Weak thermal fluctuations impede steering of chiral magnetic nanobots

Abstract

Rotating magnetic field is an efficient method of actuation of synthetic colloids in liquids. In this Letter we theoretically study the effect of the thermal noise on torque-driven steering of magnetic nanohelices. Using a combination of numerical and analytical methods, we demonstrate that surprisingly a weak thermal noise can substantially disrupt the orientation and rotation of the nanohelix, severely impeding its propulsion. The results of Langevin simulations are in excellent agreement with the numerical solution of the Fokker-Planck equation and the analytical effective field approximation.

Figures (3)

• Figure 1: Schematic drawing of the nanohelix with an affixed magnetic moment $\bm m$ actuated by an in-plane rotating magnetic field $\bm H$.
• Figure 2: Angular dynamics of of the nanohelix with elongation $p\!=\!3$ and magnetization angle $\Phi\!=\!\pi/4$, as a function of scaled actuating frequency $\omega/\omega_0$ for several values of the Langevin parameter $\xi$. (a) Average (sine of the) wobbling angle, $\langle\sin{\theta}\rangle$; (b) Average angular velocity rotation about the $z$-axis of the field rotation. (c) Average propulsion velocity $\langle U_z\rangle/(\mathrm{Ch}_\| \omega_0\ell)$ The symbols stand for the results of the Langevin simulations, the color solid lines correspond to the solution of the Fokker-Planck equation. The black solid line in (a) is the deterministic (non-Brownian) solution. The black dashed lines stand for the asynchronous regime, emerging near the step-out , $\widetilde{{\omega}}_\mathrm{s\hbox{-}o}\!\approx\!2.24$note1.
• Figure 3: The effect of the magnetization angle ($\Phi$) on the actuation of a magnetic nanohelix with $p\!=\!3$ subject to weak thermal noise for $\xi\!=\!10$: (a) average sine of the wobbling angle, $\langle \sin \theta \rangle$ vs. $\omega/\omega_0$; b) average propulsion velocity $\langle U_z\rangle/(\mathrm{Ch}_\| \omega_0 \ell)$ vs. $\omega/\omega_0$. The color solid lines correspond to the solution of the Fokker-Planck equation, the black lines in (b) correspond to the optimal non-Brownian propeller ($\Phi\!=\!\pi/2$) for synchronous (solid line) and asynchronous (dashed line) rotations. The dotted color lines are the predictions of the effective field approximation. The inset shows the dependence of the effective field magnitude $\xi_\mathrm{e}$ on frequency.