# Evaluating the Friction of Rotary Joints in Molecular Machines

## TL;DR

This paper introduces an efficient computational method to evaluate friction in molecular rotary bearings using fluctuation-dissipation theorem, applicable to short simulations and low rotation speeds, demonstrated on nanotubes and hypothetical joints.

## Contribution

A novel fluctuation-based approach for estimating molecular bearing friction that works with short simulation times and low rotational speeds.

## Key findings

- The method accurately estimates friction in molecular bearings.
- Friction for acetylenic joints is significantly lower than in nanotubes.
- Applicable to various rigid, symmetric molecular systems.

## Abstract

A computationally-efficient method for evaluating friction in molecular rotary bearings is presented. This method estimates drag from fluctuations in molecular dynamics simulations via the fluctuation-dissipation theorem. This is effective even for simulation times short compared to a bearing's energy damping time and for rotation speeds comparable to or below typical thermal values. We apply this method to two molecular rotary bearings of similar size at 300K: previously studied nested (9,9)/(14,14) double-walled carbon nanotubes and a hypothetical rotary joint consisting of single acetylenic bonds in a rigid diamondoid housing. The acetylenic joint has a rotational frictional drag coefficient of $2 \times 10^{-35}\,\mbox{kg m${}^2$/s}$. The friction for the nested nanotubes is 120 times larger, comparable to values reported by previous studies. This fluctuation-based method could evaluate dissipation in a variety of molecular systems with similarly rigid and symmetric bearings.