How not to cut cake

When my wife pointed out Francis Galton's method for cutting a cake to minimise the exposed surface and therefore improve its lifespan, I of course implemented it immediately. I hate stale cake. (I eat it anyway.)



Galton, Nature 75, pp. 173-173 (1906) doi:10.1038/075173c0

The basic principle is that you remove slices from across the middle of the cake, and then press the remaining pieces together so that there is no exposed surface to get stale.



There's an immediate drawback to this method: each progressive slice is taken from a smaller cake of a different shape, so it's hard to judge portions. It's also difficult to make even-sized pieces for multiple guests. (Galton's original publication was meant to maintain the lifespan of a cake that was only being eaten by two people.) The slices are at least neatly cuboid which solves the age-old problem of how to eat a wedge of something with a fork



The bigger problem is that this method is wholly counterproductive when applied to my wife's delicious coffee and walnut cake. It's simply not possible to produce sufficiently crisp parallel edges so that the different sides fit together and exclude the air. In fact, this method results in a greatly increased exposed surface area compared to just cutting out a wedge.



Galton's original method is applied to a Christmas cake, which has a firm texture that might be more conducive to clean edges, but I still think you're going to have difficulty getting a nice tight interface between the two exposed surfaces, even with his suggested rubber band.

Galton is known as the originator of eugenics, so perhaps it's unsurprising that this idea proves to be counterproductive. I'll stick to using the plastic cake cover.

Melting points and The French Connection

I was watching the classic 1970s crime film The French Connection recently (which is a masterpiece, by the way) and was surprised to see a bit of ordinary undergrad chemistry appear at about the half-way mark.

In lieu of the screencap that Netflix won't let me take, you'll have to load up your own copy and fast forward to the 52-minute mark.

The gang are having their chemist confirm the purity of the heroin shipment around which the whole movie revolves. He's watching for the temperature at which the compound melts - the higher, the purer, with completely pure "product" melting at its own specific melting point. I was really chuffed that the movie went to such lengths to get the technique right, which is just going to be a background detail to most viewers. It really adds to the verisimilitude.

 At the end of my undergraduate organic chemistry labs, we would do a similar procedure to show that we'd done a good job of making whatever compound we were supposed to be making. The hardware was a little different, but we were still tapping the compound into a little glass tube, heating it up, and watching for the temperature at which it melts.


Many a lab session ended with me squinting into these machines. A thermometer and a sample tube go in the top.

You might rightly wonder why impurities lower the temperature at which some chemical compound melts. The intuitive answer is that the molecules of the compound have to fit together like little lego bricks, and impurities get in the way of the molecules bonding (fitting) together, and therefore it melts more easily.

It's intuitive but it's wrong!

Actually, the bonding isn't weakened all that much by the presence of impurities. The real reason has to do with entropy. Understanding this from first principles involves a bit of thermodynamics, but I can cut to the chase a bit and introduce you to one of the neater ideas in physical chemistry.

A process in chemistry happens when the "free energy" G is lower after the process than before. So to melt, the liquid substance has to have a lower free energy, G, than the solid. G has two parts, the enthalpy H, which has to do with things like how strongly molecules are bonded together, and the entropy S, which is to do with the system's capacity for disorder. (Measured by the number of different ways we can arrange the molecules.)

G = H - T x S

The entropy S is multiplied by the temperature as you can see, so it has an additional property that its contribution to the free energy gets larger as the temperature increases.

For a process like melting, the enthalpy H has to increase. The compound is always going to be more stable locked into a neat little solid than with the molecules free to move. So this is a penalty against forming the liquid. (This is known as the enthalpy of fusion.)

However the entropy S will increase upon melting, because we can arrange the molecules in many more different ways in the liquid than in the solid. The entropy increase can be viewed as a sort of a discount on the enthalpy penalty, and because S is multiplied by the temperature, the total discount T x S is bigger at higher temperatures. Melting happens when you reach a sufficiently high temperature that entropy discount T x S is equal to the enthalpy penalty H.

So what happens when we add impurities? Well, the entropy S of the solid is a bit higher than before, because there are now even more different possible arrangements of molecules. However the entropy of the liquid is much higher than before. That means that the entropy increase associated with melting is larger, and therefore the discount we get from the entropy is bigger. Seeing as the enthalpy part H stays more or less the same, the temperature at which the entropy overbalances the enthalpy is lower.

Thinking about chemical processes in terms of thermodynamics isn't always intuitive, but it reveals a lot of subtleties that aren't immediately obvious. Kind of like a good movie.

Guillermo del Toro on getting ideas off the ground

In a recent discussion with game director Hideo Kojima (moderated by Geoff Keighley), the film director Guillermo del Toro offered the following regarding how he chooses projects:

I wish I could command the movies I want to make. The movie that gets made gets made because it's right at that time, and it doesn't matter. Anything else is completely haphazard. When people say why do you have six, seven things going at the same time, it's because one of them happens, not the seven, not the six. And I learned this the hard way. When you think about projects you think about something that came out in a dream. That's it. When you hear about it, and whether it happens or not, in between [those points] I work three, four, ten years on that thing. And sometimes, most of the time, they don't come through.

While del Toro is talking about films, I think this is good advice for anyone who's dependent upon outside support to get a project off the ground, such as scientific grants. You need to have enough ideas in progress that when the circumstances are right in terms of collaborations, funding, and the general mood of the research community, one of them can move along and give a finished result. As a corollary I'd argue that one of the things that distinguishes the really successful creative people is simply having enough ideas to be able to discard all but the best.

A second mechanism for Sn2

The S_N2 mechanism is a favourite of first-year undergraduate organic chemistry lectures. It's chunky and easy to understand, but there's a lot of subtlety in there, and it comes up all over the place. It's supposed to be well-understood (as first-year stuff it better be) but a collaboration of physicists at the University of Freiburg and Texas Tech has found another mechanism for it. (Check out the animations in the link - it makes what I'm about to prattle on about a lot clearer.)

What's S_N2? Suppose you have a molecule of methyl iodide, CH₃-I, but really you want a bromine atom, Br, in there instead of the iodine. Bromine and iodine are both in the same chemical group (the halogens) so it seems like a fair swap. You do this by shoving in some bromide anions (bromine atoms with a negative charge). The iodine that was originally in the molecule comes out as an iodide anion (which is just an iodine atom with a negative charge), balancing things out.

Br^- + CH₃-I --> Br-CH₃ + I^-

This process turns the CH₃ part of the molecule inside-out, like an umbrella. This mechanism makes a lot of sense, and explains a lot of things seen in experiment - with more complicated molecules, you can see the inverting process happening around that particular carbon atom. And of course there has to be room for the attacking nucleophile to approach - if you stick really big bulky things on that carbon, the nucleophile can't attack, and suddenly the reaction won't go.^[1]

Looking at S_N2 this way makes it easy to understand what's going on. However it always pays to check your assumptions rigorously, which is how the new mechanism was exposed. The researchers set up an idealised S_N2 reaction. They fired a beam of pure Br^- into a beam of pure CH₃-I molecules, so they know exactly how things are flying together. They monitored what direction and speed the iodide ions were coming out after the swap with in order to figure out what was happening.

In a minority of cases, rather than the bromide whalloping in one side and iodide flying out opposite (as you'd expect from the normal mechanism above), the bromide smacks into the methyl group from an angle. This sends the methyl iodide molecule spinning. The bromide can then snag the methyl part away, leaving an iodide ion. The substrate and products, and even inversion around the attacked carbon are the same (as you can see on the animation on the website).

It's a really neat idea, although the spinning action kind of depends on you having big, heavy atoms to swap in otherwise fairly light little molecules. And the new mechanism only becomes important when the collisions are happening with a lot of energy. It may seem pedantic, but exploring little oddities like this can explain odd behavior.

^[1]This kind of reaction is a nucleophilic substitution - the iodide and bromide are nucleophiles (they chase positive charges) and we're swapping one for the other. In this case, if you sit down and monitor how the reaction's speed changes with the concentration of methyl iodide or the amount of bromide, then you see that both matter - this suggests that both the attacking group and the substrate come together in one step to make the reaction go. We say that the process is bimolecular. That's where the odd name comes from - Subsitution_Nucleophilic2(Bimolecular).

Original paper. (Science)

Antoine Lavoisier and the Musee des Arts et Metiers

Antoine Lavoisier was one of the founders of chemistry. His work demonstrated the idea of "stoichiometry", that chemical compounds react in particular ratios. He's rightly enshrined as a hero of chemistry, and you can see his equipment in the excellent Musee des Arts et Metiers in Paris:



It's a great museum of science, with all sorts of interesting hardware from different eras.



It also had some historical technological figures of a different type during my visit, as part of a temporary exhibition.



As for Lavoisier, he was executed during the Terror, but is remembered with justifiable  pride by his countrymen. Look closely, and you can find his name on the Eiffel Tower.

Coulomb explosions in alkali metals

The reaction of alkali metals with water is one of the all-time classic chemistry demonstrations: a pellet of sodium or potassium is dropped onto the surface of water, where it reacts to produce hydrogen gas and a lot of heat. The heat ignites the hydrogen and melts the metal into a little ball which then jumps around on top of the water trailing flames and steam.



The basic chemistry is a reduction-oxidation reaction, that is, a reaction involving exchange of electric charges. Water isn't just a bunch of neutral water molecules H₂O. It also contains fragments in the form of positively charged hydrogen ions H⁺ and the negatively charged remainder called hydroxide OH^-.

H₂O --> H⁺ + OH^-

The alkali metals are holding onto their last negatively charged electron very weakly, and give it up very easily to the positively charged hydrogen atom. The neutral potassium atoms become positively charged potassium ions, and the positive hydrogen ions become neutral hydrogen atoms:

K + H⁺ --> K⁺ + H

Those neutral hydrogen atoms can then pair up to form hydrogen molecules, while the charge of the new positive potassium ion is balanced by the negative hydroxide ion:

K⁺ + OH^- --> KOH (in solution)
H + H --> H₂ (gas)

This is, of course, a gross simplification, but it gives you an overall idea of the processes involved. The upshot is that neutral hydrogen forms a gas that is ignited by all the heat released by the reaction, leaving behind potassium hydroxide KOH, also known as potash. This is an alkali.

However one of the great pleasures of science is checking to see what really happens. A group of researchers at the Academy of Sciences of the Czeck Republic and the Technische Unversitat Braunschweig studied the reaction between potassium and water using a high-speed camera, and they found that the metal bursts apart in a ball of spikes:



What's going on here? Well, remember that the first step in the reaction is that each potassium atom loses an electron to the water. That leaves all the atoms at the surface of the potassium with a positive charge. Similar electric charges - like matching poles on magnets - repel each other. Potassium is a pretty soft metal, so once all those surface atoms turn into charged ions, and before they have a chance to dissolve into the water, the repulsion between the ions is enough to cause the ball to blast apart into spikes. This is called a "Coulomb explosion" - Coulomb from the Coulomb force between electrical charges, and explosion because it's an explosion. The researchers performed highly sophisticated computer simulations to verify that this was indeed what's happening - no mean feat, given that they have to accurately consider the movement of electrons, metals, and water molecules.

Coulomb explosions show up in other parts of chemistry. A Mass Spectrometer which measures the masses of charged molecules flying through the instrument, so you can figure out what they are, or measure how much of a known molecule is in a mixture. However first you have to get the molecules out of the mixture so they're floating around freely, and put an electric charge on them. A classic way of doing this is to run a stream of your mixture into a powerfully electrically charged nozzle. By dumping a big charge on the mixture, you not only give the molecules the right electric charge, but you cause all of the different molecules to repel each other rapidly until you've got just individual molecules floating around in space.

I did some research work on that process in my undergraduate years. It's always great to see how universal these processes are.

Bringing this obviously ancient draft post up to date, here's Periodic Videos putting a light alkali metal - lithium - into 7-Up. The results are less spectacular, because the reaction is less aggressive.

"Here's Your Damn Jetpack"

A while ago I wrote a post about visiting LIGO, the Laser Interferometer Gravity Observatory. Actually that visit kicked off a little Tumblr project of mine, a response to people's cynicism about technological progress. No, we don't have jetpacks and flying cars, but we have scientific instruments that can detect distortions in space-time to a mind-crushingly exacting degree, portable data devices that shame the Star Trek PADD, and an impending flying robot problem.

That project ended a while ago but the recent announcement that aLIGO had detected gravitational waves jogged my memory and I decided it'd be nice to share it here. Enjoy "Here's Your Damn Jetpack".