Symmetric Lennard-Jones Research Articles

Crystal structures of symmetric Lennard-Jones mixtures

Monte Carlo simulations of binary Lennard-Jones crystals with mole fraction x=0.5 are performed at constant temperature and pressure. In our symmetric model, the interactions between equal particles are the same (εDD=εLL and σDD=σLL). The interaction between D and L particles is changed by εDL=eεDD and σDL=sσDD. The parameters e and s represent interaction strength and distance, respectively, as deviations from the Lorentz–Berthelot mixing rules. Gibbs energies were calculated to determine the stable crystal structure as a function of e and s, separately. This resulted in demixing for e<0.93 and solid solutions for e>1, with a weak transition to a substitutionally ordered fcc at e>1.8. Variation of s resulted in various crystal structures: a CsCl structure for 0.8<s⩽0.95, NaCl structure for 0.6⩽s⩽0.8, ZnS structures with gradual transition to a double fcc structure for s<0.6. We conclude that small variations in the interactions between unlike particles in a mixture suffice to change the crystal structure completely.

Sorbate-Loading Dependence of Diffusion Mechanism in a Cubic Symmetry Zeolite of Type ZK4. A Molecular Dynamics Study

In the present work we investigated how the sorbate loading controls the diffusion of spherically symmetric Lennard-Jones molecules in a cation-free zeolite of type LTA. This effect is studied by taking into account the mechanical flexibility of the framework, which allows for the energy relaxation of the sorbed molecules along with fluctuations of the window diameters. The number density of the adsorbed molecules was increased from 1 up to 15 methane molecules per cavity, which means from 8 up to 120 particles adsorbed in one unit cell. We have shown that the sorbate loading strongly alters the diffusion mechanism by inducing a transition at seven molecules per cavity from an increasing to a decreasing mobility regime.

Critical end point behavior in a binary fluid mixture

We consider the liquid-gas phase boundary in a binary fluid mixture near its critical end point. Using general scaling arguments we show that the diameter of the liquid-gas coexistence curve exhibits singular behaviour as the critical end point is approached. This prediction is tested by means of extensive Monte-Carlo simulations of a symmetrical Lennard-Jones binary mixture within the grand canonical ensemble. The simulation results show clear evidence for the proposed singularity, as well as confirming a previously predicted singularity in the coexistence chemical potential [Fisher and Upton, Phys. Rev. Lett. 65, 2402 (1990)]. The results suggest that the observed singularities, particularly that in the coexistence diameter, should also be detectable experimentally.

Rotational energy transfer in the NOAr system and the validity of the different forms of the potential

Theoretical investigations of the rotational transitions in the NO(A 2 Σ +) state due to collisions with Ar have been carried out by testing different forms of potential functions. It is found that the cross sections predicted by the pairwise sum of the potential, V = V(NAr) + V(OAr) differs from the experimental cross sections by a factor of 3 or more if the pairwise interaction term V(NAr) as well as V(OAr) is taken as a spherically symmetric Lennard-Jones potential. The agreement, however, improves considerably if the term V(NAr) as well as V(OAr) is made dependent on the orientation of the NO bond. A general form of the potential function which is expressed as an expansion in terms of Legendre polynomials has also been investigated and compared with the former potential.

Liquid−Liquid Phase Equilibria in Porous Materials

Theoretical and experimental results are presented for the effect of confinement on liquid−liquid phase equilibria for binary mixtures. Density functional theory calculations for a symmetric Lennard-Jones mixture in pores show the following qualitative features: a reduction in the critical mixing temperature, and a shift in the coexistence curve toward the component 1-rich side of the phase diagram when molecules of component 1 are more strongly attracted to the walls. These effects become more pronounced for smaller pores. Experimental results are presented for nitrobenzene/n-hexane mixtures in a controlled pore glass having pores of mean width 100 nm. Results for the liquid−liquid coexistence in the pores are obtained using nonlinear dielectric effect (NDE) and light transmission measurements. The effect of confinement is to produce a lowering of the critical mixing temperature by 0.05 ± 0.02 K and a shift in the critical mixing composition toward the nitrobenzene-rich side of the diagram by 0.04 ± 0.01 in mole fraction. Measurements near the pore critical point show that the NDE tends to a finite value at the critical point, apparently due to the constraint on the growth of the correlation length due to the pore walls.

Three-dimensional model calculation of epitaxial growth by Monte Carlo simulation

We report on a three-dimensional model calculation of epitaxial growth by Monte Carlo simulation. Our theoretical description of the interaction between atoms is only based on an assessment of the Hamiltonian and does not require any assumption of a discrete crystal lattice. Two different types of potentials were chosen for the simulation of the interaction between the adatoms and the substrate atoms: (a) a spherical symmetric Lennard-Jones potential to describe hard spheres and (b) a directional Lennard-Jones potential with fourfold symmetry. We investigated island and layer growth in the nucleation stage. Our simulation also allowed the selection of vicinal surfaces of the substrate with respect to the usually used (111) oriented surface. The simulation showed a clear stabilisation of the growth direction by the atomic steps on the substrate and even in lattice mismatched structures the formation of twins was suppressed. In the case of the directional Lennard-Jones potential with the fourfold symmetry we found that the crystalline structure disappeared after the deposition of one monolayer.

Monte carlo simulations of adsorption equilibria at states near bulk fluid phase boundaries

Abstract We discuss the use of Monte Carlo simulations to study adsorption on solid surfaces from fluids and fluid mixtures at states near to coexistence boundaries of the bulk fluid. The work is focused primarily upon the relationship between the adsorption isotherms and the nature of the contact between the coexisting fluid phases and the solid surface, and the behavior associated with the occurrence of wetting transitions in the system. Previously we have used Monte Carlo simulations in an ensemble with constant normal pressure to study prewetting transitions in adsorption from a single component undersaturated vapor in the approach to saturation. In this paper we present comparisons of our simulations results with predictions from density functional theory. We also discuss the use of simulations to determine more precisely the conditions for phase equilibrium at the prewetting transition through determination of the surface tension at the fluid-solid interface. p] We present results which extend these studies to the case of adsorption from a liquid mixture with a miscibility gap. In this work we have considered a symmetric Lennard-Jones mixture (σ11 = σ22 = σ12; e11 = e22 = e,e12 = 0.75e). We describe Monte Carlo simulations of this mixture in contact with a wall which preferentially adsorbs one of the components. At several temperatures below the consolute temperature we studied adsorption at the solid surface for various compositions in the approach to coexistence from the phase rich in the weakly adsorbed component. Within the limited precision of the results obtained thus far, the system shows behavior suggesting complete wetting at higher temperatures and partial wetting at lower temperatures. Density functional theory predicts a first order wetting transition with a prewetting line for this system.

Polarizability effects in a four-charge model for water

A planar four-charge model for the water molecule, with a spherically symmetric Lennard-Jones potential and a point polarizability, is examined. The model parameters are determined by fitting gas-phase data for the one and two-molecule systems. A reasonable description of water clusters of up to five molecules is obtained. The model gives qualitatively accurate properties in liquid and solid phases, but not enough condensation for agreement with experiment. It is suggested that the use of a point polarizability only partially accounts for many-body effects. Alternatives to the above model are discussed.

Nonequilibrium molecular dynamics calculation of self-diffusion in a non-Newtonian fluid subject to a Couette strain field

Molecular dynamics simulations have been performed on a simple fluid in the non-Newtonian regime in order to study the nature of diffusion in the presence of shear stress. The nonequilibrium molecular dynamics (NEMD) sllod algorithm is used to generate a homogeneous boundary driven Couette flow. The elements of the tensor of diffusion coefficients have been evaluated by three different routes: through Einstein relations with the corresponding elements of the tensor of molecule displacements, through Green–Kubo expressions involving tensor of momentum autocorrelation functions and cross-correlation functions, and by utilizing an NEMD color field method. All three routes to the tensor of diffusion coefficients are shown to yield consistent results. A simple spherically symmetric Lennard-Jones fluid at its triple point was used in the simulation study. We find that in a Couette strain field of sufficiently large strain rate, diffusion in all directions is enhanced substantially. We propose and verify a new asymptotic relationship between the diagonal elements of the tensor of diffusion coefficients and the strain rate.

Epitaxial growth of thin films studied by molecular dynamics simulation

The epitaxial growth of atomic systems, interacting via the spherically symmetric Lennard-Jones potential is studied as a function of substrate temperature T S and deposition rate. The calculations reveal the microscopic structure of thin films, and give insight into the dynamics of the adsorption process. For all substrate temperatures the growth is into well ordered layers which become fully completed at intermediate T S. At very low T S the layers contain defects and voids; however, the atoms are still arranged in close-packed islands within the layers. It is shown that the films exhibit a pronounced columnar structure if deposited at low T S.

Nonequilibrium molecular dynamics calculation of the shear viscosity of carbon dioxide

Nonequilibrium molecular dynamics calculations of the shear viscosity of supercritical carbon dioxide along the 313 K isotherm are reported. Three different intermolecular potential models of increasing complexity are considered: a spherically symmetric Lennard-Jones potential, a two-site Lennard-Jones potential, and a three-site potential which includes a quadrupole-quadrupole moment. Results for the three potentials are compared with experimental data.

Effective spherical potentials for the thermodynamics of homonuclear diatomic Lennard-Jones liquids

The predictions of several effective spherical potentials for thermodynamic properties of symmetric diatomic Lennard-Jones molecules are examined. The effective potentials are obtained by splitting the molecular potential in various ways followed by adding the separate angular medians of the two parts. Luckily, the best results are obtained when each site–site interaction is divided into its individual power law terms. It is therefore possible to obtain quite accurate thermodynamic properties over a continuous range of elongations using linear combinations of just two spherical potentials for which accurate analytic fitting functions are provided.

A comparison of exact classical and quantum mechanical calculations of vibrational energy transfer. II. The effect of long-lived collision complexes

Exact classical and quantum mechanical calculations of V–T relaxation were carried out for the model system He+O2(v=1). The diatomic molecule was treated as a harmonic oscillator, and a spherically symmetric Lennard-Jones intermolecular potential was assumed. The bin and two-moment methods were used to quantize the classical energy transfer. For a deep well both classical and quantal calculations showed evidence of complex formation. In this case inelastic transitions were classically allowed even at low collision energies. The classical transition probabilities generally agreed within a factor of 2 with the quantal results. The final energy distribution of the complex trajectories was not completely random, as compared with the information-theoretic prior expectation.

Energy transfer in molecular collisions far from resonance

Transfer of one quantum of vibrational excitation from a CO molecule initially in vibrational level 10 to another CO molecule initially in its ground vibrational level, a process endothermic by about 236 cm −1, is explained by a second-order distorted-wave Born calculation. The distortion potential is taken to be the spherically symmetric Lennard-Jones (6-12) potential, and the potential causing the energy transfer is assumed to be the multipolar interaction. A key factor in the explanation is the inclusion of the phase shifts due to elastic scattering by the multipolar potential. The calculated value for the cross section may differ from the true value by about 50% due to the uncertainty in the value of the molecular quadrupole moment. The computed cross section in the exothermic direction is 3.0 × 10 −18 cm 2 compared to the experimental value of 2.6 × 10 −18 cm 2.

Distorted-wave Born calculation of near-resonant energy transfer

The distorted-wave Born calculation for transfer of one quantum of asymmetric stretch from CO2 to 14N2 and 15N2 is presented. A spherically symmetric Lennard-Jones 6–12 potential with parameters derived from transport properties is used as distorting potential. The energy transfer is assumed caused by dipole–quadrupole coupling, i.e., interaction involving the transition dipole of CO2 and the transition quadrupole of N2. The results obtained are in excellent agreement with those obtained earlier using a straight path as the trajectory during the intermolecular collision and an empirical recipe for summing over impact parameters.

Molecular collision cross sections and the effect of water vapour on vibrational relaxation in carbon dioxide

Cross sections for the vibrational excitation of carbon dioxide by collision with water vapour have been calculated for collision energies up to 2.5 ev by numerical integration of the appropriate coupled scattering equations. Coupling between five of the molecular vibrational states has been retained. The scattering potential is represented by a spherically symmetric Lennard-Jones function. Chemical forces, which have been suggested by Widom and Bauer in 1953, are not taken into account, but effects arising from the dipole moment of the water molecule have been allowed for in an approximate way by statistically averaging the induced interaction over all orientations of the polar molecule. The cross sections are used to determine the effect of water vapour on vibrational relaxation in carbon dioxide for several water vapour concentrations and temperatures from 300 °K to 1000 °K. It is found that the experimentally observed strong effect of water vapour, the occurrence of sound absorption maxima at more than one frequency and the anomalous temperature dependence of the maximum sound absorption frequencies are all accounted for by the variation of the effective vibrational specific heats with temperature and concentration. In general, comparison with experiment indicates that the cross sections may be low by about a factor of 4. This can be ascribed to the uncertainties in the empirical scattering potential. It is concluded that past disagreement between experiment and theory has arisen in large part from the inadequate theoretical treatment given to the coupling between the various molecular vibrational states.

Molecular collision cross sections and vibrational relaxation in carbon monoxide

A method for the calculation of cross sections for processes involving the exchange of vibrational and translational energy on collision of molecules with internally structureless particles is described. On the assumption that the excited molecule is a simple harmonic vibrator and that the molecular interaction potential may be represented by a spherically symmetric Lennard-Jones function, the partial wave scattering equations have been obtained in a form suitable for direct numerical integration. Coupling between any selected number of energetically accessible molecular vibrational states can be retained in this calculation. The collision cross sections are then derived in terms of the asymptotic phases and the amplitudes of the numerical solutions.

The transport properties and the equation of state of gaseous para- and ortho-hydrogen and their mixtures below 40°K

Using a spherically symmetrical Lennard-Jones potential field, the following properties of para-H2, ortho-H2 and their mixtures were quantum-mechanically calculated: 1) viscosity and heat conductivity, with special attention paid to the dependence of viscosity on the para-ortho concentration ratio; 2) coefficients of self-diffusion and of mutual diffusion; 3) thermal diffusion ratio; 4) second virial coefficient. The agreement between experiment and the calculated viscosity and heat conductivity coefficients is good. Our calculations on the concentration dependence of viscosity show that pH2 has a greater viscosity than nH2, contrary to previous theoretical predictions, but in accordance with the measurements of Becker and Stehl and Van Itterbeek and Coremans. A similar effect in the second virial coefficient must be negligibly small, according to both experiment and theory. The second virial coefficient itself is about 10% smaller than the experimental value, which is probably due to the non-spherical character of the real potential field.

Energy Exchange in Molecular Collisions

A theory was developed for computing the probability of transition, upon molecular collision, between vibrational states, involving corresponding conversion of translational energy. A spherically symmetric Lennard-Jones 6–12 potential for interaction between the colliding molecules was introduced; their relative translational motion was described classically. Further, the theory was symmetrized to permit inclusion of collisions with nonzero impact parameters. As an example, the theory was applied to the CO2–H2O system. The effective collision diameter for an inelastic event was found to be of the observed order of magnitude, demonstrating not only the selective relaxation effect of water, but also its somewhat unusual temperature dependence. Zener's solution of the problem for a head-on collision was generalized to three-dimensional collisions, assuming a spherically symmetric interaction potential; but the complete solution of this model, including a quantum-mechanical description of the relative translational motion, was not obtained. However, for such a potential it was possible to demonstrate that the semiclassical theory is an adequate approximation to the quantum theory result, whenever the relative translational energies are much greater than the energy of exchange.