Evaluating the friction of rotary joints in molecular machines

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 300 K: 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 × 10 −35 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. arXiv:1701.08202v2 [cond-mat.soft] 7 Aug 2017 2 Related Work Several studies have used molecular dynamics (MD) simulations to investigate friction in nanomachines with sliding or rotating components.In [15], four different MD simulation configurations using the LAMMPS code and AIREBO force field were used to obtain consistent friction estimates for a rotating nested nanotube bearing. Other dissipation estimates for rotating nested nanotube bearings have been determined using intralayer interactions based on the Brenner potential [9] with interlayer interactions based on the Kolmogorov-Crespi registry-dependent potential [72], and with the COMPASS force field [32]. Dissipation estimates for linear sliding nested nanotube bearings have been determined using a custom force field and custom numerical simulator in [55,56], and a custom force field based on [53] and the r-RESPA integrator in [54].A MD model of experimentally realized graphene-on-graphene sliding is presented in [33]. The self-retracting motion of sheared graphene sheets is studied with an in-house MD integrator in [52]. Energy dissipation during high speed sliding of graphene sheets is investigated with GROMACS [28] and the DREIDING force field [42] in [37].

Mechanical Computing Systems Using Only Links and Rotary Joints

“…Operating this lock involves rotation at the joints by up to ∆θ ≈ 1 rad. The model system analyzed in [40] is an excerpt of the links and joints shown in the closeup on the right of Fig. 25.…”

“…25. From [40,Eq. 2], this rotation dissipates about 2.4 × 10 −27 J per rotary joint when operating at f = 100 MHz.…”

“…From [40, Eq. 2], this constant is E dissipated t = k rd φ 2 for rotation by angle φ. Supposing a logic operation corresponds to rotating about 10 joints by about a radian, this energy-time product is about 10 −34 J s, using k rd from [40].…”

“…The friction evaluation of [40] considered complete rotations of a rotor connected to a housing solely through the rotary joints. When used in the mechanical computer discussed in this paper (and as illustrated in Fig.…”

“…Another instance of a higher-level design choice is arranging designs of neighboring rotary joints to help reduce dissipation. Specifically, the rotary joint has a small potential barrier to rotation [40] that could be a significant contribution to dissipation at low temperatures. That is, imperfect recovery of energy storage and release when moving over the rotor potential leads to dissipation.…”