Chemistry, Physics and Technology of Surface

ISSN 2518-1238 (Online), ISSN 2079-1704 (Print)

Brownian motors are a class of nanomechanisms that generate directional motion of Brownian particles under nonequilibrium perturbations. A symmetry analysis of the factors affecting the appearance of a directed current and determining its direction indicates the dependence of the motor characteristics on the phase shift between the potential reliefs of the stationary and fluctuating components of nanoparticle potential energy. The motion of a Brownian particle located in the field of action of an extremely asymmetric stationary sawtooth potential fluctuating as a result of dichotomous effects of spatially harmonic signal is considered. Since the sawtooth potential is easily realized near a surface with a series of electrodes of a certain shape buried inside it, and the dichotomous changes of a spatially harmonic signal are easily created by laser beams, the considered motion of a nanoparticle (Brownian motor) can be realized experimentally. It is known that at sufficiently high temperatures, when the thermal energy exceeds the energy barrier of the sawtooth potential, the direction of motion is determined exclusively by the phase shift of the harmonic signal relative to the extrema of the sawtooth potential.

In this article, an analytical expression for the motor average velocity has been obtained, which is valid at arbitrary temperatures, but at low frequencies of dichotomous fluctuations (adiabatic mode). An analysis of the expression has shown that there exists a critical temperature T_c below which the direction of motion loses its dependence on the magnitude of the phase shift, whereas at T > T_c the direction of motion is determined by that shift. In the region of intermediate temperatures T, for each value of the  phase shift, one can indicate a temperature T_s > T_c such that at T < T_s the particle moves in one direction, while at T > T_s in the other.

1. Reimann P. Brownian Motors: Noisy Transport far from Equilibrium. Phys. Rep. 2002. 361(2-4): 57. https://doi.org/10.1016/S0370-1573(01)00081-3

2. Hänggi P., Marchesoni F. Artificial Brownian motors: Controlling transport on the nanoscale. Rev. Mod. Phys. 2009. 81(1): 387. https://doi.org/10.1103/RevModPhys.81.387

3. Cubero D., Renzoni F. Brownian Ratchets: From Statistical Physics to Bio and Nanomotors. (Cambridge, UK: Cambridge University Press, 2016). https://doi.org/10.1017/CBO9781107478206

4. Rozenbaum V.M., Shapochkina I.V., Trakhtenberg L.I. Green's function method in the theory of Brownian motors. Physics-Uspekhi. 2019. 62(5): 496. https://doi.org/10.3367/UFNe.2018.04.038347

5. Rozenbaum V.M. Constructive role of chaos: Brownian motors and winning strategies in game theory. Him. Fiz. Tehnol. Poverhni. 2020. 11(1): 100. [in Russian]. https://doi.org/10.15407/hftp11.01.100

6. Denisov S., Flach S., Hänggi P. Tunable transport with broken spacetime symmetries. Phys. Rep. 2014. 538: 77. https://doi.org/10.1016/j.physrep.2014.01.003

7. Cubero D., Renzoni F. Hidden symmetries, instabilities, and current suppression in Brownian ratchets. Phys. Rev. Lett. 2016. 116(1): 010602-1-6. https://doi.org/10.1103/PhysRevLett.116.010602

8. Rozenbaum V.M., Shapochkina I.V., Teranishi Y., Trakhtenberg L.I. Symmetry of deterministic ratchets. Phys. Rev. E. 2019. 100(2): 022115-1-16. https://doi.org/10.1103/PhysRevE.100.022115

9. Korochkova T.E., Rosenbaum V.M., Mashira V.A., Shakel E.V., Shapochkina I.V., Ikim M.I., Gerasimov G.N., Gromov V.F., Bugaev A.S. Spatial-temporal symmetry of Brownian motors controlled by a dichotomous process. Surface. 2019. 11(26): 382. [in Russian]. https://doi.org/10.15407/Surface.2019.11.382

10. Vysotskaya V.A., Shapochkina I.V., Korochkova T.E., Rosenbaum V.M. Stochastic Brownian motors with small fluctuations in potential energy. Him. Fiz. Tehnol. Poverhni. 2017. 8(3): 299. [in Russian]. https://doi.org/10.15407/hftp08.03.299

11. Rozenbaum V.M., Shapochkina I.V., Teranishi Y., Trakhtenberg L.I. High-temperature ratchets driven by deterministic and stochastic fluctuations. Phys. Rev. E. 2019. 99(1): 012103-1-10. https://doi.org/10.1103/PhysRevE.99.012103

12. Roth J.S., Zhang Y., Bao P., Cheetham M.R., Han X., Evans S.D. Optimization of Brownian ratchets for the manipulation of charged components within supported lipid bilayers. Appl. Phys. Lett. 2015. 106(18): 183703 (1-4). https://doi.org/10.1063/1.4919801

13. Lau B., Kedem O., Schwabacher J., Kwasnieski D., Weiss E.A. An introduction to ratchets in chemistry and biology. Mater. Horiz. 2017. 4(3): 310. https://doi.org/10.1039/C7MH00062F