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.     

A self-consistent density-functional approach to the structure of electric double layer: charge-asymmetric electrolytes

A self-consistent density-functional approach has been employed to study the structure of an electric double layer formed from a charge-asymmetric (2:l) electrolyte within the restricted primitive model which corresponds to charged hard sphere ions and a continuum solvent. The particle correlation due to hard-core exclusions is evaluated by making use of the universality of the density functionals and the correlation function of the uniform hard sphere fluid obtained through the integral equation theory with an accurate closure relation whereas mean spherical approximation is employed for the electrical contribution. Numerical results on the diffuse layer potential drop, ionic density profile, and the mean electrostatic potential near the electrode surface at several surface charge densities are found to be in quantitative agreement with the available simulation data.     

Enhanced KR-Fundamental Measure Functional for Inhomogeneous Binary and Ternary Hard Sphere Mixtures

An enhanced KR-fundamental measure functional (FMF) is elaborated andemployed to investigate binary and ternary hard sphere fluids near a planarhard wall or confined within two planar hard walls separated by certaininterval. The present enhanced KR-FMF incorporates respectively, for aim ofcomparison, a recent 3rd-order expansion equation of state (EOS) and aBoublik's extension of Kolafa's EOS for HS mixtures. It is indicated that the two versions of the EOS lead to, in the framework of the enhanced KR-FMF, similar density profiles, but the 3rd-order EOS is more consistent with an exact scaled particle theory (SPT) relation than the BK EOS. Extensive comparison between the enhanced KR-FMF-3rd-order EOS predictionsand corresponding density profiles produced in different periods indicatesthe excellent performance of the present enhanced KR-FMF-3rd-order EOS incomparison with other available density functional approximations (DFAs).There are two anomalous situations from whose density profiles all DFAsstudied deviate significantly; however, subsequent new computer simulationresults for state conditions similar to the two anomalous situations are invery excellent agreement with the present enhanced KR-FMF-3rd-order EOS. The present paper indicates that (i) the validity of the ``naive' substitutionelaborated in the present paper and peculiar to the original KR-FMF is stillin operation even if inhomogeneous mixtures are being dealt with; (ii) thehigh accuracy and self-consistency of the third order EOS seem to allow forapplication of the KR-FMF-third order EOS to more severe state conditions;and (iii) the ``naive' substitution enables very easy the combination of theoriginal KR-FMF with future's more accurate but potentially more complicatedEOS of hard sphere mixtures.     

On the compressibility equation of state for multi-component adhesive hard sphere fluids

The compressibility equation of state (EOS) for a multi-component sticky hard sphere model alternative to Baxter's one is investigated within the mean spherical approximation (MSA). For this model and this closure, as well as for a more general class of models and closures leading to Baxter functions q_ij(r) with density-independent stickiness coefficients, no compressibility EOS can exist for mixtures, unlike the one-component case (in view of this, an EOS recently reported in the literature turns out to be incorrect). The reason is the failure of the Euler reciprocity relation for the mixed second-order partial derivatives of the pressure with respect to the partial densities. This is in turn related to the inadequacy of the approximate closure (in particular, the MSA). A way out to overcome this drawback is presented in a particular example, leading to a consistent compressibility pressure, and a possible generalization of this result is discussed.     

SAFT-D theory for hard sphere and hard disc chain fluids

SAFT-dimer (SAFT-D) theory is reformulated to yield an improved equation of state for the hard sphere chain fluid. Two sets of the equation of state are proposed by employing Chiew's expressions for the contact values of the m hard sphere site-site correlation function g(σ). Comparison with molecular simulation data shows that the improved SAFT-D equation of state predicts the compressibility factor more accurately than Ghonasgi and Chapman's equation of state. It has been shown that SAFT-dimer theory can be applied readily to fused hard sphere chain fluids by considering the correct value of the effective chain length (m*). SAFT-dimer theory is also extended to the 2-dimensional tangent and fused hard disc chain fluids. For the fused hard disc dimer fluid, the SAFT equation of state is found to be more accurate than the Boublik hard disc dimer equation of state. For tangent hard disc chain fluids, the results obtained from SAFT-dimer theory are compared with Monte Carlo results for 5-mers and with GFD theory for 4-mers, 8-mers and 16-mers.     

New accurate binary hard sphere mixture radial distribution functions at contact and a new equation of state

New and very accurate formulae for additive binary hard sphere (HS) mixture radial distribution functions (RDFs) at contact are proposed in a simple analytical form. Using the virial theorem, the formulae also provide a new HS mixture equation of state (EOS). The new RDF formulae are the most accurate currently available. The new EOS is of comparable accuracy with that of Malijevsky, A., and Veverka, J. (1999, Phys. Chem. chem. Phys., 1, 4267), which is the most accurate HS mixture EOS currently available. However, the new EOS proposed here is of much simpler analytical form.     

纳米结构泡沫金冲击响应的分子动力学模拟

采用分子动力学计算程序对纳米结构泡沫金(Au)的冲击响应进行了模拟,得到了不同疏松度条件下泡沫Au的冲击压缩特性。通过获取不同势函数条件下实密Au的冲击Hugoniot关系以及泡沫结构稳定性测试选取适合描述Au泡沫冲击过程中原子的相互作用势。采用密堆积球壳的方式建立泡沫Au的初始构型。通过改变空心球壳的尺寸得到不同疏松度的稳定的泡沫Au结构。对泡沫Au的冲击过程进行分子动力学模拟,获得了不同疏松度泡沫Au在不同冲击压缩强度下的热力学状态参数。将模拟结果与已有的状态方程数据库以及疏松物质冲击压缩模型进行比较,结果表明,计算和理论模型给出的结果仍然存在明显的差异性,亟需通过进一步实验研究来验证模拟计算和理论模型结果的可靠性。     

TPT2 and SAFTD equations of state for mixtures of hard chain copolymers

We present the second-order thermodynamic perturbation theory (TPT2) and the dimer statistical associating fluid theory (SAFTD) equations of state for mixtures consisting of hetero-nuclear hard chain molecules based on extensions of Wertheim's theory for associating fluids. The second-order perturbation theory, TPT2, is based on the hard sphere mixture reference fluid. SAFTD is an extension of TPT1 (= SAFT) and is based on the non-spherical (hard disphere mixture) reference fluid. The TPT2 equation of state requires only the contact values of the hard sphere mixture site-site correlation functions, while the SAFTD equation of state requires the contact values of site-site correlation functions of both hard sphere and hard disphere mixtures. We test several approximations for site-site correlation functions of hard disphere mixtures and use these in the SAFTD equation of state to predict the compressibility factor of copolymers. Since simulation data are available only for a few pure copolymer systems, theoretical predictions are compared with molecular simulation results for the compressibility factor of pure hard chain copolymer systems. Our comparisons show a very good performance of TPT2, which is found to be more accurate than TPT1 (= SAFT). Using a modified Percus-Yevick site-site correlation function SAFTD is found to represent a significant improvement over SAFT and is slightly more accurate than TPT2. Comparison of SAFTD with generalized Flory dimer (GFD) theory shows that both are equivalent at intermediate to high densities for the compressibility factor of copolymer systems investigated here.     

Universal cubic equation of state and contact values of the radial distribution functions for multi-component additive hard-sphere mixtures

A universal cubic equation of state (UC EOS) is proposed based on a modification of the virial Percus-Yevick (PY) integral equation EOS for hard-sphere fluid. The UC EOS is extended to multi-component hard-sphere mixtures based on a modification of Lebowitz solution of PY equation for hard-sphere mixtures. And expressions of the radial distribution functions at contact (RDFC) are improved with the form as simple as the original one. The numerical results for the compressibility factor and RDFC are in good agreement with the simulation results. The average errors of the compressibility factor relative to MC data are 3.40%, 1.84% and 0.92% for CP3P, BMCSL equations and UC EOS, respectively. The UC EOS is a unique cubic one with satisfactory precision among many EOSs in the literature both for pure and mixture fluids of hard spheres.     

Solution of the mean spherical approximation for hard ions and dipoles of arbitrary size

The general solution of the mean spherical approximation (MSA) for an arbitrary mixture of hard spherical ions and dipoles, in which the ions can be of different size, is found. This solution is given in terms of three parameters that are calculated by solving an algebraic equation. Two of these parameters are scaling parameters required to satisfy the general symmetry of the pair correlation functions, and are similar to the one introduced in the solution of the MSA for an ionic mixture in earlier work. For equal size and low ionic concentration, we get a rather explicit solution of the MSA, which is formally similar to the Waisman-Lebowitz solution of the restricted primitive model, but with a concentration-dependent dielectric constant.Supported in part through NSF grant 77-04597.     

Nonlinear dielectric effect of dipolar fluid mixtures

The linear and nonlinear dielectric effect for two- and three-component dipolar fluid mixtures are studied within the framework of the mean spherical approximation (MSA) of dipolar hard sphere mixtures. In our approach, equally sized dipolar hard spheres with different dipole moments are considered. Based on earlier results for the electric field dependence of the polarization our analytical equations show the so-called normal saturation effects, which are in good agreement with corresponding canonical ensemble Monte Carlo simulation data. Comparisons between the MSA based theoretical results and the corresponding Langevin and Debye-Weiss theories are also made.     

Correlation of volumetric properties of binary mixtures of some ionic liquids with alcohols using equation of state

In our previous paper, we extended the Tao and Mason equation of state (TM EOS) to pure ionic liquids. Here we apply TM EOS based on statistical?Cmechanical perturbation theory to binary mixtures of ionic liquids. Three temperature-dependent quantities are needed to use the equation of state: the second virial coefficient, B ₂, effective van der Waals co-volume, b, and a scaling factor, ??. The second virial coefficients are calculated from a correlation that uses the normal boiling temperature and normal boiling density. ?? and b can also be calculated from the second virial coefficient by scaling. In this procedure, the number of input parameters, for calculation of B ₂, ??, and b reduced from 5 (i.e., critical temperature, critical pressure, acetric factor, Boyle temperature T _B, and the Boyle volume ?? _B) to 2 (i.e., T _bp and ?? _bp). At close inspection of the deviations given in this work, the TM EOS predicts the densities with a mean AAD of 1.69%. The density of selected system obtained from the TM EOS has been compared with those calculated from perturbed-hard-sphere equation of state. Our results are in favor of the preference of the TM EOS over another equation of state. The overall average absolute deviation for 428 data points that calculated by perturbed-hard-sphere equation of state is 2.60%.     

Effect of ionic size on the structure of spherical double layers: a Monte Carlo simulation and density functional theory study

The effect of ionic size on the diffuse layer characteristics of a spherical double layer is studied using Monte Carlo simulation and density functional theory within the restricted primitive model. The macroion is modelled as an impenetrable charged hard sphere carrying a uniform surface charge density, surrounded by the small ions represented as charged hard spheres and the solvent is taken as a dielectric continuum. The density functional theory uses a partially perturbative scheme, where the hard sphere contribution to the one particle correlation function is evaluated using weighted density approximation and the ionic interactions are calculated using a second-order functional Taylor expansion with respect to a bulk electrolyte. The Monte Carlo simulations have been performed in the canonical ensemble. The detailed comparison is made in terms of zeta potentials for a wide range of physical conditions including different ionic diameters. The zeta potentials show a maximum or a minimum with respect to the polyion surface charge density for a divalent counterion. The ionic distribution profiles show considerable variations with the concentration of the electrolyte, the valency of the ions constituting the electrolyte, and the ionic size. This model study shows clear manipulations of ionic size and charge correlations in dictating the overall structure of the diffuse layer.     

Structure and thermodynamics of the classical one-component plasma

An exact solution of the mean spherical approximation for charged hard spheres in a neutralizing background is used to calculate various static properties of the classical one-component plasma in the strong coupling regime. The expressions involved are simple and analytic, and involve the charged hard sphere diameter as the only unknown parameter, which we determine using an approximate scaling property of the direct correlation function. Results obtained for structural correlation functions and various thermodynamic quantities are in very good agreement with the Monte Carlo simulation data.     

Thermodynamic properties of the Lennard-Jones FCC solid: perturbation theory parameterisation and Monte Carlo simulation

This work is concerned with a valid representation of the solid-phase equation of state (EOS), the validity of which is evaluated by comparing to Monte Carlo (MC) simulation results. The proposed EOS has been developed by employing an optimal division of the Lannard-Jones (LJ) potential and an effective temperature- and density-dependent diameter into the framework of the simplified perturbation theory. Then, with the aim of extending to the chain systems, the conventional chain contribution (i.e. TPT1) is added to the proposed model (i.e. the atomic LJ system). Finally, the solid-state EOS based on Helmholtz free energy will be introduced for low temperature and high density conditions. To verify the accuracy of the proposed model, its performance is compared with the results of MC simulation. The comparison between the obtained results from the proposed model and the MC simulations shows that the EOS can satisfactorily predict the properties of the solid LJ system, both for the atomic system and for the chains.     

热质的运动与传递-热子气状态方程

基于相对论原理,提出能量的运动可以产生压强．在热质概念的基础上,针对理想气体,根据分子动理论建立了热子气状态方程,从而得到理想气体分子的热运动动能压强的表达式．基于硬球势能模型通过分子动力学模拟验证了热子气状态方程的正确性．     

Theoretical Investigation of Uniform and Non-uniform Penetrable Sphere Fluid

A bridge function approximation is proposed for a single-component fluid consisting of penetrable sphere interacting via a potential that remains finite and constant for center-center distance smaller than the particle diameter and is zero otherwise. The radial distribution function from the Ornstein-Zernike integral equation combined with the present bridge function approximation is in satisfactory agreement with the corresponding simulation data for all of the investigated state points. The presently calculated excess Helmholtz free energy respectively based on virial route and compressibility route is highly self-consistent, and is in very good agreement with simulational results for the case of low temperatures. The present bridge function approximation, combined with the bridge density functional approximation,can reproduce very accurately density profiles of the penetrable sphere fluid confined in a hard spherical cavity for all the cases where simulational results are available.     

Theoretical Investigation of Uniform and Non-uniform Penetrable Sphere Fluid

A bridge function approximation is proposed for a single-component fluid consisting of penetrable sphere interacting via a potential that remains finite and constant for center-center distance smaller than the particle diameter and is zero otherwise. The radial distribution function from the Ornstein-Zernike integral equation combined with the present bridge function approximation is in satisfactory agreement with the corresponding simulation data for all of the investigated state points. The presently calculated excess Helmholtz free energy respectively based on virial route and compressibility route is highly self-consistent, and is in very good agreement with simulational results for the case of low temperatures. The present bridge function approximation, combined with the bridge density functional approximation, can reproduce very accurately density profiles of the penetrable sphere fluid confined in a hard spherical cavity for all the cases where simulational results are available.     

Thermophysical properties of ionic liquids and their mixtures from a new equation of state

In our previous work, a perturbed hard-trimer-sphere equation of state (PHTS EOS) was developed for modeling the phase equilibria of pure ionic liquids (ILs) (M.M. Alavianmehr et al., Ionics 22 (2016) 2447–2459). In this work, we have successfully extended the model to the mixtures of IL + IL and IL + solvent. Two temperature-dependent parameters appearing in the EOS are correlated with two microscopic scaling constants σ, the effective hard-sphere diameter, and ε, the non-bonded interaction energy. The overall average absolute deviation (AAD) of the estimated densities from the literature data using the proposed model with and without non-additivity parameter (λ _ij) was found to be 0.44 and 0.79%, respectively. A modified Enskog equation and rough hard-sphere (RHS) theory are combined with our proposed equation of state to calculate the viscosity coefficient of ionic liquids and their mixtures. Finally, from the results obtained, a linear relation between logarithm of surface tension and viscosity property of ionic liquid was developed.     

A modified equation of state for Xe at high pressures by molecular dynamics simulation

The exact equation of state （EOS） for the fission gas Xe is necessary for the accurate prediction of the fission gas behavior in uranium dioxide nuclear fuel, However, the comparison with the experimental data indicates that the applicable pressure ranges of existing EOS for Xe published in the literature cannot cover the overpressure of the rim fission gas bubble at the typical UO2 fuel pellet rim structure. Based on the interatomic potential of Xe, the pressure-volume-temperature data are calculated by the molecular dynamics （MD） simulation. The results indicate that the data of MD simulation with Ross and McMahan＇s potential [M. Ross and A. K. McMahan 1980 Phys. Rev. B 21 1658] are in good agreement with the experimental data. A preferable EOS for Xe is proposed based on the MD simulation. The comparison with the MD simulation data shows that the proposed EOS can be applied at pressures up to 550 MPa and 3 GPa and temperatures 900 K and 1373 K respectively. The applicable pressure range of this EOS is wider than those of the other existing EOS for Xe published in the literature.