Science, cinema, and Sci-Fi-inspired materials

Scientific inspiration and creativity has many sources. As a professor vis-à-vis ’teacher’ educating undergraduates in engineering (specifically materials science), one always seeks ways to pique the students’ interest by whatever means necessary. I’ve always found that drawing examples from movies and film serves as an effective attention-grabbing exercise.

For example (potential spoilers ahead if you’ve never seen the films):

• Would Arnold Schwarzenegger’s T-800 Terminator — which is made of titanium alloy — really melt in the vat of molten steel at the end of Terminator 2: Judgement Day (1991)? (Note 1)
• How strong would the vampire Edward Cullen’s forearms have to be to resist the impact of a van to save Bella Swan in Twilight (2008)? (Note 2)

These serve as nice discussion points, typically illustrated by some ‘engineering’ equations and math to produce some rough numbers. The point is to get the students ‘noticing’ science and engineering concepts in the world, be it physical or fictional.

Caution should be taken, however, as the creativity flexibility of fictional worlds leads to a lot of, umm, ‘poor’ science in movies. See, for example, the prevalent use of ‘unobtanium’ — a rare or fictional material with ideal properties — used as a plot device in Avatar (2009) and lamp-shaded in The Core (2003). (Note 3)

Typically, sci-fi stories require some element of ‘futuristic’ science – ships that travel faster than light (e.g., Star Wars’ Millennium Falcon), sources of near-unlimited power (e.g., Star Trek’s dilithium crystals), and, of course, high-performance materials (e.g., Game of Throne’s Valyrian steel). There is a surplus of creativity in the world of fiction – particularly if you need a material-based deus ex machina.

The recent (and ever expanding) Marvel Cinematic Universe (MCU) provides a wealth of such examples…

Superheros need supermaterials

Exotic materials play a unique role in superhero lore, particularly when feats of extreme strength, toughness, and resilience are necessary — i.e., extreme mechanics.

Comic aficionados may refer to the adamantium claws of Wolverine, or the vibranium shield of Captain America (from Wakanda, of course). The defining quality of adamantium is its practical indestructibility. For vibranium, absorbing sound waves and kinetic energy makes this metal stronger. Such properties are quite useful when fending off supervillains, but difficult to produce in practice.

Watching The Avengers (2012), I was first introduced to the Tesseract. In the film, the Asgardian Loki wields the Tesseract — a powerful energy source of unknown potential — leading a Chitauri army to subjugate Earth (luckily, the Avengers assembled and put a stop to such treachery!)

It turned out (watching subsequent MCU films) that the Tesseract is a crystalline cube-shaped containment vessel for the Space Stone, one of the six Infinity Stones that predate the universe and possess unlimited energy. To harness the power of an Infinity Stone, the hypercube itself must be made of an extreme strong material!

In the upcoming Avengers film (Avengers: Infinity War), the main antagonist, Thanos, seeks all of the Infinity Stones for a gauntlet that will allow him to bend reality to his will. In the recently released trailer, Thanos is depicted single-handedly crushing the Tesseract with little effort.

Clearly, Thanos’ strength must be formidable.

Being a bit of a nerd (common amongst engineering professors), I was also aware that a tesseract is, in fact, a geometric shape that is a four-dimensional analogue of a cube — a tesseract is to a cube as a cube is to the square. Another name for such a polytope is a hypercube. These 4D geometries are difficult to imagine in our 3D world, but a hypercube is typically depicted as a cube-within-a-cube (as in the picture).

My own research focuses on the mechanical characterization of emerging nanomaterials, such as graphene and carbon nanotubes (CNTs). Using simulation methods, I can also (attempt to) construct materials that currently do not exist (as long as the chemistry is somewhat possible from a modeling perspective). Inspiration from cinema was merely awaiting a key ‘Eureka!’ moment.

Watching Thanos destroy a previously indestructible material, combined with my experience with high-strength carbon materials and the geometry of a hypercube… sparked an idea.

Thinking inside the box

OK, so an all-carbon hypercube. Let’s piece this thing together at the molecular scale.

The interior cube is based on an interesting molecule known as cubane. Cubane is simply a small cube with eight carbon atoms at the vertices. Since carbon atoms typically don’t like to bond at 90-degree angles, it is a relatively high-energy molecule, but it can be synthesized, typically as C₈H₈. Due to its unique geometry, it is a relatively ‘cool’ molecule. Now, how can we construct the exterior cube structure?

I have previously worked on carbyne, or linear carbon. Essentially, while carbon atoms typically ’like’ four balanced bonds (as in diamond and even cubane), they have options: single, double, and even triple bonds (as well as aromatic for those keeping track). The different bond hybridizations is what makes carbon one of the more interesting elements for developing a vast assortment of materials. Back to carbyne, if you happen to line up carbon atoms in a chain configuration, they form alternating single and triple bonds in a row. This satisfies the bond requirement, and results in a linear structure. Extend this structure indefinitely, and you get carbyne (whether we can synthesise large amounts of carbyne in practice is still a matter of debate).

Thus, I used two-carbon carbyne groups to connect the interior cubane to exterior vertices via diagonal links, and then larger four-carbon carbyne groups to connect the vertices of the exterior cube and form the edges.

Presto – an all carbon hypercube!

When I initially modeled the structure, I made sure all the angles were 90-degrees. However, that is not the structure I ultimately attained.

As mentioned, carbon atoms do not like to be connected at 90-degrees. The angles between diamond carbons in a tetrahedral configuration is about 110-degrees. For the cubane, the molecule is tightly bonded, and the carbons are rigid in an orthogonal arrangement. However, the carbyne edges are more flexible – they can bend slightly. As a result, when the structure was relaxed, the angles at each vertex deviated slightly from 90-degrees. The end result is a hypercube with slightly curved edges.

Due to the carbyne links, I labeled the structure a hypercubyne, which I believe is the first proposed all-carbon tesseract molecule!

Modeling

Once the model hypercubyne molecule was constructed, I had to run some simulations to assess its physical stability and mechanical strength. This was done using full atomistic molecular dynamics, which effectively tracks the atomistic bonding, energies, and motions amongst individual atoms. No problem. (Note 4)

Stability can be judged by atom energies — a high-energy state is bad, and the structure is likely to be unstable. It turns out that the hypercubyne is in a relatively high-energy state (compared to more common carbon materials such as diamond or graphite). The high energies are due to the angles imposed by the cube geometry. This stability issue is potentially alleviated by the Space Stone in the comic universe, as the relatively large atomistic energy from the distorted configurations can be relaxed in higher dimensions. Our Earth-based technology is limited.

Next, to compute the strength, a simple compression test is performed. As in a compression test of concrete, the molecule is squeezed until the maximum force is observed. The force and displacement of the molecule are recorded and plotted (as in the figure below).

A maximum force of 10.6 nN is achieved.

That is about the weight of 1/10,000^th of a grain of sand.

That is not a lot of force at all.

Or is it?

Strength of Thanos

Let us presume that the strength of a nanocomponent can be expressed at the macroscale — the creators of the Tesseract, after all, have access to multidimensional laboratories and methods. We therefore assume the Tesseract is constructed from a hierarchical assembly of hypercubynes, without any loss of strength. The ultimate strength is then simple to calculate. If each hypercubyne has a face with an area on the order of 64 Ų, and the Tesseract (based on the images and movie scenes) has dimensions of (approximately) a 6” cube (15 cm per side), then the total force necessary to crush it would be approximately 42,000 tons! This would (roughly) be the force Thanos would have to apply to crush the Tesseract.

The average measured male grip can be conservatively approximated on the order of 50 kg. It would thus take more than the combined grip strength of the entire population of Boston ( 673,184) to crush the Tesseract. Thanos grip is 750,000 times greater than the average man!

Weightlifting experts estimate that an average male can lift approximately 155 pounds without training. If overall strength is proportional, that would mean Thanos could deadlift a weight of about 120 million pounds. That is roughly the weight of the Titanic (52,310 tons).

Let us say (conservatively) that Tony Stark is a strong male, with an above average grip strength of 200 kg (four times average). His Iron Man suit only enhances his strength by a factor of 85, resulting in a total gripping force of a mere 17,000 kg. It would take over two thousand (!) Mark 46 Iron Man suits to work in unison to crush the Tesseract. Yikes!

We finally note this is the minimum strength of Thanos, seen to destroy the Tesseract with ease.

The Avengers will have a very hard time defeating him in the upcoming film. Perhaps not all Avengers will survive…

Real-world implications

Clearly, the prediction of the strength of Thanos is intended to be entertaining. As a thought-experiment, it provides an interesting limit for the theoretical strength of upscaled novel nanomaterials. However, the methods applied are rigorous and scientifically sound. What can we learn from such exotic materials? To start with, it was demonstrated that atoms of high energy indicate likely locations of potential instability, for both thermal and mechanical behavior. This could potentially guide the development of de novo material systems.

Perhaps, in the near future, we will be able to unlock similar methods, and sci-fi-inspired materials will lead to our own version of  ’marvel’ materials, from fiction to reality. Until then, the next time you find yourself reading comics, you can say you’re simply performing thorough literature review…

Notes:

1. The melting point of steel is (about) 1400 °C, whereas the melting point of titanium is (about) 1700 °C. Of course, it depends on the alloy… which is the discussion point in class.
2. A rough back-of-the-envelope calculation assuming Edward’s forearm size, mass and speed of van puts the minimum strength of a vampire at roughly 1 GPa. Out of known materials with such strength as a minimum, one potential candidate is diamond – thus explaining why vampires sparkle in the sunlight!
3. The Core is typically considered on of the least scientifically accurate movies of all time. Spotting the scientific inaccuracy is a fun game to play (just Google, for example, “bad science in film” for numerous articles and examples).
4. Simulations were implemented using the open source molecular dynamics (MD) software package LAMMPS (http://lammps.sandia.gov/). The ReaxFF force field was utilized to model carbon geometries to be as accurate as possible (as described by Chenoweth et al., ReaxFF Reactive Force Field for Molecular Dynamics Simulations of Hydrocarbon Oxidation. The Journal of Physical Chemistry A, 2008. 112(5): p. 1040-1053). Standard minimization and relaxation techniques were used. For full simulation details, please contact s.cranford@northeastern.edu.

Post by Steven W. Cranford, Northeastern University.