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.     

Equation of state for pure fluids at critical temperature

In this paper, we employ the concept of probability for creating a cavity with diameter d in fluid along with the perturbation and variation approach, and develop an equation of state (EOS) for a hard sphere (HS) and Lennard– Jones (LJ) fluids. A suitable axiomatic form for surface tension S(r) is assumed for the pure fluid, with r as a variable. The function S(r) has an arbitrary parameter m. S(r) = A + B(d/r)/[1 + m(d/r)]. We use the condition in terms of radial distribution function G(λd, η) containing the self-consistent parameter λ and the condition of continuity at r = d/2 to determine A and B. A different EOS can be obtained with a suitable choice of m and the EOS has a lower root-mean-square deviation than that of Barker–Henderson BH2 for LJ fluids.     

Thermodynamic study of fluid in terms of equation of state containing physical parameters

We introduce a simple condition for one mole fluid by considering the thermodynamics of molecules pointing towards the effective potential for the cluster.Efforts are made to estimate new physical parameter f in liquid state using the equation of state containing only two physical parameters such as the hard sphere diameter and binding energy.The temperature dependence of the structural properties and the thermodynamic behavior of the clusters are studied.Computations based on f predict the variation of numbers of particles at the contact point of the molecular cavity(radial distribution function).From the thermodynamic profile of the fluid,the model results are discussed in terms of the cavity due to the closed surface along with suitable energy.The present calculation is based upon the sample thermodynamic data for n-hexanol,such as the ultrasonic wave,density,volume expansion coefficient,and ratio of specific heat in the liquid state,and it is consistent with the thermodynamic relations containing physical parameters such as size and energy.Since the data is restricted to n-hexanol,we avoid giving the physical meaning of f,which is the key parameter studied in the present work.     

一种简化维里型状态方程预测高温甲烷PVT关系

为满足描述爆轰环境下高温气体高温、中高压状态的需求,本文提出了一种基于Lennard-Jones(LJ)势能函数的简化维里型状态方程Han-Long(HL).应用HL状态方程计算了甲烷1000 K以上112组理论和实验数据,计算所得体积平均绝对偏差约为1%,最大误差为3.28%,远低于DMW状态方程和BS状态方程的计算偏差.采用HL状态方程计算了甲烷冲击试验的热力学数据,计算所得体积偏差均小于3%.结果表明,HL状态方程能够很好的描述高温甲烷的热力学状态.     

液态镓在石墨烯表面的润湿性及形貌特征

液态Ga及其合金的熔点低、毒副作用小、导电率高,使得这类液态金属能像石墨烯一样被广泛应用于微流器件、柔性电子器件中,制备这些器件的关键在于有效控制各生产环节中液态金属在固体界面上的润湿性及形貌特征.基于Lennard-Jones(L-J)势函数,利用分子动力学模拟方法研究了金属Ga在石墨烯表面的润湿性,根据模拟结果拟合的L-J势参数能正确描述Ga原子与衬底之间的相互作用并得到了与实验值极为接近的润湿角,发现衬底与液膜间相互作用的微小改变都会对最终润湿形态产生极大影响,平衡态的润湿角和脱离衬底速度随着Ga-C间势能的减小而增大,并成功获得了不同厚度的Ga液膜在石墨烯表面的形态演变规律,极为符合液态Ga的基本特性.利用所得L-J势函数参数模拟了液态Ga在粗糙度相同但纳米柱尖端形貌不同的C材料表面的润湿演变,发现纳米柱尖端形貌对液态Ga的润湿过程及状态影响极大.     

Influence of dispersive long-range interactions on properties of vapour–liquid equilibria and interfaces of binary Lennard-Jones mixtures

The influence of dispersive long-range interactions on properties of vapour–liquid equilibria and interfaces of six binary Lennard-Jones (LJ) mixtures was studied by molecular dynamics (MD) simulations and density gradient theory (DGT). The mixtures were investigated at a constant temperature T, at which the low-boiling component, which is the same in all mixtures, is subcritical. Two different high-boiling components were considered: one is subcritical, the other is supercritical at T. Furthermore, the unlike dispersive interaction was varied such that mixtures with three different types of phase behaviour were obtained: ideal, low-boiling azeotrope, and high-boiling azeotrope. In a first series of simulations, the full LJ potential was used to describe these mixtures. To assess the influence of the long-range interactions, these results were compared with simulations carried out with the LJ truncated and shifted (LJTS) potential applying the corresponding states principle. The dispersive long-range interactions have a significant influence on the surface tension and the interfacial thickness of the studied mixtures, whereas the relative adsorption and the enrichment are hardly affected. Furthermore, the influence of the long-range interactions on Henry's law constants and the phase envelopes of the vapour–liquid equilibrium was investigated. The long-range interactions have practically no influence on the composition dependency of the investigated mixture properties.     

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.     

The infinite-volume ground state of the Lennard-Jones potential

We consider a finite chain of particles in one dimension, interacting through the Lennard-Jones potential. We prove the ground state is unique, and approaches uniform spacing in the infinite-particle limit.Research supported in part by NSF grant MCS 78-01520.     

On the compatibility of polarisable and non-polarisable models for liquid water

The properties of water at physiological conditions can be modelled at different levels of resolution: (1) sub-atomic models that take into account electronic degrees of freedom, (2) atomic models that only account for atomic degrees of freedom and (3) supra-molecular models that only involve some supra-molecular degrees of freedom. To enhance the computational efficiency of molecular simulation, models at different levels of resolution should be simultaneously usable for different parts of a system for which the level of detail of interest is different. This requires these different types of models to be compatible with each other. In the present study, the compatibility of two polarisable models for liquid water, COS/G2 and COS/D, with a non-polarisable model for liquid water, SPC, is investigated. It is shown that these models are compatible. The polarisable models can thus be used to solvate biomolecules described by a biomolecular force field that is compatible with the SPC water model.     

Oscillation of the radial distribution function

We prove that the radial distribution function oscillates at low density in a system with a short-range nonnegative potential and investigate the branching of the solutions of an approximate equation of state.     

Computation of high-order virial coefficients in high-dimensional hard-sphere fluids by Mayer sampling

The Mayer sampling method was used to compute the virial coefficients of high-dimensional hard-sphere fluids. The first 64 virial coefficients for dimensions 12 < D ? 100 were obtained to high precision, and several lower dimensional virial coefficients were computed. The radii of convergence of the virial series in 13, 15, 17 and 19 dimensions agreed well with the analytical results from the Percus–Yevick closure.     

ANALYTIC EQUATION OF STATE FOR GENERALIZED LENNARD-JONES SOLID INCLUDING LOWEST-ORDER ANHARMONIC AND CORRELATION CORRECTIONS

Based on the cell model, the general formula for the free energy of solids is derived analytically with the lowest order anharmonic modification and correlation effect taken into account. Combining a method of summing over lattice sites, the analytic equation of state for generalized Lennard-Jones solid is derived. The calculations show that the agreement between theory and computer simulation is quite good and is significantly improved as compared with the numerical results in literature. The comparison of different effects shows the theory including all neighbors but only considering the lowest anharmonic and correlation effects may be a good and convenient approximation for practical solids. The approximation can be easily extended to the quantum case and other generalized potentials.     

Analytic Debye-Grüneisen equation of state for a generalized Lennard-Jones solids

The approximate method to treat the practical quantum anharmonic solids proposed by Hardy,Lacks and Shukla is reformulated with explicit physical meanings.It is shown that the quantum effect is important at low temperature,it can be treated in the harmonic framework.and the anharmonic effect is important at high temperature and tends to zero at low temperature,it can be treated by using a classical approximation.The alternative formulation is easier for various applications,and is applied to a Debye-Grueneisen solid with the generalized Lennard-Jones intermolecular interaction.The expressions for the Debys temperature and Grueneisen parameter as a function of volume are analytically derived.The analytic equation of state is applied to predict the thermodynamic properties of solid xenon at normal-pressure with the nearest-neighbour Lennard-Jones interaction,and is further applied to research the properties of solid xenon and krypton at high pressure by using an all-neighbour Lennard-Jones interaction.The theoretical results are in agreement with the experiments.     

Equation of state and interaction potential of helium under high temperatures and high densities

Based on the thermodynamics statistic method, the improved variational perturbation theory and the modified quantum mechanics correction model have been used to calculate the equation of state of liquid helium at pressure from 0.7 to 108 GPa. The calculation results are in good agreement with the experimental data. The EXP-6 potential (α = 13.1) can more accurately describe the interaction of helium atoms than other potentials in the scheme. Finally, a comparison is shown between our interatomic potentials and other potentials.     

Simple analytic equations of state for the generalized hard-core Mie(α, β) and Mie(α, β) fluids from perturbation theory

New, simple and analytic perturbation theory equations of state for generalized hard-core Mie HCMie(α, β) and Mie(α, β) fluids are proposed. They are based on the second-order Barker-Henderson perturbation theory in the macroscopic compressibility approximation and the new analytical expression of the radial distribution function of hard spheres, g^HS(r), developed by Sun in terms of a polynomial expansion of base functions adapted to the square-well and Sutherland potentials [Can. J. Phys. 83 (2005) 55], the combination of which yields the HCMie(α, β) and Mie(α, β) functions. The compressibility factors, the residual internal energies and the radial distribution function at contact with the hard core are then obtained from this equation of state for the HCLJ(12, 6) potential, which is a particular case of the HCMie(α, β) potentials with α = 12 and β = 6. The results are in good agreement with the existing Monte Carlo (MC) simulation data, and compare favorably with those obtained from five other equations of state, three of which contain numerical coefficients fitted to the Monte Carlo results. For the Mie(α, 6) (α = 8, 10, 12), fluids, the present equation of state is a good representation of recent molecular dynamics (MD) simulations of the pressure and internal energy. It is more accurate than the statistical associating fluid theory of variable range (SAFT-VR Mie(n, 6)) theory for n = 8, and 10, while for n = 12 the SAFT-VR theory is best. For the Mie(14, 7) fluid, which is outside the range of application of the SAFT-VR theory, the results for the pressure are in good agreement with the analytical equation of state obtained from the MC simulation data.     

混合物冲击温度的数值模拟

介绍温度的数值模拟方法,采用三维动力学有限元程序模拟冲击压缩状态,分析了数值模拟的准确性。模拟了铜和铝两种金属单质组成混合物的冲击压缩性能,在分析了热传导影响后,计算了混合物的冲击温度和冲击绝热线。     

Sixth,seventh and eighth virial coefficients of the Lennard-Jones model

We report values of the virial coefficients B _n of the Lennard-Jones (LJ) model, as computed by the Mayer Sampling Monte Carlo method. For n = 4 and 5, values are reported for 103 temperatures T = 0.62 to 40.0 (in LJ units); for n = 6, 31 values are reported for T = 0.625 to 20.0; for n = 7, 15 values are reported from T = 0.625 to 10; and for n = 8, four values are reported from T = 0.75 to 10. Data are used to estimate the location of the LJ critical point, and the critical temperature estimated this way is given to within 0.8% of the established value, while the critical density is too low by 10%. Data derived from the virial equation of state (VEOS) are compared to pressures and internal energies calculated by Monte Carlo simulation. Simulations of systems ranging from 125 to 30,000 particles are extrapolated to infinite system size, and it is shown that the VEOS–when applied at densities where the series has reached convergence–provides results closer to the infinite-system values than obtained by any of the finite-system simulations. For n = 6, convergence of VEOS (within a 1% tolerance) is obtained for densities up to the spinodal for subcritical temperatures and up to ρ = 0.4 (in LJ units) in the vicinity of the critical temperature; the range of applicability of VEOS increases with temperature, reaching for example densities of 0.65 for T = 5.0 and 0.8 for T = 8.0 when truncated at n = 6.     

液氦冲击压缩特性的理论计算

用量子力学修正的WCA液体变分微扰理论计算了液氦冲击压缩曲线,计算中体系分子间相互作用势选择EXP-6有效两体势模型,两体势参数通过对实验数据的拟和优选。计算结果在一次冲击压力范围内,冲击温度及压力与Nellis等人的实验数据符合很好,二次冲击数据与实验值稍有偏差,但也在其误差范围内,由于二次冲击只有一个实验点,因此实验数据不能提供更多的信息以供比较。计算结果表明与其他分子间相互作用势相比,选择值为12.7的EXP-6势更为准确地反映了液氦分子间的相互作用。     

A particle method with adjustable transport properties—the generalized consistent Boltzmann algorithm

The consistent Boltzmann algorithm (CBA) for dense, hard-sphere gases is generalized to obtain the van der Waals equation of state and the corresponding exact viscosity at all densities except at the highest temperatures. A general scheme for adjusting any transport coefficients to higher values is presented.