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Journal articles on the topic 'Lennard-Jones interaction potential'

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Author: Grafiati

Published: 6 September 2023

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1

Qu, Dayi, Zixu Zhao, Chunyan Hu, Tao Wang, and Hui Song. "Car-Following Dynamics, Characteristics, and Model Based on Interaction Potential Function." Journal of Advanced Transportation 2022 (January 29, 2022): 1–11. http://dx.doi.org/10.1155/2022/5274056.

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To model the car-following behavior more accurately, we carried out the molecular similarity analysis between the vehicles on the road and the inert gas system, comparing vehicles with microscopic particles in long and narrow pipes. The complex car-following interaction behavior is simplified into a dynamic process of the follower car that is constantly seeking to maintain the required safety distance from the leading vehicle. Through mathematical derivation of the Lennard–Jones potential function suitable for thermodynamic analysis of inert gas systems, the influence of each variable on the potential energy is clarified, and the existing problems of the existing molecular car-following model are analyzed, referring to the general Lennard–Jones potential function to build the vehicle interaction potential function. Considering the impact of the road wall potential generated by the lane boundary, a car-following model based on Lennard–Jones interaction potential is presented. The simulation test results show that compared with the existing molecular car-following model and IDM model, the average absolute error and root mean square error of the vehicle acceleration results obtained by this model and the actual data are lower, which proves that the vehicle is based on the Lennard–Jones interaction potential. The vehicle-following model based on Lennard–Jones interaction potential has a better fitting effect on the real vehicle-following behavior.

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2

LIM, TEIK-CHENG. "UNITED ATOM MODEL APPROACH FOR DESCRIBING C60 INTERACTION ENERGY IN MOLECULAR MECHANICS." Journal of Theoretical and Computational Chemistry 10, no. 04 (August 2011): 423–34. http://dx.doi.org/10.1142/s0219633611006554.

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A unified atom model for describing interaction energy between C60 molecules was obtained by Liu and Wang based on the Smith–Thakkar potential function. In view of the mathematical resemblance between the Liu–Wang and the conventional Lennard-Jones (12-6) function (used in computational chemistry software for describing van der Waals energy), modified versions of the Lennard-Jones function are proposed for quantifying the potential energy between C60 molecules. In this way, the Liu–Wang parameters can be converted into Lennard-Jones parameters for ready execution in commercially available computational chemistry software with minimal hard-coding involved. It was found that the Lennard-Jones function reasonably approximates the Liu–Wang model when the former's indices are increased by a factor of (7/4), without introducing any change to the coefficients. A better agreement was found when m = 4n = 35.4857, which also requires the change in repulsive and attractive indices from 1 and 2 to (1/3) and (4/3), respectively.

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3

Saxena, Vivek. "Molecular dynamics simulation of interhalogen compounds using two potential models 2. Liquid bromine trifluoride (BrF3) — structure and thermodynamics." Canadian Journal of Chemistry 71, no. 12 (December 1, 1993): 2189–93. http://dx.doi.org/10.1139/v93-274.

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This paper reports on the molecular dynamics simulation results of liquid bromine trifluoride (BrF3) at 299, 315, and 363 K. We have assumed that the molecules interact via Lennard–Jones 12–6 site–site pair potential and Lennard–Jones site–site + fractional charges over atomic sites. Lennard–Jones potential parameters of Singer et al. (Mol. Phys. 33, 1757 (1977)) have been used for Br–Br, and F–F interactions and cross interaction terms are calculated using Lorentz–Berthelot mixing rules. Fractional charges are assigned to reproduce the experimentally determined gaseous-state molecular dipole moment. Various structural and thermodynamic properties for liquid state are reported and compared in detail with results from diffraction studies (Mittkin et al. J. Struct. Chem. 28, 60 (1987)). Some mechanical properties such as mean-square force and torque, self-diffusion coefficient have also been calculated. The repulsive part of the proposed atom–atom pair potential is a good approximation since both molecular configurations are in good agreement with experimental results.

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4

Adeniji, A. A., I. A. Fedotov, J. O. Ehigie, M. Y. Shatalov, and S. A. Surulere. "Nonlinear Interactions in Nanolattices Described by the Classical Morse, Biswas – Hamann and Modified Lennard – Jones Potentials." Nelineinaya Dinamika 18, no. 2 (2022): 183–201. http://dx.doi.org/10.20537/nd220203.

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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.

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5

Wójcicki, Piotr, and Tomasz Zientarski. "APPLICATION OF THE LENNARD-JONES POTENTIAL IN MODELLING ROBOT MOTION." Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska 9, no. 4 (December 15, 2019): 14–17. http://dx.doi.org/10.35784/iapgos.45.

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The article proposes a method of controlling the movement of a group of robots with a model used to describe the interatomic interactions. Molecular dynamics simulations were carried out in a system consisting of a moving groups of robots and fixed obstacles. Both the obstacles and the group of robots consisted of uniform spherical objects. Interactions between the objects are described using the Lennard-Jones potential. During the simulation, an ordered group of robots was released at a constant initial velocity towards the obstacles. The objects’ mutual behaviour was modelled only by changing the value of the interaction strength of the potential. The computer simulations showed that it is possible to find the optimal value of the potential impact parameters that enable the implementation of the assumed robotic behaviour scenarios. Three possible variants of behaviour were obtained: stopping, dispersing and avoiding an obstacle by a group of robots.

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6

Okabe, Tsuneyasu, and Hiroaki Yamada. "Lyapunov Instability in One-Dimensional Lennard-Jones System." International Journal of Modern Physics B 12, no. 09 (April 10, 1998): 901–20. http://dx.doi.org/10.1142/s0217979298000508.

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We study a transition from quasiperiodic to stochastic motion in one-dimensional classical systems consisting of N particles with the nearest-neighbor Lennard–Jones interaction, extensively by computer simulation. We find a new feature in the change of the Lyapunov spectrum and the maximal Lyapunov exponent by changing its energy in the intermediate region between quasiperiodic and stochastic motions. The characteristics of the Lennard–Jones system in the intermediate region is considered by means of properties of Hessian matrix of potential function. The applicability of random matrix approximation for high energy region is also investigated, comparing with the case of soft-core potential.

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7

Fuwa, Masahiro, and Masahide Sato. "Effect of impurities on tiling in a two-dimensional dodecagonal quasicrystal." Japanese Journal of Applied Physics 61, no. 4 (March 17, 2022): 045504. http://dx.doi.org/10.35848/1347-4065/ac5530.

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Abstract Langevin dynamics simulations are performed to examine how impurities affect two-dimensional dodecagonal quasicrystals. We assumed that the interaction potential between two particles is the Lennard–Jones–Gauss potential if at least one of these particles is a matrix particle and that the interaction potential between two impurities is the Lennard–Jones potential. Matrix particles and impurities impinge with constant rates on the substrate created by a part of a dodecagonal quasicrystal consisting of square and triangular tiles. The dependences of the twelve-fold rotational order and the number of shield-like tiles on the impurity density are examined after sufficient solid layers are grown. While the change in the twelve-fold rotational symmetry is small, the number of shield-like tiles in the solid increases greatly with increasing impurity density.

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8

He, Ke Rong. "Optimaization of Single-Walled Carbon Nanotube for Adsorption of Methane." Advanced Materials Research 291-294 (July 2011): 490–93. http://dx.doi.org/10.4028/www.scientific.net/amr.291-294.490.

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In this paper, methane adsorption in single-walled carbon nanotube (SWNT) has been simulated by using the grand canonical ensemble Monte Carlo (GCMC) method. Lennard-Jones (LJ) potential is used to represent the fluid-fluid interaction, Lennard-Jones potential and integral method are used to calculation of the potential between fluid molecules and carbon atoms, respectively. In the simulation, two methods of calculation of potential between fluid molecules and SWNT are compared. The potential calculated by the two methods are almost the same. Then the influence of diameter of SWNT on the usable capacity ratio (UCR) is analyzed, and the parameters of the SWNT which has the best adsorption performance at 300K is recommended under certain pressure.

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9

VAIA, RUGGERO, and VALERIO TOGNETTI. "EFFECTIVE POTENTIAL FOR TWO-BODY INTERACTIONS." International Journal of Modern Physics B 04, no. 13 (October 1990): 2005–23. http://dx.doi.org/10.1142/s0217979290001005.

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A new kind of effective potential, which permits the calculation of the quantum equilibrium averages of configuration dependent observables in a classical-like way, is used for calculating the quantum pair correlation function of a two-body system. The main feature of this effective potential is the capability to fully account for the quantum harmonic effects, so it proves much more efficient than the analogous one defined by the Wigner expansion. Applications and comparisons with exact data are made for the Lennard-Jones interaction, with the characteristic parameters of helium atoms and hydrogen molecules.

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10

Okabe, Tsuneyasu, and Hiroaki Yamada. "Instability of One-Dimensional Lennard–Jones System — Particle Density Dependence." Modern Physics Letters B 12, no. 16 (July 10, 1998): 615–22. http://dx.doi.org/10.1142/s021798499800072x.

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We report dynamical instability of one-dimensional system with the nearest-neighbor Lennard–Jones interaction. A presence of new certain region between weakly and strongly chaotic region has been found in energy dependence of the maximal Lyapunov exponent. It is numerically shown that the presence of the region is enhanced by decrease of the particle density. The characteristics of the Lennard–Jones system, which are different from the FPU and soft-core system, are explained by means of a local instability of the potential surface. In addition, the relation between the presence of the new region and spatio-temporal pattern is also discussed in the low density cases.

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11

Alshehri, Mansoor H., Faisal Z. Duraihem, and Mohammed A. Aba Oud. "Instability and translocation through nanopores of DNA interacting with single-layer materials." RSC Advances 10, no. 61 (2020): 36962–70. http://dx.doi.org/10.1039/d0ra06359b.

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Using classical applied mathematical modelling to employ the 6–12 Lennard-Jones potential function along with the continuous approximation to investigate the interaction energy between dsDNA and 2D-nanomaterials, namely GRA, h-BN, MoS₂ and WS₂ sheets.

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12

Lim, Teik-Cheng. "Alignment of Buckingham Parameters to Generalized Lennard-Jones Potential Functions." Zeitschrift für Naturforschung A 64, no. 3-4 (April 1, 2009): 200–204. http://dx.doi.org/10.1515/zna-2009-3-406.

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Abstract The Lennard-Jones(12-6) and the Exponential-6 potential functions are commonly used in computational softwares for describing the van der Waals interaction energy. Some softwares allow switching between these two potentials under prescribed condition(s) that attempt to connect the parameter relationship between the two functions. Here we propose a technique by which the parameter relationship between both potentials is extracted by simultaneously imposing an equal force constant at the well depth’s minimum and an equal mean interatomic energy from the point of equilibrium to the point of total separation. The former imposition induces good agreement for the interatomic compression and a small change in the interatomic distance near the equilibrium while the latter enables good agreement for large interatomic separation. The excellent agreement exhibited by the plots validates the technique of combined criteria proposed herein

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13

Maslov, V. P. "Thermodynamics of fluids for imperfect gases with Lennard-Jones interaction potential. I." Mathematical Notes 86, no. 3-4 (October 2009): 522–29. http://dx.doi.org/10.1134/s0001434609090296.

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14

Maslov, V. P. "Thermodynamics of fluids for imperfect gases with Lennard-Jones interaction potential: III." Mathematical Notes 87, no. 1-2 (February 2010): 79–87. http://dx.doi.org/10.1134/s0001434610010104.

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15

Sidorenkov, A. V., S. V. Kolesnikov, and A. M. Saletsky. "Graphene on Cu(111) at the nonzero temperatures: Molecular dynamic simulation." Modern Physics Letters B 31, no. 31 (November 6, 2017): 1750289. http://dx.doi.org/10.1142/s021798491750289x.

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We present results of molecular dynamic simulation of continuous graphene monolayer on Cu(111). In this paper, we investigate the dependencies of the average binding energy and the average binding distance on the temperature. The interaction between carbon and copper atoms was described by Lennard-Jones potential. It is shown that the binding energy practically remains constant in a wide range of temperatures 0–800 K. However, in the same temperature range, the binding distance of graphene on Cu(111) surface has a linear dependence on temperature. The dependence of the linear thermal expansion coefficient of the binding distance on Lennard-Jones parameters has been calculated. We suggest a simple theoretical model to explain this dependence qualitatively.

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16

Kansal, MK, and SK Trikha. "Effect of Short-range Repulsive Interactions on the Dynamics of the Methane Molecule." Australian Journal of Physics 46, no. 2 (1993): 305. http://dx.doi.org/10.1071/ph930305.

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Using a computer simulation technique, an attempt has been made to explain the A-type transition in the specific heat of solid methane at around 20 K in terms of the changes in the dynamical behaviour of the methane molecule under the influence of its nearest neighbours. Different exponents of the short-range repulsive interaction occurring in the expression for the potential energy have been tried in order to select the appropriate value. The well known Lennard-Jones (6-12) and (6-15) potentials are found to reveal a phase transition in a well defined region. From an analysis of the direction cosine data, the three-dimensional motion of the central methane molecule has been visualised before and after the transition. Pertaining to the Lennard-Jones potential, the period of the torsional oscillation (libration) of the methane molecule comes out to be of the order of 0�3xlO-12 s. From the computed critical rotational kinetic. energy, the transition temperature is found to be 20�2 K which agrees well with experimental observations.

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17

Předota, Milan, Ivo Nezbeda, and Stanislav Pařez. "Coarse-grained potential for interaction with a spherical colloidal particle and planar wall." Collection of Czechoslovak Chemical Communications 75, no. 5 (2010): 527–45. http://dx.doi.org/10.1135/cccc2009542.

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An effective coarse-grained interaction potential between a point particle and a spherical colloidal particle with continuously distributed inverse power-law interaction sites is derived. The potential covers all ranges of spherical particle size, from a point particle up to an infinitely large particle forming a planar surface. In the small size limit, the point-to-point interaction is recovered, while in the limit of an infinitely large sphere the potential comes over to the known particle–wall potentials as, e.g., the 9–3 potential in the case of the Lennard–Jones interaction. Correctness and usefulness of the derived potential is exemplified by its application to SPC/E water at a graphite sphere and wall.

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18

HAGHIGHI, BEHZAD, ALIREZA HASSANI DJAVANMARDI, MOHSEN NAJAFI, and MOHAMMAD MEHDI PAPARI. "CALCULATION OF THE DIFFUSION COEFFICIENTS FOR MIXTURES OF NO WITH He, Ne, Ar AND Kr AT LOW DENSITY USING SEMI-EMPIRICAL INVERSION METHOD." Journal of Theoretical and Computational Chemistry 02, no. 03 (September 2003): 371–83. http://dx.doi.org/10.1142/s0219633603000689.

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Diffusion coefficients for four equimolar binary gaseous mixtures of NO–noble gases are determined from the principle of corresponding states of viscosity by the inversion technique. The Lennard–Jones 12-6 (LJ 12-6) potential energy function is used as the initial model potential required by the technique. The interaction potential energies from the inversion procedure reproduce diffusion coefficients within 5%.

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19

Maulana, Alan, Zaki Su'ud, Hermawan K. Dipojono, and Khairurrijal Khairurrijal. "Corrosion Study of Steels In Liquid Lead-Bismuth Cooled Nuclear Reactors by Computer Simulation using Moldy Code." Indonesian Journal of Physics 18, no. 2 (November 3, 2016): 53–58. http://dx.doi.org/10.5614/itb.ijp.2007.18.2.3.

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The corrosion of steel in liquid lead-bismuth has been studied by computer simulation using MOLDY code. The diffusion processes among atoms are assumed to be the key issues to understand the corrosion mechanism microscopically. In order to simulate these diffusion processes, the inter-atomic potential between Fe-Fe, Pb-Pb, Bi-Bi, Cr-Cr and Ni-Ni are assumed to obey the Lennard-Jones potential. The Lennard-Jones potential parameters of above pairs of atom have been derived by fitting the data available in the literature with the Lennard-Jones equation. The initial positions of the system are taken from the crystal structures data including the cell parameters. The simulation cell was a box with the volume 60x30x30 Å3 that were filled by 2864 atoms. Nickel and chromium atoms were substituted into Fe crystal with the percentage 10% and 16 % respectively to construct the systems of SS-316 which contacted by 50%Pb-50%Bi. The molecular dynamic simulations have been carried out for surface interaction between steel crystal with liquid lead-bismuth for several temperatures. After done the above simulation, the simulation is then tried by using 45%Pb-55%Bi (Pb-Bi Eutectic). The results of molecular dynamic simulations for several temperatures and the effect of variation of Pb and Bi above will be presented in this paper.

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20

Du, Xiao Ming, Yong Huang, and Er Dong Wu. "Study of the Molecular Hydrogen- Zeolites Interaction." Advanced Materials Research 239-242 (May 2011): 1283–86. http://dx.doi.org/10.4028/www.scientific.net/amr.239-242.1283.

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An expression of monolayer capacity for hydrogen adsorption was derived on the basis of Ono-Kondo lattice theory. And then, the interaction energies between hydrogen molecules and pore surface atoms in the zeolite were calculated by using Lennard-Jones (12-6) potential model for spherical pores. The results show that the monolayer capacity is dependent on adsorbate–adsorbent and adsorbate–adsorbate interaction energies, and that the interaction energies of hydrogen-zeolite agree with the previously reported isosteric heat of hydrogen on zeolites.

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21

Matsuoka, Hiroshige, Niki Kitahama, and Shigehisa Fukui. "MoP-7 THEORETICAL STUDY OF SURFACE INTERACTION PRESSURES OF TWO-DIMENSIONAL PERIODIC MATERIAL DISTRIBUTIONS BASED ON THE LENNARD-JONES POTENTIAL." Proceedings of JSME-IIP/ASME-ISPS Joint Conference on Micromechatronics for Information and Precision Equipment : IIP/ISPS joint MIPE 2015 (2015): _MoP—7–1_—_MoP—7–3_. http://dx.doi.org/10.1299/jsmemipe.2015._mop-7-1_.

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22

Simões, Ricardo, Júlio C. Viana, Gustavo R. Dias, and António M. Cunha. "Influence of the Interaction Potential Parameters on the Mechanical Response of Simulated Semi-Crystalline Polymeric Materials." Materials Science Forum 514-516 (May 2006): 810–14. http://dx.doi.org/10.4028/www.scientific.net/msf.514-516.810.

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The tensile deformation of a semi-crystalline lamellar structure was simulated using coarse-grain molecular dynamics. Interactions between statistical segments are described by Lennard-Jones potentials, with two types of interactions (primary and secondary bonds) defined for the amorphous and crystalline phases. The choice of the correct interaction potentials in coarsegrain simulations requires an understanding of the influence of each interaction potential parameter on the mechanical response. The present paper reports results from that study, following a design of experiments approach. It was found that the apparent modulus is mainly determined by the width of the secondary bond potential. The yield stress and the extent of deformation of the material at a fixed force level are influenced both by the width of the secondary bond potential and the depth of the potential well of the amorphous region. Thus, the tensile mechanical properties and behaviour of the specific lamellar structure under study seems to be mainly determined by the secondary interactions in the amorphous region.

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23

Vogelsang, R., and C. Hoheisel. "Influence of the interaction potential on defect jumps in a Lennard-Jones lattice." Journal of Physics C: Solid State Physics 20, no. 35 (December 20, 1987): 5933–42. http://dx.doi.org/10.1088/0022-3719/20/35/009.

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24

Shen, Lingyue, Ping Lin, Zhiliang Xu, and Shixin Xu. "Diffuse interface model for cell interaction and aggregation with Lennard-Jones type potential." Computer Methods in Applied Mechanics and Engineering 415 (October 2023): 116257. http://dx.doi.org/10.1016/j.cma.2023.116257.

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25

Malyshev, V. L., C. I. Mikhaylenko, and E. F. Moiseeva. "Modeling the establishment of a saturated state of argon by molecular dynamics." Proceedings of the Mavlyutov Institute of Mechanics 8, no. 1 (2011): 172–81. http://dx.doi.org/10.21662/uim2011.1.016.

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Mathematical modeling of evaporation of liquid and condensation of gaseous argon is performed for small deviations from the saturation state. The simulation is performed using molecular dynamics methods, using the Lennard-Jones interaction potential. The thermodynamic parameters are calculated from the wide-range equation of state. The results of the calculations are compared with known experimental data.

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26

Khilchuk, M. D., and E. A. Tarasov. "Numerical modeling of interaction of water molecule and fullerene C₆₀." Journal of Physics: Conference Series 2211, no. 1 (March 1, 2022): 012015. http://dx.doi.org/10.1088/1742-6596/2211/1/012015.

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Abstract In this paper, the main subject of research is the interaction of nanostructures and water molecules. The method of molecular dynamics is used, which calculates the trajectory of a water molecule inside fullerene C60. The forces acting in the system are determined through the potential energy of the interaction of particles. The Lennard-Jones interaction potential is used. The trajectories of the movement of the water molecule for different initial conditions are obtained, the change in the speed of its movement is estimated, and the size of the movement area is estimated.

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27

HAGHIGHI, BEHZAD, ALIREZA HASSANI DJAVANMARDI, and MOHAMMAD MEHDI PAPARI. "CALCULATION OF THE TRANSPORT PROPERTIES OF GASEOUS MIXTURES OF CF4 WITH O2, N2, CH4 AND CO2 AT LOW DENSITY USING SEMI-EMPIRICAL INVERSION METHOD." International Journal of Computational Methods 04, no. 01 (March 2007): 59–80. http://dx.doi.org/10.1142/s0219876207000716.

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Viscosity and diffusion coefficients for four equimolar binary gaseous mixtures of CF 4 with O 2, N 2, CH 4 and CO 2 are determined from the extended principle of corresponding states by the inversion technique. The Lennard–Jones 12-6 (LJ 12-6) potential energy function is used as the initial model potential required by the technique. The interaction potential energies from the inversion procedure reproduce viscosity within 1% and diffusion coefficients within 5%.

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28

Miyake, Ryoya, Teppei Tanaka, Hiroshige Matsuoka, and Shigehisa Fukui. "MoP-6 THEORETICAL ANALYSES OF INTERACTION STRESSES ACTING BETWEEN SOLID SURFACES WITH ONE-DIMENSIONAL MATERIAL DISTRIBUTION BASED ON LENNARD-JONES POTENTIAL." Proceedings of JSME-IIP/ASME-ISPS Joint Conference on Micromechatronics for Information and Precision Equipment : IIP/ISPS joint MIPE 2015 (2015): _MoP—6–1_—_MoP—6–3_. http://dx.doi.org/10.1299/jsmemipe.2015._mop-6-1_.

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29

Kuterba, P., H. Christiansen, Z. Danel, and W. Janke. "Molecular dynamics simulations of the monomer density profiles of knotted ring polymer chains confined in a slit of two parallel walls with one attractive and another repulsive surface." Journal of Physics: Conference Series 2436, no. 1 (January 1, 2023): 012031. http://dx.doi.org/10.1088/1742-6596/2436/1/012031.

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Abstract We have used Molecular Dynamics simulations to obtain the monomer density profiles for real linear and ring polymer chains of 360 monomers length with different topological structures such as simple knots: 31, 61, 91, 10124, complex knots 313151 and twisted knots with n = 10 and n = 20 in a slit geometry of two parallel walls with one attractive and another repulsive surface. We have used Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) software to perform simulations with the Verlet integration algorithm. The interactions between monomers were simulated as Lennard-Jones 12-6 potential, for bonds we have used Finitely Extensible Nonlinear Elastic (FENE) potential and the interaction with the walls was taken into account via Lennard-Jones 9-3 potential. We observed that topologically complex polymers have lower monomer density profiles near the attractive wall, but at some distance in the direction to the repulsive wall this tendency changes to the opposite. We showed that most complex twisted knots have two maxima in narrow slits. In the wide slits we do not observe such relation for twisted knots at higher temperatures. These results are important for better understanding the nature of the depletion forces which arise in a slit geometry of two parallel walls with one attractive and one repulsive wall.

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30

Chan, Nicholas, Carrie Lin, Tevis Jacobs, Robert W. Carpick, and Philip Egberts. "Quantitative determination of the interaction potential between two surfaces using frequency-modulated atomic force microscopy." Beilstein Journal of Nanotechnology 11 (May 6, 2020): 729–39. http://dx.doi.org/10.3762/bjnano.11.60.

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The interaction potential between two surfaces determines the adhesive and repulsive forces between them. It also determines interfacial properties, such as adhesion and friction, and is a key input into mechanics models and atomistic simulations of contacts. We have developed a novel methodology to experimentally determine interaction potential parameters, given a particular potential form, using frequency-modulated atomic force microscopy (AFM). Furthermore, this technique can be extended to the experimental verification of potential forms for any given material pair. Specifically, interaction forces are determined between an AFM tip apex and a nominally flat substrate using dynamic force spectroscopy measurements in an ultrahigh vacuum (UHV) environment. The tip geometry, which is initially unknown and potentially irregularly shaped, is determined using transmission electron microscopy (TEM) imaging. It is then used to generate theoretical interaction force–displacement relations, which are then compared to experimental results. The method is demonstrated here using a silicon AFM probe with its native oxide and a diamond sample. Assuming the 6-12 Lennard-Jones potential form, best-fit values for the work of adhesion (W adh) and range of adhesion (z 0) parameters were determined to be 80 ± 20 mJ/m2 and 0.6 ± 0.2 nm, respectively. Furthermore, the shape of the experimentally extracted force curves was shown to deviate from that calculated using the 6-12 Lennard-Jones potential, having weaker attraction at larger tip–sample separation distances and weaker repulsion at smaller tip–sample separation distances. This methodology represents the first experimental technique in which material interaction potential parameters were verified over a range of tip–sample separation distances for a tip apex of arbitrary geometry.

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31

Давыдов, С. Ю. "Оценки констант электрон-фононной связи графена с металлическими и неметаллическими подложками." Физика твердого тела 60, no. 4 (2018): 808. http://dx.doi.org/10.21883/ftt.2018.04.45698.267.

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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.

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32

He, Ke Rong, and Zhi Chu Lu. "Computational Simulation of Methane Adsorption in Single-Walled Carbon Nanotube." Applied Mechanics and Materials 63-64 (June 2011): 983–86. http://dx.doi.org/10.4028/www.scientific.net/amm.63-64.983.

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In this paper, methane adsorption in single-walled carbon nanotube (SWNT) has been simulated by using the grand canonical ensemble Monte Carlo (GCMC) method. Lennard-Jones (LJ) potential is used to represent the fluid-fluid interaction, and integral method is used to calculation of the potential between fluid molecules and carbon atoms. In the simulation, adsorption isotherms of methane in the (15, 15), (20, 20), (25, 25) and (30, 30) SWNT are simulated.

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Belim, Sergey V., Ilya V. Tikhomirov, and Igor V. Bychkov. "Simulation of Epitaxial Film–Substrate Interaction Potential." Coatings 12, no. 6 (June 17, 2022): 853. http://dx.doi.org/10.3390/coatings12060853.

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The formation of the substrate surface potential based on the Lennard-Jones two-particle potential is investigated in this paper. A simple atom’s square lattice on the substrate surface is considered. The periodic potential of the substrate atoms is decomposed into a Fourier series. The amplitude ratio for different frequencies has been examined numerically. The substrate potential is approximated with high accuracy by the Frenkel–Kontorova potential at most parameter values. There is a field of parameters in which the term plays a significant role, with a period half as long as the period of the substrate atoms. The ground state of the monoatomic film is modeled on the substrate potential. The film may be in both crystalline and amorphous phases. The transition to the amorphous phase is associated with a change in the landscape of the substrate potential. There are introduced order parameters for structural phase transition in the thin film. When changing the parameters of the substrate, the order parameter experiences a jump when changing the phase of the film.

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HAGHIGHI, BEHZAD, ALIREZA HASSANI DJAVANMARDI, MOHAMAD MEHDI PAPARI, and MOHSEN NAJAFI. "PREDICTION OF THE TRANSPORT PROPERTIES OF SF6 WITH O2, CO2, CF4, N2 AND CH4 MIXTURES AT LOW DENSITY BY THE INVERSION METHOD (PART II)." Journal of Theoretical and Computational Chemistry 03, no. 01 (March 2004): 69–90. http://dx.doi.org/10.1142/s021963360400091x.

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Viscosity and diffusion coefficients for five equimolar binary gas mixtures of SF 6 with O 2, CO 2, CF 4, N 2 and CH 4 gases are determined from the extended principle of corresponding states of viscosity by the inversion technique. The Lennard–Jones 12-6 (LJ 12-6) potential energy function is used as the initial model potential required by the technique. The obtained interaction potential energies from the inversion procedure reproduce viscosity within 1% and diffusion coefficients within 5%.

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Stevens, Kyle, Thien Tran-Duc, Ngamta Thamwattana, and James M. Hill. "Modeling Interactions between Graphene and Heterogeneous Molecules." Computation 8, no. 4 (December 21, 2020): 107. http://dx.doi.org/10.3390/computation8040107.

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The Lennard–Jones potential and a continuum approach can be used to successfully model interactions between various regular shaped molecules and nanostructures. For single atomic species molecules, the interaction can be approximated by assuming a uniform distribution of atoms over surfaces or volumes, which gives rise to a constant atomic density either over or throughout the molecule. However, for heterogeneous molecules, which comprise more than one type of atoms, the situation is more complicated. Thus far, two extended modeling approaches have been considered for heterogeneous molecules, namely a multi-surface semi-continuous model and a fully continuous model with average smearing of atomic contribution. In this paper, we propose yet another modeling approach using a single continuous surface, but replacing the atomic density and attractive and repulsive constants in the Lennard–Jones potential with functions, which depend on the heterogeneity across the molecules, and the new model is applied to study the adsorption of coronene onto a graphene sheet. Comparison of results is made between the new model and two other existing approaches as well as molecular dynamics simulations performed using the LAMMPS molecular dynamics simulator. We find that the new approach is superior to the other continuum models and provides excellent agreement with molecular dynamics simulations.

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36

Dubovsky, O. A., and A. V. Orlov. "Compression solitons of two types in crystals with the Lennard-Jones interatomic interaction potential." JETP Letters 87, no. 8 (June 2008): 414–18. http://dx.doi.org/10.1134/s0021364008080055.

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Zhang, Xianren, Wenchuan Wang, and Guangfeng Jiang. "A potential model for interaction between the Lennard–Jones cylindrical wall and fluid molecules." Fluid Phase Equilibria 218, no. 2 (April 2004): 239–46. http://dx.doi.org/10.1016/j.fluid.2004.01.005.

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38

Munguía-Valadez, Jorge, Marco Antonio Chávez-Rojo, Edward John Sambriski, and José Antonio Moreno-Razo. "The generalized continuous multiple step (GCMS) potential: model systems and benchmarks." Journal of Physics: Condensed Matter 34, no. 18 (March 1, 2022): 184002. http://dx.doi.org/10.1088/1361-648x/ac4fe8.

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Abstract The generalized continuous multiple step (GCMS) potential is presented in this work. Its flexible form allows for repulsive and/or attractive contributions to be encoded through adjustable energy and length scales. The GCMS interaction provides a continuous representation of square-well, square-shoulder potentials and their variants for implementation in computer simulations. A continuous and differentiable energy representation is required to derive forces in conventional simulation algorithms. Molecular dynamics simulations are of particular interest when considering the dynamic properties of a system. The GCMS potential can mimic other interactions with a judicious choice of parameters due to the versatile sigmoid form. In this study, our benchmarks for the GCMS representation include triangular, Yukawa, Franzese, and Lennard-Jones potentials. Comparisons made with published data on volumetric phase diagrams, liquid structure, and diffusivity from model systems are in excellent agreement.

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Masturi and Sunarno. "Estimation of Van der Waals Interaction Using FTIR Spectroscopy." Advanced Materials Research 1123 (August 2015): 61–64. http://dx.doi.org/10.4028/www.scientific.net/amr.1123.61.

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Van der Waals (vdW) interaction is one of the important properties in the composite. The usual measurement used to investigate the vdW interaction between filler and polymeric binder is FTIR spectroscopy where the result obtained is the band shift appearance, however, it has not been used yet to estimate the vdW magnitude. Using the Lennard-Jones potential, we developed a new analysis method to obtain approximately its magnitude and further the distance between filler atoms and polymeric group. We used our model proposed to several data reported by some authors, and interestingly we also found an appearance of anharmonic vibration of the atoms.

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He, Ke Rong. "Computer Simulation in Actived Carbon Pores for Methane Storage." Applied Mechanics and Materials 63-64 (June 2011): 1022–25. http://dx.doi.org/10.4028/www.scientific.net/amm.63-64.1022.

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In this paper, adsorption of methane in actived carbon pores has been simulated by using the grand canonical ensemble Monte Carlo (GCMC) method. In the simulation, Lennard-Jones (LJ) potential is used for represent the fluid-fluid interaction, and the 10-4-3 potential is used for represent the interaction between fluid molecules and a slit carbon wall. Firstly, the adsorption isotherms of methane in actived carbon pores and local density profiles of methane in slit pore are obtained. Then, the interaction energy of methane in slit carbon pores with nine different pore sizes is obtained. Finally, the temperature, pressures, pore sizes affect the adsorption amount was studied, respectively.

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KITA, YUKIUMI, KEI WAKO, ISAMU OKADA, and MASANORI TACHIKAWA. "AB INITIO CALCULATIONS OF INTERMOLECULAR INTERACTION POTENTIALS OF FULLERENE-FRAGMENTS SYSTEMS." Journal of Theoretical and Computational Chemistry 04, no. 01 (March 2005): 49–58. http://dx.doi.org/10.1142/s0219633605001313.

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We have performed the ab initio molecular orbital calculations for combinations of the fullerene-fragments as the models of the nonbonding interaction of C 60 dimer at the preferred configurations in the simple cubic phase. The intermolecular interaction potentials have been calculated using several basis sets with MP2 level of the electron correlation energy and the basis set superposition error correction. The strong dispersion attractions that is dominant in the van der Waals interaction has been found for the combinations of the fullerene-fragments. The equilibrium intermolecular distances obtained are in good agreement with the corresponding experimental value. The repulsive region of the intermolecular interaction calculated by ab initio method is found to be express by an atom–atom interaction potential with an anisotropic exponential type repulsive term, which is less steep than the conventional Lennard–Jones type potential.

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Рехвиашвили, С. Ш., and М. М. Бухурова. "Молекулы фуллерена C-=SUB=-60-=/SUB=- под однослойным графеном на металлической подложке." Физика и техника полупроводников 55, no. 7 (2021): 592. http://dx.doi.org/10.21883/ftp.2021.07.51024.9570.

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The article discusses a hybrid nanomaterial - a monolayer of C60 molecules, which is located between a single-layer graphene and a metal substrate. Using the Lennard-Jones potential, formulas for the specific interaction energy of C60 fullerene molecules with single-layer graphene and a thick substrate are obtained. The specific energy of graphene adhesion and the equilibrium parameters of the considered nanostructure are calculated. The obtained theoretical results agree with the available experimental results.

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DOBRESCU, GIANINA, IUDIT FANGLI, and MIRCEA RUSU. "SIMULATION OF CO CHEMISORPTION ON Pt SUPPORTED ON FRACTAL SURFACES." Journal of Theoretical and Computational Chemistry 04, no. 03 (September 2005): 769–85. http://dx.doi.org/10.1142/s0219633605001829.

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CO chemisorption on Pt supported on fractal surfaces was simulated in order to compute chemisorption dimension and active sites fractal dimension. Pt deposition was simulated using different models on both fractal and planar surfaces. The potential energy surface with two adsorption positions model was used to compute Pt–CO interaction and a Lennard–Jones 6–12 potential was used to simulate CO–CO interaction. Two Pt phases on fractal surface, one at low concentration — the dispersed phase and the second at high concentration — the aggregated phase characterized by weak interactions with support are obtained. The results are in accord with experimental data of CO chemisorption on Pt supported on γ-alumina. Computed data obtained for planar support are compared with those obtained on fractal support. The effect of fractal support on chemisorption data is underlined.

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44

Adisa, Olumide O., Barry J. Cox, and James M. Hill. "Modelling the Adsorption of Methane Molecules into Carbon Nanotubes." Materials Science Forum 700 (September 2011): 104–7. http://dx.doi.org/10.4028/www.scientific.net/msf.700.104.

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We investigate the prospect of methane gas storage in carbon nanotubes, and in particular we determine the interaction energy between a methane molecule and (9, 5), (8, 8) and (10,10) carbon nanotubes. Employing the Lennard-Jones potential together with the continuous approximation, we determine analytically the interaction energy for a methane molecule inside a carbon nanotube. Our results indicate that larger tubes are highly favoured sites for methane storage although smaller tubes might be superior for methane adsorption at higher temperatures, especially in the range 400 − 500 K.

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Bubenchikov, Michael, Alexey Bubenchikov, and Alexander Malozemov. "Studying permeability of nanostructures obtained from polyethylene threads." Thermal Science 23, Suppl. 2 (2019): 463–69. http://dx.doi.org/10.2298/tsci19s2463b.

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The paper studies process of interaction of a moving molecule with structure atoms. The mathematical description is based on application of Hamiltonian systems model and numerical methods for solving the basic problem of molecular dynamics. The interaction between individual atoms and the simplest molecules is cared out using the classical Lennard-Jones potential. Polyethylene nanostructures are considered as filtering elements for selective separation of natural gas mixtures, in particular, their light components: hydrogen and helium. The influence of geometric dimensions and geometric features of a nanostructure on selectivity of gas mixtures separation is studied.

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46

GRIDNEV, K. A., S. YU TORILOV, D. K. GRIDNEV, V. G. KARTAVENKO, and W. GREINER. "MODEL OF BINDING ALPHA-PARTICLES AND APPLICATIONS TO SUPERHEAVY ELEMENTS." International Journal of Modern Physics E 14, no. 04 (June 2005): 635–43. http://dx.doi.org/10.1142/s0218301305003387.

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A model of nuclear matter built from alpha-particles is proposed. In this model, nuclei possess the molecular-like structure. Analyzing the numbers of bonds, one gets the formula for the binding energy of a nucleus. The structure is determined by the minimum of the total potential energy, where interaction between alpha-particles is pairwise and the pair-potential is of Lennard–Jones type. The calculated binding energies show a good agreement with experiment. Calculations predict the stability island for superheavy nuclei around Z=120.

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Mamedov, Bahtiyar Akber, Ebru Karatas, and Elif Somuncu. "Calculation of the Second Virial Coefficient of The TMGa Molecule." International Conference on Applied Engineering and Natural Sciences 1, no. 1 (July 20, 2023): 317–19. http://dx.doi.org/10.59287/icaens.1013.

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In this work, interaction energy values were calculated using ab initio method for Trimethylgallium (TMGa) molecule. For the Trimethylgallium molecules, the minimum energy values obtained by the ab initio method have been used to calculate second virial coefficient by placing in Yukawa potential. The obtained second virial coefficient results are compared to theoretical data reported in the literature. Furthermore, the obtained results for Yukawa potential compared to with other potentials such as Lennard Jones (12-6) potential and Morse potential in the literature. For most of the varied temperatures of the investigated TMGa molecule, the second virial coefficient predicted by theoretical result computations showed reasonable agreement with theoretical second virial coefficient values.

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Chen, Yue, Wei Chen, and Xiaosong Chen. "A classical density functional approach to depletion interaction of Lennard-Jones binary mixtures." Communications in Theoretical Physics 74, no. 3 (February 24, 2022): 035602. http://dx.doi.org/10.1088/1572-9494/ac4511.

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Abstract In this article, we apply classical density functional theory to investigate the characteristics of depletion interaction in Lennard-Jones (LJ) binary fluid mixtures. First, to confirm the validity of our adopted density functional formalism, we calculate the radial distribution functions using a theoretical approach and compare them with results obtained by molecular dynamics simulation. Then, this approach is applied to two colloids immersed in LJ solvent systems. We investigate the variation of depletion interaction with respect to the distance of two colloids in LJ binary systems. We find that depletion interaction may be attractive or repulsive, mostly depending on the bulk density of the solvent and the temperature of the binary system. For high bulk densities, the repulsive barrier of depletion force is remarkable when the total excluded volume of colloids touches each other and reaches a maximum. The height of the repulsive barrier is related to the parameters of the LJ potential and bulk density. Moreover, the depletion force may exhibit attractive wells if the bulk density of the solvent is low. The attractive well tends to appear when the surface–surface distance of colloids is half of the size of the polymer and deepens with temperature lowering in a fixed bulk density. In contrast with the hard-sphere system, no oscillation of depletion potential around zero is observed.

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Kharlamov, G. V. "Molecular diffusion in gases and liquids." Journal of Physics: Conference Series 2119, no. 1 (December 1, 2021): 012122. http://dx.doi.org/10.1088/1742-6596/2119/1/012122.

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Abstract The diffusion coefficients in gases and liquids calculated by the molecular dynamics method with the use of the hard absolutely rough elastic spheres model are compared with those calculated using the Lennard-Jones potential. It is shown that dependences of reduced diffusion coefficients on density are similar, but differ numerically for different intermolecular interaction models. The simulation results have been compared with the experimental data on the diffusion in gaseous and liquid argon and in liquid benzene.

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Affouard, F., M. Descamps, L. C. Valdes, J. Habasaki, P. Bordat, and K. L. Ngai. "Breakdown of the Stokes–Einstein relation in Lennard-Jones glassforming mixtures with different interaction potential." Journal of Chemical Physics 131, no. 10 (2009): 104510. http://dx.doi.org/10.1063/1.3204063.

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