The glass transition of polymers, Tg has always been a little difficult to talk about because it seems to violate so much basic physical chemistry. For instance, the measured Tg depends on the rate of cooling. And sometimes the measuring technique. And then there is the whole whole physical aging thing, where a glassy polymer, in which the polymer chains can't move [*], shrinks over time, with the amount of shrinkage also depending on the initial cooling rate. As I've said many time before, I seen 3 settings where I thought arguing scientists would start throw fists, and two of them involved the glass transition.
So imagine my surprise when I saw this wonderful illustration:Source
All of the macroscopic observations of the glass transition in one simple diagram. Let me give you a rundown. Temperature is on the x-axis, and volume or another thermodynamic quantity is on the y-axis. Glass transitions are usually thought of as occurring during cooling, so the plot is best viewed right to left. Starting in the upper right, the cooling polymer initially follows the thick, solid line - the "equilibrium liquid". At some point the temperature drops below the melting temperature, Tm and the liquid polymer is now supercooled. The slope of the volume vs. temperature between in these two zones is the same, but at some point, the kinetics can't keep up anymore with the thermodynamics and so that slope starts to lessen forming the "Out of equilibrium glass". The spot where the slope bends is the infamous Tg.
You can continue to cool the polymer further along this new slope until you run out of cooling power or you can hold it at a temperature below Tg and observe something even more amazing. The glassy polymer, which we already know is out equilibrium, slowly but surely progresses towards equilibrium - the extrapolated conditions of the initial cooling step. While chains in a glassy polymer cannot move past each other, they can all move en masse to occupy a smaller volume. This is known as physical aging (a term that I personally consider to be the worst term in all of polymer science, and there is plenty of competition.)
For a polymer that has undergone physical aging, it is possible to describe it with a new temperature, Tf, the fictive temperature, as shown in the illustration. Chains with the same fictive temperatures all have the same thermodynamic state, one that is equal to a polymer with Tg = Tf. Lastly, in the lower left corner is the Kauzmann temperature, Tk which is when the glass polymer has the same thermodynamic state as the crystalline one. A controversial idea to say the least and one that has never been physically observed.
To quickly comment on the energy landscapes on the right hand side of the image, the polymer initially cools in state (a). If it could, it would go to state (c) and crystallize, but it ends up in state (b), where it slowly works back towards state (a). At a cool enough temperature, the two valleys of states (a) and (c) have the same minimum value.
So there you have it. The glass transition clearly presented. While I've seen figures before that have various bits and pieces of this information, I've never seen it all come together in such a fashion before. This doesn't eliminate any of the controversies, but it does make it clearer to see where they lie and what significance they have.
[*] To paraphrase Galileo, "But they do move!"