Why does Brownian motion happen

Movement out of molecular chaos

Brownian motors can move in one direction in a targeted manner by taking advantage of the undirected and random thermal tremor motion in warm environments. What at first glance might look like a perpetual motion machine provides exciting insights into processes that nature may also use for movement on a molecular level.

Brownian motion

A warm body is full of energy. That already made quite a few heads hot who wanted to tap into this energy. But unfortunately there is the second law of thermodynamics. This prohibits a machine that does work by simply reducing the heat of a body - a so-called perpetual motion machine of the second kind.

The German Patent and Trademark Office in Munich therefore attaches great importance to mentioning the hopelessness of patent applications for such machines. For as eternally as a perpetual motion machine would do work, the futile attempts to outsmart nature and the second law of law are constant.

Albert Einstein also worked in this position when he published his thoughts on heat movement in 1905: In warm gases and liquids, atoms and molecules are in confused and chaotic motion due to the heat energy, collide with one another and transfer energy. This Brownian motion is what we experience as heat.

Even at normal temperatures, molecules are exposed to an enormous bombardment from other particles. Nevertheless, nature succeeds in maintaining transport processes in biological cells, although calculations show that the thermal energy exceeds the chemical energy required for this many times over. For molecules, it's like a walk in a tornado, which they master with astonishing purposefulness. The exact processes are by no means known, but for many researchers it is clear that a better understanding can be very helpful when building motors and pumps for the nanoworld. Peter Hänggi from the University of Augsburg is one of them. He researches in the field of so-called Brownian motors, of which he is also the namesake. Last year, Hänggi and Fabio Marchesoni published a widely acclaimed review article on the field of research.

Ratchet I.

Feynman ratchet

It was shown in the 1960s that the Brownian movement cannot be used that easily. At that time, the physicist Richard Feynman was investigating a machine - a molecular ratchet - in response to the question of whether it could pull up a flea using only Brownian motion. This machine consists of a kind of windmill, the blades of which are hit by the molecules of a gas. A ratchet (a component that causes the bicycle to idle or, in the case of the tool of the same name, converts a back and forth movement into a directional rotary movement), the windmill is limited in its movement so that it can only turn in one direction. If particles hit from the wrong side, nothing happens, otherwise the mill will turn one step further and this could pull up a weight.

If that were all, Feynman would have constructed a perpetual motion machine. But Feynman showed that the ratchet sometimes has to fail due to the heat (e.g. when particles hit the spring and release the locking mechanism). Then the ratchet also allows movements in the other direction, so that it stands still in the middle. With such a machine, no energy can be obtained from heat. The second law of thermodynamics was saved once again.

Ratchet II

However, physicists have studied other ratchets - albeit more abstract ones. And found what they were looking for. Brownian motors can move in a sawtooth-shaped, time-changing energy field with the help of Brownian motion in a targeted manner in one direction. On average, there is no force acting on the particles. But it is important that the sawtooth shape is not completely symmetrical. As a motor with an effective degree of efficiency, this arrangement is effective when work is carried out with an additionally applied external load.

Brownian engine

The trick works as follows: When the energy field is switched on, it ensures that the particles collect in its hollows. They are trapped there. If the energy field is now switched off, the Brownian motion causes the particles to drift apart. Some get so far that they end up in the next energy valley when the energy field is active again. If the energy field is switched on and off periodically, the direction with the shorter path between the hollow and the mountain is somewhat preferred, with which a directed movement is realized on average. In this way, particles can march from valley to valley and, on average, move in a directed manner. (See also the simulation linked in the right column.)

Even with Brownian motors, the laws of thermodynamics are not violated. These only relate to systems that are in so-called thermodynamic equilibrium, in which there are no external disturbances. When the energy field is switched on, however, it is precisely this balance that is disturbed. The particle is raised to a higher energy level and therefore such a ratchet is not a perpetual motion machine.

Possible applications

These ratchets no longer exist only as thought experiments, but have also been implemented in physics laboratories around the world. Versatile applications can be found in both the classical and the quantum mechanical world.

Technology is advancing into ever smaller areas. If you want to do things on a molecular level, you need the right motors and pumps. Anyone who simply wants to shrink a conventional gasoline engine quickly runs into the wall - the thermal wall. Brownian motors of all kinds, on the other hand, are promising candidates for such nanomachines. But the separation of healthy and diseased cells should also be possible in the future with the help of Brownian motors and enable exciting applications in medicine. One thing is clear: Brownian motors have already set things in motion in the nano world.

Bibliography

Review article by Peter Hänggi and Fabio Marchesoni on artificial Brownian motors: P. Hänggi; F. Marchesoni: "Artificial Brownian motors: Controlling transport on the nanoscale", Reviews of Modern Physics, Volume 81