "old style" solid state capacitors can last almost forever, the fancy new supercapacitors around 10 years, with hundreds of thousands of charge cycles).
When I found supercaps for cheap on Aliexpress, it was like finding a new shiny toy. So I got myself a 10-pack, and started playing with them. No photos here, all of them look alike, go click on some of the links.
What to do with a supercap?
I have a dream: to power something useful using a supercap and a solar cell. I currently have both, so my first test is to simply test charging it. I'll write more about this topic, so I'll just say that today is a cloudy and rainy day, and it took about an hour to charge the above 1.5 F 5.5 V supercap using this solar cell to around 4 V.
I've measured that this supercap charged to 5 V can power an ordinary red LED (through an 1 kOhm resistor) for about 2 hours. I will repeat this experiment with a Joule thief, where I expect it to last much longer.
My next goal is to find out how long would it power an Arduino, and to do that efficiently I need some more circuitry (a voltage booster). I will report what I find here when I get it.
What I will need next, and I currently have no experience with these kinds of circuits, is some kind of a battery charge controller or something similar, which would basically allow the supercap to charge, then when it is charged to about 5V, allow it to be discharged by an Arduino (or whatever else) until a certain lower voltage (say, 1V). In effect, I need something which would have a hysteresis in charging and discharging the supercap, so the Arduino can run occasionally, do some work, and go back to sleep / charging cycle. If you know of something like it (preferably as an ready-made PCB module), let me know!
Edit: I've started writing about electronics on a dedicated blog, so this one remains clear for other stuff.