When I first started researching what was already out there for carbon removal, I came across this paper published out of Rice University just last summer:
The lab of Rice chemist Andrew Barron found last year that carbon-60 molecules (aka buckyballs, discovered at Rice in the 1980s) gain the ability to sequester carbon dioxide when combined with a polymer known as polyethyleneimine (PEI).
Basically, they take carbon-60 molecules (buckyballs, a type of fullerene), superheat them in an environment absent of oxygen, and then cool them back down to room temperature. After that, they were able to get the buckyballs to passively absorb 12% of their mass in carbon dioxide.
The key part of this is that it's passive absorption at 25 degrees Celsius, or, room temperature. There's a huge energy output required to do the superheating, but no more energy is required after the pyrolyzing is completed.
Energy is at the heart of any efforts to remove carbon dioxide from the atmosphere. For obvious reasons, any process or product that removes CO2 will have to do so in a way that doesn't require more carbon emissions than it removes.
This technology isn't ready for commercial use yet, not by a long shot. But it's research into ideas like this that will lead to future innovations to remove CO2. Imagine if some ubiquitous product like a smartphone case had a built-in filter with these buckyballs that were passively filtering CO2 out of the air. Or if you could paint buildings with a paint that included this material. It might be difficult to see the path from hyper-specific scientific research papers to fully developed commercial product, but it is these sorts of discoveries that are going to be at the root of any technological solutions.