Seems like the chemical process has been a solved equation for a while. Rather than directly splitting the molecule, they use high pressure and heat to incorporate a hydrogen atom into it, converting it into Methane which can then be broken down with high heat to carbon and hydrogen.
From the page https://chemistry.stackexchange.com/questions/915/how-can-ca...
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React carbon-dioxide with hydrogen in the Sabatier (https://en.wikipedia.org/wiki/Sabatier_reaction) process to get methane. 400 °C, high pressure and Nickel catalyst needed. The process is slightly exothermic so it can keep going on its own:
CO2+4H2→CH4+2H2O
This process have been proposed to generate fuel on Mars, and used on the ISS to process exhaled carbon-dioxide.
Split the resulting water (use electrolysis or some other thermochemical cycle) take the oxygen, bring the hydrogen back to Step 1:
2H2O→2H2+O2
Electricity for this may come off solar panels.
Methane decomposes at high temperatures. The process goes to completion around 1200°C. Collect the condensed carbon, bring the hydrogen back to step 1.
CH4→C+2H2
This process is proposed as an emissions free alternative to produce hydrogen from natural gas. Heat may come from concentrated solar light.
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The missing ingredients are excess CO2 from the atmosphere and a machine system to do the full process with, and of course the math about economies of scale regarding how fast a machine that uses this method combined with the powder in the article can actually strip carbon from CO2 in the atmosphere.
It likely would neither be cheap nor fast, but since it uses nickle as a catalyst at least it is not fancy rarefied expensive hard to find materials, just more an issue of getting all of the parts together and making the whole machine run as efficiently and effectively as possible.
Also, if the methane is generated from CO2, then burning it is nearly carbon neutral, so in places where fossil fuels are the ideal energy source it would allow us to use Green energy to make transportable low-carbon fossil fuels for them to use.