Ok, but, if I've understood correctly , at the end of article they suggest that the CO2 captured while the battery was in recharging state is released when the same battery is in use. In other words the battery doesn't capture permanently the CO2 as the gas stream method you just mentioned: the battery isn't like a black hole for CO2, it simply "breath" releasing the CO2 when it's discharging. So in what way that should be a solution for the global warming ? If they want capture the CO2 in discharging phase, they need to store a big number of coin size batteries in an industrial facility that needs batteries for some reason, plus you are using electricity that likely was produced burning fossil combustibles to remove CO2 from air. So no laptop or cellphone removing CO2 from our atmosphere.
The best answer right now for CO2 disposal is to compress it to 1500 psi and inject into a saline aquifer. The gas has to be really pure to do that and that kind of device could do that purification.
