Chemical potentials and phase equilibria of Lennard-Jones chain fluids

Computer simulations (molecular dynamics) were performed for ensembles of flexible tangent Lennard-Jones chains consisting of n sites (n = 1, 2, 4, 8, and 16). From these simulations, the orthobaric liquid and vapour densities were calculated not only with the traditional method of simulating a liquid film in coexistence with vapour, but also using the rigorous thermodynamic condition of satisfying the chemical potential equality between the phases in equilibrium. The agreement with literature data, as far as such exist, is excellent.     

Dynamic properties of Lennard-Jones fluids and liquid metals

The dependence of the dynamic properties of liquid metals and Lennard-Jones fluids on the characteristics of the interaction potentials is analyzed. Molecular-dynamics simulations of liquids in analogous conditions but assuming that their particles interact either through a Lennard-Jones or a liquid-metal potential were carried out. The Lennard-Jones potentials were chosen so that both the effective size of the particles and the depth of the potential well were very close to those of the liquid-metal potentials. In order to investigate the extent to which the dynamic properties of liquids depend on the short-range attractive interactions as well as on the softness of the potential cores, molecular-dynamics simulations of the same systems but assuming purely repulsive interactions with the same potential cores were also performed. The study includes both single-particle dynamic properties, such as the velocity autocorrelation functions, and collective dynamic properties, such as the intermediate scattering functions, the dynamic structure factors, the longitudinal and transverse current correlations, and the transport coefficients.     

A comprehensive approach to an equation of state for hard spheres and Lennard-Jones fluids

We present a simple method of obtaining various equations of state for hard sphere fluid in a simple unifying way.We will guess equations of state by using suitable axiomatic functional forms (n=1,2,3,4,5) for surface tension S n m (r),r ≥ d/2 with intermolecular separation r as a variable,where m is an arbitrary real number (pole).Among the equations of state obtained in this way are Percus-Yevick,scaled particle theory and Carnahan-Starling equations of state.In addition,we have found a simple equation of state for the hard sphere fluid in the region that represents the simulation data accurately.It is found that for both hard sphere fluids as well as Lennard-Jones fluids,with m=3/4 the derived equation of state (EOS) gives results which are in good agreement with computer simulation results.Furthermore,this equation of state gives the Percus-Yevick (pressure) EOS for the m=0,the Carnahan-Starling EOS for m=4/5,while for the value of m=1 it corresponds to a scaled particle theory EOS.     

Perturbation and variational approach for the equation of state for hard-sphere and Lennard-Jones fluids

The present work uses the concept of a scaled particle along with the perturbation and variation approach, to develop an equation of state (EOS) for a mixture of hard sphere (HS), Lennard–Jones (LJ) fluids. A suitable flexible functional form for the radial distribution function G(R) is assumed for the mixture, with R as a variable. The function G(R) has an arbitrary parameter m and a different equation of state can be obtained with a suitable choice of m. For m = 0.75 and m = 0.83 results are close to molecular dynamics (MD) result for pure HS and LJ fluid respectively.     

Coexistence and interfacial properties of triangle-well fluids

Coexistence and interfacial properties of triangle-well fluids are determined by combining the slab technique and the replica exchange algorithm for different interaction ranges (λ = 1.5, 1.75, 2.0, 2.5, and 3). This is implemented using both Monte Carlo and molecular dynamics methods. We make use of a recently proposed substitution of the hard-core repulsion by a linear function with a large negative slope. This makes possible to gain access through the virial route to thermodynamical properties and to employ widely spread packages such as Gromacs. Coexistence curves of these systems were calculated with both implementations and compared to those previously reported in the literature. A good agreement was found among them. Surface tension data obtained from Monte Carlo and molecular dynamics techniques also show a good agreement.     

A modified soft-core fluid model for the direct correlation function of the square-shoulder and square-well fluids

We propose a simple analytical expression of the direct correlation function for the square-shoulder and square-well fluids. Our approximation is based on an ansatz for the direct correlation function of a modified soft-core fluid, whose parameters are adjusted by fitting the data obtained from Monte Carlo computer simulations. Moreover, it is complemented with a Wertheim-like parametrization to reproduce correctly the direct correlation inside the hard-core. We demonstrate that this approach is in quantitative agreement with the numerical solution of the Ornstein–Zernike equation within the Percus–Yevick approximation. We also show that our results are accurate in a large regime of densities for different interaction ranges and potential strengths. Therefore, this opens up the possibility of introducing the square-shoulder or the square-well potentials as new reference systems in advanced theoretical approximations.     

An equation of state contribution for dipolar and quadrupolar square-well fluids

A dipolar–quadrupolar contribution to the residual Helmholtz energy for a polar square well (a square well plus either a point dipole or a point quadrupole) fluid is developed based on the Padé approximation. Taking the square well system as reference, the contribution is formulated using an expansion for radial distribution function of the reference system. In addition to square well potential parameters the contribution depends only on dipole and quadrupole moments. This term is added as perturbation to a generalized equation of state for square well fluids. The results are then compared with the available simulation data in the literature. With the new equation obtained, it was possible to predict liquid–vapour equilibrium properties and critical properties of polar square well fluids more accurately than with available perturbation theories for multipolar square well systems. Application of the equation of state to a real dipolar (water) and a real quadrupolar (carbon dioxide) fluid indicated that the polar contribution greatly improved the predictions of saturation properties. Accurate prediction of critical properties for polar square well fluids remains as a challenge. This work can be useful in the development of better equations of state.     

A unified approach to phase diagrams in field theory and statistical mechanics

We construct the phase diagram of any system which admits a low-temperature polymer or cluster expansion. Such an expansion turns the system into a hard-core interacting contour model with small, but not necessarily positive, activities. The method uses some of Zahradnik's ideas [Z1], but applies equally well to systems with complex interactions. We give two applications. First, to low-temperatureP()₂ models with complex couplings; and second, to a computation of asymptotics of partition functions in periodic volumes. If the index of a supersymmetric field theory is known, the second application would help determine the number of phases in infinite volume.Alfred P. Solan Research Fellow. Supported in part by the National Science Foundation under Grants PHY87-064220, DMS 88-58073, and PHY/DMS 86-45122     

Surface effects and diffusive phase transition in ferroelectric thin films: A self-consistent approach

A self-consistent Landau phenomenological approach has been used to study the ferroelectric transition in films in the presence of various surface effects such as depolarization and strain. The polarization distribution of the film is computed and its variation with respect to temperature, thickness and strain is determined. The gradual decrease in polarization across the transition shows the diffusive behavior which is confirmed from the soft mode and the dielectric susceptibility analysis. The critical thickness below which ferroelectricity disappears is also computed. The degree of diffuseness in the transition is obtained from the susceptibility exponent which shows more and more diffusive behavior for smaller and smaller film thickness.     

Lennard-Jones binary fluids: A comparative study between the molecular dynamics and Monte Carlo descriptions of their structural properties

Molecular dynamics and Monte Carlo techniques are employed for the study of binary Lennard-Jones fluids. Systematic comparisons between the predictions of both techniques are discussed, with particular emphasis on the dependency of the structural properties with respect to temperature and Lennard-Jones potential parameters.     

Density functional study of the pressure tensor for inhomogeneous Lennard—Jones fluids

Based on classical density functional theory,an expression of the pressure tensor for inhomogeneous fluids is presented.This takes into account greater correlation between particles,especially for systems that are geometrically confined or involve an interface.The density and pressure components of Lennard-Jones fluids confined in hard and softened nano-cavities are calculated.A comparison between the results of this work and IK expression suggests that the agreement depends on temperature.The interfacial tension for hard sphere fluids agrees well with the Monte Carlo result when the bulk density is not too large.The results of the solid-fluid interfacial tension for Lennard-Jones fluids demonstrate that different types of external potentials modulate the interfacial tension in different manners.     

Modeling of adsorption and phase diagrams for stepped surfaces: Transfer matrix approach

The simplest model of stepped surface has been constructed and scrutinized with different values of model parameters. The transfer matrix method was shown to be a very effective approach. Phase diagrams and local isotherms have been obtained. It was shown that the local coverage can be the non-monotonous function of the total coverage or the chemical potential.     

Theoretical investigations of the vapour-liquid equilibrium and dielectric properties of dipolar Yukawa fluids in an external field

In a low field approximation, using the dipolar Yukawa fluid model (in mean spherical approximation as a reference system) a consistent field-dependent free energy expression is proposed for the calculation of the vapour-liquid equilibrium of polar fluids in an applied electric field. A perturbation theory high field approximation expression of the free energy is also proposed to study the field-dependent properties of fluids. In the high field approximation, equations for the field-dependent polarization and for the nonlinear dielectric constant (or Piekara constant) are also predicted. It has been discussed that our approximations are appropriate to describe the vapour-liquid-like phase equilibria and the magnetization curves of magnetic fluids.     

Gas-liquid interface of a Lennard-Jones binary mixture controlled by differential activity: phase transition and interfacial stability

The European Physical Journal E - We perform molecular dynamics simulations of a two-dimensional binary mixture of Lennard-Jones particles, characterized by some degree of “activity”...     

A general local composition and coordination number model for square-well fluids with variable well width and diameter ratio

A radial distribution function for attractive hard-core systems is obtained from the equilibrium of a molecular pair between local and bulk environments. With this function, a general model is established for the coordination number (CN) and local composition (LC) of square-well fluids. It meets the low-density, high-density and high-temperature limit conditions, as well as the unlike pair conservation and quasi-chemical equilibrium conditions. It also has some other features that many other models do not have: (1) its CN and LC expressions contain all pair potentials; (2) it yields temperature-dependent CN and LC for closely packed mixtures with different pair potentials; (3) its energy parameter is the difference of the total potentials of one pair in local and bulk environments, not the difference of two pair potentials. This model can accurately predict the CN, LC and compressibility factors of square-well fluids from computer simulation over a wide range of density, well width (λ?=?1–2) and diameter ratio. For the case λ?=?1.5, this model is better than or comparable with semi-empirical models; in other cases, it is far better than semi-empirical models. It does not need any empirical parameter for LC prediction. For the prediction of CN and compressibility factors, it only needs the smoothed radial distribution function of pure hard-sphere fluids. It also gives excellent results for lattice gases and highly nonideal lattice mixtures.     

Mode-coupling theory for the lattice dynamics of anharmonic crystals: self-consistent damping and the 1d Lennard-Jones chain

We present a self-consistent theory for the dynamical one-phonon structure factor in anharmonic crystals. The theory is the phonon analogue of the mode-coupling theory of liquid dynamics of Götze and his coworkers. Starting point is the lattice dynamics treatment based on the Mori- Zwanzig technique as formulated by Götze and Michel. We apply the theory to the one-dimensional (1d) Lennard-Jones chain and show that the nonlinear mode-coupling equations can be readily solved in the time domain. The vertices entering the equations as input are calculated exactly by a Monte Carlo technique. We compare our findings with molecular dynamics (MD) simulations and the results of other theoretical approaches.     

Mixed valencies: Structure of phase diagrams,lattice properties and the consequences of electron hole symmetry

Symmetry properties and phonon phenomena of mixed valence compounds are discussed within the framework of the periodic Anderson model which was extended to include the interaction of 4f electrons with longitudinal optical phonons. The temperature anomaly in the thermal expansion found in CeSn₃ (positive thermal expansion coefficient) and YbCuAl (negative) is correctly described. Within the model the anomaly is a consequence of the particle hole symmetry of the underlying Hamiltonian. Moreover, the theory gives the positive slope of the phase boundary in the pressure-temperature phase diagram (dP/dT>0), for example for Ce, and predicts a negative slope (dP/dT<0) for Yb compounds.Furthermore, the quite unusual low temperature features of the pressure-temperature phase diagram have been calculated. It is found that the lattice vibrational contribution renormalizes the two essential parameters of the periodic Anderson model. The hybridization energyV ₀ of 4f and 5d–6s states is changed to =V ₀–a–b ² whereas the energy of the 4f stateE ₀ with respect to the 5d band becomes =E ₀–a–b ²., being proportional to the lattice constant, is determined by minimizing the Gibbs free energy, while ² is proportional to the mean square displacement of the rare earth ions. The strong temperature dependence of and ² determines the behaviour of the phase boundary and for large enough coefficientsb andb the phase boundary terminates at two critical points. An argument is given why the unusual low temperature features are more expressed in dirty mixed valence compounds as Sm_1–x Gd _x S than in the pure compound SmS. Furthermore, the theory predicts a quite unusual behaviour of the plasma-like phonon mode in the mixed valence phase: It softens at the critical temperature and at an intermediate temperature.Work performed within the program of the Sonderforschungsbereich 125, Aachen-Jülich-Köln