scholarly journals Оценки констант электрон-фононной связи графена с металлическими и неметаллическими подложками

2018 ◽  
Vol 60 (4) ◽  
pp. 808
Author(s):  
С.Ю. Давыдов
Keyword(s):  
Covalent Bond ◽  
Orbital Method ◽  
Phonon Interaction ◽  
Jones Potential ◽  
Electron Phonon Interaction ◽  
Dielectric Substrates ◽  
Lennard Jones ◽  
Strong Covalent Bond ◽  
Two Parameters ◽  
Analytical Expressions

AbstractTwo modes of graphene–substrate interaction have been considered: a weak van der Waals bond and a strong covalent bond. The Lennard–Jones potential and Harrison bond-orbital method are used in the former and latter cases, respectively. Analytical expressions for the electron–phonon interaction constants, which contain only two parameters (binding energy E _ B for graphene and a substrate and distance d between them) have been obtained. The constants have been calculated for metallic, semiconductor, and dielectric substrates.

A THEORETICAL INVESTIGATION ON 10–12 POTENTIAL OF HYDROGEN–HYDROGEN COVALENT BOND

2013 ◽  
Vol 27 (11) ◽  
pp. 1350076
Author(s):  
SENCER TANERI
Keyword(s):  
Binding Energy ◽  
Hydrogen Molecule ◽  
Covalent Bond ◽  
Power Laws ◽  
Analytical Investigation ◽  
Lennard Jones Potential ◽  
Internuclear Separation ◽  
Jones Potential ◽  
Lennard Jones ◽  
Almost Everywhere

This is an analytical investigation of well-known 10–12 potential of hydrogen–hydrogen covalent bond. In this research, we will make an elaboration of the well-known 6–12 Lennard–Jones potential in case of this type of bond. Though the results are illustrated in many text books and literature, an analytical analysis for these potentials is missing almost everywhere. The power laws are valid for small radial distances, which are calculated to some extent. The internuclear separation as well as the binding energy of the hydrogen molecule are evaluated with success.

scholarly journals A Review of Geometry, Construction and Modelling for Carbon Nanotori

2019 ◽  
Vol 9 (11) ◽  
pp. 2301 ◽  
Author(s):  
Pakhapoom Sarapat ◽  
James Hill ◽  
Duangkamon Baowan
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanostructures ◽  
Single Walled Carbon Nanotubes ◽  
Continuum Approximation ◽  
Interaction Energies ◽  
Jones Potential ◽  
Lennard Jones ◽  
Walled Carbon Nanotubes ◽  
Analytical Expressions ◽  
The Continuum

After the discovery of circular formations of single walled carbon nanotubes called fullerene crop circles, their structure has become one of the most researched amongst carbon nanostructures due to their particular interesting physical properties. Several experiments and simulations have been conducted to understand these intriguing objects, including their formation and their hidden characteristics. It is scientifically conceivable that these crop circles, nowadays referred to as carbon nanotori, can be formed by experimentally bending carbon nanotubes into ring shaped structures or by connecting several sections of carbon nanotubes. Toroidal carbon nanotubes are likely to have many applications, especially in electricity and magnetism. In this review, geometry, construction, modelling and possible applications are discussed and the existing known analytical expressions, as obtained from the Lennard-Jones potential and the continuum approximation, for their interaction energies with other nanostructures are summarised.

On the transport properties of simple liquids

1986 ◽  
Vol 64 (2) ◽  
pp. 211-214
Author(s):  
S. K. Datta
Keyword(s):  
Shear Viscosity ◽  
Pair Potential ◽  
Viscosity Coefficient ◽  
Simple Fluids ◽  
Jones Potential ◽  
Simple Liquids ◽  
Lennard Jones ◽  
Approximate Nature ◽  
Real Fluids ◽  
Analytical Expressions

Closed analytical expressions for the diffusion coefficient and shear-viscosity coefficient of dense, simple fluids characterized by the Lennard-Jones potential function have been obtained using the Weeks, Chandler, and Andersen criterion for the division of the pair potential. The expressions are then used to calculate these properties for some real fluids. The deviations between the estimated and measured values of the coefficients are attributed mostly to the approximate nature of the Kirkwood and Rice expressions for shear viscosity and the friction coefficient used to calculate those properties.

scholarly journals Exponentially Correlated Gaussians for Simulating Of Localized and Autolocalized States in Polar Media

2017 ◽  
Vol 12 (2) ◽  
pp. 273-301 ◽  
Author(s):  
Н.И. Каширина ◽  
N.I. Kashirina
Keyword(s):  
Energy Spectrum ◽  
Localized States ◽  
Continuum Approximation ◽  
Electron Systems ◽  
Phonon Interaction ◽  
Phonon Field ◽  
Electron Phonon Interaction ◽  
Polar Media ◽  
Analytical Expressions ◽  
The Continuum

Localized and autolocalized states and their simplest two-electron complexes in polar media are considered in the continuum approximation. The electron-phonon interaction is taken into account in the Pekar-Fröhlich approximation. The exponentially correlated Gaussian basis is used for the calculation of the energy spectrum of two-electron systems in phonon field. Analytical expressions for effective functionals of paramagnetic centers and their simplest two-electron complexes are presented. Numerical examples are given for the calculations of the energy spectrum of localized and self-localized states in metal-ammonia solutions.

scholarly journals Electron-Phonon Scattering in Quantum-Sized Films with the Hyperbolic Pöschl–Teller Potential

2019 ◽  
Vol 64 (4) ◽  
pp. 336
Author(s):  
Kh. A. Gasanov ◽  
J. I. Guseinov ◽  
I. I. Abbasov ◽  
D. J. Askerov ◽  
Kh. O. Sadig
Keyword(s):  
Electron Scattering ◽  
Phonon Scattering ◽  
Transition Probability ◽  
Bulk Crystals ◽  
Dimensional Electron ◽  
Phonon Interaction ◽  
Electron Phonon Interaction ◽  
Dimensional Electron Gas ◽  
Analytical Expressions ◽  
Electron Phonon Scattering

A quantitative theory of electron-phonon interaction in the two-dimensional electron gas in a quantum-sized film with the hyperbolic P¨oschl–Teller confining potential has been developed. Analytical expressions for the transition probability are derived in the case of electron scattering by deformation-induced acoustic, piezoacoustic, and polar optical phonons. The results obtained for various scattering mechanisms in the film are compared with the results obtained for bulk crystals.

scholarly journals Modelling of Nickel Atoms Interacting with Single-Walled Nanotubes

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Mansoor H. Alshehri
Keyword(s):  
Cross Section ◽  
Nickel Atom ◽  
Boron Nitride Nanotubes ◽  
Interaction Energies ◽  
Jones Potential ◽  
Single Walled Nanotubes ◽  
Lennard Jones ◽  
Continuous Approach ◽  
Minimum Interaction ◽  
Analytical Expressions

Herein, the encapsulation mechanism of nickel atoms into carbon and boron nitride nanotubes is investigated to determine the interaction energies between the nickel atom and a nanotube. Classical modelling procedures, together with the 6-12 Lennard-Jones potential function and the hybrid discrete-continuous approach, are used to calculate the interaction of a nickel atoms with (i,i) armchair and (i,0) zigzag single-walled nanotubes. Analytical expressions for the interaction energies are obtained to determine the optimal radii of the tubes to enclose the nickel atom by determining the radii that give the minimum interaction energies. We first investigate the suction energy of the nickel atom entering the nanotube. The atom is assumed to be placed on the axis and near an open end of a semi-infinite, single-walled nanotube. Moreover, the equilibrium offset positions of the nickel atoms are found with reference to the cross-section of the nanotubes. The results may further the understanding of the encapsulation of Ni atoms inside defective nanotubes. Furthermore, the results may also aid in the design of nanotube-based materials and increase the understanding of their nanomagnetic applications and potential uses in other areas of nanotechnology.

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