Subscribe

Subscribe to our Newsletter and get informed about new publication regulary and special discounts for subscribers!

ILCPA > ILCPA Volume 86 > Motion in the Restricted Three-Body Problem at the...
< Back to Volume

Motion in the Restricted Three-Body Problem at the Nanoscale

Full Text PDF

Abstract:

This paper studies the classical restricted three-body problem of a carbon atom in the vicinity of two carbon 60 fullerenes (  fullerenes) at the nanoscale. The total molecular energy between the two fullerenes is determined analytically by approximating the pairwise potential energies between the carbon atoms on the fullerenes by a continuous approach. Using software MATHEMATICA, we compute the positions of the stationary points and their stability for a carbon atom at the nanosacle and it is observed that for each set of values, there exists at least one complex root with the positive real part and hence in the Lyapunov sense, the stationary points are unstable. Since only attractive Van der Waals forces contribute to the orbiting behavior, no orbiting phenomenon can be observed for , where the Van der Waals forces becomes repulsive. Although the  orbital is speculative in nature and also presents exciting possibilities, there are still many practical challenges that would need to be overcome before the  orbital might be realized. However, the present theoretical study is a necessary precursor to any of such developments.

Info:

Periodical:
International Letters of Chemistry, Physics and Astronomy (Volume 86)
Pages:
1-10
Citation:
J. Singh and T. K. Richard, "Motion in the Restricted Three-Body Problem at the Nanoscale", International Letters of Chemistry, Physics and Astronomy, Vol. 86, pp. 1-10, 2021
Online since:
April 2021
Export:
Distribution:
References:

[1] D. E. H. Jones, Hollow molecules. New science 32 (1966) 245.

[2] H. W. Kroto, J.R. Heath, S.C. O'Brien, R.F. Curl, R. E. Smalley, C60 Buckminster fullerene. Nature 318 (1985) 162-163.

[3] Q. Zhen, J. Z. Liu, Q. Jiang, Excess Van der Waals interaction energy of a multi-walled carbon nanotude with an extruded core and the induced core oscillation. Phys. Rev. B. 65 (2002) 245.

DOI: https://doi.org/10.1103/physrevb.65.245409

[4] P. Liu, Y.W. Zhang, C. Lu, Oscillatory behavior of C60-nanotube oscillators. A molecular dynamics study. Journal of applied physics 97 (2005).

DOI: https://doi.org/10.1063/1.1890451

[5] B. J. Cox, N. Thamwattana, J. M. Hill, Mechanics of atoms and fullerenes in single-walled carbon nanotubes. Acceptance and suction energies. Proc. Roy. Soc. London A. 463 (2007) 461.

DOI: https://doi.org/10.1098/rspa.2006.1771

[6] Y. Chan, G. M. Cox, J. M. Hill, A carbon orbiting around the outside of a carbon nanotube. In proceedings of International Conference on Nanoscience and Nanotechnology ICONN 2008 (2008) 152-155.

DOI: https://doi.org/10.1109/iconn.2008.4639269

[7] Y. Chan, N. Thamwattana, J. H. Hill, Restricted three-body problems at the nanoscale. Conditional mathematics-material science 62 (2009) 25.

[8] J.E.L. Jones, The determination of molecular fields. From the variation of the viscosity of a gas with temperature. Proc. Roy. Soc., 106A (1924) 441.

[9] C.N. Douskos, V.V. Markellos, Out-of-Plane equilibrium points in the restricted three-body problem with oblateness. Astronomy and Astrophysics, 466 (2006) 357-362.

DOI: https://doi.org/10.1051/0004-6361:20053828

[10] M.K. Das, P. Narang, S. Mahajan, M. Yuasa, On out of plane equilibrium points in Photo-Gravitational restricted three-body problem Astrophys. Astr. 30 (2009) 177-185.

DOI: https://doi.org/10.1007/s12036-009-0009-6

[11] J. Singh, A. Umar, On the stability of triangular equilibrium points in the elliptic R3BP under radiating and oblate primaries. Astrophys. Space Sci. 341 (2012) 349-358.

DOI: https://doi.org/10.1007/s10509-012-1109-3

[12] J. Singh, A. Umar, On out of plane equilibrium points in the Elliptic restricted three-body problem with radiation and oblate primaries. Astrophys. Space Sci. 344 (2013) 13-19.

DOI: https://doi.org/10.1007/s10509-012-1292-2

[13] J. Singh, T.O. Amuda, Out-of-Plane equilibrium points in the photogravitational circular restricted three-body problem with oblateness and P-R Drag. Astronomy and Astrophysics 36 (2015) 291-305.

DOI: https://doi.org/10.1007/s12036-015-9336-y

[14] J. Singh, K. R. Tyokyaa, Stability of triangular points in the elliptic restricted three-body problem with oblateness up to zonal harmonic J4 of both primaries. Eur. Phys. J. Plus, 131 (2016) 365.

DOI: https://doi.org/10.1140/epjp/i2016-16365-2

[15] J. Singh, K. R. Tyokyaa, Stability of collinear points in the elliptic restricted three-body problem with oblateness up to zonal harmonic J4 of both primaries. Eur. Phys. J. Plus, 132 (2017) 330.

DOI: https://doi.org/10.1140/epjp/i2017-11604-8
Show More Hide
Cited By:
This article has no citations.