[another_someone]

Maybe this should be classed under crackpot ideas - or maybe there is already a product out there that does something exactly like this, but it was an idea that occurred to me, so I thought I'd ask whether it could, and maybe already does, work?

Could one manufacture by lithography a surface that when it has a voltage applied to it would create an electrical filed that has the same surface shape as a crystal of a given material (e.g. a crystal of water ice, or of CO₂ dry ice)?

The idea being that if (for instance) you pass humid air over the electrically activated surface, the shape of the electric charge on the surface could be such as to attract the oxygen and hydrogen to particular localities on the surface, and so align the water molecules to begin forming an ice crystal.  The effect of this would both be to dehumidify the air, but also as the ice crystal forms, it will release generate heat through the latent heat of fusion, and this heat could be carried away through the substrate on which the ice is formed, and so cool the air from which the ice was extracted.  Thus the mechanism can be used both for removing water from the air, and as a heat pump to cool the air.

The same idea could be used to remove CO₂ from the air as to remove water from the air - you just need a different electrical shape on the surface, one that would match a crystal of CO₂ rather than a crystal of water ice.

[Bored chemist]

As soon as you have a layer of ice on the surface the molecules of water vapour in the air above it cannot tell what the surface underneath is.
So they will only stick to it and form more ice crystals if it's cold enough.
If you have the surface that cold then it pretty much doesn't matter what it's like- you will get ice on it.
I don't think you gain anything this way compared to a bigger plate of stuff that's less cold, but still below the dew point of the air. You will cool the air and remove water from it. If you let that water run away down the drain then you don't need to expend more energy freezing it.
A wet surface will proably trap dust better too which might help.

[another_someone]

As soon as you have a layer of ice on the surface the molecules of water vapour in the air above it cannot tell what the surface underneath is.
So they will only stick to it and form more ice crystals if it's cold enough.
If you have the surface that cold then it pretty much doesn't matter what it's like- you will get ice on it.
I don't think you gain anything this way compared to a bigger plate of stuff that's less cold, but still below the dew point of the air. You will cool the air and remove water from it. If you let that water run away down the drain then you don't need to expend more energy freezing it.
A wet surface will proably trap dust better too which might help.

I was aware that the thickness of the crystal would have to be limited, and the crystals regularly removed from the surface (possible simply by switching of the voltage momentarily, and letting the crystal drop off).

You could possibly increase the size of the crystal grown by using a substrate that is not totally flat, but contains spikes or V cuts, so that the crystal could be grown on 2 or more sides from a corner rather than just expecting it to grow down from a single surface of the crystal.

On the other hand, if you have a crystal of ice already there, would that not to some extent provide a seed for more ice, even when it is already some way from the surface?

The reason for not simply using cooling is two fold.

Firstly, the present means of using coolers for dehumidifiers is either by using condensers and expansion chambers, which is large and complex, or using the Peltier effect, which is inefficient (although I agree that newer cooling technologies are being developed, and these may provide better alternatives).

The second issue, and this is an intrinsic difference, is that using fractional condensation will effect a range of substances, and is sometime difficult to target one particular constituant of a mixture unless it is the constituent with the highest melting/boiling point (i.e. if you have air containing water and CO₂, you cannot freeze the CO₂ in a single step without also freezing the water - while the above could target a CO₂ crystal while leaving the water untouched).