Rotaxane Molecular Shuttle Simulator

Stimulus (pH-like switch)

Bias ΔG (station B − A) −8.0 kJ/mol

Environment

Temperature 298 K

Barrier height (central macrocycle) 18.0 kJ/mol

Ensemble (N = 30)

Station A: 30Station B: 0

Predicted K_eq = [B]/[A]

0.05

Observed hops (total)

Thermal energy k_BT

2.48 kJ/mol

How it works

A [2]rotaxane is a macrocycle (ring) mechanically trapped on a dumbbell-shaped axle by two bulky stopper groups — it can't come off, but it can slide. The axle carries two binding stations; the ring's position along the axle sits in a double-well free-energy landscape:

U(x) = h·((x² − a²)/a²)² + ΔG·x/(2a)

h  = barrier height between stations (kJ/mol)
a  = half the station separation
ΔG = free-energy bias of station B relative to A

Each ring obeys overdamped Langevin dynamics — deterministic drift down the free-energy slope plus thermal noise:

γ·dx/dt = −dU/dx + √(2·γ·k_BT)·ξ(t)

Random thermal kicks occasionally carry a ring over the central barrier — an activated (Kramers-type) hop, exactly like real ¹H-NMR-observed station-switching in Stoddart- and Leigh-style shuttles. At equilibrium the population ratio follows a Boltzmann distribution:

K_eq = [B]/[A] = exp(−ΔG / k_BT)

Favor Station A / B — jumps the bias to a preset, modelling a chemical stimulus (protonation, redox, light) that changes which station binds the ring more strongly — the real switching mechanism used in synthetic molecular shuttles and muscles.
Bias ΔG slider — fine control of the same free-energy tilt.
Temperature — sets k_BT = R·T and hence the noise amplitude; higher T means faster, more frequent hops.
Barrier height — how much steric/electrostatic resistance the ring feels crossing the axle's midpoint; a taller barrier suppresses hopping even when ΔG strongly favors one station.

Time here is illustrative simulation time, not real picoseconds — the qualitative behavior (biased random hopping, Boltzmann-weighted populations) is physically accurate; the absolute hop rate is not calibrated to a real solvent viscosity.

Station A Station B Macrocycle (ring)

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