Rotational ratchet controlled by dichotomous changes in applied field orientations
Abstract
We explore the unidirectional rotation of a polar rotor (rotational ratchet) in a hindered-rotation potential (HRP), controlled by the dichotomous fluctuations of the orientation of the electric field. A symmetry analysis is carried out, which shows the absence of the ratchet effect for either an odd number of wells of the HRP or for an even number of wells if the average angle of the fluctuating orientations of the electric field coincides with any symmetry axes of the HRP. Analytical expressions are obtained for the average rotation velocity of the rotor in the double-well HRP in the low-temperature adiabatic approximation, when the hopping rotation occurs and thermodynamic equilibrium has time to be established in each state of the dichotomous process, and in the high-temperature approximation at arbitrary fluctuation frequencies, when the thermal energy is much greater than both the reorientation barrier of the HRP and the energy of the dipole rotor – electric field interaction. We showed that the maximum rotation velocity is achieved at large electric fields that fluctuate in sign, and the dependence of the rotation velocity on the amplitude of the angular fluctuations is bell-shaped, the width of which and the presence of the plateau can be tuned by the value of the average fluctuation angle. The dependence of the rotation velocity on the fluctuation frequency is also bell-shaped, wide for the stochastic fluctuations and narrow for the deterministic dichotomous ones, with the same linear low-frequency asymptotics.
References
- Julicher F, Ajdari A, Prost J. Modeling molecular motors. Reviews of Modern Physics.1997;69(4):1269–1281. DOI:10.1103/ RevModPhys.69.1269.
- Reimann P. Brownian motors: noisy transport far from equilibrium. Physics Reports. 2002;361(2–4):57–265. DOI:10.1016/ S0370-1573(01)00081-3.
- Astumian RD, Hanggi P. Brownian motors. Physics Today. 2002;55(11):33–39. DOI: 10.1063/1.1535005.
- Bressloff PC, Newby JM. Stochastic models of intracellular transport. Reviews of Modern Physics. 2013;85(1):135–196. DOI: 10.1103/RevModPhys.85.135.
- Hoffmann PM. How molecular motors extract order from chaos (a key issues review). Reports on Progress in Physics. 2016; 79(3):032601. DOI: 10.1088/0034-4885/79/3/032601.
- Cubero D, Renzoni F. Brownian ratchets: from statistical physics to bio- and nano-motors. Cambridge: Cambridge University Press; 2016. 200 p.
- Gulyaev YuV, Bugaev AS, Rozenbaum VM, Trakhtenberg LI. Nanotransport controlled by means of the ratchet effect. Physics – Uspekhi. 2020;63(4):311–326. DOI: 10.3367/UFNe.2019.05.038570.
- Dekhtyar ML. Brownian photomotors based on organic compounds: a review. Theoretical and Experimental Chemistry. 2022; 58(2):90–104. DOI: 10.1007/s11237-022-09726-5.
- Pierce S. Life’s mechanism. Life. 2023;13(8):1750. DOI:10.3390/life13081750.
- Kottas GS, Clarke LI, Horinek D, Michl J. Artificial molecular rotors. Chemical Reviews. 2005;105(4):1281–1376. DOI:10.1021/ cr0300993.
- Michl J, Sykes ECH. Molecular rotors and motors: recent advances and future challenges. ACS Nano. 2009;3(5):1042–1048. DOI:10.1021/nn900411n.
- Yang T, Zhang R. STM studies for surface-mounted molecular rotors: a mini review. AAPPS Bulletin. 2024;34:6. DOI:10.1007/ s43673-023-00107-1.
- Gao L, Liu Q, Zhang YY, Jiang N, Zhang HG, Cheng ZH, et al. Constructing an array of anchored single-molecule rotors on gold surfaces. Physical Review Letters. 2008;101(19):197209. DOI:10.1103/PhysRevLett.101.197209.
- Stolz S, Groning O, Prinz J, Brune H, Widmer R. Molecular motor crossing the frontier of classical motion to quantum tunneling motion. PNAS. 2020;117(26):14838–14842. DOI: 10.1073/pnas.1918654117.
- Rozenbaum VM, Ogenko VM, Chuiko AA. Vibrational and orientational states of surface atomic groups. Soviet Physics Uspekhi. 1991;34(10):883–902. DOI:10.1070/PU1991v034n10ABEH002525.
- Rozenbaum VM, Lin SH. Spectroscopy and dynamics of orientationally structured adsorbates. Singapure: World Scientific; 2002. 208 p.
- Koumura N, Zijlstra WJ, van Delden RA, Harada N, Feringa BL. Light-driven monodirectional molecular rotor. Nature.1999; 401(6749):152–155. DOI: 10.1038/43646.
- Sheng J, Danowski W, Sardjan AS, Hou J, Crespi S, Ryabchun A, et al. Formylation boosts the performance of light-driven overcrowded alkene-derived rotary molecular motors. Nature Chemistry. 2024;16(8):1330–1338. DOI:10.1038/s41557-024-01521-0.
- Rozenbaum VM, Vovchenko OYe, Korochkova TYe. Brownian dipole rotator in alternating electric field. Physical Review E. 2008;77(6):061111. DOI: 10.1103/PhysRevE.77.061111.
- Shapochkina IV, Rozenbaum VM. Adiabatic discrete ratchet effect of a rotor in the N-well potential of hindered rotation. Nonlinear Phenomena in Complex Systems. 2024;27(2):199–207. DOI:10.5281/zenodo.12621736.
- Zhang J, Con C, Cui B. Electron beam lithography on irregular surfaces using an evaporated resist. ACS Nano. 2014;8(4): 3483–3489. DOI:10.1021/nn4064659.
- Zharik GA, Dagesyan SA, Soldatov ES, Presnov DE, Krupenin VA. Nanometer scale lithography with evaporated polystyrene. Moscow University Physics Bulletin. 2017;72(6):627–632. DOI: 10.3103/S0027134917060224.
- Rozenbaum VM, Shapochkina IV, Trakhtenberg LI. Green’s function method in the theory of Brownian motors. Physics – Uspekhi. 2019;62(5):496–509. DOI: 10.3367/UFNe.2018.04.038347.
- Reimann P. Supersymmetric ratchets. Physical Review Letters. 2001;86(22):4992–4995. DOI: https://doi.org/10.1103/PhysRevLett.86.4992.
- Denisov S, Flach S, Hanggi P. Tunable transport with broken space – time symmetries. Physics Reports. 2014;538(3):77–120. DOI:10.1016/j.physrep.2014.01.003.
- Rozenbaum VM, Shapochkina IV, Teranishi Y, Trakhtenberg LI. Symmetry of deterministic ratchets. Physical Review E. 2019; 100(2):022115. DOI: 10.1103/PhysRevE.100.022115.
- Shapochkina IV, Savina ND, Rozenbaum VМ, Korochkova ТYe. Symmetry properties of a Brownian motor with a sawtooth potential perturbed by harmonic fluctuations. Journal of the Belarusian State University. Physics. 2021;1:41–49. Russian. DOI:10.33581/ 2520-2243-2021-1-41-49.
- Rozenbaum VM, Yang D-Y, Lin SH, Tsong TY. Catalytic wheel as a Brownian motor. Journal of Physical Chemistry B. 2004; 108(40):15880–15889. DOI: 10.1021/jp048200a.
- Reimann P, Grifoni M, Hanggi P. Quantum ratchets. Physical Review Letters. 1997;79(1):10–13. DOI:10.1103/PhysRevLett.79.10.
- Rozenbaum VM, Shapochkina IV, Trakhtenberg LI. Tunneling mechanism for changing the motion direction of a pulsating ratchet temperature effect. JETP Letters. 2023;118(5):369–375. DOI: 10.1134/S002136402360235X.
- Rozenbaum VM, Shapochkina IV, Trakhtenberg LI. Adiabatic ratchet effect in systems with discrete variables. JETP Letters. 2020;112(5):316–322. DOI: 10.1134/S0021364020170075.
- Rozenbaum VM. High-temperature Brownian motors: deterministic and stochastic fluctuations of a periodic potential. JETP Letters. 2008;88(5):342–346. DOI:10.1134/S0021364008170128.
- Shapochkina IV, Rozenbaum VM. High-temperature diffusion transport: transition processes in symmetric deterministic dichotomic fluctuations of a potential energy. Vestnik BGU. Seriya 1, Fizika. Matematika. Informatika. 2009;2:43–47. Russian.
- Shapochkina IV, Rozenbaum VM. High-temperature diffusion transport: asymmetric transition processes in symmetric deterministic dichotomic fluctuations of a potential energy. Vestnik BGU. Seriya 1, Fizika. Matematika. Informatika. 2010;2:41–45. Russian.
- Rozenbaum VM, Shapochkina IV, Teranishi Y, Trakhtenberg LI. High-temperature ratchets driven by deterministic and stochastic fluctuations. Physical Review E. 2019;99(1):012103. DOI: 10.1103/PhysRevE.99.012103.
- Shapochkina IV, Savina ND, Zaytseva ЕМ, Rozenbaum VM, Ikim MI, Bugaev AS. Adiabatic Brownian motor with a stepwise potential perturbed by a dichotomous harmonic signal. Journal of the Belarusian State University. Physics. 2021;2:71–80. Russian. DOI: 10.33581/2520-2243-2021-2-71-80.
- Makhnovskii YuA, Rozenbaum VM, Yang D-Y, Lin SH, Tsong TY. Flashing ratchet model with high efficiency. Physical Review E. 2004;69(2):021102. DOI: 10.1103/PhysRevE.69.021102.
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