I’d think you’d want the VOCs to be captured by something, rather than floating around in the air where you could breathe them in. Combined with a HEPA filter in the air circulation system, this should be a good solution.
Absorption is usually not a one-way street, though: Surfaces absorb gasses when the concentration in the air is higher than that on the surface boundary, but often also release them back into the air otherwise (which is why you can e.g. smell cigarette smoke in clothes – if they only captured it, there would be nothing for you to smell).
The only difference are some materials like charcoal, which does permanently bind many substances (but as a result can also saturate).
No idea which kind lime and clay are (i.e. "absorb and permanently bind with limited capacity" or "act as a buffer both ways").
> Combined with a HEPA filter in the air circulation system
Actually not that many types of things will bind to the carbon permanently, mostly it's the affinity for such a wide variety of contaminants to the carbon, combined with the porosity of the carbon structure which can have a very impressive amount of surface area to come in contact with the fluid being filtered. Whether filtering air or water. It hangs onto contaminants tightly.
Because carbon is such an effective adsorbent for contaminants, the partitioning coefficient for contaminants to remain in the solvent being filtered is lowered quite dramatically compared to so many other kinds of affordable alternative filtration media.
Most times people do need to afford to discard the carbon eventually, but it doesn't even really absorb contaminants like it's supposed to unless it is activated carbon to a good degree.
Activation only means that is it porous enough to begin with so it has enough surface area to be effective, then it is heated with adequate air exchange to about 250 Celsius for as many hours as it takes for virtually all of the VOC's or moisture it may have accumulated to be baked out. Then sealed up tightly, otherwise it can sit around for ages and gradually become saturated passively with any contaminants or humidity admitted through leaks to the ambient environment.
Sometimes, you can reactivate almost indefinitely to keep reusing the same carbon, and it works with VOCs because by their volatile nature they are basically baked back out easily and virtually completely each time. Different amounts of time if using different temperatures though, if equipped.
The stronger the activation, the more tightly with higher capacity the carbon wants to absorb things it encounters that are dissimilar to the fluid being filtered.
I assume they absorb VOC until you tear down the chalk or clay plaster.
With clay the indoor problem is more about radioactivity, but it's best in terms of humidity control. Chalk creates an alkaline environment on the surface which makes it inhabitable for mold (however the wooden furniture you put in front of it can still get mold if the indoor air humidity is too high).
