Percus-Yevick theory for the structural properties of the seven-dimensional hard-sphere fluid

The direct correlation function and the (static) structure factor for a seven-dimensional hard-sphere fluid are considered. Analytical results for these quantities are derived within the Percus-Yevick [Phys. Rev.110, 1 (1958)] theory.     

Equation of state for hard-sphere fluid in restricted geometry

Many practical applications require the knowledge of the equation of state of fluids in restricted geometry. We study a hard-sphere fluid at equilibrium in a narrow cylindrical pore with hard walls for pore radii R<((square root 3)+2)/4 (in units of the hard sphere diameter). In this case each particle can interact only with its nearest neighbors, which makes possible the use of analytical methods to study the thermodynamics of the system. Using a transfer operator formalism and expanding in low- and high-pressure regions, we can obtain a simple analytical equation of state for almost all ranges of pressure. The results agree with Monte Carlo simulations. Additionally, it is shown that a convenient analytical representation can be chosen to accurately describe the equation of state within the error of the Monte Carlo simulation.     

NMR relaxation parameters of a Lennard-Jones fluid from molecular-dynamics simulations

Ensembles of soft spheres or of Lennard-Jones atoms were studied by molecular dynamics at reduced temperatures from 0.8 to 3, and radial distribution functions, diffusion coefficients, and magnetic dipole-dipole correlation functions were measured as functions of system size. The expected relation between the values of the correlation functions at zero lag time and the integrals of the radial distribution was verified for each system. The measured correlation functions were compared with theoretical expressions derived by [Ayant et al., J. Phys. (Paris) 36, 991 (1975)] and by [Hwang and Freed, J. Chem. Phys. 63, 4017 (1975)]. It was shown that, in order to recover the long-time behavior characteristic of diffusion-controlled relaxation processes, the simulation must comprise at least 10 000 particles. By fitting the simulation results to the Hwang-Freed function, independent values of the diffusion coefficient were obtained, similar but not identical to those computed using the Green-Kubo formalism. The spectral densities of the dipole-dipole interaction were computed as Fourier transforms of the correlation functions. These quantities are less sensitive to model imperfections and reproduce quite well the values derived from theory. The dimensionless spin-lattice and spin-spin relaxation rates were derived from the spectral densities. It was shown that the spin-lattice (longitudinal) relaxation rate goes through a maximum as the temperature increases, while the spin-spin (transverse) rate decreases monotonously.     

Equation of state of nonadditive d-dimensional hard-sphere mixtures

An equation of state for a multicomponent mixture of nonadditive hard spheres in d dimensions is proposed. It yields a rather simple density dependence and constitutes a natural extension of the equation of state for additive hard spheres proposed by us [A. Santos, S. B. Yuste, and M. Lopez de Haro, Mol. Phys. 96, 1 (1999)]. The proposal relies on the known exact second and third virial coefficients and requires as input the compressibility factor of the one-component system. A comparison is carried out both with another recent theoretical proposal based on a similar philosophy and with the available exact results and simulation data in d=1, 2, and 3. Good general agreement with the reported values of the virial coefficients and of the compressibility factor of binary mixtures is observed, especially for high asymmetries and/or positive nonadditivities.     

Equation of state and liquid-vapor equilibria of one- and two-Yukawa hard-sphere chain fluids: theory and simulation

The accuracy of several theories for the thermodynamic properties of the Yukawa hard-sphere chain fluid are studied. In particular, we consider the polymer mean spherical approximation (PMSA), the dimer version of thermodynamic perturbation theory (TPTD), and the statistical associating fluid theory for potentials of variable attractive range (SAFT-VR). Since the original version of SAFT-VR for Yukawa fluids is restricted to the case of one-Yukawa tail, we have extended SAFT-VR to treat chain fluids with two-Yukawa tails. The predictions of these theories are compared with Monte Carlo (MC) simulation data for the pressure and phase behavior of the chain fluid of different length with one- and two-Yukawa tails. We find that overall the PMSA and TPTD give more accurate predictions than SAFT-VR, and that the PMSA is slightly more accurate than TPTD.     

Tests of the homogeneous nucleation theory with molecular-dynamics simulations. I. Lennard-Jones molecules

Two kinds of the homogeneous nucleation theory exist at the present: the classical nucleation theory and the semiphenomenological model. To test them, we performed molecular-dynamics (MD) simulations of nucleation from vapor to liquid with 5000-20,000 Lennard-Jones-type molecules. Simulations were done for various values of supersaturation ratios (from 2 to 10) and temperatures (from 80 to 120 K). We compared the size distribution of clusters in MD simulations with those in the theoretical models because the number density of critical clusters governs the nucleation rate. We found that the semiphenomenological model achieves excellent agreements in size distributions of the clusters with all MD simulations we done. The classical theory underestimates the number density of the clusters in the temperature range of 80-100 K, but overestimates in 100-120 K. The semiphenomenological model also predicts well the nucleation rate in MD simulations, while the classical nucleation theory does not. Our results confirmed the validity of the semiphenomenological model for Lennard-Jones-type molecules.     

Percus-Yevick theory of adsorption

We study adsorption of hard sphere particles on to a plane surface with a delta function adsorption potential. The calculation takes account of exclusion via the Percus-Yevick approximation. At low and intermediate bulk adsorbate densities, both type II and type III BET adsorption isotherms can be found for the surface excess density and for the monolayer surface density. The surface excess isotherm agrees with an expansion of the exact surface excess isotherm to second order in the density. We mention some biochemical ramifications of the results.     

Communication: inferring the equation of state of a metastable hard-sphere fluid from the equation of state of a hard-sphere mixture at high densities

A possible approximate route to obtain the equation of state of the monodisperse hard-sphere system in the metastable fluid region from the knowledge of the equation of state of a hard-sphere mixture at high densities is discussed. The proposal is illustrated by using recent Monte Carlo simulation data for the pressure of a binary mixture. It is further shown to exhibit high internal consistency.     

Layered interfaces between immiscible liquids studied by density-functional theory and molecular-dynamics simulations

We present a study of the structure in the interface between two immiscible liquids by density-functional theory and molecular-dynamics calculations. The liquids are modeled by Lennard-Jones potentials, which achieve immiscibility by suppressing the attractive interaction between unlike particles. The density profiles of the liquids display oscillations only in a limited part of the simple liquid-phase diagram (rho,T). When approaching the liquid-vapor coexistence, a significant depletion appears while the layering behavior of the density profile vanishes. By analogy with the liquid-vapor interface and the analysis of the adsorption this behavior is suggested to be strongly related to the drying transition.     

基于化学缔合统计理论的链状流体状态方程

基于化学缔合统计理论的链状流体状态方程(EOS)能够反映实际分子的形状、链节成链、缔合等具体信息,在实际流体热力学性质计算中有着广泛应用.一般的链状流体EOS仅考虑相邻链节间的相关性,我们则借助统计力学和计算机模拟结果在模型中纳入了相间链节间的相关性,获得的硬球链流体(HSCF)模型能够更好地预测模型流体的压缩因子和第二维里系数.以HSCF为参考,引入方阱色散微扰项获得了实际方阱链流体(SWCF)EOS;结合根据黏滞球模型导得的缔合项,进一步构建了缔合流体EOS.最近,我们根据微扰理论和积分方程方法又开发了一新的变阱宽方阱链流体(SWCF-VR)模型.SWCF和SWCF-VREOSs可很好地用于计算小分子、聚合物、离子液体等纯流体及混合物的相行为、热焓、表面张力、黏度等热力学及传递性质,显示了模型良好的工程应用价值.本文就本课题组多年来在自由空间范畴内基于化学缔合统计理论开发链状流体EOS及其实际应用作系统的总结.     

Equation of state for expanded fluid mercury: variational theory with many-body interaction

A variational associating fluid theory is proposed to describe equations of state for expanded fluid mercury. The theory is based on the soft-sphere variational theory, incorporating an ab initio diatomic potential and an attractive many-body potential; the latter is evaluated with quantum chemical methods and expressed as a function of the local atomic coordination number and the nearest-neighbor distance. The resultant equation of state can reproduce the observed gas-liquid coexistence curve with good accuracy, without introducing phenomenological effective pair potentials. Various thermodynamic quantities such as pressure, isocloric thermal pressure coefficient, adiabatic sound velocity, and specific heat are calculated over a wide density-temperature range and compared with available experimental data.     

Density-functional-based molecular-dynamics simulations of molten salts

The physicochemical properties of two molten salts, namely, KCl and NaCl, have been studied with a molecular-dynamics approach using a density-functional-based tight-binding (DFTB) model. The obtained results have been compared with a number of previously reported simulations, carried out on smaller systems and using classical force-field techniques. A good agreement has been found for both structural parameters and macroscopic properties, such as self-diffusion coefficients. Furthermore, our DFTB results are very close to the available experimental data. From a more general point of view, our results demonstrate the applicability of DFTB as an efficient tool in the modeling of melts. At the same time, the quality of the obtained results supports the use of this as a reliable alternative to the more expensive ab initio dynamics approaches, if accurate parameters are provided.     

Perturbed hard-sphere equations of state of real fluids. II. Effective hard-sphere diameters and residual properties

Effective hard-sphere diameters for argon, krypton and xenon have been calculated from the currently most accurate perturbation theories using accurate pair-potential models. Based on the theoretical diameters and on pressure—volumes—temperature data for the real fluids, the van der Waals parameter a_p is examined and two conjectures generalizing the behavior of a_p are formulated. These conjectures make it possible to evaluate the effective hard-sphere diameters of simple liquids at the triple-point temperature from data for a few low-temperature pressure—volume isotherms. This fact, together with a corresponding-states principle that emerges from results for the theoretical diameters, forms the basis of a simple method which we propose for evaluating temperature-dependent effective hard-sphere diameters of a perturbed hard-sphere equation of state, independently of any pair-potential model and any perturbation theory. The applicability of the method is demonstrated for methane and its extension to nonsimple liquids is discussed. It is also shown that the use of an approximate theory and/or approximate pair-potential model may often result in a qualitatively misleading picture of a_p behavior.     

Estimation of the parameters in the Kirkwood-Buff theory of solution using Percus-Yevick fluid mixtures

Parameters G _ij in the Kirkwood-Buff theory of solution were calculated for binary fluid mixtures of Lennard-Jones (LJ) 6–12 molecules by using the Percus-Yevick theory. Calculations were carried out for various parameters in the LJ potential. Under the Lorentz-Berthelot rules, G ₁₁ and/or G ₂₂ -composition curves do not show a maximum for any parameters in the LJ potential. When the intermolecular interaction between different species becomes much weaker than that expected from the Berthelot rule, G ₁₁ and G ₂₂ show a maximum and G ₁₂ a minimum. The pressure effect on G _ij was examined and calculations at constant pressure were also carried out. G _ij is almost independent of the pressure when the ratio of the molecular volume of two components is in the range 1.0 to 2.5. Comparison was made between experimental and calculated G _ij for cyclohexane-2,3-dimethylbutane and acetonitrile-toluene systems. For the latter system, the quantitative agreement between the calculated and experimental could not be obtained but showed that the characteristics of G _ij -composition curves can be explained qualitatively by using the PY theory.Adjunct Associate Professor of Institute for Molecular Science (April 1982–March 1984)     

Equation of state of hexagonal hydroxylapatite (P63) as obtained from density functional theory simulations

Hydroxylapatite is an important calcium phosphate phase whose knowledge is useful in different fields, for instance in bone biology, development of biomaterials and even cultural heritage. In this work, the equation of state of this mineral was calculated by using the quasi‐harmonic approximation, also including for the first time the temperature effect. In athermal conditions (0 K), we found that the pressure dependence of the hydroxylapatite unit cell volume is well described by a third‐order Birch–Murnaghan formulation, with parameters K₀ = 115.9(1), K' = 4.47(6), and V₀ = 524.323(27). The inclusion of temperature led to a lower bulk modulus, for example, KT₀ = 109.55 GPa at 300 K. The thermal expansion coefficient between 0 and 1000 K was also reported. The results are in good agreement with the few available experimental data reported in literature and further extend the knowledge of the mechanical and thermal behavior of this important mineral.     

Extending the simple weighted density approximation for a hard-sphere fluid to a Lennard-Jones fluid II. Application

A simple weighted density approximation (SWDA) was extended to nonuniform Lennard-Jones fluids by following the spirit of a partitioned density function theory [S. Zhou, Phys. Rev. E 68 (2003) 061201] and mapping the hard-core part onto an effective hard-sphere fluid whose higher order terms beyond the second order of the functional perturbation expansion are treated by the SWDA. The resultant DFT formalism performs well for Lennard-Jones fluids under the influence of diverse external fields. With the present DFT formalism, we investigate in detail the structure and adsorption properties of a low-density LJ gas in a spherical cavity with a wall consisting of hard-sphere or LJ particles. It was found that when the cavity wall exerts an attractive external potential on the LJ particles in the cavity, the excess adsorption decreases as the temperature increases, while when the cavity wall exerts a hard repulsive external potential on the LJ particles in the cavity, the excess adsorption increases as the temperature increases.     

Slow dynamics and re-entrant melting in a polydisperse hard-sphere fluid

Extensive molecular dynamics simulations are performed at 6% polydispersity to investigate the phase diagram of a polydisperse hard-sphere fluid and the dynamical behavior in each phase. As the volume fraction phi is increased, the existence of a supercooled liquid is suggested above phi = 0.5524 by the mean-field analysis proposed recently. The first-order phase transition from supercooled liquid to crystal is then shown to occur around phi = 0.5630. The occurrence of re-entrant melting, a first-order phase transition from crystal to supercooled liquid, is also found around phi = 0.5715. The existence of the glass transition is thus suggested, even in the hard-sphere fluid with small polydispersity.     

Equation of state and structural properties of the Weeks-Chandler-Andersen fluid

Molecular dynamics simulations have been carried out for the equation of state and percolation properties of the Weeks-Chandler-Andersen (WCA) system in its fluid phase as functions of density and temperature. The compressibility factor Z collapses well for the various isotherms, using an effective particle diameter for the WCA particle which is (in the usual WCA reduced units) sigma(e)=2(16)(1+T)(16), where T is the temperature. A corresponding "effective" packing fraction is zeta(e)=pisigma(e) (3)N6V, for N particles in volume V, which therefore scales out the effects of temperature. Using zeta(e) the simulation derived Z can be fitted to a simple analytic form which is similar to the Carnahan-Starling hard sphere equation of state and which is valid at all temperatures and densities where the WCA fluid is thermodynamically stable. The data, however, are not scalable onto the hard sphere equation of state for the complete packing fraction range. We explored the continuum percolation behavior of the WCA fluids. The percolation distance sigma(p) for the various states collapses well onto a single curve when plotted as sigma(p)sigma(e) against zeta(e). The ratio sigma(p)sigma(e) exhibits a monotonic decrease with increasing zeta(e) between the percolation line for permeable spheres and the glass transition limit, where sigma(p)sigma(e) approximately 1. The percolation packing fraction was calculated as a function of effective packing fraction and fitted to an empirical expression. The local coordination number at the percolation threshold showed a transition between the soft core and hard core limits from ca. 2:74 to 1:5, as previously demonstrated in the literature for true hard spheres. A number of simple analytic expressions that represent quite well the percolation characteristics of the WCA system are proposed.     

Information theory approach to the isothermal–isobaric ensemble. 1. Monte Carlo simulations with the hard-sphere and square potentials

Monte Carlo (MC) simulations were performed on the isothermal–isobaric partition functions for both argon and methane gas. A newly implemented form was applied to the calculation of the volume for a variety of pressures, from which many potential applications can be derived.