 So for a pair of partially miscible solvents, if I have a solvent A and a solvent B that are miscible above some temperature that we call the consulate temperature and immiscible below that temperature in some concentrations, then the phase diagram looks like this, as we've talked about previously. For example, in a case like phenol with water, this consulate temperature is around 67 Celsius. Above 67 Celsius, I can mix phenol and water in any proportions I want. Below 67 Celsius, they'll phase separate into phenol-rich and or water-rich phase. That's very typical behavior for immiscible or partially miscible solvents, but it's not the only way these solvents can behave. And to understand that, let's think about what these two curves mean on the sides of this miscibility diagram. So let's say this is the case with phenol and water. So a mole fraction of phenol is increasing from zero to one. So we have pure phenol on this side, pure water on this side. The points on this curve are telling us how soluble one of these solvents is in the other. So for example, over here on the phenol-rich side, where I'm pure phenol or phenol with a little bit of water added to it, then what this tells me is at this temperature I can dissolve this much water into pure phenol. If I raise the temperature, I can dissolve more water. If I raise the temperature further, I can dissolve more water. Might be easier to see on this side. In the water-rich phase, nearly pure water, I can dissolve a mole fraction of a few percent of phenol. At this temperature, if I raise the temperature a little bit, I can dissolve a little bit more phenol. If I raise the temperature more, I can dissolve more phenol. And then once again, when I get to the consulate temperature of 67 Celsius, then I can dissolve an infinite amount of phenol into water or an infinite amount of water into phenol. So these diagrams are sometimes called solubility charts or miscibility diagrams in addition to a temperature composition phase diagram. But as I've said, the diagrams don't always look like this, because solubility doesn't always increase as we increase the temperature. That's the typical way that solubility behaves, but as you may know from doing experiments in the lab sometimes for some combinations of solutes and solvents, the solubility will decrease as I increase the temperature. And when that happens, we get a phase diagram that's qualitatively quite different. So let's consider a case and a specific case that behaves like this is triethylamine. So nitrogen with three ethyl groups attached to it, so triethylamine, I plot the mole fraction of triethylamine against temperature. I again get partially miscible solvents if I combine this with water. So this would be pure triethylamine. This would be pure water. In this case, what the phase diagram looks like is this. So the solubility of triethylamine in water, so over here I have again a water-rich solution. Over here I have a triethylamine-rich solution. If I take pure water and I add progressively more and more triethylamine to it, eventually I'll get to the point on this phase diagram that tells me I can't add any more triethylamine without phase separation, phase separation into a solution of this concentration and a solution of this concentration. That solubility, if I go from a low temperature up to a high temperature, that solubility is actually decreasing. I can put less triethylamine into water as I increase the temperature. Likewise over here, as I increase the temperature, I can put less and less water into a solution of triethylamine as I increase the temperature. This phase diagram is essentially upside down version of this phase diagram. So I have a single liquid phase that's fully miscible below this special temperature and only partially miscible above that temperature. And for triethylamine, that temperature, I'll look up the specific value, is 18 Celsius. So fully miscible below 18 Celsius, partially miscible above that value of 18 Celsius. We still call this a consulate temperature or a critical solution temperature, but since the qualitative behavior of these two cases is very different in cases like phenol and water, which is the more common case, we call it an upper consulate temperature because this consulate temperature represents the upper limit of when I can phase separate the two solvents. Here because it's at the lower boundary of this phase coexistence region, we call that a lower consulate temperature or a lower critical solution temperature. So same idea just whether it's an upper bound or a lower bound on the phase coexistence region. And it gets more complicated still. There are particular combinations of solvents that have both an upper and a lower consulate temperature. So I'll draw another phase diagram. This one is not too atypical for polymer blends. So again, a temperature composition diagram. Here I won't name any particular solvents, but you can find cases where there's a single liquid phase. But if I increase beyond an upper, sorry, a lower consulate temperature, I get phase separation between the two liquids or conversely, if I cool below this upper consulate temperature, I get phase separation into the two, an A-rich and a B-rich forms of the two solutions. So this would be a case where there's both an upper and a lower consulate temperature. This diagram is for the case where the lower consulate temperature is a higher value than the upper consulate temperature. And that's certainly one possibility, but there are solvents, pairs of solvents for which the opposite is true, for which the upper consulate temperature is above the lower consulate temperature. So this is an upper consulate temperature, this is a lower consulate temperature. And I will give you a specific example with some specific values for this case. The stereotypical sort of famous example of a system that has its upper consulate temperature above the lower consulate temperature is a solution formed by mixing nicotine and water. So again, we'll have a temperature composition diagram, this particular diagram, I'll plot the mole fraction of nicotine on this axis. So the upper consulate temperature on this diagram is 210 Celsius, the lower consulate temperature is 60 degrees Celsius. And remember, beneath the upper consulate temperature, I have phase separation. Above the lower consulate temperature, I have phase separation. And I'll try to draw this at least roughly to scale. If I'm at a temperature hotter than 60 Celsius, but below 210, and at compositions of roughly a 50-50 mixture of the two solvents, the two solvents are not missable. I can't mix nicotine and water in arbitrary concentrations between these two temperatures. But I can mix them at various concentrations, either a very water-rich solution, a very nicotine-rich solution, or at any composition I want, as long as the temperature is above 210 or below 60. You may have noticed that 210 is already above the boiling point of water. So this is a phase diagram that is true at high pressures. I have to compress the solution to pressures high enough that the boiling point of water is above 100 Celsius, well above 100 Celsius, so that I can actually observe this upper consulate temperature. But it's certainly interesting that this pair of solvents has both an upper and a lower consulate temperature, and they have arranged themselves such that there's this sort of island of the mims' ability. But they're fully missable both above that and below that. So liquid-liquid miscibility, liquid-liquid temperature composition diagrams show a wide range of different behaviors, but once you understand this idea of a consulate temperature and you can identify whether it's an upper or lower consulate temperature, it makes it easy to understand these diagrams.