Lab Notes – Sarah Dawson (McMaster University)

Lab Notes is a series about researchers and the work they do. Each entry will focus on a different researcher with the goal of getting a birds-eye view of their area of expertise.

For this installment I spoke to Sarah Dawson, a PhD student at McMaster University in Hamilton Canada. Sarah studies phase transitions via computer simulation with applications to block copolymer patterning.  Ok, deep breath. Relax. There is a high probably that this doesn’t mean anything to you. Not just yet at least.

IMG_20170721_111545.jpg
Sarah, coffee, and Hamilton. Name a more iconic trio.

 

Phase transitions

I bet you know some examples of this. Water can transition between liquid, solid, and gas depending on what you do to it. Naturally, decreasing the temperature of water will send it from a gas (vapor) toward the solid phase (ice), likely passing though the liquid phase. The difference between these phases is the orientation of water molecules with respect to each other. When they are spread out and moving quickly, you have a gas. When they are packed tight, you will get ice.

IMG_20170725_125304
Interesting aside – typical ice is a crystal, meaning there is long-range order among the molecules, often packing in hexagonally. This is not the only way they can do it. 16 types of crystalline ice are known, and in fact, interstellar ice typically doesn’t even HAVE long-range order. This means the ice we know and love is actually quite rare in the universe…

So we know if we start with liquid water and want to end up with ice, the molecules will have to pack into the right structure. We have an initial state, and a final state, so the question is “How do we go from A to B?” Surely a volume of water, when cooled to a temperature such that it will become ice, doesn’t spontaneously become ice all over, at the exact same time. We expect that the transition will start somewhere and spread across the whole volume. Where this transition starts or “nucleates” and how it spreads is the aspect of the phase transition that Sarah is interested in.

This is only one example of phase transitions, but you find similar phenomenon all over. Sarah doesn’t study water specifically, but it is an intuitive example that illustrates the basic idea. As usual, the devil’s in the details, so we won’t dwell on specifics of the above example, but instead paint in broad strokes how Sarah does what she does.

Simulations

The scientific holy grail (in my highly biased, experimentalist opinion) is validating theory through experiment. You come up with an idea of how a phenomenon works (theory) and you test your theory in the real world with experiments. Ideally your experiment will be able to directly test your theory, like, if I do A to my sample, I expect it to do B. Then I go and get a sample, do A to it, and see if B happens. Sometimes you either can’t do A, or you can’t observe B. This is where simulation comes in. For example, we can’t experimentally “form galaxies” from different initial conditions, so many scientists who study galaxy formation use computer simulations.

Imagine you had an infinitely powerful, ridiculously fast Super-Duper ComputerTM. You could write a program that follows each atom of your system, calculates is motion, how it interacts with other atoms, its energy – everything about it – as well as all these details for every other atom in the system. In a litre of water, this would mean tracking ##### atoms (### *[H2O] = ###*[3 atoms] = #####). These atoms are very small, very dense and move fairly quickly, so you would want to evaluate the position, energy, etc. of these guys quite often. If you let them go for even one second, you would expect one atom to run into an incredible number of neighbors, so we need to evaluate all of our atoms on the order of femto seconds. Provided you could do this, Sarah would be out of a job.

Fortunately for her, computers are simply nowhere close to being able to do calculations like this for anything but the smallest systems and the shortest time scales. Most systems are simply too large and too slow to make this sort of simulation computationally possible, so Sarah has to be clever. Scientists like Sarah need to find a way to simplify the simulation. They need to sweep as many details under the rug as they can. However, sweep too many, and you won’t be left with a physically sensible simulation. So what techniques are available to simplify this system?

Statistical Mechanics

Ok, put on your Super-Duper Microscope-GlassesTM. These babies let you see on the atomic scale. Now make sure your sample has a uniform temperature throughout and take a look. Check out all those atoms. Check out all the bumping and grinding between those molecules. You can actually see all the collisions and see the relative speeds of molecules. From this you can calculate the energy of all the molecules. Move your focus to a different area of your sample. How does this look compared to the first spot? It looks pretty much the same. A few molecules are moving faster, a few slower, but on average they’re all about the same. Move focus again. It looks the same as the first spot. Maaan, maybe these Super-Duper Microscope-GlassesTM weren’t worth it after all…

Ok, the point here is the specific details of individual molecules might not be the most important thing here.

This is the fundamental idea behind Statistical Mechanics. We admit that there are too many things to keep track in our system, so we say “all these molecules are individuals and have their own properties, but on average they behave like this.” And after all, what we want to know is what the whole sample is doing, not each individual molecule.

This results in a trade-off though. Without getting into the nitty gritty, when we average over large numbers of molecules, we can say a good deal about what’s going on in general in the system, but we lose the ability to know exactly what each molecule is doing. This means we can’t say with certainty exactly what the system is up to, but instead we have to talk about its average properties, and how likely it is to fluctuate around this average.

Now the last step is thinking about what this means with respect to a phase transition. With our understanding of statistical mechanics, if our sample is in one state, we understand this really means on average, the molecules in the system have the required properties to be in that state. But that doesn’t mean they all are. We realize that the natural fluctuations in the system result in small regions “transitioning” into the other state, then fluctuating back into the original state. Statistical mechanics allows us to predict how often these fluctuations happen. If they happen at a high enough rate, then it becomes quite likely that a big enough region of the sample will transition before it reverts back to its original state. If regions of the new state emerge faster than they take to disappear, you are going to end up with the new phase spreading. THIS is a phase transition. Sarah tries to predict how likely these transitions are to occur depending on the sample properties like temperature, pressure, interfaces etc.

Ok, so I said Sarah thinks about “block copoloymer patterning” then I told you to not worry about it, that we would get to it. Well here we go!

Block copolymers and the shapes they make

A polymer is a chain of repeating molecular units. For our purposes, imagine they are simple very very small spaghetti noodles. Plastics and rubbers and elastics are made up of polymers. Think of these materials as big messy, tangled bunches of spaghetti noodles. As you manipulate your material, as well as through thermal fluctuations, these noodles naturally shift around and worm past each other, but just like a blob of spaghetti, if you grab and pull on one noodle quickly, all the noodles follow. So despite a blob of rubber appearing solid, the molecules it is made from actually have some small mobility within the bulk.

Now, not all of these polymer spaghetti noodles are simply one molecular unit repeated. Some of them are made of different units along the chain. These are called block copolymers because they have different “blocks” of polymers.

IMG_20170725_125755
Top: a tangle of spaghetti. Wait, no, it’s a bunch of polystyrene molecules. This is what your disposable coffee cup is made of. You should really consider a reusable one though. Bottom: an imaginary diblock copolymer. Diblock because it is made of two blocks – a polystyrene block, and a “different” block.

While the A block and the B block may be fused, often times these blocks would rather lie next to blocks of the same type. This means A blocks will want to line up with A blocks and B blocks will want to line up with B blocks. Typically polymers are dense enough and the the chains (or noodles) move slow enough that there is very little polymer rearrangement in the sample. That’s why rubbers and plastics appear solid. However, you can heat these up, or dissolve these materials to give the polymers a chance to flow and rearrange.

Now, if you could unfuse the A and B, you  could imagine that they would want to “phase separate”, or, you would imagine the A’s would drift to one side leaving the B’s alone with the other B’s.  However, that’s not the world we live in. An A is stuck to a B and that’s that. This results in a frustrated system (that’s actually a technical term, I’m not being cute), and as a rule of thumb, when nature becomes frustrated, you often get cool results.

IMG_20170725_130141
Randomly ordered diblocks and rearrange into different “phases”. These phases may repeat throughout the bulk of a large sample.

I’ve drawn a couple phases diblocks can take on. The important thing to notice is the A’s attempt to line up with A’s and B’s try to line up with B’s. Depending on the relative lengths, sizes, etc. of these blocks, the polymer can be found in a wide variety of states.

So finally, we arrive at the crux of what Sarah studies. Basically, though statistical mechanics and simulation, Sarah wants to be able to predict under what conditions diblock copolymers will transition from a random mess of spaghetti noodles into ordered states. She also wants to be able to predict what states these polymers will be found in.

What’s it good for?

C’mon man. Don’t give me that “what’s it good for” stuff. Isn’t that cool enough?

Fine. I have something ready for this.

You know computer chips? They’re really hard to make. They require layers and layers of micropatterened materials, and usually this is done via lithography, masks and etching . However, these processes are very difficult, can be expensive, and we are kind of at the limit of how small we can make them.

Enter copolymer patterning.

Make a copolymer of different blocks, have them orient themselves in a way you want, the selectively dissolve on of the blocks. You’ll be left with a tiny, micropatterned device, and the beauty is that nature kind of did it for you.

This could represent a great revolution in the production of computers. It could let us reduce the size and cost of many computer parts, allowing us to put them in way more things.

…and I know you’re just dying to have more computers in more things…

 

 

Thanks for reading! Questions? Comments? Want to talk to Sarah? Leave me a comment below!

fortais.


Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s