# Sublimation and Phases.

Q:
why does some substance sublime at room temperature? What does air pressure got to do with it?
- Anonymous
Singapore
A:

Good question!  As you may know, sublimation is the process of a solid becoming a gas without being a liquid in between.  A common example of this is dry ice where solid carbon dioxide becomes gaseous at room temperature. Have a look at the phase diagram for CO2, courtesy of Wikimedia Commons. At atmospheric pressure (p~1 bar) and room temperature (T~295 K) the CO2 is in a gaseous state. If you raised p to a few atmospheres (e.g. 10 bar) you can see that warming the CO2 would take it through the liquid on the way to the gas. Other materials (e.g. water) have phase diagrams that look pretty much like this. For water, if you lower p to about 1/160 of atmospheric pressure, it will go straight from solid to gas.

It turns out that for each solid, at low enough p it will go straight to the gas, but at higher p will go through the liquid in between.  At low pressure p, raising temperature T takes the material directly from solid to gas. The pressure where that behavior changes turns out to be a lot different for different materials, so at atmospheric p some behave one way, some the other.

Unfortunately here we get a little long-winded. It's easiest to understand this via a little thermodynamics. The stable state at any temperature T and pressure p is the one that makes the free energy smallest. The "free energy" is G= H-ST, where H=U+pV, called the enthalpy, depends on energy (U)  p and volume (V), and S is the entropy.    (See via Wikipedia for more on this.)

Here's the key point: S is a measure of how many states the particles can wander around in. It's much bigger for a gas than for a liquid or solid. It's somewhat bigger for a jumbled-up liquid than for an ordered solid. H is smallest for the solid, in which the molecules fall into compact, low-energy states, and biggest for the gas. (Experts- forget He3.)

At low pressure, particles have lots of room to roam in the gas so joining the gas greatly increases their S. So the gas become the stable state even at pretty low T. At low enough T the low-H solid is more stable than the higher-H liquid. Therefore at low enough p, the liquid state just isn't stable- the material goes straight between gas and solid.

OK, so why is that triple-point pressure, needed to make the liquid stable, so different for different materials? This depends on details of the liquid-solid difference. In most case, the volumes of these phases are close, so let's just think about their energy differences. If the molecules or atoms can lose almost as much U by clustering near each other in a liquid as by lining up in a solid, then the higher-S liquid is stable at fairly low T. If a lot of the energy loss can't be reached without the molecules actually lining up into a solid, then the liquid only becomes stable at higher T.  At low p, that T is already too high- the solid has turned to gas.

Mark and Mike W.

(published on 05/16/2013)

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