Dynamics of molecular shock-absorbers: energy dissipation and the Fluctuation Theorem

We study the non-equilibrium behaviour of piston-rotaxane molecules under compression and extension. These soft molecules consist of several free rings threaded onto a rod, with the position of one ring controlled by an external piston. A Langevin simulation shows that at a slow speed of compression and expansion, the force on the piston agrees well with the previously calculated equilibrium result. However at speeds larger than a characteristic speed, non-equilibrium effects become important, and these give rise to an asymmetric energy dissipation. We construct distributions for compressive and expansive work, and using Crooks Fluctuation Theorem, we determine the equilibrium free energies of compression/ expansion, and hence, the dissipative work. This analysis demonstrates how Fluctuation Theorems can be used to interpret non-equilibrium behaviour from force spectroscopy of soft molecules. Specifically, we demonstrate the use of the Crooks Fluctuation Theorem to determine the piston-rotaxane design that maximises energy dissipation per stored energy.