Lennard-Jones Potential Energy Function Research Articles

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.

The extended Lennard-Jones potential energy function: A simpler model for direct-potential-fit analysis

An analytical model for the diatomic potential energy function that was recently tested as a universal function (Hajigeorgiou, 2010) has been further modified and tested as a suitable model for direct-potential-fit analysis. Applications are presented for the ground electronic states of three diatomic molecules: oxygen, carbon monoxide, and hydrogen fluoride. The adjustable parameters of the extended Lennard-Jones potential model are determined through nonlinear regression by fits to calculated rovibrational energy term values or experimental spectroscopic line positions. The model is shown to lead to reliable, compact and simple representations for the potential energy functions of these systems and could therefore be classified as a suitable and attractive model for direct-potential-fit analysis.

Molecular dynamics simulations of momentum and thermal diffusion properties of near-critical argon along isobars

Three basic diffusion properties of argon – shear viscosity, bulk viscosity and thermal conductivity – were studied in the neighborhood of the critical point using molecular dynamics (MD) and the Lennard-Jones potential energy function. MD simulations were performed along the 1.0Pc and 1.2Pc isobars. Green-Kubo relations and a Lennard-Jones pair potential were used. Four different sets of Lennard-Jones parameters were used. A comparison of computed shear viscosity and thermal conductivity values with data available from the National Institute of Standards and Technology (NIST) displayed a good agreement. Results for bulk viscosity indicated that values of this property cannot be neglected in this thermodynamic region, a result that violates the traditional and much-assumed Stokes hypothesis in classical fluid mechanics. Furthermore, it was shown that in the neighborhood of the critical region the bulk viscosity can have larger values than the shear viscosity.

Vibrations of single- and double-walled carbon nanotubes with layerwise boundary conditions: A molecular dynamics study

In the present work, the vibration characteristics of single- and double-walled carbon nanotubes under various layerwise boundary conditions at different lengths are investigated. This is accomplished by the use of molecular dynamics simulations based on the Tersoff-Brenner and Lennard-Jones potential energy functions. The effects of initial tensile and compressive strains on the resonant frequency of carbon nanotubes are also taken into consideration. From the results generated, it is observed that the natural frequency of carbon nanotubes is strongly dependent on their boundary conditions especially when tubes are shorter in length. The natural frequency and its dependence on tube end conditions reduce by increasing the tube length. The natural frequency of DWCNTs lies between those of the constituent inner and outer SWCNTs and is nearer to those of the outer one. It is further observed that the natural frequency is highly sensitive to tensile and compressive strains. The frequency shift occurring in the presence of small initial strains is positive for tensile strains and negative for compressive strains. The results obtained provide valuable information for calibrating the small scaling parameter of the nonlocal models for the vibration problem of carbon nanotubes.

A perturbed hard-sphere equation of state for liquid metals

A perturbed hard-sphere equation of state, developed previously for liquid alkali metals and liquid refractory metals, has been applied for PVT calculation of some pure liquid metals including alkaline earth metals, tin, lead, antimony, bismuth, and rubidium over a wide range of temperatures and pressures. Two temperature-dependent parameters appear in the equation of state, which are universal functions of the reduced temperature, i.e. two scale parameters are sufficient to calculate the temperature-dependent parameters. The scaling parameters can be easily obtained by employing a corresponding-states principle based on a Lennard-Jones potential energy function. Employing the present equation of state, the liquid densities of aforementioned metals at temperatures ranging from the melting point to 2000 K and at pressures ranging from vapour pressure up to 40,000 bar have been calculated and compared with experimental data. The average absolute deviation in predicted densities compared with experimental data is 1.54%.

Physical model for the growth of amorphous carbon nanotubes

A physical model for the growth mechanism of amorphous carbon nanotubes (ACNTs) (namely, “open tips growth and carbon clusters (Cn,n>6) adding”) has been proposed in this letter. Based on Tersoff–Brenner [Phys. Rev. B 37, 6991 (1988) and Phys. Rev. B 42, 9458 (1990)] and Lennard-Jones potential energy functions, a mathematic relationship for the growth of ACNTs was established. The predicted diameters of ACNTs from this physical model were in the range of 5–25 nm. The predicted values were in agreement with the experimental measurements in the range of 7–20 nm.

Effects of the Nanostructural Geometry at a Liquid-Solid Interface on the Interfacial Thermal Resistance and the Liquid Molecular Non-Equilibrium Behaviors

The effects of the structural geometry at the nanometer scale on the thermal resistance at a liquid molecule-solid interface, as well as the interfacial energy transport mechanism of liquid molecules, were investigated directly by the nonequilibrium classical molecular dynamics simulations. The 12-6 Lennard-Jones potential energy functions for liquid molecules and the channel structure at the nanometer scale are employed so as to discuss the effects of the surface geometry at the nanometer scale on the interfacial thermal resistance in comparison with a flat surface. The thermal resistance between solid and liquid molecules was calculated by the temperature discontinuity at the liquid-solid interface and the energy flux that was added or subtracted by the Langevin method per unit area so as to maintain a constant boundary temperature of solid walls. The substantial interfacial thermal resistance reduction depending on the interaction parameters between solids and liquid molecules was observed in the case of the nanostructure surface in comparison with the flat surface. The liquid-solid interfacial thermal resistance reduction in the case of nanostructure surface relates to the energy transport mechanism change at the liquid-solid interface and the surface area magnification.

An extended Lennard-Jones potential energy function for diatomic molecules: Application to ground electronic states

A new simple analytical diatomic potential energy function that can be considered an extension of the prototypical Lennard-Jones model is proposed and tested. Five- and six-parameter models are considered and these can be easily constructed from widely available low-order vibrational–rotational constants and the dissociation energy. Accuracy tests are carried out on the ground electronic states of sixteen diatomic molecules. The proposed six-parameter function is found to be more accurate than other available few-parameter analytical models for the diatomic potential energy, and has accuracy comparable to that of modern high-level ab initio functions.

Long range relationship between Morse and Lennard–Jones potential energy functions

Arising from the use of the Morse function–which is well-known for its applicability for describing bonded interaction energy–in van der Waals systems, an attempt is made herein to express parameters of the Lennard–Jones potential function in terms of the Morse function to enable normalized comparison. In a departure from previous work where the parameter relationships enforce equal curvature at the minimum well-depth, the present approach replaces this rule with equal area above the curves for 1 ≤ (r/R) ≤ ∞. Results show good approximations of the Morse function to the Lennard–Jones curve and vice versa. Comparison with the previous relation for short range interaction shows that the present relations offer superior agreement with the Lennard–Jones function over a longer range. The conversion relations provide a cost-effective, less time-consuming and reasonably reliable method for obtaining Morse parameters from those of the Lennard–Jones function and vice versa.

Biologically Plausible Computational Neurogenetic Models: Modeling the Interaction Between Genes, Neurons and Neural Networks

Using extensive molecular dynamics simulations, we have investigated the extensivity of the internal energy and entropy as well as the intensivity of temperature and pressure in small thermodynamic systems. Atomic systems consisting of n3 n = 2 3 10 argon-like particles interacting through the Lennard-Jones potential energy function have been studied. It is found that in small systems, contrary to macroscopic systems, internal energy and entropy are nonextensive whereas temperature and pressure are nonintensive. These deviations from macroscopic thermodynamics, that continue to remain detectable even in systems containing as many as 1000 particles, are in agreement with theoretical predictions.

Investigation of the thermoelastic phase transformation in a NiAl alloy by molecular dynamics simulation

The Ni x Al 1− x alloys exhibit shape memory effect, for which thermoelastic phase transformations are essential, in the composition range of 60< x<65. The analytical studies are very difficult on the thermoelastic phase transformations because these types of transformations exhibit anharmonic behaviour. In order to overcome this difficulty, it is possible to benefit from the molecular dynamics (MD) calculations based on interatomic interaction potentials. In the present study, the interatomic interactions of Ni 62.5Al 37.5 alloy have been modelled by means of Lennard–Jones potential energy function. A MD cell of 1024 atoms in B2 super lattice has been chosen and the structural changes were investigated on this system with changing temperature. It has been observed that the model alloy exhibits the thermoelastic phase transformation with thermal cycling. A hysteresis has been determined between forward and backward transformation temperatures. The structural analysis is also done before and after the transformation.

Pressure effects on martensitic transformation under quenching process in a molecular dynamics model of NiAl alloy

The solid–solid phase transitions in NiAl alloys occur by the temperature changes and application of a pressure on the system. Both types of transitions are called martensitic transformation and have displacive and thermoelastic characters. Pressure effects on thermoelastic transformation in Ni 62.5Al 37.5 alloy model have been studied by means of molecular dynamics method proposed by Parrinello–Rahman. Interaction forces between atoms in the model system were calculated by Lennard–Jones potential energy function. Thermodynamics and structural analysis of the martensitic transformations under hydrostatic pressure during the quenching processes have been performed. The simulation runs have been carried out in different hydrostatic pressures changing from zero to 40.65 GPa during the quenching process of the model alloy. At the zero and nonzero pressures, the system with B2-type ordered structure undergoes the product phase with L1 0-type ordered structure by Bain distortion in the first step of martensitic transformation under the quenching process. The increase in hydrostatic pressure causes decrease in the formation time of the product phase, and twin-like lattice distortion is observed in low temperature L1 0 phase.

Energetic and Entropic Contributions to the Surface Energy of a Free-Standing Thin Film of n-Tetracontane

The surface free energy, γμ, calculated from the chemical potential, μ, and the contribution of the internal energy to the surface energy, γU, are compared for a molecular model of a free-standing thin film of n-tetracontane. The coarse-grained chains are represented on a high-coordination lattice with a step length of 2.5 A. Each occupied site on this lattice represents a two-carbon unit of n-tetracontane. The configurations of the coarse-grained chains are governed by two types of energies. Short-range intramolecular conformations are weighted using first- and second-order interactions in the classic rotational isomeric state model of Abe et al. for polyethylene (J. Am. Chem. Soc. 1966, 88, 631). Intermolecular, as well as long-range intramolecular, interactions are weighted with a discretized Lennard-Jones potential energy function, truncated after the third shell. The contribution of these two energies to γU of the amorphous free-standing thin film is 22 erg/cm2 at 400 K. The chemical potential of the...

Monte Carlo simulation of the crystallization and annealing of a freestanding thin film of n-tetracontane

A freestanding thin film of n-tetracontane chains is simulated by a Monte Carlo (MC) method on a high coordination lattice. The coarse-grained chains, represented by 20 beads each, can be reverse-mapped into the fully atomistic description, C40H82. The Hamiltonian includes a short-range interaction based on a rotational isomeric state model and a long-range interaction obtained from a Lennard-Jones potential energy function. When the melt is instantaneously quenched from 473 to 298 K, crystallization initiates in the surface region and propagates into the interior of the film, as was found in a prior molecular dynamics simulation of a united atom model of polyethylene [M. Ito, M. Matsumoto, and M. Doi, Fluid Phase Equilibria, 144, 395 (1998)]. Several repetitions of the MC simulation, starting from different configurations of the melt at 473 K, reveal that two distinctly different structures can be obtained. Usually the independently initiated crystals at the two surfaces of the thin film produce a disordered grain boundary when they impinge on one another as a consequence of propagation into the interior of the film. This grain boundary was also observed by Ito et al. However, if the MC simulation is repeated many times, there are a few instances in which the independently initiated crystals happen to have a similar orientation, and then crystallization propagates completely through the thin film without producing a grain boundary in the interior. A well-defined melting phenomenon is observed at about 390 K when the film without the grain boundary is heated. Annealing at 380 K of the film with the grain boundary causes growth of one crystal at the expense of the other. This growth eventually leads to a completely crystalline film, with elimination of the grain boundary. Therefore, the stable structure of the thin film is the one that is completely crystalline, with no grain boundary in the interior, even though rapid quenching is more likely to lead to a structure with a grain boundary. The MC simulation can anneal the imperfect structure into the more perfect one.

Equivalent formulations and necessary optimality conditions for the Lennard–Jones problem

The minimization of molecular potential energy functions is one of the most challenging, unsolved nonconvex global optimization problems and plays an important role in the determination of stable states of certain classes of molecular clusters and proteins. In this paper, some equivalent formulations and necessary optimality conditions for the minimization of the Lennard–Jones potential energy function are presented. A new strategy, the code partition algorithm, which is based on a bilevel optimization formulation, is proposed for searching for an extremal Lennard–Jones code. The convergence of the code partition algorithm is proved and some computational results are reported.

Monte Carlo Simulation of Head-to-Head, Tail-to-Tail Polypropylene and Its Mixing with Polyethylene in the Melt

Simulations have been performed at 473 K for one-component melts of polyethylene (PE) and head-to-head, tail-to-tail polypropylene (hhPP) as well as a mixture of the two species. The densities are 0.760, 0.753, and 0.756 g/cm3 for these three NVT simulations, respectively. The Monte Carlo simulation uses coarse-grained representations of the chains on a sparsely occupied high coordination lattice. The short-range intramolecular interactions are controlled by rotational isomeric state models for the two types of chains, and the intermolecular interactions are represented by a discretized version of Lennard-Jones potential energy functions. Equilibrated coarse-grained replicas are reverse-mapped to atomistically detailed models in continuous space. The pair correlation functions clearly demonstrate the onset of demixing for the two-component melt, which is qualitatively consistent with the conclusion from small-angle neutron scattering reported by Jeon et al. [Macromolecules 1998, 31, 3340]. Analysis of the components of the energy in the simulations shows that the positive energy change on mixing is completely dominated by the intermolecular Lennard-Jones contributions, with negligible contributions from the short-range intramolecular interactions in the rotational isomeric state models. Quantitative comparison with experiment shows that the χ deduced from the simulations is larger than the χ deduced from the experiments. Several factors in the experiments and in the simulations may contribute to the quantitative difference.

Translational diffusion in Monte Carlo simulations of polymer melts: center of mass displacement vs. integrated velocity autocorrelation function

Translational diffusion has been simulated in monodisperse melts of four linear alkanes, C2xH4x+2, x=6,30,50,158, and two cyclic alkanes, C2xH4x, x=30,50, at 473K. The alkanes are expressed in a coarse-grained representation using x beads on a high coordination lattice, one bead for every two carbon atoms. Short-range intramolecular interactions are controlled by an adaptation of the rotational isomeric state model for unperturbed polyethylene, and the long-range interactions are controlled by a step-wise three-shell potential energy function derived from a continuous Lennard-Jones potential energy function. Acceptance of trial moves, each of which changes the coordinates of a single bead only, is governed by the Metropolis rule. Translational diffusion coefficients, D, are estimated from the mean square displacement of the center of mass and the integral of the velocity autocorrelation function. Both approaches yield the same value for D, which demonstrates that the velocity has been defined in a reasonable manner in the Monte Carlo simulation. A method is proposed for the estimation of D when the trajectory is not quite long enough to have achieved the behavior characteristic of the limit as time approaches infinity.

Detection of the onset of demixing in simulations of polypropylene melts in which the chains differ only in stereochemical composition

Simulations have been performed at 480 K for pure melts of atactic, isotactic and syndiotactic polypropylene chains with a degree of polymerization of 50 and composition C150H302, and also for the three 50:50 mixtures of two of these species. The simulations are performed on a high coordination lattice, with incorporation of short range intramolecular interactions from a rotational isomeric state model of polypropylene, and incorporation of long range interactions defined by a Lennard-Jones potential energy function for the interaction of pairs of molecules of propane. Both the rotational isomeric state model and Lennard-Jones parameters were taken directly from the literature (Suter et al. and Prausnitz, respectively). The efficiency of the simulation on the sparsely occupied high coordination lattice facilitates the equilibration of the one- and two-component melts within accessible computer time. Onset of a tendency for demixing of isotactic and syndiotactic polypropylene is apparent in the intermolecular pair correlation functions. No such demixing occurs with isotactic and atactic polypropylene. Both of these predictions from the simulation are consistent with experimental results in the literature (Maier et al. and Lohse, respectively). The simulation produces an ambigious prediction for the melt of atactic and syndiotactic polypropylene. This melt has been reported (Maier et al.) to exhibit phase separation, but less strongly than the isotactic-syndiotactic system, for which the simulation makes an unambiguous (and correct) prediction. The physical origin of the tendency for demixing in the simulations is identified as the differences in the preferred local conformations of polypropylene chains with various stereochemical sequences. This driving force is an example of “conformational asymmetry” induced solely by differences in stereochemical sequence.

A model for predicting the solubility of 1,3,5-trinitro-1,3,5- s-triazine (RDX) in supercritical CO 2: isothermal–isobaric Monte Carlo simulations

Isothermal–isobaric Monte Carlo (NPT-MC) simulations and the Widom test particle method were used to predict the solubility of the explosive 1,3,5-trinitro-1,3,5- s-triazine (RDX) in supercritical CO 2. A Lennard–Jones potential energy function was chosen to describe the interaction between RDX and CO 2, and calibrated using two experimental solubility values. NPT-MC simulations using this interaction potential predicted solubilities of RDX in CO 2 over a temperature range of 308 to 353 K and pressures ranging from 10.4 to 48.3 MPa that were in good agreement with experimental values.

Molecular Dynamics Simulation of Argon in Solid\raLiquid Phase Transition Region

The microstructure of 256 argon atoms located on ideal fcc lattice sites on which periodic boundary conditions have been applied at the vicinity of transition temperature has been investigated. The forces among atoms have been derived from Lennard-Jones potential energy function and the equations of motion of the system have been solved by using the Verlet algorithm. The variations in microstructure have been investigated by means of radial distribution function and real-space atomic trajectories. It has been found from the results of simulation at zero pressure that solid-liquid transition temperature is 86K, the change of enthalpy is 1202 J/mol and relative volume change is 0.14.