Abstract
Most macroscopic machines rely on wheels and gears. Yet, rigid gears are entirely impractical on the nano-scale. Here we propose a more useful method to couple any rotary engine to any other mechanical elements on the nano- and micro-scale. We argue that a rotary molecular motor attached to an entangled polymer energy storage unit, which together form what we call the "tanglotron" device, is a viable concept that can be experimentally implemented. We derive the torque-entanglement relationship for a tanglotron (its "equation of state") and show that it can be understood by simple statistical mechanics arguments. We find that a typical entanglement at low packing density costs around 6kT. In the high entanglement regime, the free energy diverges logarithmically close to a maximal geometric packing density. We outline several promising applications of the tanglotron idea and conclude that the transmission, storage and back-conversion of topological entanglement energy are not only physically feasible but also practical for a number of reasons.
Highlights
Molecular machines are everywhere around us and run our lives on the sub-cellular scale
The tanglotron's chains can act as a practical energy conversion and storage unit as well as a long range energy transmission medium
The tanglotron can be seen as an active topological nanoscale gear that acts as a so and “geometry insensitive” nano-mechanical element able to adapt to any relative reorientation and repositioning of the motor and “consumer”
Summary
Molecular machines are everywhere around us and run our lives on the sub-cellular scale. Interlocked motors with gears and wheels, connected with force transmitting chains and belts form the practical basis for most large scale mechanical devices They appear like a very awkward, hard to realize way to build nano-machines in the uctuating realm of the so and small. The central idea that we want to advance is that of torque transmission by the process of topological entanglement of polymer chains attached to the active rotary device (motor), cf., Fig. 1. Besides DNA, other natural laments, like single actin rings, are known to display similar supercoiling
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