Lennard-Jones Potential Function Research Articles

Investigating the effect of welding tool length on mechanical strength of welded metallic matrix by molecular dynamics simulation

The welding process and the properties of welding instruments may improve the mechanical performance of an item. One of these properties is the length of the welding tool. This approach has a substantial effect on the mechanical strength of the metallic matrix. The current study used molecular dynamics modeling and LAMMPS software to evaluate the effect of welding tool length on the mechanical properties of a welded Cu–Ag metallic matrix. This simulation makes use of the Lennard-Jones potential function and the embedded atom model. First, the equilibrium phase of modeled samples was verified by changing the computation of kinetic and total energies. Next, the mechanical properties of the welded matrix were studied using the stated Young's modulus and ultimate strength. The stress-strain curve of samples demonstrated that the mechanical strength of atomic samples increased as the length of the welding tool (penetration depth) increased. Numerically, by increasing the tool penetration depth of Fe tools from 2 Å to 8 Å, Young's modulus and ultimate strength of the matrixes sample increase from 34.360 GPa to 1390.84 MPa to 38.44 GPa and 1510 MPa, respectively. This suggested that the length of the Fe welding tool significantly affected the mechanical properties of the welded metallic matrix. The longer the length of Fe welding tools, the more particles were involved, and consequently, more bonds were formed among the particles. Bonding among the particles caused changes in mechanical properties, such as greater ultimate strength. This method can optimize mechanical structures and be useful in various industries.

A Minimalistic 3D Self-Organized UAV Flocking Approach for Desert Exploration

In this work, we propose a minimalistic swarm flocking approach for multirotor unmanned aerial vehicles (UAVs). Our approach allows the swarm to achieve cohesively and aligned flocking (collective motion), in a random direction, without externally provided directional information exchange (alignment control). The method relies on minimalistic sensory requirements as it uses only the relative range and bearing of swarm agents in local proximity obtained through onboard sensors on the UAV. Thus, our method is able to stabilize and control the flock of a general shape above a steep terrain without any explicit communication between swarm members. To implement proximal control in a three-dimensional manner, the Lennard-Jones potential function is used to maintain cohesiveness and avoid collisions between robots. The performance of the proposed approach was tested in real-world conditions by experiments with a team of nine UAVs. Experiments also present the usage of our approach on UAVs that are independent of external positioning systems such as the Global Navigation Satellite System (GNSS). Relying only on a relative visual localization through the ultraviolet direction and ranging (UVDAR) system, previously proposed by our group, the experiments verify that our system can be applied in GNSS-denied environments. The degree achieved of alignment and cohesiveness was evaluated using the metrics of order and steady-state value.

The study of ideal/defected graphene nanosheet roughness after atomic deposition process: Molecular dynamics simulation

In this work, molecular dynamics (MD) approach was performed to study the surface roughness of ideal/defected graphene nanosheet after carbon atoms deposition at various temperatures and pressures. In our calculations, the atomic interactions of nanostructures are based on TERSOFF and Lennard-Jones potential functions. The results show that the temperature of simulated structure is an important parameter in atomic deposition process and initial temperature enlarges, intensifies atomic deposition ratio. Numerically, by temperature increasing to 15 K, the surface roughness amplitude increase to 0.98 Å/0.83 Å after atomic deposition in ideal/defected structure. The roughness power in MD simulations converges to 0.64/0.55 in ideal/defected sample at maximum temperature. Furthermore, the pressure effects on dynamical behavior of simulated samples were reported in our study. We conclude that, by increasing initial pressure from 0 to 2 bar, the surface roughness amplitude in ideal/defected atomic arrangement increases to 1.01 Å/0.84 Å after deposition process and the roughness power of simulated structures reaches to larger value. Numerically, by initial pressure setting at 2 bar, the roughness power value converged to 0.72/0.56 in ideal/defected graphene. Reported numeric results in various temperature and pressures predicted the initial condition can be manipulated the atomic deposition process in ideal/defected graphene nanostructures.

Design of High-Frequency Carbon Nanotube-Carbon Nanotorus Oscillators for Energy Harvesting: A Molecular Dynamics Study.

The objective of this study is to examine the feasibility of using carbon-based nanostructures as nano-oscillators for future nanoelectromechanical applications such as energy harvesting devices and vibration sensing. The proposed nano-oscillator is comprised of a carbon nanotube (CNT) oscillating through a fixed carbon nanotorus molecule. For the first time in the literature, molecular dynamics (MD) simulations in conjunction with the Tersoff-Brenner (TB) and 6-12 Lennard-Jones (LJ) potential functions are adopted to determine the molecular interactions of the introduced nanodevice. To simulate the oscillatory behavior, two different schemes, namely, rigid and flexible, are considered. A detailed parametric study is performed to investigate the effects of rigidity, flexibility, and size of nanostructures as well as initial velocity on the force distribution and time histories of displacement and velocity of the core. Numerical results reveal that unlike the rigid oscillators, the flexible oscillators damp out within a few cycles. It is shown that the escape velocity of the flexible scheme is ∼6 times greater than that of the rigid scheme. The operating frequency and the generated power of rigid and flexible schemes under different system parameters are also calculated and compared. It is demonstrated that with increasing the ratio of nanotube-to-nanotorus diameter, the operating frequencies of both schemes decrease, while the generated powers do not behave monotonically. For a determined system parameter, it is observed that the flexible scheme provides higher operating frequencies compared to the rigid one. Moreover, considering that the initial velocity of the system is identical to the escape velocity, the generated power of the flexible scheme is calculated to be ∼14 times greater than that of the rigid scheme.

Nano-friction behavior and deformation study of hydroxyapatite in ultra-precision polishing process.

In order to study the effect of ultra-precision machining on the surface quality of hydroxyapatite semiconductor materials as well as the material removal mechanism of hydroxyapatite, the mechanical polishing behaviors of hydroxyapatite at different polishing depths were studied by molecular dynamics method. The results show that the subsurface damage of hydroxyapatite increases with increasing polishing depth. The polishing temperature and the polishing force showed a positive correlation with the polishing depth, and the variation of the polishing force was related to the accumulation-release effect of the potential energy of hydroxyapatite material. In addition, the variation of stresses in hydroxyapatite during polishing is mainly influenced by the thermal softening effect. With a smaller polishing depth, the hydroxyapatite semiconductor material has fewer structural defects, fewer atoms undergoing phase transitions, lower surface roughness, and better surface quality. Therefore, to ensure the long-lasting service life of hydroxyapatite semiconductor materials, a small polishing depth should be used in ultra-precision machining. Additionally, this study also provides a theoretical reference for future research on the mechanical properties of hydroxyapatite-based composites. A Large-Scale Atomic/Molecular Parallel Simulator (LAMMPS) was utilized to perform molecular dynamics simulations. The output was visualized and analyzed by the Open Visualization Tools (OVITO) software. The intermolecular interactions were described by the polymer consistent force-field and the 12/6 Lennard-Jones potential functions. The workpiece was polished under a micro-canonical ensemble with the temperature settled at 300 K. Periodic boundary conditions were adopted and the velocity-Verlet algorithm was used to integrate the atomic motion with a timestep of 0.1 femtoseconds (fs).

Research on azeotropic breaking extraction technology for High-Value chemicals from wash oil

In response to the challenge of achieving high-purity separation within a mixture containing acenaphthene, dibenzofuran, fluorene, and biphenyl in coal tar wash oil fractions, the azeotropic behavior of this mixture was investigated through phase equilibrium experiments to elucidate the azeotropic system. Once the azeotropic system was identified, attention shifted to intermolecular forces, and simulation calculations utilizing the Lennard-Jones potential energy function were employed to reveal the mechanism underlying high-purity separation in the azeotropic system. Building upon this foundation, the feasibility of solvent crystallization was explored as a means to break the azeotrope and achieve high-purity separation. This involved a thorough analysis of the intermolecular interactions between the crystallization solvent and the mixture system. Ethanol, methanol, and pentanol were chosen as potential solvents for conducting solvent crystallization experiments.Results demonstrate that ethanol performs admirably within the solvent crystallization method, exhibiting a high degree of crystallization selectivity for acenaphthene. On the other hand, pentanol demonstrates advantages in the separation and crystallization for removing biphenyl. Using ethanol as the solvent for crystallization, the acenaphthene content can be refined to 99.17%, while the biphenyl content can be reduced to a mere 0.002%. These findings underscore the effectiveness of ethanol as a solvent in effectively addressing the azeotropic challenge arising from the coexistence of biphenyl and acenaphthene, ultimately achieving an efficient separation of the targeted substances. Considering both crystallization selectivity and yield, ethanol emerges as the most suitable crystallization solvent for this intricate multi-component system. This study presents a practical solution for the efficient separation of acenaphthene, dibenzofuran, fluorene, and biphenyl—all of which constitute azeotropic systems within the heavy distillate fraction of wash oil.

Analysis of the mechanism of enhanced heat transfer by nanofluids.

Industrial production and humans cannot exist without energy, but the low efficiency of the heat transfer in the excessive use of energy is the most significant aspect of energy saving and emission reduction. Molecular dynamics simulation methods are devoted to simulate the heat transfer efficiency of a nanofluid system with different particle sizes, and the heat transfer enhancement mechanism of the nanofluid is simulated and studied from a microscopic perspective. The analysis showed that as nanoparticle size increases, the thermal conductivity of the Al-Ar nanofluid tends to decrease, but all of them are still higher than the thermal conductivity of the liquid argon system. According to the findings of the density and radial distribution function analyses, it can be seen that the microstructure of the system changes after putting solid nanoparticles to the original fluid. This alteration in the system's microstructure is the primary component responsible for the increased heat transfer efficiency of nanofluids. In this paper, based on the theory of molecular dynamics, the simulation calculations were mainly performed using LAMMPS software, which is a commonly used open source computational program in the field of MD simulation research. VMD is used for visualization and analysis. The Lennard-Jones potential function was used in the simulation to accurately describe the forces acting between the atoms.

Molecular Simulation of the Crystallization of Polyethylene Nanocomposites: The Effect of Surface Affinity of Nanofillers

AbstractMonte Carlo simulation of coarse‐grained models is used to investigate the effect of polymer–nanofiller interaction on the structural formation of polyethylene nanocomposites with stepwise cooling from the melts. Polyethylene (PE) is represented by the rotational isomeric state (RIS) model and the Lennard–Jones potential function for intrachain energetics and non‐bonded interactions, respectively. Crystallization is monitored using the fraction of trans state and the orientation order parameter at bond and chain scale. The results show that PE nanocomposites with repulsive polymer–surface interaction can enhance faster structural formation and induce larger degree of the ordered structures. On the other hand, nanofiller with attractive polymer–surface interaction causes the chain with lower amount of trans conformation resulted in less ordered structures.

Investigation of the mechanical properties of different amorphous composites using the molecular dynamics simulation

Metal matrix composites have various structural and thermal applications in terms of their unique mechanical and thermal properties compared to their counterparts. These nanoparticle (NP)-reinforced composites have received much attention due to their relatively low production costs and excellent mechanical properties. In the present research, modeling and studying the effects of adding reinforcing NP on the hardness of aluminium-based composites is done using the molecular dynamics (MD) simulation. The expressed structures' equilibration, temperature, and potential energy are calculated and reported in the first simulation stage. In this regard, the parameters of Lennard-Jones potential function for the particles in the MD simulation of aluminium and oxygen. Finally, the results show that the hardness of pure nanocomposite (NC) was equal to 100, and by adding NP with a mass ratio of 6%, the hardness of NC increased from 100 to 190 HV. The radial distribution function (RDF) showed that the composition was in the solid phase at a temperature of 300 K, indicating the proper balance of simulated atomic systems. The results show that the maximum value of RDF decreased by increasing the amount of reinforcement. The results show that the yield stress decreased as the volume fraction of reinforcement increased in the crystal structure. Finally, it is expected that the results obtained from MD simulations will be considered in the practical use of aluminium NCs reinforced with alumina nanoparticles in various industrial, engineering and medical uses.

A new correlation model for predicting the melting and boiling temperatures of the Lennard-Jones systems

The Lennard-Jones (LJ) potential function is widely employed in molecular dynamics simulations. In this study, the LJ potentials under different characteristic diameter σ and characteristic energy ε were simulated, and the changes in properties such as number density, total energy, phase transition latent heat, and phase transition temperature were detailed. With the increase of σ, the melting and boiling temperatures of the LJ systems and the thermodynamic temperature range corresponding to liquid decrease, while with the increase of ε, the melting and boiling temperatures and the thermodynamic temperature range of liquid increase. Moreover, the phase transition latent heat hardly changes with the increase of σ, but significantly increases with ε. The number densities at the melting and boiling temperatures are only dependent on σ, and are not nearly influenced by ε. Furthermore, based on a modified Lindemann’s melting criterion, a new empirical correlation model is proposed to predict the melting and boiling temperatures of the LJ systems, where the phase transition points are in good agreement with the experimental values. For the melting point, the absolute error between the formula and the experimental measurement for inert gas and methane is no more than 10 K, and for the boiling point, the absolute error is less than 15 K. By this new presented model, some thermophysical properties of the LJ potential systems can be quickly obtained and evaluated.

An Analytical Model for Lithium Storage in Spherical Fullerenes

In this paper, the encapsulation of lithium atoms in spherical fullerenes of varying sizes is investigated. The 6–12 Lennard–Jones potential function and the continuum approximation, in which it is assumed that the atoms can be replaced with a uniform distribution across the surface of the molecules, are exploited to model the interaction energies between lithium atoms and spherical fullerenes. Thus, the total interaction energies can be approximated by applying surface integrations. The results show that for a lithium atom interacting inside a spherical fullerene, the interaction energies are minimized at a position that approaches the fullerene wall as the size of the fullerene increases. However, the results show that an external force would need to be applied to a lithium atom in order to overcome the repulsive energy barrier so that it can be encapsulated in CN fullerenes with a radius of less than 2 Å. The present study indicates that the optimal radius that gives the minimum energy for the storage of Li inside CN fullerenes occurs for a fullerene with a radius of ≈2.4 Å. Overall, this study provides an analytical formulation that may facilitate rapid computational results, and an application of this work is in the design of future high-energy-density batteries that utilize CN fullerenes.

A multiscale analysis framework for formation and failure of the thermoplastic interface

Formation and failure of the interface determine the quality of thermoplastic composite structures. However, accurate prediction of interface strength evolution during advanced manufacture is still challenging due to the multiscale feature of thermoplastics, which hinders the design of composites processing and analysis of structure reliability. Here, we develop a multiscale model for formation and failure of thermoplastic interface. The reptation model of polymer chains is used to describe the chain density evolution at the interface during manufacture. Then, by releasing the rigid-bond assumption in the traditional freely-jointed-chain model, the Lennard-Jones potential function is incorporated to model polymer chain scission. Finally, chain-length dispersity, individual chain scission, and chain density reduction are incorporated to model the interface failure. The model predictions are in good agreement with the experimental results of composites welding, indicating that the developed model can be used to analyze the interface strength evolution of thermoplastics in the advanced manufacturing processes.

Car-Following Dynamics, Characteristics, and Model Based on Interaction Potential Function

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.

The Size and Shape Effects on the Melting Point of Nanoparticles Based on the Lennard-Jones Potential Function.

A model is proposed to calculate the melting points of nanoparticles based on the Lennard-Jones (L-J) potential function. The effects of the size, the shape, and the atomic volume and surface packing of the nanoparticles are considered in the model. The model, based on the L-J potential function for spherical nanoparticles, agrees with the experimental values of gold (Au) and lead (Pb) nanoparticles. The model, based on the L-J potential function, is consistent with Qi and Wang’s model that predicts the Gibbs-Thompson relation. Moreover, the model based on the non-integer L-J potential function can be used to predict the melting points of nanoparticles.

Continuum Modelling for Encapsulation of Anticancer Drugs inside Nanotubes

Nanotubes, such as those made of carbon, silicon, and boron nitride, have attracted tremendous interest in the research community and represent the starting point for the development of nanotechnology. In the current study, the use of nanotubes as a means of drug delivery and, more specifically, for cancer therapy, is investigated. Using traditional applied mathematical modelling, I derive explicit analytical expressions to understand the encapsulation behaviour of drug molecules into different types of single-walled nanotubes. The interaction energies between three anticancer drugs, namely, cisplatin, carboplatin, and doxorubicin, and the nanotubes are observed by adopting the Lennard–Jones potential function together with the continuum approach. This study is focused on determining a favourable size and an appropriate type of nanotube to encapsulate anticancer drugs. The results indicate that the drug molecules with a large size tend to be located inside a large nanotube and that encapsulation depends on the radius and type of the tube. For the three nanotubes used to encapsulate drugs, the results show that the nanotube radius must be at least 5.493 Å for cisplatin, 6.452 Å for carboplatin, and 10.208 Å for doxorubicin, and the appropriate type to encapsulate drugs is the boron nitride nanotube. There are some advantages to using different types of nanotubes as a means of drug delivery, such as improved chemical stability, reduced synthesis costs, and improved biocompatibility.

Computational Study on the Interaction and Moving of ssDNA through Nanosheets

The adsorption characteristics and moving through nanopores of a single-stranded deoxyribonucleic acid (ssDNA) molecule on monolayers, such ashexagonal boron nitride and graphene nanosheets, were studied using the continuous approach with the 6–12 Lennard–Jones potential function. The ssDNA molecule is assumed to be at a distance l above the sheet, and the relation between the minimum energy location and the perpendicular distance of the ssDNA molecule from the nanosheet surface is found. In addition, by assuming that there is a hole in the surface of the nanosheet as a pore, the interaction energies for the ssDNA molecule moving through the pore in the surface of the nanosheet (used to calculate the radius p of the hole) are obtained, which provides the minimum energies. Furthermore, a comparative study with graphene was performed in order to compare with hexagonal boron nitride nanosheets. Our results indicate that the binding energies of the ssDNA onto graphene and hexagonal boron nitride nanosheets are approximately 15.488 and 17.582 (kcal/mol), corresponding to perpendicular distances of l=20.271 and l=20.231 Å, respectively. In addition, we observe that the ssDNA molecule passes through graphene and hexagonal boron nitride nanopores when the gap radius p>7.5 Å. Our results provide critical insights to understand and develop the interactions and translocation of DNA molecules with and through nanosheets.

Investigation of Interaction of Noble Metals (Cu, Ag, Au, Pt and Ir) with Nanosheets.

Two-dimensional nanomaterials, such as graphene and hexagonal boron nitride nanosheets, have attracted tremendous interest in the research community and as a starting point for the development of nanotechnology. Using classical applied mathematical modeling, we derive explicit analytical expressions to determine the binding energies of noble metals, including copper, silver, gold, platinum and iridium (Cu, Ag, Au, Pt and Ir) atoms, on graphene and hexagonal boron nitride nanosheets. We adopt the 6–12 Lennard–Jones potential function, together with the continuous approach, to determine the preferred minimum energy position of an offset metal atom above the surface of the graphene and hexagonal boron nitride nanosheets. The main results of this study are analytical expressions of the interaction energies, which we then utilize to report the mechanism of adsorption of the metal atoms on graphene and hexagonal boron nitride surfaces. The results show that the minimum binding energy occured when Cu, Ag, Au, Pt and Ir were set at perpendicular distances in the region from 3.302 Å to 3.683 Å above the nanosheet surface, which correspond to adsorption energies in the region ranging from 0.842 to 2.978 (kcal/mol). Our results might assist in providing information on the interaction energies between the metal atoms and the two-dimensional nanomaterials.

Self-Organized UAV Flocking Based Only on Relative Range and Bearing

In this work, we address the problem of convergence and cohesiveness of an unmanned aerial vehicle (UAV) flocking. Thus, we propose a proximal control-based method for UAV self-organized flocking. Our method efficiently achieves flocking in the absence of alignment control and moves into an arbitrary direction without any direction control or informed robots. Robots use a Lennard-Jones potential function to maintain the cohesiveness of the flocking while avoiding collision within the teammates. We evaluate our approach using the order metric, the steady-state value, and the settling time that can be used as a cohesiveness indicator.

Molecular modeling of Ti-6Al-4V alloy shot peening: the effects of diameter and velocity of shot particles and force field on mechanical properties and residual stress

Shot peening is a surface treatment process that is used for the improvement of the mechanical properties of metallic alloys. The effects of sphere particle diameter and impact velocity on residual stress and mechanical properties of Ti-6Al-4V as titanium alloy are investigated in this study using molecular dynamics simulation. In this research, titanium atoms are simulated as a surface layer and the carbon steel atomic structure is modeled as the impacting particle in the shot peening process. Two types of molecular potential functions including embedded atom method (EAM) and Lennard-Jones (LJ) are used for molecular modeling of colliding atoms and the effect of these force fields on residual stress, hardness, surface roughness is investigated. Moreover, the effects of impacting particle velocity and diameter on these parameters are studied. The results show the amount of residual stress in the titanium surface layer increased by increasing the particle diameter and velocity of particles. The diameter and velocity of particles in the shot peening process has a significant effect on the mechanical behavior of the simulated titanium surface layer. The value of maximum compressive residual stress is −413 MPa which occurs in depth of 10 Å from the surface layer for 1 Å fs−1 velocity and 10 Å diameter of shot particle. Furthermore, the results show that the Vickers hardness of the titanium is increased by increasing the size and velocity of the carbon steel particle in both EAM and LJ potential functions.

Size-Dependent Vibration Problem of Two Vertically-Aligned Single-Walled Boron Nitride Nanotubes Conveying Fluid in Thermal Environment Via Nonlocal Strain Gradient Shell Model

The free vibration behavior of two fluid-conveying vertically-aligned single-walled boron nitride nanotubes are studied in the present paper via the nonlocal strain gradient piezoelectric theory in conjunction with the first-order shear deformation shell assumption in thermal environments. It is supposed that the two adjacent boron nitride nanotubes are coupled with each other in the context of linear deformation by van der Waals interaction according to Lennard–Jones potential function. To achieve a more accurate modeling for low-scale structures, both hardening and softening effects of materials are considered in the nonlocal strain gradient approach. The motion equations and associated boundary conditions are derived by means of Hamilton’s variational principle, then solved utilizing differential quadrature method. Numerical studies are done to reveal the effect of different boundary conditions, size scale parameters, aspect ratio, inter-tube distance, and temperature change on the variations of dimensionless eigenfrequency and critical flow velocity.