Resizing Matter: Part 1

Happy Pi Day!

In my most recent blog post, I started to consider how chemistry might change if an object was resized magically (Engorgio and Reducio spells in Harry Potter) or technologically (Marvel’s Ant-Man). My plan is to explore this issue in more detail in a multi-part series.

Let’s start with a simple case, a cube of table salt (sodium chloride). The chemical formula of table salt is NaCl and the solids form cubic crystals. The figures above and below are from the Atoms In Motion website and give you a sense of the lengthscale.

If I (the wizard Hufflepuff Hippo) cast Engorgio on a cube of table salt, I could make it magically grow in size. The question is HOW the cube grows in size. First let’s take an atom-level view. NaCl is an example of an ionic solid, i.e., positive ions (cations) and negative ions (anions) are arranged in a 3-dimensional lattice (see above). Note that the Na(+) ions are smaller in size than the Cl(–) ions.

Possibility #1. The amount of matter increases to match the increase in size. The sizes of the ions themselves do not change.

The advantage of this approach is that there is no change to the chemical behavior of table salt. The strength of the ionic bonds due to the attraction between the cations and anions does not change. If I doubled the number of ions, I would double its mass – but other than being more massive, it would still behave in the same way I would expect table salt to behave. The large cube does not behave differently than the small cube. How might this spell work? If you’re near the sea, Na(+) and Cl(–) ions in the salt water can be summoned and added to the crystal lattice of the cube. This is likely easier than creating new matter from scratch – the problem of Gamp’s Law.

In this scenario, the object changes in inertia, but otherwise functions in exactly the same way. This is typically how we imagine the effect of an Engorgio spell. When a spider increases in size, to Ron Weasley’s horror, it still functions the same way a spider would. We see similar mechanics in Ant-Man when he increases or decreases in size. Any behavioral difference is due to the difference in inertial mass. But in the case of a spider or Ant-Man, it’s much harder to picture how you might add existing matter or create new matter to match the features of the spider or Ant-Man. It was much easier to imagine this for the structurally simpler NaCl cube with its ordered arrangement of ions in a lattice.

Possibility #2. The size of matter increases locally to the object being resized. In NaCl, this means that the size of the individual ions increases with Engorgio.

This is what we typically have in mind when we imagine a spider or Ant-Man increasing in size. But now there’s a problem. If atom or ion sizes increase, this affects the strength of chemical bonds.

Glossing over the details for how an atom would increase in size, let’s make the following initial assumptions. The mass increases proportionally as the size of all particles that make up the atom (protons, neutrons, electrons) increase. The charges stay the same since as far as we know, charges are treated as labels unrelated to size. Thus, the relative charges of protons and electrons remain as +1 and –1. Consequently, an enlarged Na(+) and Cl(–) will have the same charges but the ionic bonds would lengthen as the sizes increase. According to Coulomb’s Law, this would weaken the ionic bonds since the bond strength is inversely proportional to the bond length. (Technically, the force between a pair of ions is proportional to 1/r² while the potential energy is proportional to 1/r. The Madelung force in the lattice will also be a contributing factor.)

While there are many ions in our body, there aren’t many ionic compounds with a lattice structure. Hydroxyapatite in bone is the closest thing I can think of. So if you engorgio-ed yourself into a giant, you would have weaker bones relative to your increased inertial mass. Something to think about in case you thought it would make you stronger. You might cripple yourself very quickly instead.

It’s less clear how other interactions involving ions would play out. The solubility and transport of ions is also dependent on the attractive strength between an ion and (polar) water molecules, and how large the solvation shell orders itself around the ion. Other examples include metal ions that play a vital role in enzymes or porphyrins. Mg(2+) and Ca(2+) ions have numerous interactions with polar molecules and macromolecules, including the backbone of your DNA. I’ve also restricted the above discussion to a simple classical view of ionic bonds. More importantly, how would resizing impact covalent bonds and intermolecular interactions that govern the chemistry of life?

Resizing is a complicated matter (pun intended!) but we will explore several possibilities in subsequent blog posts. Stay tuned!

P.S. Pi features in Coulomb’s Law!