Lennard-Jones Interaction Potential Research Articles

Thermal Conductivity of Liquid Lead for the Fast Nuclear Reactor Coolant, Calculated by the Green-Kubo Method Using Molecular Dynamics Simulation

Comprehensive information about nuclear reactor coolant materials for application in heat-transfer systems is very important. One important physical property that needs to be known is the thermal conductivity. The goal of this work is to predict the thermal conductivity value of the liquid lead, which is one of the important candidates for cooling materials for Gen-IV fast nuclear reactor designs. The thermal conductivity of liquid lead in this study was predicted using the Green-Kubo scheme and the molecular dynamics (MD) computational method to collect the simulation data. The MD simulation was done in the NVT ensemble, using the Lennard-Jones interaction potential. We observe the thermal conductivity of the liquid lead can be studied based on the diffusion physical process. The thermal conductivity of the liquid lead obtained from this research is λ = 0.0113T + 8.8539 [W/mK]. As a conclusion, this result is very suitable, compared with the available experimental data, then the Green-Kubo method can be used to calculate the thermal conductivity of liquid metal as lead.

Numerical modeling of interaction of water molecule and fullerene C60

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.

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.

Instability of the body-centered cubic lattice within the sticky hard sphere and Lennard-Jones model obtained from exact lattice summations.

A smooth path of rearrangement from the body-centered cubic (bcc) to the face-centered cubic (fcc) lattice is obtained by introducing a single parameter to lattice vectors of a cuboidal unit cell. As a result, we obtain analytical expressions in terms of lattice sums for the cohesive energy where the interaction is described by a Lennard-Jones (LJ) interaction potential or a sticky hard-sphere (SHS) model with a r^{-n} long-range attractive term. These lattice sums are evaluated to computer precision by expansions in terms of a fast converging Bessel function series. Applying the whole range of lattice parameters for the SHS and LJ potentials we prove that the bcc phase is unstable (or, at best, metastable) toward distortion into the fcc phase in the low temperature and pressure limit. Even if more accurate potentials are used, such as the extended LJ potential for argon or chromium, the bcc phase remains unstable. This strongly indicates that the appearance of a low temperature bcc phase for several elements in the periodic table is due to higher than two-body forces in atomic interactions.

Structure of a nanodrop of a binary mixture on a solid surface

The structure of a nanodrop composed of the binary mixture and sitting on the smooth solid surface is examined on the basis of a nonlocal canonical ensemble density functional theory. The molecules of two components have different diameters, masses and energy parameters of Lennard–Jones interaction potential. The properties of density distributions of the fluid components and local composition of the mixture inside and on the boundary of the drop are analysed in details for various net compositions of the mixture at various temperatures, parameters of intermolecular interaction and gravitational acceleration. The results might be of interest in developing drug delivery methods as one component of the mixture can be considered as a solvent and another one (solute) as a drug.

Non-local phase field revisited

The phase field model is revisited as an approximation of a full non-local approach. We focus on van der Waals fluids, where the non-local interaction potential consists of short-range repulsion and long-range attraction, characterized by distances d (i.e. a typical molecular size d ≈ 10−9 m) and ℓ ≫ d. The first non-local correction to the thermodynamic limit introduces a density square gradient free energy, expressed in terms of a characteristic length, a. Imposing that the line integral of the non-local free energy functional across an interfacial region must equal the surface tension, we find that a is up to two orders of magnitude larger than the molecular size, in agreement with the local equilibrium assumption. Instead, by finding a directly from the interaction potential, when the attractive force follows a power-law, as in the Lennard-Jones potential, then a ≅ d, which contradicts that a ≈ 10−7 m as from surface tension measurements. Conversely, when the attractive force follows a Debye-like exponentially decaying potential of range ℓ, then a ≈ ℓ ≫ d, in agreement with surface tension measurements and the mean field theory assumption. The other point that we have addressed is determining when the mean field model can be applied. By directly simulating the phase separation of a far-from-critical van der Waals fluid mixture, we find that the growth laws of the mean nuclei size are not modified when higher-order gradient terms are retained. An exponentially decaying attractive potential must be used since the higher-order gradient terms diverge when power-law potentials are considered, confirming that a Lennard-Jones interaction potential is not compatible.

Distributed charge models of liquid methane and ethane for dielectric effects and solvation

Liquid hydrocarbons are often modelled with fixed, symmetric, atom-centred charge distributions and Lennard-Jones interaction potentials that reproduce many properties of the bulk liquid. While useful for a wide variety of applications, such models cannot capture dielectric effects important in solvation, self-assembly, and reactivity. The dielectric constants of hydrocarbons, such as methane and ethane, physically arise from electronic polarisation fluctuations induced by the fluctuating liquid environment. In this work, we present non-polarisable, fixed-charge models of methane and ethane that break the charge symmetry of the molecule to create fixed molecular dipoles, the fluctuations of which reproduce the experimental dielectric constant. These models can be considered a mean-field-like approximation that can be used to include dielectric effects in large-scale molecular simulations of polar and charged molecules in liquid methane and ethane. We further demonstrate that solvation of model ionic solutes and a water molecule in these fixed-dipole models improve upon dipole-free models.

Optimized Magnesium Force Field Parameters for Biomolecular Simulations with Accurate Solvation, Ion-Binding, and Water-Exchange Properties.

Magnesium ions play an essential role in many vital processes. To correctly describe their interactions in molecular dynamics simulations, an accurate parametrization is crucial. Despite the importance and considerable scientific effort, current force fields based on the commonly used 12–6 Lennard-Jones interaction potential fail to reproduce a variety of experimental solution properties. In particular, no parametrization exists so far that simultaneously reproduces the solvation free energy and the distance to the water oxygens in the first hydration shell. Moreover, current Mg2+ force fields significantly underestimate the rate of water exchange leading to unrealistically slow exchange kinetics. In order to make progress in the development of improved models, we systematically optimize the Mg2+ parameters in combination with the TIP3P water model in a much larger parameter space than previously done. The results show that a long-ranged interaction potential and modified Lorentz–Berthelot combination rules allow us to accurately reproduce multiple experimental properties including the solvation free energy, the distances to the oxygens of the first hydration shell, the hydration number, the activity coefficient derivative in MgCl2 solutions, the self-diffusion coefficient, and the binding affinity to the phosphate oxygen of RNA. Matching this broad range of thermodynamic properties, we present two sets of optimal parameters: MicroMg yields water exchange on the microsecond timescale in agreement with experiments. NanoMg yields water exchange on the nanosecond timescale facilitating the direct observation of ion-binding events. As shown for the example of the add A-riboswitch, the optimized parameters correctly reproduce the structure of specifically bound ions and permit the de novo prediction of Mg2+-binding sites in biomolecular simulations.

Role of Attractive Interactions in Structure Ordering and Dynamics of Glass-Forming Liquids

A key question in glass physics is what the origin of slow glassy dynamics is. The liquid structure is a natural candidate; however, an apparently severe counterexample has been known. Two model glass-forming liquids, with the standard Lennard-Jones interaction potential and its Weeks-Chandler-Andersen variation without the attractive tail, exhibit very similar structures at the two-body level but drastically different dynamical behaviors in the supercooled states. Here we look at the liquid structure through a (many-body) structural order parameter Θ characterizing the packing capability of local particle arrangements. We show that the structures of these two systems seen by Θ are actually very different at a many-body level, but, quite surprisingly, the macroscopic structure (Θ)-dynamics (τ_{α}) relationships commonly follow a Vogel-Fulcher-Tammann-like function. Furthermore, the mutual information analysis reveals strong local structure-dynamics correlations. Therefore, we conclude that attractive interactions affect the liquid structure in a nonperturbative manner, but a general structural origin of slow dynamics holds for these systems.

Thermophysical properties of supercritical [formula omitted] from Molecular Dynamics simulations

The ability to predict thermophysical properties of molecular hydrogen with high accuracy, especially at high pressures, is crucial to design and to operate processes involving compressed hydrogen. Molecular simulations comprise an adequate tool to investigate both thermodynamic and transport properties of different molecular systems using a single potential energy surface model. Such a potential is called a force field. Here we propose a new single-site force field for pure hydrogen using a Mie potential to describe the intermolecular interactions. The proposed force field yields better predictions of thermodynamic properties when compared to other available force fields that use Lennard-Jones interaction potential. The new force field is also able to predict transport properties with reasonable accuracy.

Stochastic simulation of transport processes in liquids

The subject of this paper is molecular stochastic modeling the transport processes in liquids. The proposed method and the corresponding algorithm are an alternative to the molecular dynamics method. However, unlike the latter the system of Newtonian equations is not solved for modeling the phase trajectories of the system studied. The phase trajectories of the molecular system are simulated stochastically. For this purpose, the database of the intermolecular forces acting on each molecule of the system during the considered time interval has been created. The distribution function of these forces has been built. It was shown that this distribution function can be approximated by certain analytic function. The dependency of the parameters of this function on the liquid temperature and parameters of the intermolecular interaction potential (the Lennard-Jones interaction potential is used) is determined. Using this distribution function the force acting on each molecule at given time is determined. After that the coordinates and velocity of all molecules of the system are calculated. As a result, the full information about the phase variables of the molecular system is obtained. All macroscopic characteristics of the system (temperature, pressure, transport coefficients etc.) are calculated by means of the methods of nonequilibrium statistical mechanics. The transport coefficients are calculated using fluctuation-dissipation theorems that relate transport coefficients to the evolution of the corresponding correlation functions. The algorithm was tested on the calculation of the viscosity of several simple liquids.

Empirical potential for molecular simulation of graphene nanoplatelets

A new empirical potential for layered graphitic materials is reported. Interatomic interactions within a single graphene sheet are modeled using a Stillinger-Weber potential. Interatomic interactions between atoms in different sheets of graphene in the nanoplatelet are modeled using a Lennard-Jones interaction potential. The potential is validated by comparing molecular dynamics simulations of tensile deformation with the reported elastic constants for graphite. The graphite is found to fracture into graphene nanoplatelets when subjected to ∼15% tensile strain normal to the basal surface of the graphene stack, with an ultimate stress of 2.0 GPa and toughness of 0.33 GPa. This force field is useful to model molecular interactions in an important class of composite systems comprising 2D materials like graphene and multi-layer graphene nanoplatelets.

Interaction energy of a pair of identical coplanar uniformly charged nanodisks

We consider a nanosystem consisting of two coplanar uniformly charged nanodisks that are coupled via Coulomb forces. Such a model represents a typical situation encountered in two-dimensional semiconductor quantum dot systems of electrons. We provide an exact integral expression for the interaction energy between the two coplanar nanodisks as a function of their separation distance. It is found that the difference between a standard Coulomb potential and the current one has features reminiscent of a Lennard-Jones interaction potential. The results derived can be useful to understand formation of clusters and/or aggregates in systems of coplanar charged nanodisks that contain electrons.

MODELING OF HYDRAULIC FRACTURING ON THE BASIS OF THE PARTICLE METHOD

A technique of calculating the deformation of the soil environment when it interacts with a liquid on the basis of the particle method a is realized. To describe the behavior of the solid and liquid phases of the soil, a classical two-parameter Lennard-Jones interaction potential and its modified version proposed by the authors were chosen. The model problem of deformation and partial destruction of a soil massif under strong pressure from the liquid pumped into it is solved. Analysis of the results shows that the use of the modified Lennard-Jones potential for describing the solid phase of the soil environment makes it possible to describe the process of formation of cracks in the soil during hydraulic fracturing of the formation.

Modeling of deformation of ground media on the basis of the particle method in a two-dimensional formulation

A two-dimensional version of the soil deformation method based on the particle method is implemented in this paper. For describing the behavior of a continuous medium, the previously used two-parameter “modified” Lennard-Jones interaction potential was chosen. A number of model problems describing the loss of stability of the soil embankment in the field of gravity and the destruction of the soil under the action of the liquid phase are solved.

Effect of temperature on the corrosion inhibition of iron in liquid lead using oxygen inhibitor: studied by MD simulation

For corrosion mitigation of steels used in a fast nuclear reactor power plant, oxygen gas is one of promising candidates of inhibitors. Many experiments have been conducted to reveal the mechanism of corrosion and mechanism of how to overcome the corrosion. In the previous work, we had shown computationally that the oxygen atom can be used to reduce the corrosion and we had predicted the oxygen contents. In the current work, not only to explore deeeper the ability of oxygen gas to reduce the corrosion, but also to include the variation of used temperature. We still used iron material to represent a real steels. Using MD (molecular dynamics) simulation based on the Lennard-Jones interaction potential, we sought to understand the concentration of oxygen gas as variation of temperature used in the reactor for the best corrosion mitigation. From this work, we conclude that the temperature does not give effect in related with how concentration of injected oxygen. The temparature merely affects to rise the diffusion coefficient of iron in liquid lead, yet it does not influence how much oxygen needed for corrosion mitigation. In this work, all simulations on different series of temperatures (1023°K, 1073°K, 1123°K, 1173°K) reveals that oxygen content of 0.1151wt% will cause the lowest corrosion level of iron in liquid lead.

Accurate calculation of near-critical heat capacities CP and CV of argon using molecular dynamics

Molecular dynamics (MD) employing the Lennard-Jones (LJ) interaction potential was used to compute the heat capacities of argon at constant volume CV and constant pressure CP near the critical point very close to the asymptotic region. The accurate MD calculation of critical divergences was shown to be related to a careful choice of the cutoff radius rc and the inclusion of long-range corrections in the LJ potential. The computed CP and CV values have very good agreement as compared to available NIST data. Furthermore, values of CV in a range of temperatures for which NIST data is not available could be computed. In the investigated range of temperatures, both CP and CV MD results were fitted to a simple mathematical expression based on an empirical model that describes the critical effects when the asymptotic models are not appropriate. The present approach is of general applicability and robust to compute thermophysical properties of fluids in the near-critical region.

Molecular thermal energy transfer in binary mixture of simple liquids

Molecular thermal energy transfer in liquid mixtures was investigated using non-equilibrium molecular dynamics (NEMD) simulations of heat conduction in a series of binary mixture liquids with various compositions. Mixtures of argon and krypton were selected as simple liquids which were modeled using the Lennard-Jones (LJ) interaction potential. Thermal conductivities for these mixtures in a saturated state at a constant temperature (127 K) were compared with respect to mixture composition, i.e., molar fraction of each component. According to the molecular energy transfer mechanism, microscopic heat conduction flux can be decomposed into two molecular-scale contributions: one from self-transportation, which includes transport of kinetic energy and potential energy by molecular motion, and the other via the contribution of intermolecular energy transfer based on intermolecular interaction. The intermolecular energy transfer, which is the dominant source of macroscopic heat conduction flux in liquids, can be decomposed into contributions from various pair interactions, which in the present study are energy transfers via the paths ArAr, ArKr, and KrKr. The above contributions to heat conduction were evaluated quantitatively. It was found that the composition dependence of the first self-transportation contribution is mostly caused by the differences of their thermodynamic states, and the variation of total thermal conductivity with the composition is dominated by the second intermolecular energy transfer contribution, which accounts for about 80% of the total. The contributions of individual interaction paths were analyzed with our new concept of atomistic heat path [Matsubara et al., J. Chem. Phys., 142 (2015), 164509]. It was found that these contributions are mostly affected by the number densities of the interaction paths in the first neighbor shell. The molecular-scale internal structure of the liquid is changed by changes in composition, which affects the efficiency of the energy transfer by a single intermolecular interaction. A sensitivity analysis of LJ cross-molecular parameters was done using various combining rules. We found that the decomposed energy transfer contribution of interaction paths, ArAr and KrKr may be affected by changing the LJ parameters of ArKr.

Cutoff nonlinearities in the low-temperature vibrations of glasses and crystals.

We present a computer simulation study of glassy and crystalline states using the standard Lennard-Jones interaction potential that is truncated at a finite cutoff distance, as is typical of many computer simulations. We demonstrate that the discontinuity at the cutoff distance in the first derivative of the potential (corresponding to the interparticle force) leads to the appearance of cutoff nonlinearities. These cutoff nonlinearities persist into the very-low-temperature regime thereby affecting low-temperature thermal vibrations, which leads to a breakdown of the harmonic approximation for many eigenmodes, particularly for low-frequency vibrational modes. Furthermore, while expansion nonlinearities which are due to higher order terms in the Taylor expansion of the interaction potential are usually ignored at low temperatures and show up as the temperature increases, cutoff nonlinearities can become most significant at the lowest temperatures. Anharmonic effects readily show up in the elastic moduli which not only depend on the eigenfrequencies, but are crucially sensitive to the eigenvectors of the normal modes. In contrast, those observables that rely mainly on static structural information or just the eigenfrequencies, such as the vibrational density of states, total potential energy, and specific heat, show negligible dependence on the presence of the cutoff. Similar aspects of nonlinear behavior have recently been reported in model granular materials, where the constituent particles interact through finite-range, purely repulsive potentials. These nonlinearities have been ascribed to the nature of the sudden cutoff at contact in the force law. As a consequence, we demonstrate that cutoff nonlinearities emerge as a general feature of ordered and disordered solid state systems interacting through truncated potentials.

Theoretical study of thermal conductivities of various gas mixtures through the generalized Lennard-Jones interaction potential for application in gas-discharge lasers

Thermal conductivities of helium, neon, bromine, and hydrogen are calculated on the basis of the (12-6) Lennard-Jones interaction approximation. Where necessary for a more precise approximation, a generalized (n-m) Lennard-Jones interaction potential is used. Thermal conductivities of binary gas systems are calculated and compared through two different empirical methods for the case of gas discharges in He, Ne, and Ne-He mixtures with small admixtures of bromine and hydrogen. A new simple method is proposed for the thermal conductivity determination for the 3- and 4-component gas mixtures of our interest.