Chemistry, Physics and Technology of Surface, 2016, 7 (4), 444-452.

Molecular rotor as a high-temperature Brownian motor



DOI: https://doi.org/10.15407/hftp07.04.444

O. Ye. Tsomyk, T. Ye. Korochkova, V. M. Rozenbaum

Abstract


The aim of the present work is to develop a theory of high-temperature polar molecular rotors, the rotation of which is initiated by an external alternating electric field. Such rotors can be considered as Brownian motors in the sense that a unidirectional translatory motion of motor particles is similar to the unidirectional rotation of moving part of a rotor; that allows using, at calculations, the high-temperature theory of Brownian motors. The potential energy of a rotating particle, as a function of time and rotation angle, is represented in additive-multiplicative form. The approximation of the two first harmonics suffices to describe a smooth potential profile. Indeed, they are the minimum number of harmonics to simulate the asymmetry of the potential relief and to describe molecular rotors since the first harmonic is conditioned by the interaction of the rotor with the alternating field and the second one – by the potential of hindered rotation. With these conditions, the velocity of rotation of polar molecular rotors is calculated, and the analytical dependences of the velocity on the parameters of the model is analyzed for the two cases of time dependence of the applied alternating electric field, harmonic and stepped. It is shown that, at a stepped change of an alternating electric field, the values of the angular velocity are higher, for any frequency of the applied field, than those at a harmonic change, and a dichotomic mode of the electric field changing is generally more efficient one, resulting in the optimal mode of rotor operation. Moreover, there exists a qualitative difference, in the low-frequency asymptotics of the rotor velocity, between harmonic and stepwise external field: the average velocity of rotation is proportional to the square of the field modulation frequency in the former case, and it is the linear function of the frequency in the later case.

Keywords


molecular rotor; Brownian motor; ratchet; diffusion kinetic; potential fluctuations

Full Text:

PDF

References


1. Rozenbaum V.M., Ogenko V.M., Chuiko A.A. Vibrational and orientational states of surface atomic groups. Sov. Phys. Usp. 1991. 34(10): 883. https://doi.org/10.1070/PU1991v034n10ABEH002525 

2. Rozenbaum V.M., Lin S.H. Spectroscopy and Dynamics of Orientationally Structured Adsorbates. (Singapure: World Scientific, 2002).

3. Kottas G.S., Clarke L. I., Horinek D., Michl J. Artificial molecular rotors. Chem. Rev. 2005. 105(4): 1281. https://doi.org/10.1021/cr0300993 

4. Vacek J., Michl J. Artificial surface-mounted molecular rotors: molecular dynamics simulations. Adv. Funct. Mater. 2007. 17(5): 730. https://doi.org/10.1002/adfm.200601225 

5. Rozenbaum V.M., Vovchenko O.Ye., Korochkova T.Ye. Brownian dipole rotator in alternating electric field. Phys. Rev. E. 2008. 77(6): 061111. https://doi.org/10.1103/PhysRevE.77.061111 

6. Rozenbaum V.M., Tsemik O.E. Analytical description of thermally stimulated polarization and depolarization currents. Phys. Solid State. 2010. 52(10): 2192. https://doi.org/10.1134/S106378341010029X 

7. Lemouchi C., Iliopoulos K., Zorina L., Simonov S., Wzietek P., Cauchy Th., Rodríguez-Fortea A., Canadell E., Kaleta J., Michl J., Gindre D., Chrysos M., Batail P. Crystalline arrays of pairs of molecular rotors: correlated motion, rotational barriers, and space-inversion symmetry breaking due to conformational mutations. J. Am. Chem. Soc. 2013. 135(25): 9366. https://doi.org/10.1021/ja4044517 

8. Comotti A., Bracco S., Ben T., Qiu Sh., Sozzani P. Molecular rotors in porous organic frameworks. Angew. Chem. Int. Ed. 2014. 53: 1043. https://doi.org/10.1002/anie.201309362 

9. Lien Ch., Seck Ch. M., Lin Y.-W., Nguyen J. H.V., Tabor D.A., Odom B. C. Broadband optical cooling of molecular rotors from room temperature to the ground state. Nature Commun. 2014. 5: 4783. https://doi.org/10.1038/ncomms5783 

10. Raeburn J., Chen L., Awhida S., Deller R.C., Vatish M., Gibson M.I., Adams D.J. Using molecular rotors to probe gelation. Soft Matter. 2015. 11: 3706. https://doi.org/10.1039/C5SM00456J 

11. Jiang X., O'Brien Z.J., Yang S., Lai L.H., Buenaflor J., Tan C., Khan S., Houk K.N., Garcia-Garibay M.A. Crystal fluidity reflected by fast rotational motion at the core, branches, and peripheral aromatic groups of a dendrimeric molecular rotor. J. Am. Chem. Soc. 2016. 138(13): 4650. https://doi.org/10.1021/jacs.6b01398 

12. Khodorkovsky Y., Steinitz U., Hartmann J.-M., Averbukh I.Sh. Collisional dynamics in a gas of molecular super-rotors. Nature Commun. 2015. 6: 7791. https://doi.org/10.1038/ncomms8791 

13. Kaleta J., Michl J., Mézière C., Simonov S., Zorina L., Wzietek P., Rodríguez-Fortea A., Canadell E., Batail P. Gearing motion in cogwheel pairs of molecular rotors: weak-coupling limit. Cryst. Eng. Comm. 2015. 17:7829. https://doi.org/10.1039/C5CE01372K 

14. Puigmartí-Luis J., Saletra W.J., González A., Pérez-García L., Amabilino D.B. Assembling Supramolecular Rotors on Surfaces under Ambient Conditions. Advances in Atom and Single Molecule Machines. (Berlin: Springer Int. Pub, 2015).

15. Cherioux F., Galangau O., Palmino F., Repenne G. Controlled directional motions of molecular vehicles, rotors, and motors: from metallic to silicon surfaces, a strategy to operate at higher temperatures. Chen. Phys.Chem. Minirewievs. 2016. 17: 1742. https://doi.org/10.1002/cphc.201500904 

16. Tsomik O.Ye., Chernova A.A., Rozenbaum V.M. Near-surface Brownian motors, controlled by an alternating electric field. Dopov. Nat. akad. nauk Ukr. 2009. 12: 83. [in Russian]

17. Rozenbaum V.M. High-temperature brownian motors: Deterministic and stochastic fluctuations of a periodic potential. JETP Letters. 2008. 88(5): 342. https://doi.org/10.1134/S0021364008170128 

18. Shapochkina I.V., Rozenbaum V.M. High-temperature diffusion transport: transient processes in symmetric dichotomous deterministic fluctuations of the potential energy. Vestnik BGU. 2009. 1(2): 43. [in Russian]

19. Prudnikov A.P., Brychkov Yu.A., Marichev O.I. Integrals and series. (NY: Gordon and Breach Science Publishers, 1992).




DOI: https://doi.org/10.15407/hftp07.04.444

Copyright (©) 2016 O. Ye. Tsomyk, T. Ye. Korochkova, V. M. Rozenbaum

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.