The Standing Invitation

Posts Tagged ‘Science

The Origin of Opacity

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Daniel C Dennett: Consciousness Explained

Richard Dawkins: Unweaving the Rainbow

Arthur C Clarke: Report on Planet Three and Other Speculations


Written by The S I

May 6, 2012 at 1:10 am

The Cost of Perfection

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Take two particles.*

Particles are fussy things. They don’t like being too close to each other because atomic nuclei repel each other very strongly; at the same time, the shifting clouds of electrons surrounding the nuclei can be mildly attractive to one another, so they don’t like being too far apart either. This balance of attractive and repulsive forces is familiar from all social gatherings: when you’re talking to someone at a party you want to be close enough to hear them, but if they’re standing right in your face it’s uncomfortable.

What this means for particles is that there’s a sweet spot, an optimum separation between the two particles that makes them both happy. It’s the lowest-energy arrangement of particles, in that once they’re at this distance, it would require an input of energy to push them closer together or pull them further apart.

So this idea of the optimum distance between two particles is straightforward. And the same thing applies when you have billions of particles at once. They will move around at random until they find the lowest-energy arrangement, where the average distance between particles is as close as possible to the ideal separation.

When billions of particles try to reach their lowest-energy arrangement, they will try to form a lattice.

Lattices are three-dimensional patterns of points in space. They are infinitely large, infinitely repeating, purely mathematical constructs that can only be approached, never exactly attained. A lattice is a map of where particles should sit in space in order to be at the right distance from each other.

When particles arrange themselves on a lattice, we call this a crystal. Crystals, like diamond, are simply regular arrangements of particles – and they really are very regular, repeat themselves almost perfectly for millions and millions of layers.

But remember, lattices are mathematical ideals, perfect and Platonic, while crystals are real-world lumps of matter. The particles in a crystal may try to reach the perfect state of a lattice, but they will never reach it. There will always be defects – points at which an atom is not sitting where the lattice says it should be. These are the microscopic imperfections that mean the ideal of a lattice will never be attained. Even though all particles in a crystal would benefit from being in a perfect lattice (achieving the optimum separation from other particles), the defects are nevertheless unavoidable.

There are two kinds of defects: extrinsic and intrinsic. Extrinsic defects are easy to understand. They are simply impurities. A diamond crystal is supposedly a regular arrangement of carbon atoms, but since no source of carbon is perfectly pure, no diamond will be perfectly pure. The most common impurity in diamond is a nitrogen taking the place of a carbon. Diamonds, supposedly pure carbon, are typically 1% nitrogen. As well as being impurities in themselves, the presence of a nitrogen atom causes local distortions in the crystal surrounding it, as the adjacent carbons move slightly from their ideal lattice positions in order to compensate for it.

But even if some perfectly pure source of carbon could be found and a diamond crystal grown from it, would that crystal approach a perfect lattice? Not quite, because of the second kind of defect – intrinsic defects. An intrinsic defect occurs when a particle isn’t where it should be.

These intrinsic defects are interesting because they are unavoidable. They are the inevitable consequence of the great trade-off between enthalpy and entropy. Because although there is an energetic benefit to having particles sitting an ideal distance from each other, there is also an energetic cost to having them perfectly ordered. This again makes sense to anybody who has ever tried to organise anything. Of course you want things organised; things are more efficient when they are organised, and so the more organised, the better – but organising things takes time, effort, and energy. Ultimately a compromise has to be reached: you accept the amount of organisation you can achieve for the amount of energy you’re willing to expend on putting things in order.

Although particles like to be separated by an ideal distance, they also like moving around, particularly at high temperatures. For this reason, truly perfect crystals are impossible to grow. Imperfections will always sneak in. In fact, imperfections are necessary. Crystals exist because it is energetically favourable for particles to be organised; but because of the inevitable cost of organising anything, it is also energetically favourable for there to be defects. And the interesting thing is that because the imperfections are the result of particle movement, and movement depends on temperature, it is possible to predict how many imperfections there will be in a crystal at a given temperature. You can’t say where they will be, but you can say how many there will be per cubic centimetre. The defects obey exact laws that can be understood and exploited. They are perfect imperfections.


* In this post, by particles I mean atoms, ions, molecules or some colloids; things smaller than atoms behave rather differently.

Written by The S I

April 9, 2012 at 10:18 am

No Nonsense

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Written by The S I

April 1, 2012 at 2:34 pm

Things That Don’t Look Like Anything

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When I talk about things like molecules, atoms and particles with nonscientists, a question I am often asked is what these things look like. And they never seem satisfied with my response: that, really, they don’t look like anything at all. It’s not that they’re invisible as such; it’s just that sentences involving what they look like don’t make any sense. You can’t describe their appearance because they don’t have an appearance to describe.

The thought makes people uncomfortable.

The idea of something not looking like anything is not a new one. Sounds do not look like anything. We know that sounds exist, but that physical appearance is not something we can ascribe to them. When we talk about sounds, we describe them in nonvisual terms.

Sounds, or ideas or desires or smells, have a certain abstract quality that seems to excuse this. But particles are stuff. They are physical objects whose masses are known to remarkable degrees of accuracy, and since everything we can see is made up of aggregates of them, it seems impossible that they cannot be described visually.

Let’s consider what happens when you see something, step by step.

An object is illuminated by a bombardment of photons. These photons interact with the surface of the object. Some are absorbed by the object – it is this absorption that gives the object its colour. The photons that are not absorbed are scattered around in all directions, and many of them enter through the pupil of your eye. These photons reach the retina, where they cause chemical changes in molecules like 11-cis-retinal; electrical reports of these changes are transmitted to the brain, where they are interpreted as ‘seeing’ those photons.

So to ‘see’ something means that photons bouncing off the thing cause chemical changes in your eye. This is fine for large objects like apples and oranges, but what if the object is smaller? Most people can’t see objects smaller than 0.1 mm, because there aren’t enough photons reflecting off them to react with our eyes. We get around this problem by using stronger illumination and magnifying lenses, allowing us to see things like blood cells.

But what about objects that are even smaller?

Well, here we start to have a problem. For objects smaller than 0.002 mm, photons of visible light start to be too big to see things clearly. In order to resolve details at this size level, smaller, higher-energy particles than photons need to be used. This is how electron microscopy works: instead of using reflected photons, you use reflected electrons, which are much smaller and better able to probe the surface of what you’re examining.

Is this really ‘seeing’ the object? The microscopic object under examination is not being studied with light, remember. This is why electron microscope images are monochrome. Light isn’t involved in the process at any point until a computer screen shows you, with light, the pattern of reflected electrons. Still, we are presented with pictures of the object’s surface, so it’s certainly like seeing, and the object certainly has an appearance that can be discovered, even if only indirectly.

What if the object is smaller?

Eventually an object can be so small that not even electrons can give you good enough resolution, and even more indirect means of gathering information must be used. One of them, atomic force microscopy, is more analogous to touch than sight: it drags a tiny needle across a surface to register bumps in the surface where the individual atoms are. But apart from the atoms’ location in space, there’s no information here about their appearance. Atoms do not interact with light in a way that gives meaning to the word ‘looks like’. They do absorb light and so might be said to have colour in a technical sense, but no picture of an atom could ever be drawn based on their interaction with light. And smaller particles than atoms don’t interact with light at all. You can’t see them, ever, because there is nothing there to see.

But still, some picture of a very tiny object might be drawn. Questions about its shape, for example, are not meaningless – but on a small enough scale, questions of shape become questions about properties rather than appearance. The question ‘is x round?’ becomes ‘are all the points on x’s surface the same distance from one central point?’. This is a question that can be answered, but only because it is a mathematical question about the properties of a certain type of object. And it turns out that the equations describing these objects reveal the them to be strange and wonderful things – things that behave in ways that make absolutely no sense to people used to objects the size of apples and oranges. They cannot be seen, but they can be described, and this description is better than seeing them. A mathematical description of a particle is more precise and less fallible than the clumsy tool of vision that evolution gave us to survive in a world full of large-scale objects. And we can reach this level of acquaintance with these particles that no one has ever seen because even though we can’t see them, we can imagine them.

Written by The S I

March 26, 2012 at 3:00 am

Functions of State

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What one thing would you change about the world?







But really interesting to me is a graph like this one.







Written by The S I

November 6, 2011 at 11:59 pm

The Smell of Money

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There really is nothing quite like writing a doctoral thesis for increasing your interest in things other than your thesis. Today I wondered: why do some metals have a smell?

Go through your small change right now. The pennies have a distinct metallic smell. But how can this be?

In order to smell something, particles of it have to get to your nose. This is easily understandable with liquids, because all liquids are continuously shedding molecules to the air around them through the process of evaporation. The tendency of a liquid to release gas by evaporation is given by its vapour pressure, which varies with temperature: the higher the temperature, the higher the vapour pressure, faster the liquid evaporates.

Solids, on the other hand, do not evaporate in this way, although there is an analogous process called sublimation, in which particles leave the solid’s surface as gas without passing through a liquid state. This means that solids do have vapour pressures, but these are extremely low for things like metal coins, which do not have a noticeable tendency to evaporate when left on the pavement on a hot day.

So what is it about coins that gives them this smell of metal? Marvellously, there is a paper in Angewandte Chemie from 2006 that answers exactly this question. The authors focus on iron, which is often described as having a ‘musty’ aroma. What they find is that iron is in fact odourless, both as a solid lump of metal and as a solution.

They are unable to resist the pun: “Ironically, the iron odour on skin contact is a type of human body odour.”

The experiments involved the sweat and blood of researchers. Sweat is corrosive: it attacks the surface of the metal and partially dissolves it, forming small amount of the ion Fe2+. This is reacts within seconds with oxygen give to Fe3+, but also causes a reaction with the sweat itself. Lipidperoxides occurring naturally in sweat are  broken down into volatile carbonyl hydrocarbons that we are able to smell. Metal smells, but only because it has been touched by people.

The same mechanism explains the metallic smell of blood – one of the researchers’ own blood was used in the experiment, apparently. Blood contains iron, which decomposes lipidperoxides in the blood.

The typical “musty” metallic odor of iron metal touching skin (epidermis) is caused by volatile carbonyl compounds (aldehydes, ketones) produced through the reaction of skin peroxides with ferrous ions (Fe2+) that are formed in the sweat-mediated corrosion of iron. Fe2+ ion containing metal surfaces, rust, drinking water, blood etc., but also copper and brass, give rise to a similar odor on contact with the skin. The human ability to detect this odor is probably a result of the evolutionarily developed but largely dormant ability to smell blood (“blood scent”).

It’s a nice everyday example of the scientific problem of correlation implying causation. You might describe the smell as ‘metallic’, but that’s only because you only smell it around metals. In reality, the metal is not what you’re smelling; you’re smelling the decomposition of chemicals produced by your own skin.

In reality, the copper coins you’ve been sniffing have a smell we call ‘coppery’ because they are smeared with the chemically decomposed sweat and oils from the hundreds of greasy, sweaty fingers that have touched them. A lovely thought, isn’t it?


Written by The S I

October 31, 2011 at 11:59 pm

Chemistry in 1911 Was Just Adorable

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What was the cutting edge of chemical research a century ago? Fortunately the Journal of the American Chemical Society stores PDFs of papers published as early as 1879. What was contained in the issue from one hundred years ago this month?

The paper that stands out for me is by Otto Folin and Fred F Flanders, and is called simply The Determination of Benzoic Acid. I find it adorable beyond words.

Benzoic acid is a simple compound that occurs naturally in many plant and animal species. Extracting it from an aqueous solution is now a common experiment for first-year undergraduates: add a little HCl and a lot of chloroform, and the benzoic acid will migrate to the chloroform layer; then separate the chloroform layer, evaporate off the chloroform and you’ll be left with pure compound. When all you’re doing is getting benzoic acid out of water, it’s almost impossible to get it wrong (although somehow, when I was an undergraduate, I managed…); but if there are a whole bunch of other, similar compounds in the water too, then obtaining the benzoic acid pure is much more difficult.

So Folin and Flanders dedicated themselves to developing techniques for obtaining pure benzoic acid from cranberries (I love this so much). They were able to find the amount of benzoic acid in the chloroform layer directly by measuring the acidity of the solution – an improvement over removing the chloroform by evaporation since, in the days before rotary evaporators, this would have involved just leaving the flask open on a bench for a couple of days.

But cranberries were too easy, they say. They demanded a harder challenge. And so they turned their attention to catchup.

Reading this I had no idea what ‘catchup’ was. It turns out to be an early alternative spelling of ‘ketchup’ (they also spell ‘definite’ and ‘volatile’ without the final e). Catchup is essentially tomatoes preserved by acid: the acid prevents bacterial growth.

Extracting benzoic acid from catchup was made complicated by the presence of these various acids. They tended to end up in the chloroform layer alongside the benzoic acid and needed to be taken care of. Folin and Flanders eventually removed these impurities with carefully pH-controlled aqueous washes; by recording the pH at which each acid came out, they were able to identify many of the acids.

Using this technique they were able to find the amount of benzoic acid in two of the sauces – Snider’s catchup and Heinz’s catchup. Their technique wasn’t perfect – the benzoic acid never came off entirely clean (the impurity was probably the chemically similar cinnamic acid), and wasn’t accurate for levels higher than 0.1%, but as a simple test that only takes 90 minutes and lets you recover the chloroform afterwards, they seem rightly pleased with it.

Rather cute, really, isn’t it?



Original paper:

See the Wikipedia pages for benzoic acid, cinnamic acid, and a surprisingly detailed discussion of the etymology of the word ketchup.

Written by The S I

October 27, 2011 at 11:59 pm