The entropic sieve

Here’s another of my (pre-edited) earlier pieces for the BBC Future site. Must catch up on these now – there are several more.
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Sorting out tiny particles and molecules of different sizes is necessary for various technologies, from gene sequencing to nanotechnology. But it sounds like a pretty tedious business, right?

It’s no surprise, then, that a recent paper describing a new technique for doing this garnered no headlines. But it’s well worth a closer look. For one thing, it sounds like sheer magic.

Physicist Peter Hänggi at the University of Augsburg in Germany and his colleagues show that you can take a tube containing a mixture of big and small particles, apply some force to pull them through in one direction (an electric field would do the job for charged particles, say), and then give it a shake. And hey presto – the small particles will drop out of the end towards which the force pulls them, whereas the big particles drop out of the other end (D. Reguera et al., Phys. Rev. Lett. 108, 020604 (2012)).

Not only is this trick very clever but it’s also rather profound, touching on some of the most fundamental principles of physics. The device stems from a loophole proposed in the nineteenth century for evading the second law of thermodynamics, in effect making a perpetual motion machine. Needless to say, the new particle separator isn’t that, but the explanation of why not requires an excursion into the recondite field of information theory. Deep stuff from what is basically a grain sorter.

There are already ways to separate molecules by size. You can literally sieve them using solid materials with tiny pores of uniform size, such as the zeolite minerals used to separate and selectively alter some hydrocarbons in crude oil. And a technique called gel electrophoresis is used to separate strands of DNA chopped into different lengths – a standard procedure for sequencing genes – according to their size-dependent speed of being dragged along by an electric field. These techniques work well enough for most purposes. But that devised by Hänggi and colleagues is potentially more efficient.

Like all good magic, you have to look inside to see how it’s done. The tube is divided into a series of funnel-shaped chambers connected by narrow necks – looked at in cross-section, it resembles two saw blades with the teeth not quite touching. This sawtooth profile is all it takes to make the large and small particles move in opposite directions in response to a combination of the force and the shaking.

The tube is what physicists call a Brownian ratchet. The name derives from Brownian motion, the random movement of tiny particles such as pollen grains in water, or indeed water molecules themselves, due to the jiggling of heat. (For pollen grains, it’s actually the random collisions of jiggling water molecules that cause the movement.) Normal Brownian motion doesn’t favour any direction over any other – the particles just wander at random. But a bias can be introduced by putting the particles in asymmetric surroundings, such as lodging them in a series of grooves with a sawtooth profile, the slopes steeper in one direction than the other.

When Brownian ratchets were first proposed, they caused consternation because they seemed to violate the laws of thermodynamics and allow perpetual motion. In 1912 the Polish physicist Marian Smoluchowski suggested that a tiny ratchet-and-pawl might be induced to turn in just one direction by random thermal shaking. 50 years later, Richard Feynman showed why it wouldn’t work, if the temperature of the apparatus is the same everywhere.

But Brownian ratchets aren’t easily dismissed. They seem to represent an example of a Maxwell demon, which also violates thermodynamics. In the nineteenth century, James Clerk Maxwell suggested how heat might travel from cold to hot, in contradiction of the second law of thermodynamics, if a little ‘demon’ opened a trapdoor between two compartments each time a ‘hot’ molecule happened to reach it, thereby accumulating heat in one compartment. It wasn’t until the 1980s that the reason prohibiting Maxwell’s demon was understood: you have to take into account the information that the demon uses to make its choices, which itself incurs a cost in entropy – in disorder – that balances the thermodynamic books.

Yet Brownian ratchets can work if they don’t rely on random thermal ‘noise’ alone – if there is some other factor that tips the balance, so that the system is out of thermodynamic equilibrium. It seems likely that Brownian ratchets exist in molecular biology, inducing directional motion of components of the cell driven by a combination of biochemical energy and noise.

What makes the ratchet described theoretically by Hänggi’s team different from previous incarnations is that they have shown how to make the different particles move in wholly different directions. Normally they’d just move in the same direction at different speeds, because the small particles find it easier to ‘climb’ the steep slopes than the big particles. Another way of saying this is that the big particles are more strongly repelled by entropy from the vicinity of the steep slopes. The researchers show that the force pulling the particles against the ratcheting flow can be adjusted to a level just big enough to overcome the tendency of the small molecules’ random jiggling to move them preferentially in the direction of the shallow slopes, but not big enough to counteract this for the big molecules. And voilà: they head off in opposite directions, separated by entropy. The team show that, after several passes through the tube, a mixture of two particles of slightly different sizes – two chopped-up, screwed-up strands of DNA like those encountered in gene sequencing, say – can be segregated damned near perfectly.