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Nonlinear physics and mechanics
Nonlinear Interactions in Nanolattices Described
by the Classical Morse, Biswas – Hamann
and Modified Lennard – Jones Potentials
S. A. Surulerea, M. Y. Shatalova, J. O. Ehigieb, A. A. Adenijia, I. A. Fedotova a Department of Mathematics and Statistics, Tshwane University of Technology,
Private Bag X680 Pretoria 0001, Staatsartillerie Road, Pretoria West, South Africa
b Department of Mathematics, University of Lagos,
University Road Lagos Akoka, Yaba 101017, Lagos, Nigeria
Abstract:
The oscillatory motion in nonlinear nanolattices having different interatomic potential energy
functions is investigated. Potential energies such as the classical Morse, Biswas – Hamann
and modified Lennard – Jones potentials are considered as interaction potentials between atoms
in one-dimensional nanolattices. Noteworthy phenomena are obtained with a nonlinear chain,
for each of the potential functions considered. The generalized governing system of equations for
the interaction potentials are formulated using the well-known Euler – Lagrange equation with
Rayleigh’s modification. Linearized damping terms are introduced into the nonlinear chain. The
nanochain has statistical attachments of 40 atoms, which are perturbed to analyze the resulting
nonlinearities in the nanolattices. The range of initial points for the initial value problem
(presented as second-order ordinary differential equations) largely varies, depending on the interaction
potential. The nanolattices are broken at some initial point(s), with one atom falling off
the slender chain or more than one atom falling off. The broken nanochain is characterized by an
amplitude of vibration growing to infinity. In general, it is observed that the nonlinear effects in
the interaction potentials cause growing amplitudes of vibration, accompanied by disruptions of
the nanolattice or by the translation of chaotic motion into regular motion (after the introduction
of linear damping). This study provides a computationally efficient approach for understanding
atomic interactions in long nanostructural components from a theoretical perspective.
Keywords:
nonlinear interactions, 1D lattices, Euler – Lagrange, interatomic potentials,
nanostructures.
Received: 04.10.2021 Accepted: 11.01.2022
Citation:
S. A. Surulere, M. Y. Shatalov, J. O. Ehigie, A. A. Adeniji, I. A. Fedotov, “Nonlinear Interactions in Nanolattices Described
by the Classical Morse, Biswas – Hamann
and Modified Lennard – Jones Potentials”, Rus. J. Nonlin. Dyn., 18:2 (2022), 183–201
Linking options:
https://www.mathnet.ru/eng/nd786 https://www.mathnet.ru/eng/nd/v18/i2/p183
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Abstract page: | 54 | Full-text PDF : | 16 | References: | 11 |
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