Schlegel Diagrams

These beautiful Lewis structures are essentially 2-dimensional projections of Buckminsterfullerene (C60)–buckyballs flattened out. They represent the same molecule, but from different perspectives, one centered on a hexagonal face and one on a pentagonal face. I just think they’re pretty. Might even make nice tattoo motifs, if one were inclined towards ultra-dorky chemistry tattoos. There are other Schlegel diagrams representing the higher fullerenes, but they are not so pretty as these, IMO.


Even educated non-scientists know about fullerenes, the novel allotropes of elemental carbon resembling soccer balls or geodesic domes. C60, a spherical structure containing 60 carbon atoms, is the archetype. Each carbon atom in a classical fullerene is sp2 hybridized, meaning essentially that it is bound to three other atoms arranged more-or-less in a plane with it. A carbon atom is said to be “saturated” if it has four bonds (sp3 hybridization), and any carbon with less than four–like those in fullerene structures–is said to be “unsaturated” because it could, at least in terms of classical valence bond theory, accept at least one more bond. These are the same “saturated” and “unsaturated” that gives us the terms “saturated fat” and “unsaturated fat.” The chemistry to take an unsaturated carbon to a saturated one is rudimentary and is practiced every day on vast industrial scales.

So I’m driving along the other day and it occurs to me that fullerenes are unsaturated–they’re just carbon. Could we dump them in a reactor with hydrogen and a metal catalyst, just like we do with the vegetable oil that ends up in your oreo cookie filling, and produce the saturated hydrocarbon equivalents of fullerenes? Hydrofullerenes? So I went to the library and, per Hirsch and Brettreich’s excellent book Fullerenes, found out that the short answer is “Yes, but not exhaustively.” While partially-hydrogenated fullerenes like C60H36 can be produced and are relatively stable, exhaustive hydrogenation has not been achieved and is probably impossible, at least under practical conditions. This is believed to be a consequence of steric crowding on the exterior of the carbon shell; the more positively-charged protons you stick on to it, after a point, the less stable it gets.

The next-most intuitive question, at least for me, is “How about fluoridation?” The realization that flourine atoms can be treated analogously to hydrogen atoms in hydrocarbon chemistry gave us Teflon and the whole modern field of fluorocarbon chemistry. So if we can’t make perhydrofullerenes, how about their perfluoro analogs? A sort of “Teflon sphere” idea? Turns out, again per Hirsch and Brettreich, that the answer is “No.” Again, while partially-fluorinated fullerenes can be and have been produced, perfluorination turns out to be unfavorable for reasons which are analogous to those which disfavor perhydrogenation. The only difference is a sign change: While the surface of perhydrofullerene is too positively charged to be stable under practical conditions, the surface of perfluorofullerene is too negatively charged to be stable under practical conditions.

So my hare-brained idea is this: Try to fully saturate C60 using a “hetero-fluoro-hydro” strategy, so that the complimentary positive and negative partial charges of protons and fluorine atoms on the sphere’s surface stabilize the structure. You could either hydrogenate and then fluoridate, or fluoridate and then hydrogenate. My intuition favors the latter, because while it’s known that fluorine will displace hydrogen, the opposite reaction does not occur, to my knowledge.

I’m not an expert in the field by any means but I’ve done some rudimentary literature searches using phrases like “hydrofluorofullerene,” “fluorohydrofullere,” etc. and not found any precedent.

As to benefit, who knows? My readings to date indicate that fully saturated fullerenes of any type have been produced only in trace quantities, if at all. It would be a significant achievement to produce saturated fullerene in significant yield. Then you study its properties and start to think applications. If nothing else, being the first to make lots of saturated C60 could be good for one’s scientific career.

The point has been made that the fullerenes and fullerene type structures are highly stable. They are even more stable, in fact, than carbon in its adamantane geometry (i.e. diamond), because the sp2 hybridization of the carbon atoms in fullerenes allows for an enormous amount of resonance stabilization when the double bond electrons delocalize through the enormous pi-system. (Which is what makes them conductive.) This is something I glossed over earlier in discussing the energy costs of saturating fullerenes, when I only mentioned steric repulsion at the surface. If you saturate a fullerene, you’re also breaking a very large resonance stabilization. This is why, as some have suggested, it appears to be feasible to exhaustively perfluoridate diamond surfaces–adamantane carbon is sp3. But it is not safe to assume that because diamond can be perfluoridated, so can fullerenes, again because diamond is not resonance stabilized and fullerenes are.

The hetero-fluoro-hydro strategy I propose might offset the steric costs of saturation with complimentary electrostatic interactions on the surface, but I don’t think it’ll help much with the resonance-breaking problem. However, because the studies I’ve seen suggest that it’s really not too hard to at least partially saturate C60, my intuition is that the steric problem is much more significant than the resonance-breaking problem. After all, the first double bond should be the hardest to break, because it will have the most extended resonance and hence the most stabilization. And since they’ve already made it to C60H36 by conventional hydrogenation techniques, it follows that sterics are the limiting factor, not resonance.

Peroxidation appears to be a workable strategy, c.f. Chemical Physics Letters 384 (2004) 283-287. Tsukuda and co-workers demonstrate convincingly that they can produce C60On with n <= 30 by corona discharge ionization. Again, it hasn't been done in quantity, but Hirsch and Brettreich seem to think it could be. The paper includes a really cool figure showing C60O30. I would also note that traditional "wet" metal catalytic epoxidation has been tried many ways, and they can't seem to get more than 6 oxygen atoms installed.

An Amarillo Armadillo

Maybe the folks who live in Amarillo, Texas, aren’t really so proud of the fact that their city means “yellow” in Spanish. If I were on the city council, however, I think I’d want to embrace the fact, and move to make Arty here the city mascot.

On rumination, however, it occurs to me that there are at least three reasons why such a move is unlikely. I’ve already mentioned one, which is the association of yellow with cowardice. The second reason, as has been pointed out to me elsewhere, is that an animal that curls into a ball or runs away when threatened only worsens the implications. Finally, there’s the fact that public admission of the Spanish origin of the city’s name is likely to be unpopular given the present political climate in Texas–especially rural Texas–regarding Mexican influence in American culture.


My girlfriend, like so many of the really smart people I know, is something of an insomniac. It’s understood between us that she is free to use my computer, watch my TV, eat out of my kitchen, read my books, and generally make herself at home during her sleepless small hours at my condominium. Often I find endearing bits of evidence of her vigils during the daylight hours–a DVD left in the player, a book out of place, an empty cracker box in the kitchen trash. Last week I woke up one morning and found that she’d left Google Earth open on my desktop. The search queue immediately caught my attention, as the top three entries were “Auschwitz,” “Buchenwald,” and “Dachau.” I had to ask her about this later.
“Why,” I put to her, “were you looking at satellite pictures of concentration camps in the middle of the night?”
“Oh,” she replied, with complete nonchalance. “I wanted to see what they looked like from God’s point of view.”

On The Possibility of a "Heat Pill"

It was suggested on that a pill could be created that would generate a comfortable heat in a person’s gut. These are my thoughts on the subject.

The first problem is going to be finding a reaction that is sufficiently exothermic that the amount of stuff we can pack into a pill will give off the necessary heat. Obviously, the reaction should have no toxic or gaseous products. We might call this the “thermodynamic” part of the problem.

To give an idea of how much heat we need, let’s adopt drinking a cup of hot tea as a model system. An 8 oz cup of hot tea at a “comfortable drinking temperature” of 65C contains 8 oz = 237 mL of water at 65 C – 37 C = 28 C above body temperature. The heat required to elevate 237 mL of water by 28 C is (237mL)(28C)(1 cal/CmL) = 6636 calories, or about 7 Kcal.

Dry calcium chloride (CaCl2) gives off about 18 Kcal/mol when dissolved in water. Dividing the required heat by the heat of solution of CaCl2 gives us (7 Kcal)/(18 Kcal/mol) = 0.39 moles of CaCl2 that we must dissolve to give off 7 Kcal. Unfortunately, the molar mass of CaCl2 is 111 g/mol, so 0.39 moles of it weighs 43 grams! With a density for CaCl2 of 2.15 g/mL, we’re left with 20 mL of dry salt that we must consume. Even though the solution products are the harmless and physiologically ubiquitous ions Ca2+ and Cl-, the consumption of this much salt is bound to produce a strongly hypertonic solution in the gut, which will almost certainly cause dehydration and diahhrea.

A better candidate is calcium oxide (CaO), also known as quicklime. Although the hydration of calcium oxide is slightly less exothermic than that of calcium chloride at 15.5 Kcal/mol, it also has a significantly lower molar mass of 55 g/mol, meaning we can pack more reactivity into the same mass. It has higher density, too. What’s more, besides heat, hydration of calcium oxide produces calcium hydroxide (CaOH2), a medium-strong base that will react exothermically with bile acid (HCl) to give off even more heat, water, and *hydrolyzed* calcium chloride (i.e. we’re not going to get any more heat out of CaCl2 at this point).

Assuming that the biggest horse-pill we can swallow is 3 mL, multiplying by CaO’s density of 3.35 g/mL gives us about 10g of CaO that we can reasonably ingest in a single pill. 10g CaO is 0.18 moles, so the hydration step alone should produce (0.18 moles)(15.5 Kcal/mol) = 2.8 Kcal. What’s more, each mole of Ca(OH)2 is 2-normal in hydroxide, so we end up with 0.36 moles of base. Acid neutralization of hydroxide liberates 13.7 Kcal/mol as a rule, so we can expect an additional (0.36 mol)(13.7 Kcal/mol) = 4.9 Kcal from the acid-base chemistry. Summing contributions from hydration and neutralization of CaO gives us 2.8 Kcal + 4.9 Kcal = 7.7 Kcal given off by our 10g quicklime pill. From a strictly thermodynamic point of view, we could actually afford to make our horse-pill a bit smaller. Incidentally, the hydration of quicklime is, I believe, the same reaction that is used to heat MREs.

So it looks like we’ve solved the first part of the problem. We’ve found a reaction with the necessary energy density that is without toxic or gaseous byproducts. We’re still basically eating a salt pill and have to contend with the expected consequences of that, but we haven’t produced any particular substance that’s going to poison us. The problem now is one of kinetics, i.e. it has to do with how fast things happen. The hydration and neutralization of quicklime in the stomach are going to happen lickety-split fast, and so we’re essentially going to get all 7 Kcal dumped into the gut over the course of a few seconds. This will probably produce sufficient local heating to generate steam. What we need is a sustained release (SR) formulation for our pill that will prevent all of it from reacting at once.

More insight can be had from our model system. Although I’ve never tried it myself, my guess is that, while 65C may be a comfortable “sipping” temperature for hot tea, a person who took a whole cup at that temperature and slammed it down his or her throat all at once, which is approximately the same effect our pill would have, wouldn’t be very happy or very comfortable. This, of course, is not how people drink hot beverages. It takes minutes to drink a cup of hot tea, during which time it probably cools considerably. To get a realistic idea of how much heat we actually absorb from a cup of hot tea, and how long it takes us to do it, it would be necessary to measure the temperature time-course of a real cup of tea as it is being consumed and integrate to get the area under the curve. This would not be a difficult experiment. Once we knew the absolute heat absorbed from a real hot beverage, we could adjust the absolute energy goal for our pill accordingly. More importantly, once we knew how long it takes to comfortably drink that beverage, we’d know the time-course over which our pill was expected to give off its energy. This information, in turn, would determine the composition of our SR formulation.

SR formulation entails a slowly-dissolving matrix which releases the active ingredient into the gut at a measured rate. This matrix, unfortunately, is going to add mass and volume to an already ungainly pill. Because we don’t need a particularly long-lasting SR formulation, however, it’s probably possible to keep the volume gain as low as 100%, i.e. we can probably safely assume that SR formulation will no more than double the volume of the pill. If we then half our target heat, so that one pill equals about half-a-cup of tea, we’ve both solved the pill-size problem and provided a more versatile dosing system: One pill for light warmth, two for full strength, and three for extra strength.

This is an interesting inquiry both because it is fairly easy to model and because it suggests a couple of simple experiments. The first, mentioned above, involves measuring the real heat absorbed by a real body from a real cup of hot tea, and the second, readily implied, is to pack 10g of quicklime into one or more gelcaps, dump them in an unstirred container of 0.1N HCl, and see what happens to the temperature and other observables.

He of Pants Unsuitable

Several years ago I designed a couple of chess sets, and among the feedback I received there was an e-mail from a gentleman named Ray, who also made chess sets and had, in fact, won some awards for his “themed” chess sets, which included a set made from various makes and sizes of fire hydrants. Ray was an interesting guy; during the course of our correspondence, I learned that he was about 50, that he lived with or near his mother, and that he’d served in Vietnam. He was single, and one of the last times I heard from him he’d taken off around the world to meet a Russian mail-order bride he’d been conversing with via e-mail. He got as far as Paris, as I recall, before chickening out. He sent a long group e-mail to myself and others of his friends describing the journey in lavish and sometimes eccentric detail. As an example of the latter, I recall a confrontation he described between himself and an airline employee at the Denver airport in which he was told that his “pants were not suitable for flying.” His e-mail did not include a description of the pants in question, leaving the nature of their unsuitability for us to imagine. The incident is described in passing, as Ray’s experience of the Denver airport was simply in passing, but I found the phrase evocative and it has since become one of my favorite idioms: “His pants are not suitable for flying” has, in my mind, approximately the same meaning as “his elevator does not go all the way to the top” and “he’s one card short of a full deck.” I say “approximately” because, while the latter expressions clearly imply lunacy characteried by deficiency, of one sort or another, “his pants are not suitable for flying” seems to lack this perjorative connotation. One whose pants are not suitable for flying is crazy in an entirely benign way; as long as there are responsible personnel to remind him to change them before boarding an aircraft, no harm can come of him.

A Subtle Kindness

I knew I liked Dr. M_______ the second week I was in the Chemistry department. I was riding the elevator up from the basement. It stopped at the ground floor and a college-age male with some kind of neurodegenerative disease rolled onto the elevator in his wheelchair, together with a woman who was obviously there to assist him. The doors closed, and at the next floor Dr. M_______ got on. The kid in the wheelchair was parked right in front of the buttons. Without missing a beat, and with a slightly impatient tone, Dr. M_______ says “Five, please.” “Sure,” the kid replies amiably, and reaches out a trembling, scrawny arm and, with some difficulty, presses the button for five. Nobody said anything for the rest of the ride up, but you could feel both the kid and his assistant, who might’ve been a sister, flush with gratitude. Most people, in that situation, they look at the kid and feel like they can’t ask anything of him, so maybe they nod politely and smile awkwardly while they reach around him to press the button for themselves. Dr. M_______ saw, in the second between the time the elevator doors opened and the time he stepped on, how rarely this kid would find himself in a situation–ANY situation–in which HE could be the one helping out, instead of the one asking for help. He saw an opportunity to make the kid feel like a normal person, and he took it, without being patronizing, without trying to politely tippy-toe around the glaring fact of the kid’s handicap, and without second-guessing himself. He saw all that, and he did it, and he never once let on that he knew what he was doing. But he did, and everybody on that elevator knew he did, and every one of us, including me, had a brief glimpse of authentic human kindness. From that moment on I knew he was someone I wanted to know better.

Memphis, Tennessee

Recorded in 1959 and released as the B-side of “Back in the USA,” Chuck Berry’s song “Memphis, Tennessee” was not an immediate hit in the US, but would creep as high as #6 on the British pop charts in 1960(?). Although diametrically opposed in tone, the song’s story foreshadows Berry’s 1965 hit “Promised Land” (covered by Elvis in 1973) with its protagonist negotiating a cross-country long-distance phone call with the operator. In “Promised Land,” the narrator’s tone is jubilant and triumphant, but in “Memphis, Tennessee” it is somber and morose. “Memphis” is the story of a young man returning a long-distance call to a girl named “Marie,” who lives in Memphis, “on the south side/high up on a ridge/just a half-a-mile from the Mississippi bridge,” with whom the narrator had been emotionally involved, and subsequently separated “because her Mom did not agree.” The songs plays with listeners’ expectations; based on the typical content of pop songs from that era, most people automatically assume that the narrator is a young man, just starting out in the world, who remembers Marie as an early sweetheart, perhaps from his teenage years, with whom he was forced to part because of her mother’s disapproval. The last line of the song, however, turns our expectations on their heads:

“Marie is only six years old. Information, please: try to put me through to her in Memphis, Tennessee.”

The song so effectively misleads us that this line commonly horrifies first-time listeners–he was involved with a six-year-old girl? On repeated listening, however, we realize that the idea of a romantic or sexual involvement between the narrator and Marie is never stated, and come to understand that Marie is not the narrator’s former sweetheart, but his child. The “Mom” mentioned in the lyrics is not a tyrannical mother-in-law figure, but the narrator’s ex-wife, who “tore apart our happy home in Memphis, Tennessee” not by meddling, but by divorcing the narrator and maintaining custody of their daughter, Marie. And so in one line the song gains a tremendous gravity, transmogrifying from an adolescent paen to puppy love (which is what most other pop songs of the era actually were) into a much more serious lament of a much more mature situation. A young man (and he must be young, for how else could his sweetheart’s *mother* effectively exert control over their relationship?) who loses a sweetheart is consolable–he has a long life ahead of him and should be able to find another. An older man who has missed the formative early years of his daughter’s life due to an acrimonious divorce is not so quick to find solace, and his is a situation that most grown men, regardless of age, could at least relate to (if not actually identify with.)

Coming as it did in 1959, this one key line in this one particular song anticipated, in its affect, the metamorphosis of Rock ‘n’ Roll itself from children’s music to adult fare, a process which would not be well underway until the advent of Cream in the late ’60s. That the song was released as a B-side and did not find widespread acceptance until covered by Lonnie Mack in 1963 is perhaps, at least in part, due to the anachronism of its theme. Rock ‘n’ Roll audiences were younger, then, and not ready for the emotional weight of a subject as serious as divorce and the pangs of fatherhood. With its incestuous blurring of the line between mother and lover, the song, of course, is ripe fodder for Freudian analysis, and especially given the pedophiliac tone of some of Berry’s other songs (e.g. “Sweet Little Sixteen”) and the sex scandals that rocked his career (“C’mon, baby, just let me pee on you!”) the way is clearly open for disappointing moralistic interpretations of “Memphis, Tennessee.” Such tawdry readings miss the more profound meanings of the song and of its position in cultural space.