When asked to explain, the spokesman says things like "we use new physics". That alone peaked my bullshit detector.
Every battery tech I'm also aware of cannot handle high amperage charging without things like outgassing, battery seperation, heating effects, and explosions. Even the venerable NiFe battery has problems with high current charging.
But this startup has beat it? [Citation needed]
My concern is over using supercaps: their density is still very low compared to Li-ions on a volume basis.
Also, I noticed they are using a Samsung phone. Last time I used a supercap in a project, I had to build a complex circuit that compensates for exponential voltage drop but outputs constant voltage and amperage. I want to know how they got around that issue as well.
I would have believed it more if they used a MediaTek chip based phone. They could have hacked and modified those all they wanted.
Techcrhuch had some articles about them this year http://techcrunch.com/2014/04/07/storedots-bio-organic-batte...
That said, smartphones don't use these batteries, and anyone who tried to put a couple of amperes into a standard lithium polymer battery is going to have an amusing experience.
Minor correction: battery capacity is measured in ampere-hour, i.e. ampere * hour.
I feel like you've mixed up LiFePO4 and LiPo. LiFe has low charge rates, lower energy density, lower voltage, and higher cost compared to LiPo. For R/C aircraft, it's typically used only for the receiver and servos of the really large helis/planes, because its lower voltage is tolerated by the servos whereas a LiPo needs a regulator to step down to 5-6V for driving servos. I can't speak for expensive hand tools, but "everyone" in the R/C community uses LiPo.
There are specialist lipos used for RC planes/cars/boats that can handle 100C burst discharges but even those can't be charged at more than ~10-20C - and these cells have very high self-discharge and short cycle life, so they're quite unsuitable for mobile phones.
(Edit: Clarification)
Gassing (or smoke, not sure which) starts around 15 sec. Plenty of results for 'LiPo explosion', 'overcharge lipo', etc.
A LiPo fire is a chemical reaction, it cannot be extinguished by traditional fire extinguishers (i.e. smothering does not extinguish, it's creating its own fuel) -- you have to wait for the battery to burn out and then extinguish the remains on fire. Treat your batteries (and electronics with batteries in them) well, folks.
That's the only thing that will save you.