Perfluorononane is a fluorocarbon with a density of 1.8 g/mL and a melting point of -16⁰ C.
According to this paper it has a vapor pressure of about 0.7 kPa at 15⁰ C, so in regions with low altitude at the northern latitudes of Mars where ice just below the surface is expected, perfluorononane should be mostly solid and when liquid it would barely evaporate away into the atmosphere.

As an example, a small bowl-shaped crater with a depth of 20 m could contain a 14 m deep perfluorononane lake that would have a pressure of about 1 atm at the floor of the crater.
To use as least as possible of the costly substance, an iceberg, that at its bottom would have more or less the same curvature as the bowl-shaped crater, could float on it, with much of its mass below the surface.
The amount of the iceberg above the liquid surface could be adjusted such that between the floor of the crater and the bottom of the iceberg there would be enough space to house a settlement, while the space between the sides of the iceberg and the sides of the crater would make entrances from the surface possible.

Some of the advantages of such a settlement opposed to one in the open air at the surface of Mars would be:

  • Water (ice) at hand in huge quantities !
    The centre of the ice ceiling could have a dome shape that would allow liquid water to float inside it on the heavier fluorocarbon.

  • Fluorocarbons have good thermal insulation properties and high emissivities, meaning thermal radiation from waste heat of the settlement would be radiated back. That would make it possible to maintain an ambient temperature just below the freezing point of water, opposed to the far below -60° C on the surface at the latitudes mentioned before.

  • the ambient pressure of the liquid would be 1 atm., so no need for spacesuits to go from one building to another, maybe even no diving equipment for this particular fluorocarbon !

  • No need for special building material that should protect against micrometeorites and UV radiation.

  • The buildings would not have to be made airtight at the surface on which they stand because of the equal pressures of the air inside and the ambient liquid.

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    $\begingroup$ related: Is it possible to colonize planetoids by using perfluorocarbon lakes? (I like the imagery of walking on the ceiling) and the following answers contain some potentially related links: 1, 2 $\endgroup$ – uhoh Oct 11 '20 at 19:10
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    $\begingroup$ I'm pretty sure this particular idea is less practical than simply building an air-filled settlement with lots of regolith or ice on the outsides of buildings (for insulation and radiation shielding). Regolith and ice already exist in nigh-infinite quantities on Mars, whereas you'd need to synthesis huge amounts of perfluorononane (for the example given, I think you'd need over 2 million litres of it). $\endgroup$ – Pitto Oct 12 '20 at 8:11
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    $\begingroup$ @Cornelisinspace What I'm saying is that this whole idea is impractical. If you want a settlement "in the open air", you can get a similar effect by enclosing a large volume in a dome and filling that with breathable air. The dome would protect against UV and act as a greenhouse, and meteorites would be a minor problem as even Mars' thin atmosphere would burn up most of them (on Earth, meteors burn up in the mesosphere, which is even thinner than Mars' atmosphere at the surface). $\endgroup$ – Pitto Oct 12 '20 at 10:09
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    $\begingroup$ Am I correct that you're proposing people live in the liquid (presumably hyperoxygenated) fluorocarbon? That would be a very bad idea. And if you're proposing the fluoro is trapping an air "bubble", then the other answers explain why that is not practical (either). $\endgroup$ – Carl Witthoft Oct 12 '20 at 12:28
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    $\begingroup$ BTW, the "iceberg" will not be a convex-bottomed thing. That's not how pressure laws work. $\endgroup$ – Carl Witthoft Oct 12 '20 at 12:29

Since this question doesn't have an actual answer yet, I guess I'll take a crack at it. The challenges of a settlement in liquid perfluorononane on Mars would be:

  • The difficulty of getting perfluorononane on Mars. There are many proposals for using local resources to produce other things, like rocket fuel and oxygen, but absolutely nothing for perfluorononane. I haven't been able to find any information on perfluorononane synthesis, but I would guess that it's more complex than producing something like oxygen, since it's a larger molecule (at the very least, you'd need to mine for fluorine-containing minerals). And you can forget about importing it from Earth: sending anything from Earth to Mars is difficult enough already, you don't want to make your task harder by importing things you don't need.
  • Perfluorononane being an irritant to the skin, eyes and respiratory tract. Doesn't sound like something you'd want to be breathing in (note that the PFCs proposed for liquid breathing are perfluorohexane and perfluorooctane).
  • Since it has a greater density than water, it would offer even more resistance to movement than water. Mars settlers would need to waste a lot of energy just moving around.
  • There being much more practical ways of doing the same things. An air-filled dome can give you a greenhouse effect and UV protection without forcing you to swim around in a dense liquid, and Mars' atmosphere would protect the dome from micrometeorites. PFCs have been proposed for terraforming Mars, this is true, but this involves spreading gaseous PFCs over the planet, not using liquid PFCs to warm up just a small settlement.

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