Molecular ratchet

A molecular ratchet or Brownian ratchet is an imaginary nanomachine that generates directed movement from Brownian molecular movement (i.e. from heat ). This can only work if additional energy is brought into the system from outside. Such systems are mostly called Brownian motors in the literature (see literature / links).

A molecular ratchet without externally supplied energy would be a perpetual motion machine of the second kind and therefore not work. The physicist Richard Feynman showed in a thought experiment in 1962 in his lectures what a molecular ratchet could look like in principle and explained with the help of the Maxwell-Boltzmann distribution why it does not work. The thought experiment is related to that of Maxwell's demon .

The model was discussed by Gabriel Lippmann before Feynman around 1900 and explained by Marian Smoluchowski in 1912. Feynman's solution was criticized by Juan Manuel Rodriguez Parrondo and Pep Español. According to the authors, Feynman incorrectly assumed quasi-static conditions in the case of different temperatures. Their own analysis was published by Parrondo, Davis and Derek Abbott in 2000. Another recent and influential analysis is by Marcelo Magnasco (1993) and Magnasco and Stolovitzky showed in 1998 that the efficiency is less than the ideal Carnot efficiency, in contrast to the analysis by Feynman . From his work on this topic, Parrondo developed the Parrondo paradox named after him as a kind of discrete version.

A variant was proposed by Léon Brillouin in 1950: the current generated by heat noise in a resistor is rectified in a diode and could in principle do work. Here, too, a precise analysis shows that the movement of heat in the diode generates an electromotive force that counteracts this.

An experimental test in a granular gas (with limited transferability to the molecular situation) was carried out in 2010 by Detlef Lohse and colleagues.

Feynman's molecular ratchet

Structure of the Feynman molecular ratchet

The figure on the right shows the basic structure. The arrangement consists of an impeller (right) and a ratchet (left) with a ratchet (gray). The entire machine must be very small (a few micrometers ) so that the impacts of the surrounding gas have a significant impact on it. The way it works is very simple: a gas particle that hits the impeller as marked by the green arrow, for example, causes a torque that is transmitted via the axis to the ratchet and can turn it one position further. A particle that hits as marked by the red arrow does not cause any rotation because the ratchet is blocking the ratchet. The molecular ratchet should therefore generate a directed movement from thermal energy , but this is not possible according to the second law of thermodynamics .

Resolution of the paradox

The ratchet only works when it is pressed against the ratchet with a spring. He too is subject to the bombardment of Brownian molecular motion. If it is deflected by this, it hits the ratchet, which leads to a net torque opposite to the previously assumed direction of rotation. The probability of the ratchet deflection large enough to skip a ratchet position is where the energy required to deflect the ratchet spring is the temperature and the Boltzmann constant . The rotation via the impeller must also tension the spring in order to get to the next position of the ratchet; that is, the probability is also . As a result, the ratchet does not turn on average. ${\displaystyle \exp(-\Delta E/k_{\mathrm {B} }T)}$ ${\displaystyle \Delta E}$ ${\displaystyle T}$ ${\displaystyle k_{\mathrm {B} }}$ ${\displaystyle \exp(-\Delta E/k_{\mathrm {B} }T)}$

The situation is different if there is a temperature difference between the wing disk and the ratchet. If the area around the impeller is warmer than that of the ratchet, the molecular ratchet rotates as previously assumed. If the area around the ratchet is warmer, the machine turns in the opposite direction. The device would then be a heat engine .

Brownian motors

The term Brownian motors was coined in 1995 by the physicist Peter Hänggi ( University of Augsburg ) in order to characterize the directed movement in periodic systems with spatial and / or temporal symmetry breaking using the source of the thermal Brownian movement. It is important that these systems operate far from thermal equilibrium. There is thus no contradiction to the 2nd law of thermodynamics .

See also

• Maxwell's demon

literature

• Richard P. Feynman: The Feynman Lectures on Physics . Volume 1, Chapter 46, Addison-Wesley, 1963, ISBN 0-201-02116-1
• R. Dean Astumian and Peter Hänggi: Brownian Motors (PDF, 473 kB). In: Physics Today . Volume 55, 2002, pp. 33-39, doi: 10.1063 / 1.1535005 .
• Peter Hänggi, Fabio Marchesoni and Franco Nori: Brownian Motors (PDF, 416 kB). In: Annalen der Physik (Leipzig) Volume 14, 2005, pp. 51–70, doi: 10.1002 / andp.200410121 .
• Peter Hänggi and Fabio Marchesoni: Artificial Brownian motors: Controlling transport on the nanoscale (PDF, 4.0 MB). In: Reviews of Modern Physics . Volume 81, 2009, pp. 387-442, doi: 10.1103 / RevModPhys.81.387 .

Web links

Commons : Molecular Ratchets  - Collection of Images, Videos, and Audio Files

Individual evidence

1. ^ Website of Parrondos Paradoxon by Derek Abbott , webarchive
2. ↑ Smoluchowski, Experimentally verifiable molecular phenomena contradicting the usual thermodynamics, Physikalische Zeitschrift, Volume 13, 1912, pp. 1068-1080
3. ↑ Parrondo, Espanol, Critique of Feynman's analysis of the ratchet as an engine, American Journal of Physics, Volume 64, 1996, pp. 1125-1130
4. ↑ Abbott, Davis, Parrondo: The problem of detailed balance for the Feynman-Smoluchowski Engine and the multiple pawl paradox, in: Unsolved Problems of Noise and Fluctuations. American Institute of Physics, 2000, pp. 213-218
5. ↑ Magnasco, Forced Thermal Ratchets, Physical Review Letters, Volume 71, 1993, pp. 1477-1481.
6. ↑ Marcelo Magnasco, Gustavo Stolovitzky: Feynman's Ratchet and Pawl, Journal of Statistical Physics, Volume 93, 1998, p. 615.
7. ↑ Brillouin, Can the Rectifier Become a Thermodynamical Demon ?, Physical Review, Volume 78, 1950, pp. 627-628.
8. ↑ Eshuis, van der Weele, Lohse, van der Meer: Experimental realization of a rotational ratchet in a granular gas, Phys. Rev. Lett., Volume 104, 2010, p. 248001, PMID 20867337