Semiclassical Dynamics and Time Correlations in Two-Component Plasmas

The semiclassical dynamics of a charged particle moving in a two-component plasma is considered using a corrected Kelbg pseudopotential. We employ the classical Nevanlinna-type theory of frequency moments to determine the velocity and force autocorrelation functions. The constructed expressions preserve the exact short and long-time behavior of the autocor-relators. The short-time behavior is characterized by two parameters which are expressable through the plasma static correlation functions. The long-time behavior is determined by the self-diffusion coefficient. The theoretical predictions are compared with the results of semiclassical molecular dynamics simulation.     

Molecular dynamics of liquid alkaline-earth metals near the melting point

Results of the studies of the properties like binding energy, the pair distribution function g(r), the structure factor S(q), specific heat at constant volume, velocity autocorrelation function (VACF), radial distribution function, self-diffusion coefficient and coordination number of alkaline-earth metals (Be, Mg, Ca, Sr and Ba) near melting point using molecular dynamics (MD) simulation technique using a pseudopotential proposed by us are presented in this article. Good agreement with the experiment is achieved for the binding energy, pair distribution function and structure factor, and these results compare favourably with the results obtained by other such calculations, showing the transferability of the pseudopotential used from solid to liquid environment in the case of alkaline-earth metals.     

Electric field dynamics at charged point in two component plasma

The autocorrelation function for the velocity and for the electric microfield of an impurity ion in a Two Ionic Component Plasma (TICP) is considered. A simple model is constructed for this purpose that preserves the exact short time dynamics and the long time global constraint of a given self-diffusion coefficient. The memory function and then the collision effects associated with the correlation function for the self-diffusion are expressed in terms of an effective two body interaction via a screened effective potential. The basic approximation used in our approach is the disconnected one that refers to the collision operator. A comparison of the prediction of this model for the self-diffusion and for the autocorrelation functions with the results of the molecular dynamics simulation developed in our laboratory (PIIM) shows an acceptable agreement over a wide range of plasma coupling, impurity ion charge and concentration.Received: 11 August 2003, Published online: 19 February 2004PACS: 52.20.Dq Particle orbits - 52.65.Cc Particle orbit and trajectory - 47.40.Nm Shock wave interactions and shock effects - 05.20.-y Classical statistical mechanics     

Exact short time dynamics for steeply repulsive potentials

The autocorrelation functions for the force on a particle, the velocity of a particle and the transverse momentum flux are studied for the power law potential v(r)=ε(σr)^ν (soft spheres). The latter two correlation functions characterize the Green–Kubo expressions for the self-diffusion coefficient and shear viscosity. The short-time dynamics is calculated exactly as a function of ν. The dynamics is characterized by a universal scaling function S(τ), where τ=t/τ_ν and τ_ν is the mean time to traverse the core of the potential divided by ν. In the limit of asymptotically large ν this scaling function leads to delta function in time contributions in the correlation functions for the force and momentum flux. It is shown that this singular limit agrees with the special Green–Kubo representation for hard-sphere transport coefficients. The domain of the scaling law is investigated by comparison with recent results from molecular dynamics simulation for this potential.     

Dynamical properties of strongly interacting Brownian particles : II. Self-diffusion

The self-diffusion process of Brownian particles is theoretically investigated for concentrated systems in the presence of strong potential interactions between particles. Starting from an N-particle diffusion equation, a formalism is developed to calculate the self-diffusion coefficient and the velocity autocorrelation function on the basis of the superposition approximation for the three-particle distribution function of non-equilibrium states. Explicit calculations are carried out for model systems of hard spheres with a screened Coulomb potential. Calculated time-dependent self-diffusion coefficients are compared with available data of the Brownian dynamics. Without introducing any phenomenological or adjustable parameters, quantitative agreement is achieved.     

The viscosity of simple dense fluids ; a memory-function approach

A gaussian memory function is used to compute the viscosity of dense fluid argon over a large region of states from the Lennard-Jones potential and the radial distribution function. The superposition approximation is used to evaluate the triplet correlation function and estimates of the errors introduced by this approximation are investigated. The agreement with experimental viscosities is quite satisfactory in the liquid region, but less so at lower densities and higher temperatures. The computed stress autocorrelation function exhibits those characteristics which are known from molecular dynamics studies. The stress autocorrelation remains monotonic even close to the triple point, where the same memory function leads to the well-known backscattering behaviour in the velocity autocorrelation function. This, too, is in agreement with the results of molecular dynamics.     

Dissipative particle dynamics study of velocity autocorrelation function and self-diffusion coefficient in terms of interaction potential strength

This research focuses on numerically investigating the self-diffusion coefficient and velocity autocorrelation function (VACF) of a dissipative particle dynamics (DPD) fluid as a function of the conservative interaction strength. Analytic solutions to VACF and self-diffusion coefficients in DPD were obtained by many researchers in some restricted cases including ideal gases, without the account of conservative force. As departure from the ideal gas conditions are accentuated with increasing the relative proportion of conservative force, it is anticipated that the VACF should gradually deviate from its normally expected exponentially decay. This trend is confirmed through numerical simulations and an expression in terms of the conservative force parameter, density and temperature is proposed for the self-diffusion coefficient. As it concerned the VACF, the equivalent Langevin equation describing Brownian motion of particles with a harmonic potential is adapted to the problem and reveals an exponentially decaying oscillatory pattern influenced by the conservative force parameter, dissipative parameter and temperature. Although the proposed model for obtaining the self-diffusion coefficient with consideration of the conservative force could not be verified due to computational complexities, nonetheless the Arrhenius dependency of the self-diffusion coefficient to temperature and pressure permits to certify our model over a definite range of DPD parameters.     

Using the Ab Initio Molecular Dynamics Method for Simulating the Peculiarities in the Temperature Dependence of Liquid Bismuth Properties

The specific features pertinent to the temperature dependence of the electronic and atomic properties of liquid bismuth that have been observed in experiments are investigated according to the ab initio molecular dynamics method using the SIESTA open software package. The density of electronic states, the radial distribution function of atoms, and the self-diffusion coefficient are calculated for the temperature range from the melting point equal to 545 K to 1500 K. The calculated data are in good agreement with the experimental data. It is found that the position of the first peak in the radial distribution function of atoms and the self-diffusion coefficient are characterized by a nonmonotonic dependence under the conditions of superheating by approximately 150 K above the melting temperature. In the authors’ opinion, this dependence feature is attributed to a change in the liquid short-range order structure.     

Time correlation functions in classical dense fluids

The velocity autocorrelation functions and memory functions of dense classical fluids may be directly obtained from the static radial distribution function g(r) in an approximate way. Following the Mori projection operator formalism, the memory functions may be related to the fluctuating force correlation. At low densities, these functions may be evaluated by following the trajectories of particle pairs in the interatomic potential. At higher densities, the force correlation functions can be evaluated approximately from particle pair trajectories via the potential of the mean force. The contributions to the memory function come mainly from particle pairs with rather specific and rather short interatomic distances. At higher temperatures, this specific distance is even shorter, hence the memory function decays quickly with time. At lower temperatures, a negative region of the memory function may develop. On the other hand, there is relatively little density dependence of the normalized memory function. The results for argon fluids at various densities and temperatures agree satisfactorily with the molecular dynamics and the Enskog values. The decrease of the diffusion coefficient with density is partly due to the nature of g(r) which reflects the stronger clustering of atoms at higher densities.     

Molecular collisions and self-diffusion in liquids

The velocity autocorrelation function and coefficient of self-diffusion are derived for a hard-sphere fluid. An earlier quasi-lattice model of self-diffusion in liquids is re-examined and a less restrictive expression for the self-diffusion coefficient is derived. The coefficient of self-diffusion of a light or heavy isotope in the normal liquid is considered both for hard spheres and in the quasi-lattice approximation. An experiment is proposed to clarify the nature of the isotope effect in self-diffusion.     

Determination of the friction coefficient via the force autocorrelation function. A molecular dynamics investigation for a dense Lennard-Jones fluid

For a large region of dense fluid states of a Lennard-Jones system, we have calculated the friction coefficient by the force autocorrelation function of a Brownian-type particle by molecular dynamics (MD). The time integral over the force autocorrelation function showed an interesting behavior and the expected plateau value when the mass of the Brownian particle was chosen to be about a factor of 100 larger than the mass of the fluid particle. Sufficient agreement was found for the friction coefficient calculated by this way and that obtained by MD calculations of the self-diffusion coefficient using the common relation between these coefficients. Furthermore, a modified friction coefficient was determined by integration of the force autocorrelation function up to the first maximum. This coefficient can successfully be used to derive a reasonable soft part of the friction coefficient necessary for the Rice-Allnatt approximation for the shear viscosity of simple liquids.     

Molecular dynamics studies of an m-6-8 fluid

The pressure, energy and self-diffusion coefficient have been calculated for an 11-6-8 fluid using the method of molecular dynamics. A comparison with data for argon, krypton and xenon is presented. It is shown that agreement between theory and experiment for the thermodynamic properties is generally within the estimated precision of the calculated and experimental values, provided three-body and quantum corrections are included in the calculation, except when the density approaches the triple-point density. Agreement between theoretical and experimental self-diffusion coefficients is satisfactory at all densities after allowance is made for the long-time behaviour of the velocity autocorrelation function. We demonstrate that three-body forces are important in the liquid and that our estimates of such forces are very close to those suggested by Barker, Fisher and Watts.     

Molecular dynamics simulations of one-dimensional Lennard-Jones systems

One-dimensional Lennard-Jones systems are investigated by molecular dynamics simulations. The full Lennard-Jones potential is compared to the repulsive Lennard-Jones potential. It is found that the pair correlation function and the normalized velocity autocorrelation function agree at high densities and high temperature. However, the diffusion coefficient indicates that the attractive potential introduces additional correlations into particle dynamics which are not reflected in the statics. These results are in agreement with three-dimensional studies.     

Molecular dynamics simulation of HCl in liquid Ar

Molecular dynamics simulations of one HCl molecule in liquid Ar at three different thermodynamic states have been carried out. The dynamic properties of both the solute molecule and solvent atoms are discussed. Results for Ar in the first solvation shell of HCl are compared with those for atoms in the bulk. The study includes radial distribution functions, residence times, velocity autocorrelation functions, spectral densities, self - diffusion coefficients, reorientational time correlation functions and infrared spectra.     

Computation of some thermodynamics, transport, structural properties, and new equation of state for fluid methane using two-body and three-body intermolecular potentials from molecular dynamics simulation

Molecular dynamics simulation has been performed to obtain pressure, radial distribution function, and self-diffusion coefficient of fluid methane using one site OPLS (optimized potentials for liquid simulations), five sites OPLS-SITE, and two-body HFD (Hartree-Fock dispersion)-like potentials. To take higher-body forces into account, three-body potential of Hauschild and Prausnitz (1993) has been used with the two-body HFD-like potential. The significance of this work is that the three-body potential of Hauschild and Prausnitz extended as a function of density and temperature and used with the HFD-like potential to improve the prediction of the results of pressure of fluid methane without requiring an expensive three-body calculation. The molecular dynamics simulation of methane has been also used to determine a new equation of state. The results are in a good agreement with experimental and theoretical values.     

Computer simulations of a rough sphere fluid I

A molecular dynamics simulation of a rough sphere fluid with variable roughness is presented from which the intermediate scattering function, orientational correlation functions and velocity autocorrelation functions are calculated for several values of the density, roughness and wave number. The dependence of these correlation functions on the parameters is discussed and a comparison with a neutron scattering experiment on neopentane [C(CH₃)₄] is made, which gives good agreement between the two experiments.     

Ionic self-diffusion in concentrated aqueous electrolyte solutions

A self-consistent microscopic theory is developed to understand the anomalously weak concentration dependence of ionic self-diffusion coefficient D(ion) in electrolyte solutions. The self-consistent equations are solved by using the mean spherical approximation expressions of the static pair correlation functions for unequal sizes. The results are in excellent agreement both with the known experimental results for many binary electrolytes and also with the new Brownian dynamics simulation results. The calculated velocity time correlation functions also show quantitative agreement with simulations. The theory also explains the reason for observing different D(ion) in recent NMR and neutron scattering experiments.     

Reorientational correlation functions for computer-simulated liquids of tetrahedral molecules

Molecular dynamics simulations have been carried out on fluids of tetrahedral molecules for several sets of temperatures and pressures. The results were analysed to give reorientational and angular velocity autocorrelation functions. It was found that these could be related by a cumulant expansion in powers of the angular velocity and rotation operators. This type of analysis is likely to prove simple and useful for relating orientational correlation functions to the angular velocity correlation function in dense fluids where reorientation is hindered.     

Connection of the velocity autocorrelation function to the mean-square-displacement and to the memory function of generalized master equations

General connections between the velocity autocorrelation function and the mean-square-displacement for a special initial condition are established and shown to reduce in the high-temperature limit to earlier such results obtained by Scher and Lax. A simple and useful relation, which is valid in the high temperature limit, between the velocity autocorrelation function and memory functions in generalized master equations is given.     

The velocity autocorrelation function and self-diffusion coefficient of fluids with steeply repulsive potentials

We consider the velocity autocorrelation function, vacf, or C_v(t) and self-diffusion coefficients, D, of steeply repulsive inverse power fluids (SRP) in which the particles interact with a pair potential, ? (r) = ?(σ/r)ⁿ. The C_v(t) are calculated numerically by molecular dynamics simulations. Accurate expressions for the short time expansion of C_v(t) to order O(t⁴) for n large are derived for this fluid. We propose novel expressions for C_v (t) that, for n large, spans the transition from the short time regime (expandable in even powers of time) and the longer time exponential-like regime characteristic of hard spheres. Inter alia we introduce relaxation times that characterize the duration of a collision and the decay of the velocity correlation within the mean-collision or Enskog-like relaxation time, T_E.