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Wednesday, April 17, 2024

The Physics of Materials at Minus 80 Degrees Celsius

It's a hopeful sign. Pfizer announced that its Covid-19 vaccine could be 90 percent effective. That could really help us get past this darned pandemic. But there's a catch. The vaccine is based on mRNA (messenger RNA)—this reads the DNA in the nucleus of a cell and transports the instructions to the cytoplasm where proteins are produced. The problem is that the mRNA is normally short lived. It either interacts with oxygen or folds onto itself and then doesn't do its job. So if you want to use it in a vaccine, you need to make the mRNA last longer. That means you have to keep it cold. Really cold. The standard storage temperature for these types of vaccines is –80 degrees Celsius. Yup. So, that means we have to talk about cold stuff. Let's do it.

How Cold is –80 Degrees Celsius?

Maybe you aren't too familiar with temperature units in Celsius—I hear you. Honestly, there's nothing really wrong with the Fahrenheit unit of temperature (except that I can never remember how to spell it). The advantage of the Celsius unit is that it's easier to calibrate. The original method was to use the freezing point of water as 0°C and the boiling point of water as 100°C. However, the value of 1°C was later redefined to be determined from the Boltzman constant—a fundamental constant that gives a relationship between the average kinetic energy of particles and the temperature of a system.

If you know two corresponding temperature values in both °C and °F, you can set up an equation that converts from Celsius to Fahrenheit. You can also use your basic algebraic skills to change this into an equation that takes the temperature in Fahrenheit and converts to Celsius. Here are those two equations.

So, if you put in a temperature of –80°C you get a temperature of –112°F. Yeah, that's pretty cold. But here is my favorite temperature: minus 40. There are two great things about –40. First, you don't have to specify if it's in Celsius or Fahrenheit since –40°C = –40°F (go ahead and check it for yourself). The second awesome thing about –40 is that it's the temperature on the surface of Hoth (from Star Wars V: The Empire Strikes Back). OK, maybe not everyone agrees about the temperature on Hoth, but this is the value used on the Star Wars episode of MythBusters so I'm going to stick with it.

How Do You Get Stuff Down to –80 Degrees Celsius?

The simplest way to get something cold is to put it in thermal contact with another object that's even colder. But you might not be able to find something colder than –80°C (although there is one option that I will get to in a little bit). That means you have to use a different cooling method. Probably the most common refrigeration method is the same one your refrigerator uses. You can understand how this works with a very simple demo using a rubber band—so go get one.

OK, you have your rubber band (hopefully). Take it and stretch it with your hands, and keep it stretched. Now touch the stretched rubber band to your lip (which is very sensitive to temperature changes). You should be able to feel the rubber band is warmer than room temperature. Don't let the rubber band relax, just keep it stretched for a little while (30 seconds at least). It should cool off back down to room temperature. The next part is the best. Finally let that rubber band return to its normal length. Touch it back to your lip and you can feel the rubber band is now cold.

So, here's what happened. Stretching the rubber band makes it warm up. If you just let it return back to its original length right away, nothing interesting happens. However, by letting the stretched rubber band cool down to room temperature, it still decreases in temperature when it returns to its relaxed state—but now it ends up colder than room temperature.

This is exactly what a refrigerator does—except not with rubber bands. Instead it uses some type of liquid gas called a refrigerant (there are many different chemicals you could use here). You could start with the refrigerant as a gas and compress it until it becomes a liquid. This compression makes the refrigerant warm up. The next step is to let the compressed refrigerant cool off on the outside of the refrigerator. Now you can put the refrigerant inside the fridge and let it expand back into a gas, and it cools off—much colder than room temperature. That's how you keep your food cold.

But what's different about the –80 degree freezer for vaccine storage? It turns out that it's pretty much impossible to get the inside temperature of the freezer down to –80°C with your normal refrigerant. Instead, you need TWO sets of refrigerants. It's sort of like a freezer inside of a freezer. The outer freezer is pretty much like the one in your kitchen. The inner freezer uses a different refrigerant (maybe isopropyl alcohol) so that when it's compressed, it can cool off inside of the normal freezer. But having two compressors is what makes these more expensive. Oh, do you want to see a picture?

This is the freezer in the biochemistry lab at Southeastern Louisiana University. Now you know what it looks like.

Dry Ice

I told you there was something you might be able to find that was at –80°C, and it's dry ice—solid carbon dioxide. To make dry ice, you start with carbon dioxide gas. This carbon dioxide gas is then cooled and compressed into liquid carbon dioxide. Then, when the liquid carbon dioxide is removed from pressure, it turns into a gas again. But this phase transition also decreases the temperature and gets it cold enough to freeze at –80°C to become a solid.

But solid carbon dioxide does some weird stuff at atmospheric pressure (a pressure of 1 atm)—when it warms up, it goes straight from a solid to a gas without first becoming a liquid. This is called sublimation. I mean, that's weird. Since it doesn't turn into a liquid, it's not wet. Yes, that's where the name "dry ice" comes from.

Can H2O do this too? Yup. We like to think of the freezing and melting point of water as being at some set temperature—but it's not. It also depends on the pressure. So, it helps to make a plot of temperature vs. pressure for different chemicals. We call this a phase diagram. Here is what that would look like for H2O.

There's a lot in that diagram, so let me point out some important things. Take a look at that horizontal dotted line. That is the line that corresponds to atmospheric pressure (that's the pressure we live with on the surface of the Earth). If you look at the graph on the left side along the dotted line, this would be cold stuff and the water would be a solid (we call that ice). At point A, the temperature is 0°C and this is the temperature of a phase transition from solid to liquid. Point B is at 100°C and that's the phase transition from liquid to gas. But what about point C? That's called the triple point. If you reduce the pressure you can have solid, liquid, and gas phases all at the same time. For water, this is at a temperature of 0.1°C with a pressure of 0.006 atmospheres. It's pretty cool—check it out in this video.

You can see how carbon dioxide is different by looking at the phase diagram. It looks something like this.

If you look at the dotted line for a pressure of 1 atmosphere, it's now below the triple point. That means that a solid will make a phase change straight into a gas. That's the dry ice thing. But if you increase the pressure up to about 5 atmospheres, you CAN get solid carbon dioxide to make a phase transition into the liquid phase. As a bonus, I am going to show you this liquid carbon dioxide.

Here's how you can do it. Put dry ice into a plastic container that is sealed at both ends. I'm going to use a clear plastic drinking straw. As the dry ice warms up, it changes into a gas as dry ice likes to do. However, this carbon dioxide gas has nowhere to go, and this increases the pressure inside of the straw. Eventually the pressure gets so high that liquid carbon dioxide is formed. But ultimately the pressure gets too high and the straw explodes. It's not a big explosion—it's just a straw. Here, check it out.

I just think this is really cool. Usually when you have liquid carbon dioxide, it's in a metal pressure tank and you can't actually see it. Well, at least I had never seen it before I did this experiment.

But What About the Covid-19 Vaccine?

Yes, this is the logistical problem that's facing us right now. It's going to be quite difficult to ship and then store the vaccine so that it can be distributed. This is going to take a combination of the ultra cold freezers and storage in dry ice. But either way, it seems as though we really need a vaccine to get past this pandemic. Like any hero, it needs a side kick which, in this case, is super cold refrigeration.

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