II. Not really a Part 2, but more the second leg of my writing it. Thanks to the misfortunes of traveling in the northern United States during the winter, one flight was cancelled and another rebooked. It brings me back to a core concept that I have been forced to learned over the last two years – unique properties are nice, but where is the pain point? What need are you fixing? I will hold off on that topic for the time being and just reflect that if we were able to grow fluorinated polymer chains as a brush-like structure on aircraft wings, the threats of ice would be a thing of the past… That is worthy of a short write-up, or longer one, in the future, but I digress. Back to the nanoscale.
What I am really talking about here are nano-structured materials, or nanomaterials for short. These are materials that are so finely divided that they exhibit properties that are intermediate between the macroscale behavior we are accustomed to, and true molecular-scale behavior. They may show unique properties related to changes in electrical, optical, mechanical, and thermal phenomena (some examples to follow), or may be even more exotic, such as quantum confinement, where the size of a particle is so small that we are altering the configuration and interactions of its atoms and electrons. This can give rise to some bizarre and interesting properties, generally centered around the way that they interact with electromagnetic fields. More on that later.
One size dependent phenomena that is relatively straightforward, and which I conveniently have a graphic prepared for, is mechanical behavior. A great example is carbon fiber, which consists of semi-crystallized graphite that is partially aligned along the direction of the fiber. Graphite comes in the form of plates because it crystallizes in two dimensions, like a sheet. This is an inherent property of carbon that is near and dear to my heart, so I will leave it here for the moment and suffice it to say that in a different world, your carbon fiber iPhone case (if it wasn’t fake) could have been a diamond, which is the exact same carbon but just organized in different ways. The ability to make different structures from the same elements is known as allotropicity¸ which is a word I might have just made up. The different structures are called allotropes.
Back to carbon fiber. The stiffness of the carbon fiber is very much tied into the alignment of these graphite crystals, as well as the percentage of the carbon that’d has formed into graphite crystals. If the fiber is wide, you can have a very broad distribution in crystal orientations, so the stiffness will be more or less independent of direction. As you decrease the diameter of the fiber, the crystals can only orient in a fixed direction, along the axis of the fiber. As a result, the “stiff” parts are all pointing the same direction and the stiffness increases. This effect is only significant for fiber diameters near the size of the crystals.
A related phenomenon is strength. In a brittle material, the strength is related to the size of the biggest defect. You can think of it as a weakest link in a chain analogy. Due to various factors, most materials will have a characteristic size of the largest defect, which ends up determining the strength of the brittle material. This strength is much lower than the theoretical strength of the “perfect” material, which depends on the molecular bonds themselves. If you reduce the size of the material below this critical defect size, then the flaw size must decrease (or else the material wouldn’t be continuous). Because of this reduction in flaw size, the strength of the material increases. Eventually, you get to a point where the flaws are so small that’d they don’t matter anymore and you can have a material with strength limited only by the strength of the chemical bonds themselves (there is an interesting phenomena where the defects don't actually need to be completely gone; they just stop influencing the mechanical behavior when they are smaller than a length scale called the Griffith criterion, which is a feature of many bio-materials and something strived for with bio-mimicry- true perfection is often a waste of time).
This is near perfection – there is no other way to increase the strength of the material in this case, short of a change in crystal structure, reinforcement, or some other type of modification! This is the source of all the excitement about carbon nanotubes and graphene, and is at the heart of why they were being called the ultimate material. People were even calling this the missing link needed to build a space elevator. I’m not sure if that superfluous business ended up helping or hurting the field of CNT, as it turns out a limit is now big you can make the nanotubes while controlling their structure to the necessary degree (although some strides in this field are finally coming around), but again I digress. A final point worth making is that the carbon nanotube is the natural end of the line for the carbon fiber story – if you reduce the diameter of the carbon fiber until it is a single ring of carbon atoms, then you have a single walled carbon nanotube. Neat, right?
The second benefit of a nanoscale material is an increase in surface area relative to volume. That may sound like a mouthful, but it is an easy enough concept. Say that we have a cube in front of us. It is a nice square, a happy square, a healthy square – one meter wide, one meter deep, and one meter high. It could replace one of these lovely chairs I am sitting on at the Chicago airport. As an engineer and a physicist, I very quickly consider the volume of this cube, which is simply 1 cubic meter (to get volume, we just multiply the length by the width by the height). Note that if I were a true physicist, I would naturally assume that this cube is a sphere and that it is equivalent that all the other sphere-like cubic chairs all around me, regardless of the people sitting on it, but that is an old trope and I’m above it. Back to the cube-like chair. The volume is 1 cubic meter, so the next question is the surface area. This is important because that is the part of the chair that interacts with the outside world. If the mechanical properties aren’t significantly changed, no one would care if the cube is solid or hollow, or filled with a delicious liquid, so long as the outside surfaces all remain the same. The surface of the cube is easy to define – it is just 6 squares. The area of each of the squares is 1 square meter, so the total surface area of the cube is 6 square meters. The ratio of the surface area and volume, an important part of any discussion on nanomaterials, is then 6, with units of reciprocal meters (square meters divided by cubic meters is 1/meters, also expressible as m-1 or reciprocal meters, depending on your personal style).
Now let’s say we are bored with this simple cube and we decide to pull out our authentic Japanese katana that we somehow snuck through the TSA security checkpoint (I’m still at the airport) and we slice it up into smaller cubes. Let’s go ahead and say that each of the smaller cubes is half the size of the original cube, so the length, width, and height are now 0.5 meters. It is easy to visualize that there will be 8 cubes in this case. Using the same approach, we find that the volume is each is 0.125 cubic meters (or 1/8 of a cubic meter – get it?), so the total volume obviously hasn’t changed. The surface area of each cube is 6*0.5*0.5 square meters, which gives 1.5 square meters. So the total surface area of the newly sliced cubes is 12 square meters, which is twice as high as the original cube. We have doubled the surface area and kept the volume constant, so the surface area to volume ratio is doubled to 12 reciprocal meters.
It should be obvious where I am going here. If we go slicing again and reduce each of those cubes to half of their original size, we now have 64 total cubes, each 1/4 of a meter across, with a total volume of 1 cubic meter and a surface area of 24 square meters. If we do it again, our surface area has increased to 48 square meters, then again to 96. By the time we get each cube to about 1 inch across, we have a staggering 32,768 cubes on our handle with the exact same volume that we started with, but 32 times the surface area. Once the cubes are 1 millimeter across, we will have about 1 billion cubes with a total surface area of 6,144 square meters (1,024 times the original). To put that into context, that means we could take the cubes, which started off about the size of a grown man in the fetal position (which I may curl into soon if this flight doesn’t eventually start making some progress toward TAKING OFF), and we can more than cover an entire football field (American, of course) with it. Morbidity associated with my suggestion of spreading a grown man across a football field in 1 mm slices aside (sorry for that visual), that should be a pretty impressive figure.
That should get the point across, but since I am still waiting for my flight, I wanted to see how ridiculous I could make it. Unfortunately, it didn’t quite get as extreme as I hoped. My goal was to see how small the slices would have to be to cover the entire surface of the Earth. Alas, our katana would have to be sharp enough to get to the sub-atomic scale, which is even beyond the nanoscale analogy and therefore outside of our little foray. We wouldn't want to be accused of silliness, after all. It does turn out that we could cover the entire city of Houston with nanometer-scale cubes (of about 3.7 nm across), which will have to do for now. Fortunately, the flight is about to board, so I will have to continue at a later time. I will leave with that visual – a grown man curled in the fetal position, if reduced to nanometer-sized cubes, can completely cover the city of Houston. Science is awesome.