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Different types of protons have different properties though. Liquefied hydrogen has around a quarter of energy density compared to gasoline, so that's not really great.
It sounds like a hydrogen battery rather than just burning hydrogen as a fuel source. If I had to guess, the hydrogen positively charges the anode when it forms a hydrogen bond with TABQ, and the charge differential is what generates current.
Burning hydrogen is clean actually, you get get water as exhaust. The problem with hydrogen is that most of it isn't produced in a clean way right now. Although, it is possible to do so. Volatility is also an issue, not sure if making a hydrogen battery could address that or not.
Storing hydrogen is also very hard, the molecules are so small that they cavitate through any solid material trying to hold them. I've heard loose carbon fiber is good at holding hydrogen but I don't think they've figured out a carbon fuel cell yet.
This sidesteps the problem of cavitation by just breaking hydrogen away from the electrolyte instead of storing it as a pure fuel.
As far as I know carbon fiber is somewhat expensive to make too. That is a promising approach though. I imagine we'll see a combination of different battery approaches going forward optimized for different use cases. I do think we'll be seeing increasing amount of research going into this with electric vehicles and renewable energy becoming more common.