Truncated Lennard-Jones Potential Research Articles

Thermodynamic properties of the 3D Lennard-Jones/spline model

The Lennard-Jones (LJ) spline potential is a truncated LJ potential so that both the pair potential and the force continuously approach zero at . We present a systematic map of the thermodynamic properties of the LJ spline model from molecular dynamics and Gibbs ensemble Monte Carlo simulations. Results are presented for gas/liquid, liquid/solid and gas/solid coexistence curves, the Joule-Thomson inversion curve, and several other thermodynamic properties. The critical point for the model is estimated to be and , respectively. The triple point is estimated to and . The coexistence densities, saturation pressure, and supercritical isotherms of the LJ spline model were fairly well represented by the Peng-Robison equation of state. We find that Barker-Henderson perturbation theory works less good for the LJ spline than for the LJ model. The first-order perturbation theory overestimates the critical temperature and pressure by about 10% and 90%, respectively. A second-order perturbation theory is not much better. Our assessment is that the mean compressibility approximation gives a poor representation of the second-order perturbation term. Our main conclusion is that we at the moment do not have a theory or model that adequately represents the thermodynamic properties of the LJ spline system.

Note: A new truncation correction for the configurational temperature extends its applicability to interaction potentials with a discontinuous force.

We present a simple truncation correction for the configurational temperature which, unlike previous corrections, works even at low truncation values for the shifted and truncated Lennard-Jones potential. The success of the new correction suggests that the expression for the configurational temperature is valid also for interaction potentials with a discontinuous force, given that the discontinuity is properly accounted for.

Predicting the Thermodynamic Properties of the Modified Lennard-Jones Fluid from the Lennard-Jones Equation of State

The Lennard-Jones (LJ) potential has been widely used, even beyond fluid science, as a standard form to express interparticle interaction. However, numerical computation and simulation requires some convention for dealing with the potential's infinite tail. This delicate problem can be circumvented by adopting a truncated potential. The functional form of the latter should mimic that of the original potential as closely as possible, while simultaneously minimizing artificial effects caused by the resultant discontinuities. The advantage of choosing such a truncated LJ potential, called the modified Lennard-Jones (mLJ) potential, is that the thermodynamic behavior of fluids can be predicted from the extensive knowledge base regarding the LJ fluid. In this study, the properties of the mLJ fluid were treated as perturbations of the LJ fluid case, and the discrepancies were expressed as density series expansions. The second virial coefficient of the mLJ fluid was well reproduced by this method. Reproduction of the liquid–vapor coexisting envelope was also satisfactory, except in the vicinity of the critical point.

Acceleration of molecular dynamics simulation of multiphase systems on GPU

The paper presents results on acceleration of molecular dynamics simulations with the usage of GPUs. A system of water molecules is considered as an example of polar liquid. The intermolecular interaction is modeled with the usage of Coulomb and truncated Lennard-Jones potentials. Results of computational experiments on acceleration and performance of the developed code are presented.

Heating through the glass transition: A rigidity approach to the boson peak

Using molecular dynamics, we study the relationship between the excess of low-frequency vibrational modes (Boson peak, BP) and the glass transition for a bidispersive glass interacting through a truncated Lennard-Jones potential. The evolution of the BP with increasing temperature is correlated with the average coordination, as predicted by rigidity theory. This is due to a lack of atomic ``contacts,'' as is confirmed by taking a crystal with broken bonds. We show how the quadratic mean displacement $(⟨{u}^{2}⟩)$ is enhanced by the BP. When $⟨{u}^{2}⟩$ is obtained on short time scales or measured on inherent structures, the glass transition temperature ${T}_{g}$ is determined by the position and height of the BP. Between the melting temperature ${T}_{m}$ and ${T}_{g}$, the nature of the relaxation processes exhibit phase separation, where the backbone increases its rigidity while the smaller atoms diffuse away to form separate crystals.

Soft Wall Ion Channel in Continuum Representation with Application to Modeling Ion Currents in α-Hemolysin

A soft repulsion (SR) model of short-range interactions between mobile ions and protein atoms is introduced in the framework of continuum representation of the protein and solvent. The Poisson-Nernst-Plank (PNP) theory of ion transport through biological channels is modified to incorporate this soft wall protein model. Two sets of SR parameters are introduced. The first is parametrized for all essential amino acid residues using all atom molecular dynamic simulations; the second is a truncated Lennard-Jones potential. We have further designed an energy-based algorithm for the determination of the ion accessible volume, which is appropriate for a particular system discretization. The effects of these models of short-range interactions were tested by computing current-voltage characteristics of the α-hemolysin channel. The introduced SR potentials significantly improve prediction of channel selectivity. In addition, we studied the effect of the choice of some space-dependent diffusion coefficient distributions on the predicted current-voltage properties. We conclude that the diffusion coefficient distributions largely affect total currents and have little effect on rectifications, selectivity, or reversal potential. The PNP-SR algorithm is implemented in a new efficient parallel Poisson, Poisson-Boltzmann, and PNP equation solver, also incorporated in a graphical molecular modeling package HARLEM.

Droplet spreading driven by van der Waals force: a molecular dynamics study

The dynamics of droplet spreading is investigated by molecular dynamics simulations fortwo immiscible fluids of equal density and viscosity. All the molecular interactions aremodeled by truncated Lennard-Jones potentials and a long-range van der Waals force isintroduced to act on the wetting fluid. By gradually increasing the coupling constant in theattractive van der Waals interaction between the wetting fluid and the substrate, weobserve a transition in the initial stage of spreading. There exists a critical value of thecoupling constant, above which the spreading is pioneered by a precursor film. Inparticular, the dynamically determined critical value quantitatively agrees with thatdetermined by the energy criterion that the spreading coefficient equals zero. Thelatter separates partial wetting from complete wetting. In the regime of completewetting, the radius of the spreading droplet varies with time as , a behavior also found in molecular dynamics simulations where the wetting dynamics isdriven by the short-range Lennard-Jones interaction between liquid and solid.

Direct determination of the Tolman length from the bulk pressures of liquid drops via molecular dynamics simulations

An expression for the difference in pressure between a liquid drop in equilibrium with its vapor Deltap=p([script-l])-p(v) is derived from previous expressions for the components of the Irving-Kirkwood pressure tensor. This expression, as well as the bulk values of the pressure tensor, is then evaluated via molecular dynamics simulations of particles interacting through a truncated Lennard-Jones potential. We determine the Tolman length delta from the dependence of Deltap on the equimolar radius. We determine the Tolman length to be delta=-0.10+/-0.02 in units of the particle diameter. This is the first determination of the Tolman length for liquid droplets via the pressure tensor route through computer simulation that is negative, in contrast to all previous results from simulation, but in agreement with results from density functional theory. In addition, we study the planar liquid-vapor interface and observe a dependence of the physical properties of the system on the system size, as measured by the surface area.

Excess of low frequency vibrational modes and glass transition: A molecular dynamics study for soft spheres at constant pressure

Using molecular dynamics at constant pressure, the relationship between the excess of low frequency vibrational modes (known as the boson peak) and the glass transition is investigated for a truncated Lennard-Jones potential. It is observed that the quadratic mean displacement is enhanced by such modes, as predicted using a harmonic Hamiltonian for metastable states. As a result, glasses loose mechanical stability at lower temperatures than the corresponding crystal, since the Lindemann criteria are observed, as is also deduced from density functional theory. Finally, we found that the average force and elastic constant are reduced in the glass due to such excess of modes. The ratio between average elastic constants can be approximated using the 2/3 rule between melting and glass transition temperatures.

Calculation of the surface tension from Monte Carlo simulations: Does the model impact on the finite-size effects?

We report two-phase Monte Carlo simulations of the liquid-vapor interface of the Lennard-Jones (LJ) fluids in order to study the impact of the methodology used for the energy calculation on the oscillatory behavior of the surface tension with the system sizes. The surface tension values are illustrated through the LJ parameters of methane. The first methodology uses a standard truncated LJ potential, the second one adds a long range correction (LRC) contribution to the energy into the Metropolis scheme, and the third one uses a LJ potential modified by a polynomial function in order to remove the discontinuities at the cutoff distance. The surface tension is calculated from the mechanical and thermodynamic routes and the LRCs to the surface tension are systematically calculated from appropriate expressions within these definitions. The oscillatory behavior has been studied as a function of the size of the interfacial area and of the length of the dimension perpendicular to the surface. We show that the methodology has an important effect on the oscillatory variation in the surface tension with the system size. This oscillatory variation in the surface tension with the system size is investigated through its intrinsic and LRC contributions. We complete this work by studying the dependence of the surface tension with respect to the cutoff distance when the LRC part to the energy is considered into the Metropolis scheme.

Interfacial Properties and Adsorption of Polymer−Solvent Binary Mixtures

The phase behavior and interfacial properties of mixtures of chain molecules built of 2, 4, and 10 segments with monomeric species are studied using density functional theory. The chain molecules are modeled as fully flexible chains of tangentially bonded spherical segments. The chain segments and the solvent molecules interact via the truncated Lennard-Jones potential. Within density functional theory, we investigate the structure of the fluid−fluid interface and interfacial tension. In general we find an accumulation of the solvent particles at the interface. For mixtures with longer chains, we find the complete wetting transition at the gas−liquid interface upon approaching the triple point. We also report mean field density functional theory results for adsorption of tetramer−monomer mixtures in slit-like pores. We present density profiles, adsorption isotherms, and phase diagrams and discuss the effects of the model parameters on the capillary condensation. The main effect is that confinement gives rise to a substantial enrichment of tetramers, relative to bulk phases. However, the global phase diagrams for confined mixtures belong to the same class of phase behavior as those for bulk phases.

Effect of attractive interactions on tagged particle dynamics

We study tagged particle dynamics in a one-component simple liquidcharacterized by the Lennard-Jones (LJ) interaction potential. Extended modecoupling theory is used to obtain the correlation function which feeds back on thedynamics of the self-correlations. The cooperative dynamical effects are studied byevaluating various properties of tagged particle motion as influenced by thecollective dynamics. Comparison between the results obtained for particles withpurely repulsive interactions like the truncated LJ potential (or the hard-sphereinteraction) and that of the full LJ potential are shown. The nature of the velocityautocorrelation function and the non-Gaussian variation of the van Hoveself-correlation function is specifically highlighted here. The role of staticstructural input in the theory is considered especially in this regard.

Microscopic morphology and energy surface landscape in a supercooled soft-sphere system

We carry out a systematic study on the microscopic morphology and its relationship with the signatures of the traces swept over the potential energy surface in a soft-sphere fluid system interacting via a truncated Lennard–Jones potential. The state of the model system is tuned by changing its temperature obtained in a molecular dynamics simulation, ranging from the equilibrium fluid phase to the deeply quenched supercooled states. The density and the range of interaction are chosen so that the instantaneously barely isolated centers are present. We analyze the microscopic structural origin of the features in the instantaneous-normal-mode (INM) spectrum and search for evidence of state transformation. It is found that the presence of drastic changes in the INM spectra upon entering the deep supercooled regime is accompanied by the reduction in the spatial connectivity. We develop a method to characterize the spatial configuration in an attempt to address the origin of the temperature-dependent changes in the spectra.

On the long-range corrections to computer simulation results for the Lennard-Jones vapor-liquid interface

The long-range corrections (LRCs) to the configurational energy have been taken into consideration in the Monte Carlo simulation of the vapor-liquid interface for a pure Lennard-Jones (LJ) fluid. The simulated bulk densities agree satisfactorily with those obtained from the Gibbs ensemble method, and the simulated surface tension values agree reasonably well with those reported in the literature for a larger number of molecules and a larger cut-off distance. To compare the influence of the potential forms on the simulation results, a truncated LJ potential, and a shifted and truncated LJ potential have been examined. Although the bulk densities and surface tensions calculated for different model fluids are strongly affected by the LRC, the different potentials essentially lead to similar density values and similar surface tension values when the respective calculated values are compared on the basis of a reduced temperature scale.

Effect of Size Dispersity on the Melting Transition

ABSTRACTWe present a molecular dynamics simulation study of the liquid-solid transition in a two dimensional system consisting of particles of two different sizes interacting via a truncated Lennard-Jones potential. We work with equal number of particles of each kind and the dispersity Δ in the sizes of the particles is varied by changing the ratio of the particle sizes only. For the monodisperse case (Δ = 0) and for small values of Δ, we find a first order liquid-solid transition on increasing the volume fraction p of the particles. As we increase Δ, the first-order transition coexistence region weakens gradually and completely disappears at high dispersities around Δ = 0.10. At these values of dispersity the high density phase lacks long range translational order but possesses orientational order with a large but finite correlation length. The consequences of this effect of dispersity on the glass transition and on the melting transition in general are discussed.

The equation of state for molecules with shifted Lennard-Jones pair potentials

Compressibility factors and internal energies have been calculated for fluids with softly repulsive pair potentials by means of the Maxwell distribution method. The pair potentials used are Lennard-Jones potentials, truncated at the minimum and with the minimum shifted towards zero energy. The exponent of attraction has been varied between 4 and 8, the exponent of repulsion between 8 and 40. An empirical equation of state has been developed which permits the calculation of thermodynamic properties for all truncated Lennard-Jones potentials. When this equation of state is substituted for the hard-sphere term in simple equations of state of the var der Waals type, a better representation of caloric data is obtained, especially over the high density region.

Molecular simulation of phase coexistence: Finite-size effects and determination of critical parameters for two- and three-dimensional Lennard-Jones fluids

The subject of this paper is the investigation of finite-size effects and the determination of critical parameters for a class of truncated Lennard-Jones potentials. Despite significant recent progress in our ability to model phase equilibria in multicomponent mixtures from direct molecular simulations, the accurate determination of critical parameters remains a difficult problem. Gibbs ensemble Monte Carlo simulations with systems of controlled linear system size are used to obtain the phase behavior in the near-critical region for two- and three dimensional Lennard-Jones fluids with reduced cutoff radii of 3, 3.5, and 5. For the two-dimensional systems, crossover of the effective exponent for the width of the coexistence curve from mean field (β = 1/2 in the immediate vicinity of the critical point to Ising-like (β= 1/8) farther away is observed. Critical parameters determined by fitting the data that follow Ising-like behavior are in good agreement with literature values obtained with finite-size scaling methods. For the three-dimensional systems, no crossover to mean field-type behavior was apparent. Extrapolated results for the critical parameters are consistent with literature estimates for similar fluids. For both two- and three-dimensional fluids, system size effects on the coexistence curves away from the critical point are small, normally within simulation statistical uncertainties.

The effect of solvation on the conformation of freely jointed repulsive trimers

The effect of solvation on the conformation of a dense one-component fluid composed of freely jointed repulsive trimers is calculated theoretically and compared to results from computer simulation. All monomers in the fluid interact with one another via the purely repulsive, shifted–truncated Lennard-Jones potential. We are able to confirm an earlier suggestion that when the conformation of nonpolar flexible molecules is calculated with a site–site solvation potential and the reference interaction site model (RISM) theory, better results are obtained with the recently derived Percus–Yevick (PY) style solvation potential than the hypernetted-chain (HNC) style or Gaussian-fluctuation solvation potential. Interestingly, although RISM-based theory predicts well the general shape of the probability distribution of trimer conformations, it cannot recover a small feature observed in the simulations and expected on simple physical grounds. At high density, there are three preferred conformations of the trimer, corresponding to the three ways in which a flexible trimer can be fitted into a dense fluid with locally hexagonally close-packed (hcp) symmetry. RISM-based theories predict a preference for only two conformations of the trimer. To predict the preference for all three conformations, information about three-site correlations in the fluid must be incorporated into the theory. We present a theory that includes this information and is thereby capable of reproducing the results of our simulations.

Molecular-dynamics investigation of tracer diffusion in a simple liquid.

Extensive molecular-dynamics simulations have been carried out for a model tracer-solvent system made up of 100 solvent molecules and 8 tracer molecules interacting through truncated Lennard-Jones potentials. The influence of the size ratio between solute and solvent, of their mass ratio, and of the solvent viscosity on the diffusivity of a small tracer was investigated. Positive deviations from a Stokes-Einstein behavior are observed, in qualitative agreement with experimental observations. It was also observed that as tracer and solvent become increasingly dissimilar, their respective dynamics become decoupled. We suggest that such decouplings can be interpreted by writing the mobility of the tracer as the sum of two terms, the first one arising from a coupling between tracer dynamics and hydrodynamic modes of the solvent, and the second one describing jump motion in a locally nearly frozen environment.

Molecular dynamics study of the temperature dependence of the interfacial thickness in two-dimensional fluid phases

The thickness of the interface between two-dimensional fluid phases is determined as a function of temperature by using the method of molecular dynamics. The model fluid is one of particles interacting via a truncated Lennard-Jones potential. Periodic boundary conditions are used and no macroscopic external field such as gravity is imposed. The temperature is varied between that of the triple point to values as close to the critical point as is consistent with the finiteness of the system studied on the computer. Because of the relatively small interfacial area probed in these simulations, long-wavelength capillary waves are strongly suppressed and within statistical uncertainty, the results for the interfacial thickness are found to be consistent with the prediction of the nonclassical van der Waals theory of the intrinsic interface.