Lennard-Jones Potential Function Research Articles

Hygro-thermo-mechanical vibration of two vertically aligned single-walled boron nitride nanotubes conveying fluid

The nonlocal strain gradient theory, when combined with the first-order shear deformation theory, provides many capabilities in size-dependent structures. The aim of the present study is evaluation of the free vibration behavior of two vertically aligned fluid-conveying single-walled boron nitride nanotubes in hygrothermal environments considering slip boundary condition based on Knudsen number. These two adjacent nanotubes are coupled in the context of linear deformation through van der Waals interaction according to Lennard–Jones potential function. Actually, the contribution of the present work, compared with those previously reported, is investigating the simultaneous effect of hygrothermal loading and slip boundary condition on the dynamic behavior of two vertically aligned fluid-conveying single-walled boron nitride nanotubes. As an additional step to achieve a more accurate model of low-scale structures, both hardening and softening effects of materials are taken as important variables in the nonlocal strain gradient approach. To derive the motion equations and associated boundary conditions, Hamilton’s variational principle is used. The equations are then solved with the aid of differential quadrature method. Numerical studies are also performed to depict the effects of a number of parameters such as boundary conditions, size scale, aspect ratio, inter-tube distance, and temperature alteration on the variations of dimensionless eigenfrequency and critical flow velocity.

A multiscale simulation of amorphous polystyrene

A multiscale simulation method to investigate amorphous polymeric materials for vinyl polymer was applied for glassy polystyrene (PS) with different tacticity. PS chains were coarse-grained and then mapped onto the second nearest neighbor diamond (2nnd) lattice incorporating short- and long-range interactions from the modified rotational isomeric state (RIS) model and the discretized Lennard-Jones (LJ) potential function, respectively. Bulk PS structures composed of 14 chains with 42 monomer units was generated and equilibrated on lattice Monte Carlo (MC) simulation. The on-lattice properties including molecular size, conformational statistics and chain dynamics were compared. The chain mobility of neat PS melts with different stereochemistry are qualitatively ordered as: iPS < aPS << sPS. There is no clear correlation for these relative diffusions with molecular size and chain stiffness but can possibly be related to the intermolecular contribution i.e. chain packing among neighboring chains. Next, fully atomistic amorphous PS models at the bulk density were obtained by the reverse-mapping procedure to convert the coarse-grained chains to recover the missing atoms. After energy minimization, molecular and material properties including torsional angle distribution, solubility parameter, radial distribution function and neutron scattering intensity are determined and compared for amorphous PS structures.

A dissipative particle dynamics study:influence of fluid-solid interaction force on micro-flow in shale slits

The fluid-solid interaction force has a decisive influence on the flow characteristics of micro-nano scale. Based on the dissipative particle dynamics (DPD) method, static and flow simulations of fluid in typical shale slits were carried out. The Lennard-Jones (LJ) potential function of 96X was applied to characterize the fluid-solid interaction force. The slit width ranged 3–10nm, the wall material was quartz, the fluid was n-hexane, and the driving force of the flow simulation ranged 1–20kcal/(mol·A). The results show that due to the attraction of solid wall, the aggregation of fluid molecules near the wall was enhanced, fluid density there increased, and the diffusion coefficient there was significantly lower than that in the middle of the slit. The fluidity of the fluid near the wall is significantly reduced. In the flow model, when the fluid-solid interaction force was ignored, the flow profile was piston-like, and the velocity gradient at the edge of the slit was extremely large, showing the characteristics of slip flow. When the fluid-solid interaction force was taken into account, the velocity was reduced significantly, and the profile was parabolic. When the LJ96X was replaced by LJ126X potential function to characterize the fluid-solid interaction force, the attractive force from the wall on the fluid near the wall decreased, the fluidity was enhanced, and the velocity profile increased. When the conservative force parameter of fluid was changed, enhancing the wettability of oil phase, the affinity between fluid and solid was increased, and the velocity profile was reduced.

Van der Waals interactions and oscillatory behaviour of carbon onions interacting with a fully constrained graphene sheet

This study focuses on the van der Waals (vdW) interactions and oscillatory behaviour of nested spherical fullerenes (carbon onions) in the vicinity of a single-layer graphene (SLG) sheet. The carbon onions are of Ih symmetries and the graphene sheet is modelled as a fully constrained flat surface. Employing the continuum approximation along with the 6–12 Lennard-Jones (LJ) potential function, explicit analytical expressions are determined to calculate the vdW potential energy and interaction force. The equation of motion is solved numerically based on the actual force distribution to attain the displacement and velocity of the carbon onion. Using the conservation of mechanical energy principle, a semi-analytical expression is also derived to accurately evaluate the oscillation frequency. Numerical results are presented to examine the influences of size of carbon onion and initial conditions (initial separation distance and initial velocity) on the operating frequency of carbon onion–SLG sheet oscillators. It is shown that carbon onion executes oscillatory motion above the graphene sheet with frequencies in the gigahertz (GHz) range. It is further observed that smaller structures of carbon onions produce greater frequencies. We comment that the presented results in this study would contribute to the development of new generation of nano-oscillators.

Molecular Dynamics Simulations of the Effects of a Nanoparticle Surface Adsorption Layer on the Thermal Conductivity of a Cu–Ar Nanofluid

Nanofluids formed by adding a small volume fraction of solid nanoparticles to the conventional fluid can greatly enhance the thermal transport performance of the conventional fluid. This study reveals the mechanism of thermal conductivity by studying the microscopic effect of nanoparticles in a Cu–Ar nanofluid on the base fluid. Due to the presence of a trapped, adsorbed Ar layer on the surface of the nanoparticle, under certain volume fractions, the influence of the nanoparticles with different sizes on the thermal conductivity is analyzed. The equilibrium molecular dynamics and nonequilibrium molecular dynamics methods are used to calculate and verify the thermal conductivity of the nanofluid, and the abilities of the Lennard–Jones (LJ) and embedded atom method (EAM) potential functions to accurately describe interactions between Cu atoms are compared. By calculating the contribution of different components to the thermal conductivity of the nanofluid, it is found that the composition of the base liquid plays a leading role, while the nanoparticle composition and the solid–liquid cross-section contribute very little. Through decomposition of the Green–Kubo formula (contains potential energy term (V), the kinetic energy term (K), the collision term (V)), it is found that the PV, KV, and VV terms are related to collisions (V) when the LJ potential function is used, which play a major role in the nanofluid’s thermal conductivity. Partial enthalpy terms h, PP, and KK contribute little to the thermal conductivity, and they hinder any decrease of the thermal conductivity as the size of the nanoparticles increases; meanwhile, the KP term remains basically constant. In systems described by the EAM potential function, the contributions of KP and PP are relatively high. Therefore, this paper analyzes the mechanism of increasing the thermal conductivity of Ar-based nanofluid from the perspective of molecular dynamics simulation and obtains the results.

Dynamic behavior of chloride ion-electrically charged open carbon nanocone oscillators: A molecular dynamics study

This paper is intended to study the dynamic oscillatory behavior of chloride ion inside electrically charged open carbon nanocones (CNCs) using the molecular dynamics (MD) simulations. The small and wide ends of nanocone are assumed to be identically and uniformly charged with positive electric charges. In the simulation, the Tersoff-Brenner (TB) and the Lennard-Jones (LJ) potential functions are employed to evaluate the interatomic interactions between carbon atoms and the van der Waals (vdW) interactions between the ion and the nanocone, respectively. The Coulomb potential is also adopted to evaluate the electrostatic interactions between the ion and the electric charges distributed at both ends of nanocone. Numerical results are presented to examine the effects of magnitude of electric charges, initial separation distance and initial velocity on the mechanical oscillatory behavior of system and the obtained results are also compared with the ones related to an uncharged nanocone. It is found that operating frequency as well as escape velocity enhance considerably as a result of electrostatic interactions. It is further found that regardless of the value of electric charges, optimal oscillation frequency is achievable when no initial velocity is imposed on the ion initially located inside of nanocone with an offset of 2 Å from its small end.

Modeling and Determining the Averaged Binary Potential Fields of Five Noble Gases from Sound Speed

In terms of averaged interactive fields, this research discovered a new relation between averaged binary potential field (ABPF) and sound speed. Then, the ABPFs of five noble gases were modeled using an extended Lennard–Jones potential function. The derived equation based on the ABPF and the model potential accurately described the sound speed data of the five noble gases from the National Institute of Standards and Technology. Later, the surface of the ABPF was determined from the data, which indicated that the ABPF principally exhibited the conventional Lennard–Jones’ potential at low temperatures, but performed as a soft sphere potential at high temperatures. This temperature-based shift represents new knowledge regarding intermolecular interactions. The derived equation also provided a novel and practical method to calculate the sound speed from temperature and density.

Generalized non-integer Lennard-Jones potential function vs. generalized Morse potential function for calculating cohesive energy and melting point of nanoparticles

A generalized non-integer Lennard-Jones (L-J) potential function with an additional parameter m is proposed to calculate the cohesive energy and melting point of nanoparticles. The model based on the new generalized non-integer L-J potential function has been successful in predicting experimental values. The calculated cohesive energies show an excellent agreement with the experimental values of the cohesive energies of molybdenum (Mo) and tungsten (W) nanoparticles (Kim et al., 2002). Moreover, the calculated melting points based on the generalized non-integer L-J potential function agree with the experimental values for large gold (Au) nanoparticles including n≥1000 atoms (Buffat and Borel, 1976) and small silica-encapsulated gold (Au) nanoparticles including n≤1500 atoms (Dick et al., 2002). The stability of nanoparticles is due to two conditions: the increase of the range of the attractive force and the high gradient attractive interaction in the potential function when rij≈r0.

Nonlinear buckling analysis of double-layered graphene nanoribbons based on molecular mechanics

Double-layer graphene nanoribbons promise potential application in nanoelectromechanical systems and optoelectronic devices, and knowledge about mechanical stability is a crucial parameter to flourish the application of these materials at the next generation of nanodevices. In this paper, molecular mechanics is utilized to investigate nonlinear buckling behavior, critical buckling stress, and lateral deflection of double-layered graphene nanoribbons under various configurations of stacking mode and chirality. The implicit arc-length iterative method (modified Riks method) with Ramm’s algorithm is utilized to analyze the nonlinear structural stability problem. The covalent bonds are modeled using three-dimensional beam elements in which elastic moduli are calculated based on molecular structural mechanics technique, and the interlayer van der Waals (vdW) interactions are modeled with nonlinear truss elements. An analytical expression for Young’s modulus of nonlinear truss elements is derived based on the Lennard–Jones potential function and implemented in numerical simulation with a UMAT subroutine based on FORTRAN code to capture the nonlinearity of the vdW interactions during the buckling analysis. The results indicate that the highest critical buckling stress and the minimum lateral deflection occur for armchair and zigzag chirality, both with AB stacking mode, respectively. Moreover, the critical buckling stress is found to be directly dependent on the mode shape number regardless of in-phase or anti-phase deflection direction of layers. Lateral deflection exhibits a similar trend with mode shape in anti-phase mode; however, it is decreasing by increasing mode shape number in in-phase mode.

Free vibration problem of fluid-conveying double-walled boron nitride nanotubes via nonlocal strain gradient theory in thermal environment

This article is a comprehensive investigation into the equations of the size-dependent free vibration of a special type of fluid-conveying nanotubes, i.e., double-walled boron nitride nanotubes, in a thermal environment. The motion equations are obtained through the use of nonlocal strain gradient theory for piezoelectric materials combined with the first-order shear deformation theory and Hamilton’s principle. Lennard-Jones potential function imposes the coupling between the pair of nanotubes that are bound together via van der Waals forces. This study also considers softening and hardening effects to better understand important aspects of modeling. After setting proper boundary conditions, the differential quadrature method is exploited to solve the obtained equations. This numerical study allows us to evaluate the effects of many parameters that include delta-temperature, aspect ratio, size scale and boundary conditions on the nondimensional eigenfrequency of considered system and critical flow velocity.

Water Molecule and Atoms Inside C60 Fullerene

In this research, we are interested in the non-bonded interactions between a single water molecule and the atoms Li, Na, K, Rb, Cs, Ca, Ni, Zn and Pb inside a C60 fullerene using the Lennard-Jones potential function. We assume that a single water molecule is inside the endofullerene and determine the exact formula of the interaction energy between the water molecule and the fullerene. Then we determine the interaction energy between an atom and the endofullerene to consider the interaction behaviours of each atom inside the fullerene. The results show that a water molecule does not desire to be encapsulated inside the fullerene. Similarly, Rb, Cs and Pb act the same behaviour, where they are not stable inside the fullerene. However, some atoms which are Li, Na, K, Ca, Ni and Zn can be inside the endofullerene. Hence, the creation of endofullerene with a single water molecule or Rb, Cs and Pb inside, an external force must be applied while that force is not necessary for Li, Na, K, Ca, Ni and Zn.

Instability and translocation through nanopores of DNA interacting with single-layer materials.

In this study, we use classical applied mathematical modelling to employ the 6–12 Lennard-Jones potential function along with the continuous approximation to investigate the interaction energies between a double-stranded deoxyribonucleic acid (dsDNA) molecule and two-dimensional nanomaterials, namely graphene (GRA), hexagonal boron nitride (h-BN), molybdenum disulphide (MoS2), and tungsten disulphide (WS2). Assuming that the dsDNA molecule has a perpendicular distance Δ above the nano-sheet surface, we calculated the molecular interaction energy and determined the relation between the location of the minimum energy and Δ. We also investigated the interaction of a dsDNA molecule with the surface of each nano-sheet in the presence of a circular hole simulating a nanopore. The radius of the nanopore that results in the minimum energy was determined. Our results show that the adsorption energies of the dsDNA molecule with GRA, h-BN, MoS2, and WS2 nano-sheets corresponding to the perpendicular distance Δ = 20 Å are approximately 70, 82, 28, and 26 (kcal mol−1), respectively, and we observed that the dsDNA molecule moves through nanopores of radii greater than 12.2 Å.

The equation of state of symmetric extended Lennard-Jones fluids

This paper developed the conceptual model of symmetric extended Lennard-Jones fluid based on an extended Lennard-Jones potential function. Therein, important relationships between averaged intermolecular potential field (AIPF) and thermodynamic properties were presented, in which the equation of state was included. These formulascan not only predict the p-V-T properties of argon, nitrogen, carbon monoxide and methane that are representatives of spherical, polar and non-polar molecular fluids in acceptable accuracy, but also physically interpret the p-V-T properties from the AIPF. Obtained results have theoretical significance and can serve as reference or base in the analysis and computation of the p-V-T properties of simple fluids.

Modelling of Nickel Atoms Interacting with Single-Walled Nanotubes

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.

The effect of non-covalent functionalization on the interaction energy of carbon nanotubes

The Lennard-Jones potential function together with the continuous approximation is employed to determine the van der Waals interaction between two parallel cylindrical nanotubes. Here we determine the interaction energy between carbon nanotubes and those with non-covalent functionalization polyether ether ketone (PEEK) polymer. The distance for any two tubes does not depend on the tube radii and the number of nanotube walls. This closest distance between two surfaces for any two tubes is determined to be 0.32 nm. Furthermore, the binding energy between two tubes depends on the number of walls. Non-covalent agglomeration with polymers reduces the interaction energy between tubes and reduces agglomeration of carbon nanotubes.

A force field for MD simulations on rhenium organometallic compounds developed from enthalpy of sublimation and X-ray diffraction measurements

The standard (p° = 0.1 MPa) molar enthalpies of sublimation, at 298.15 K, of methyltrioxorhenium(VII), ΔsubHmo[CH3ReO3] = 70.2 ± 0.4 kJ mol−1, and dirhenium decacarbonyl, ΔsubHmo[Re2(CO)10] = 97.4 ± 0.9 kJ mol−1, corresponding to well characterized crystalline phases, were determined by Calvet microcalorimetry. These results, along with structural information obtained in this work by single crystal X-ray diffraction for CH3ReO3, or previously reported for Re2(CO)10, tetramethylammonium perrhenate(VII), [N1111][ReO4], and hexamethylrhenium(VI), Re(CH3)6, were used to extend our previously developed all-atom force field for organometallic compounds, to rhenium species. The new parametrization was able to reproduce the enthalpies of sublimation and unit cell parameters of the test set with maximum absolute deviations of 3.3 kJ⋅mol−1 and <3.8%, respectively. The transferability of the interaction (ε) and atomic diameter (σ) parameters of the Lennard-Jones (12–6) potential function, observed for first and second-row transition metals, was also found to be valid for rhenium and tungsten (third-row metals).

Optimal configurations for interacting carbon nanotori

The optimal or lowest energy configuration of two carbon nanotori is investigated. With the assumption that the tori are symmetrically situated and parallel with the centres lying on their common axis, the interaction energy between the two tori is evaluated using the continuum approximation and the Lennard-Jones potential function. This mathematical modelling approach provides a fast and accurate computation as compared to other simulation methods. The numerical results obtained determine the most stable configuration corresponding to the minimum energies for five different sized tori, and a relation between the major and minor radii of the tori and the equilibrium position is demonstrated. The interaction energies between two nanotori determined here might be utilised to model many promising devices for future developments in nano and biotechnology.

Physical origins of temperature continuity at an interface between a crystal and its melt.

We justify and discuss the physical origins for the assumption of temperature continuity at crystal/melt interfaces by performing atomistic simulations. We additionally answer why the crystal/melt interfaces differ from the typical solid/liquid interfaces, which usually exhibit dissimilarities and a resulting temperature drop. We present results for pure silver modeled using the embedded-atom method and Lennard-Jones potential function and contrast the results with each other. We find that the temperature continuity at an interface between a crystal and its melt originates from the perfect vibrational coupling, which is caused by the interfacial structural diffusivity. This study provides fundamental insights into the heat transfer for cases of extremely large heat flux and thermal gradients occurring during rapid melting and solidification. The findings additionally determine the role of rough surfaces in manipulating the thermal conductance in nanodevices.

Molecular dynamics study of gigahertz nanomechanical oscillators based on an ion inside a series of electrically charged carbon nanotubes

Abstract In this paper, the mechanical oscillatory behavior of a chloride ion inside a series of electrically charged carbon nanotubes (CNTs) is investigated using molecular dynamics (MD) simulations. The Tersoff-Brenner and 6–12 Lennard-Jones (LJ) potential functions are respectively employed to describe the interatomic interactions between carbon atoms and van der Waals (vdW) interactions between ion and CNT, while the Coulomb potential function is used to model the electrostatic interactions between ion and electric charges. The outer shell which is assumed to be either uncharged or positively charged is composed of identical units located concentrically with an equal distance. Two different cases named cases 1 and 2 are considered to incorporate the electrostatic interactions into the model. In the first one, both left and right ends of all units are electrically charged, whereas in the second one, only the left end of the left-most unit and the right end of the right-most unit are electrically charged. Numerical results are presented to examine the effects of type of decoration of electric charges and their magnitudes, geometrical parameters (number of units, length and radius of units and the distance between two neighboring units) and initial conditions (initial separation distance and initial velocity) on the dynamic behavior of system. A comparison is also made between the results of cases 1 and 2 with those of uncharged units. For given initial conditions, it is demonstrated that the oscillation frequency of case 1 is lower than that of case 2 and higher than that of pure nanotubes. It is further found that the highest escape velocity corresponds to case 1 followed by case 2 and uncharged nanotubes.

Analysis of topological relationships and network properties in the interactions of human beings.

In the animal world, various kinds of collective motions have been found and proven to be efficient ways of carrying out some activities such as searching for food and avoiding predators. Many scholars research the interactions of collective behaviors of human beings according to the rules of collective behaviors of animals. Based on the Lennard-Jones potential function and a self-organization process, our paper proposes a topological communication model to simulate the collective behaviors of human beings. In the results of simulations, we find various types of collective behavior and fission behavior and discover the threshold for the emergence of collective behavior, which is the range five to seven for the number of topology K. According to the analysis of network properties of the model, the in-degree of individuals is always equal to the number of topology. In the stable state, the out-degrees of individuals distribute around the value of the number of topology K, except that the out-degree of a single individual is approximately double the out-degrees of the other individuals. In addition, under different initial conditions, some features of different kinds of networks emerge from the model. We also find the leader and herd mentality effects in the characteristics of the behaviors of human beings in our model. Thus, this work could be used to discover how to promote the emergence of beneficial group behaviors and prevent the emergence of harmful behaviors.