Second-order Percus–Yevick theory for the radial distribution functions of a mixture of hard spheres in the limit of zero concentration of the large spheres

The radial distribution functions of a mixture of hard spheres are quite interesting when the ratio of diameters is large and the concentration of the large spheres is very small. In this regime, the radial distrbution functions change rapidly with concentration. The usual PercusYevick theory, which is adequate over most of the concentration range, fails at low concentrations of the large spheres. Values are reported of the radial distribution functions for zero concentration of the large spheres using the most accurate theory presently available, secondorder Percus-Yevick theory. Agreement with recent formulae for the contact values of these functions is very good except for the contact value for a pair of large spheres, where the agreement is fairly good. It is possible that the radial distribution function for a pair of large spheres may be a little larger than the already large values given by this recent formula.     

Liquid–vapour transition of the long range Yukawa fluid

Two liquid state theories, the self-consistent Ornstein–Zernike equation (SCOZA) and the hierarchical reference theory (HRT) are shown, by comparison with Monte Carlo simulations, to perform extremely well in predicting the liquid–vapour coexistence of the hard-core Yukawa (HCY) fluid when the interaction is long range. The long range of the potential is treated in the simulations using both an Ewald sum and hyperspherical boundary conditions. In addition, we present an analytical optimized mean field theory which is exact in the limit of an infinitely long-range interaction. The work extends a previous one by C. Caccamo, G. Pellicane, D. Costa, D. Pini, and G. Stell, Phys. Rev. E 60, 5533 (1999) for short-range interactions.     

Temperature range of the liquid–glass transition

It has been shown that the currently used method for calculating the temperature range of δT_g in the glass transition equation qτ_g = δT_g as the difference δT_g = (T₁₂–T₁₃) results in overestimated values, which is explained by the assumption of a constant activation energy of glass transition in deriving the calculation equation (T₁₂ and T₁₃ are the temperatures corresponding to the logarithmic viscosity values of logη = 12 and logη = 13). The methods for the evaluation of δT_g using the Williams–Landel–Ferry equation and the model of delocalized atoms are considered, the results of which are in satisfactory agreement with the product qτ_g (q is the cooling rate of the melt and τ_g is the structural relaxation time at the glass transition temperature). The calculation of τ_g for inorganic glasses and amorphous organic polymers is proposed.     

Simulating the vapour–liquid equilibria of large cyclic alkanes

Self-adapting fixed endpoint configurational-bias Monte Carlo simulations in the Gibbs ensemble were carried out to determine the vapour–liquid coexistence curves of cyclic alkanes from c-pentane to c-octadecane. In general, the critical temperatures and densities of the cyclic alkanes are substantially higher than those of their linear counterparts. Furthermore, the simulation data point to a maximum in the critical density for cyclic alkanes with about eight carbon atoms as also observed for the linear alkanes.     

Molecular dynamics simulation of the vapour → liquid transition of argon and the reaction coordinate of condensation

We have investigated the n-dependences of the rate constants of absorption and emission of monomers that are attached to and detached from the cluster of n monomers, and have determined n*, the number of monomers that form the critical nucleus of the homogeneous condensation of the Lennard-Jones?Ar vapour. The dynamics was clearly separated into two regions at the critical nucleus; n* did not, however, give the unique dividing point. The observed strong dependences of both the nucleus size and the barrier height of the nucleation on the induction time of the condensation suggest that a slowly changing variable instead of the cluster size is necessary as the reaction coordinate of the nucleation. Although the slow variable is not well characterised at the present stage of the investigation, it seems to be related to the local density of the gas atoms around the liquid-like clusters. Both the slow evolution of the radial distribution function of the gas atoms around the liquid-like atoms, and the correlation between n* and the onset of the condensation indicate that Gibbs energy curves represented in n-space change significantly with the activation of the slow variable.     

Surface tension of hydrocarbon chains at the liquid–vapour interface

Molecular dynamics simulations were performed at constant temperature to obtain the surface tension of hydrocarbon chains at the liquid–vapour interface. The Ewald sum was used to calculate the dispersion forces of the Lennard–Jones potential to take into account the full interaction. The NERD and TraPPE_UA flexible force field models were used to simulate molecules from ethane to hexadecane along the coexistence curve. The simulation results for the TraPPE_UA model are in good agreement with experimental data, whereas the NERD model predicts slightly higher values.     

Self–similar and charged spheres in the free–streaming approximation

We evolve nonadiabatic charged spherical distributions of matter. Dissipation is described by the free–streaming approximation. We match a self–similar interior solution with the Reissner–Nordstr?m–Vaidya exterior solution. The transport mechanism is decisive to the fate of the gravitational collapse. Almost a half of the total initial mass is radiated away. The transport mechanism determines the way in which the electric charge is redistributed.     

“Linearized” dynamical mean-field theory for the Mott-Hubbard transition

The Mott-Hubbard metal-insulator transition is studied within a simplified version of the Dynamical Mean-Field Theory (DMFT) in which the coupling between the impurity level and the conduction band is approximated by a single pole at the Fermi energy. In this approach, the DMFT equations are linearized, and the value for the critical Coulomb repulsion can be calculated analytically. For the symmetric single-band Hubbard model at zero temperature, the critical value is found to be given by 6 times the square root of the second moment of the free (U=0) density of states. This result is in good agreement with the numerical value obtained from the Projective Selfconsistent Method and recent Numerical Renormalization Group calculations for the Bethe and the hypercubic lattice in infinite dimensions. The generalization to more complicated lattices is discussed. The “linearized DMFT” yields plausible results for the complete geometry dependence of the critical interaction. Received 6 May 1999 and Received in final form 2 July 1999     

Calculation of the surface tension of pure tin from atomistic simulations of liquid–vapour systems

Monte Carlo simulations of heterogeneous systems of tin at liquid–vapour equilibrium have been performed at several temperatures from 600 to 1500 K, using a modified embedded atom model potential. Surface tension of the corresponding planar interfaces has been evaluated using the test area method. Calculation results are in good agreement with experiments presenting a maximum deviation of 10% from experiments. In addition, the Monte Carlo simulations provide a temperature coefficient (the derivative of the surface tension in regard with temperature) in reasonable agreement with the experimental coefficient.     

Effect of solid-state characteristics on the critical parameters of the vapor–liquid phase transition

Database for the critical point parameters of almost all metals (including transition metals) and semiconductors is used to derive a number of empirical expressions to relate these parameters to the heat of evaporation, the normal density, and the isothermal bulk modulus of these substances in a solid state under normal conditions. The database is obtained using the thermodynamic model proposed earlier.     

A generalization of the Carnahan–Starling approach with applications to four- and five-dimensional hard spheres

Development of good equations of state for hard spheres is an important task in the study of real fluids. In a way consistent with other theoretical results, we generalize the famous Carnahan–Starling approach for arbitrary dimensions and apply it to four- and five-dimensional hard spheres. We obtain simple and integer representations for virial coefficients of lower orders and accurate equations of state. Since theoretically and practically validated, these results improve understanding of hard sphere fluids.     

Equation of state SAFT-CP for vapour–liquid equilibria and mutual solubility of carbon dioxide and water

ABSTRACT

The statistical associating fluid theory (SAFT) was proposed first in 1990, and has been extended to various forms for the calculation of thermodynamic properties of complex systems, such as oil reservoir fluids, polar systems, polymers, electrolytes, near-critical systems, interfacial phenomena, solids and even biomaterials. SAFT-CP (critical point) has been established for nonpolar fluids in 2001 with excellent expression of thermodynamic properties across critical points. It was extended later for polar and associating fluids with the addition of just a dipole–dipole interaction, which leads simple calculation procedure without an association term. In this article SAFT-CP is applied to carbon dioxide, water and their mixture. Vapour–liquid equilibria for pure components CO₂ and H₂O, CO₂ solubility in water and H₂O solubility in dense CO₂ are analysed. Expression of pure CO₂ properties is improved with the dipole–dipole interaction term used, while expression of pure water is a little bit improved with the non-spherical degree parameter less than 1.0. For the high asymmetry in polarity and association between CO₂ and H₂O molecules, the Stryjek–Vera combining rule is used with different temperature-dependent parameters. With the quadratic temperature-dependent parameters, the mutual solubilities in the system are calculated with good agreement with experimental ones over the wide range of temperature as 298–474 K and of pressure as 0.1–70 MPa.     

Spatial heterogeneity in liquid–liquid phase transition

Molecular dynamics simulations are performed to investigate the liquid–liquid phase transition(LLPT) and the spatial heterogeneity in Al–Pb monotectic alloys. The results reveal that homogeneous liquid Al–Pb alloy undergoes an LLPT,separating into Al-rich and Pb-rich domains, which is quite different from the isocompositional liquid water with a transition between low-density liquid(LDL) and high-density liquid(HDL). With spatial heterogeneity becoming large, LLPT takes place correspondingly. The relationship between the cooling rate, relaxation temperature and percentage of Al and the spatial heterogeneity is also reported. This study may throw light on the relationship between the structure heterogeneity and LLPT, which provides novel strategies to control the microstructures in the fabrication of the material with high performance.     

Manifestation of spinodal singularities in the liquid–vapor phase transition during simulation of nanosecond vaporization of a liquid film

The recent results of molecular-dynamics simulation of nanosecond vaporization of a thin liquid film are analyzed within the continual approach. The analysis shows a significant increase in the thermal conductivity at the film temperature maximum before its explosive decomposition, which indicates the closeness of the achievable limiting overheating temperature to the spinodal.     

Determination of the vapor–liquid transition of square-well particles using a novel generalized-canonical-ensemble-based method

The square-well(SW) potential is one of the simplest pair potential models and its phase behavior has been clearly revealed, therefore it has become a benchmark for checking new theories or numerical methods. We introduce the generalized canonical ensemble(GCE) into the isobaric replica exchange Monte Carlo(REMC) algorithm to form a novel isobaric GCE-REMC method, and apply it to the study of vapor–liquid transition of SW particles. It is validated that this method can reproduce the vapor–liquid diagram of SW particles by comparing the estimated vapor–liquid binodals and the critical point with those from the literature. The notable advantage of this method is that the unstable vapor–liquid coexisting states,which cannot be detected using conventional sampling techniques, are accessed with a high sampling efficiency. Besides,the isobaric GCE-REMC method can visit all the possible states, including stable, metastable or unstable states during the phase transition over a wide pressure range, providing an effective pathway to understand complex phase transitions during the nucleation or crystallization process in physical or biological systems.     

The reassessment of the structural transition regions along the liquidus of Fe–Si alloys and a possible liquid–liquid structural transition in FeSi2 alloy

We reassessed the structural transition regions along the liquidus of Fe–Si alloys by using ab initio molecular dynamics simulation. Except for 50 at.% Si, structural transition compositions are found at both 30 at.% Si and 67 at.% Si (FeSi₂) which are eutectic alloys. We demonstrated that the liquid structure in the sub-region of 0～30 at.% Si is close-packed, and in the sub-region of 67～100 at.% Si liquid alloys have very open structure. From 30 at.% Si to 67 at.% Si, the close-packed structure gradually change into open one. These structure transition sub-regions are also supported by the formation enthalpy of liquid alloys. Furthermore, the predicted enthalpy change between 1585 K and 1873 K is so large that there is probably liquid–liquid transition with temperature at FeSi₂ alloy which is an important thermoelectric material. Discussions have been made on the materials phenomenon of several Fe–Si alloys based on the structural information.     

Condensation of gold vapour on silicone oil – effect of the liquid substrate

When gold vapour condenses onto a liquid substrate, the inherent structure of the liquid could influence the condensate growth and coverage. A thorough comparison between the liquid (silicone oil) and solid (amorphous carbon) substrates is reported by analysing the changes in their condensate growth. Low condensate coverage with large areas of empty regions is observed on the liquid surface in contrast to the solid carbon surface displaying uniformly distributed gold clusters at all times. This is deduced to be caused by the incoming gold atoms restricting the liquid molecules’ degrees of freedom upon binding. This effect could perturb the entire liquid structure, causing the liquid to collectively act against the adsorption of gold atoms. This could lead to differences in growth kinetics on the liquid substrate and can account for the observed dissimilarity in condensate coverage. The substrate structure effect discussed here serves as a step forward for utilizing liquid substrates for a variety of potential applications.     

Equation of state and liquid–vapour equilibrium in a triangle-well fluid

The second-order thermodynamic perturbation theory formulation of Barker and Henderson is used to derive the equation of state of the triangle-well fluid. This is combined with the rational function approximation to the radial distribution function of the hard-sphere fluid. Results are obtained for the critical parameters and the liquid–vapour coexistence curve for various values of the range of the potential. A comparison with available simulation data is presented.     

Comprehensive study of the vapour–liquid coexistence of the truncated and shifted Lennard–Jones fluid including planar and spherical interface properties

Vapour–liquid equilibria of the Lennard–Jones potential, truncated and shifted at 2.5σ, are studied using molecular dynamics simulations, an attractive option for studying inhomogeneous systems. Comprehensive simulation data are reported for three cases: no interface, a planar interface, and a spherical interface between the coexisting phases, covering a wide range of temperatures. Spherical droplets are also studied for a range of radii between 5 and 16σ. The size dependence of the surface tension, based on the Irving–Kirkwood pressure tensor, and other properties is quantified for spherical interfaces. All simulation results are correlated with a consistent set of empirical equations. A comparison with the results of other authors as well as with experimental data for noble gases and methane is also presented.