Hard body fluids again: Virial coefficients and equations of state

The table of the virial coefficientsB ₂ throughB ₄ of all hard body fluid models considered so far has been completed by calculating the missing coefficients. Applicability of these coefficients to predicting the thermodynamic behaviour of dense hard body fluids is assessed and certain discrepancies in the data for oblate spherocylinders are found. It is shown that by combining the Padé approximant with an appropriate analytic expression an accurate 3-parameter equation of state results.     

Virial series around non-null density: density dependence of virial coefficients

It is shown that the equation of state of fluid systems can be expanded around non-null densities if the well known virial series is generalized by considering its coefficients as density dependent. This in turn leads to a hierarchy of differential equations that describe the coefficients b_j (ρ). Starting from the already known equation of state for hard bodies in d = 0,1,2,3 dimensions this hierarchy is analysed and the behaviour of both the reducible b_j (ρ) and irreducible β～ _j (ρ) cluster integrals is discussed. New virial coefficients b_j (ρ) have been introduced with a simpler density dependence. Their asymptotic (j → ∞) behaviour is discussed.     

Is it possible to infer the equation of state of a mixture of hard discs from that of the one-component system?

Based on exact asymptotic properties of the composition-independent virial coefficients of a binary mixture of hard discs in the limits α = σ₂/σ₁ → 0, α → 1 and α → ∞, R. J. Wheatley (1998, Molec. Phys., 93, 965) has recently proposed an approximate interpolation equation for these coefficients. In this note, the equation of state equivalent to this interpolation is obtained, expressing the compressibility factor of the mixture in terms of that of the pure system. An extension to an arbitrary number of components is also given. The equation of state derived here is compared with another one recently proposed by following a different route (Santos, A., Yuste, S. B., and López de Haro, M., 1999, Molec. Phys., 96, 1) and with Monte Carlo simulation results. It is shown that the latter equation is more accurate than the former one, at least for not too disparate mixtures (0.7 < α < 1).     

The virial coefficients of hard hypersphere binary mixtures

The third, fourth and fifth virial coefficients of hard hypersphere binary mixtures with dimensionality d = 4, 5 have been calculated for size ratios R ≥ 0.1, R = ≡ σ₂₂/σ₁₁, where σ _ii is the diameter of component i. The composition independent partial virial coefficients have been evaluated by Monte Carlo integration of the corresponding Mayer modified star diagrams. The results are compared with the predictions of Santos, S., Yuste, S. B., and Lopez de Haro, M., 1999, Molec. Phys., 96, 1 of the equation of state of a multicomponent mixture of hard hyperspheres, and the good agreement gives strong support to the validity of that recipe.     

Thermodynamic properties of molecular fluid mixtures of hard ellipsoids

Thermodynamic properties of molecular fluid mixtures of hard ellipsoids are calculated. Numerical results are given for equation of state and excess-free energy of the binary mixture of both additive and non-additive hard ellipsoids. It is found that the equation of state and free energy of mixtures increase with increase of anisotropy parameterx ₀.     

由实验数据计算氢气的维里系数问题

我们对计算气体物态方程中维里系数的方法作了全面的探讨,提出了如何判定物态方程中项数的四个原则。这四个原则是:(1)用∑v²的大小的变化来判断项的数目应如何选取,其中v为pV的计算值减去其实验值。(2)多项式要满足逐项在数值上减少的级数性质。(3)多项式的末一项大小要与实验误差大小相同。(4)误差v的正负号数目要大致相等。我们建议在计算中要用A₀+B₀+C₀+…=1条件,但不要用A=RT条件。此外还讨论了用压强展开和用密度展开的问题,级数展开式中省去奇数幂次项问题,维里系数的有效位数问题,若干实验数据的修正问题等。我们根据上述原则和建议,重新计算了氢气的维里系数,结果与各原作者所得的有相当的不同。在同一温度用不同实验窒的数据所得的维里系数比各原作者所得的要互相接近些,一般在两倍标准误差内一致。     

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.     

使用等价轨道法计算AB型晶体的倍频系数

在忽略电子-声子相互作用的基础上,本文探讨了从能带波函数出发计算AB型晶体倍频系数的可能性。采用计算AB型晶体能带的近似方法——等价轨道法。计算了k=0点的倍频系数,然后通过带宽的修正,使k=0点的倍频系数近似地表为不同k点倍频系数的平均,这一平均值乘以第一布里渊区内k点的总数就是晶体的宏观倍频系数。计算了十七种闪锌矿型和纤维锌矿型晶体的倍频系数,计算值和实验值的吻合相当满意。从中得出几点有用的结论:(1)倍频系数的双能级跃迁模型对闪锌矿型结构是适用的;但对纤维锌矿型结构并不适用。(2)纤维锌矿型晶体的X₃₃₃^2ω系数可表示成两项之和:单重态(Γ₁,Γ₃)的贡献和双重态(Γ₅,Γ₆)的贡献。其中单重态对倍频系数贡献正值,双重态贡献负值。(3)使用Pauling的离子性标度f_i来表征A—B键的离子性是适宜的。 关键词：     

Equation of state of long chain molecules and rings

An equation of state for long chain molecules has been proposed using statistical associating fluid theory (SAFT). The formalism derived here is based on the assumption that the chain is formed by the pairs of trimers. The equations of state for 48-mers and 192-mers are formulated and compared with Monte Carlo results. The theory has been developed to treat hard sphere molecules with two attraction sites to form a ring molecule. The equations of state for trimer, hexamer and 12-mer ring molecules have been formulated. There is excellent agreement with available Monte Carlo results. Second virial coefficients of tangent chain molecules and ring molecules have been determined numerically and compared with simulation results.     

Modification of Tao–Mason equation of state to ionic liquids

In our previous paper, we extended the Tao and Mason equation of state (TM EOS) to refrigerant fluids, using the speed of sound data. Here, we predict the equation of state for ionic liquids (ILs). The considered ILs are [Bmim][PF₆], [C₂mim][NtF₂], [C₃mim][NtF₂], [C₆mim][NtF₂], [C₇mim][NtF₂], [C₂mim][EtOSO₃], [Bmim][MeSO₄], [Bmim][OcSO₄], and [C₄mim][dca]. The equation of state consists of three temperature-dependent parameters: the second virial coefficient, a constant for scaling the softness of repulsive force, and an effective hard-sphere diameter equivalent to the van der Waals co-volume. The second virial coefficients of ILs are scare and there is no accurate potential energy function to allow their theoretical calculation. In this work, the second virial coefficient have been calculated using corresponding states correlation based on temperature and density at normal boiling point. The other two parameters of the equation of state can be calculated using a scaling rule. Analysis of our predicted results shows that the Tao?CMason equation of state is capable of accurately predicting the density of ILs at any temperature and pressure. The overall average absolute deviation densities for 1,633 data points are 2.05%. Also, the density of ILs obtained from the TM EOS has been compared with those calculated from vdW?CCS?C?? and Peng?CRobinson (PR) equation of state. Our results are in favor of the preference of the TM EOS over the two other equations of state. The overall average absolute deviation for 1,633 data points calculated by vdW?CCS?C?? and PR equation of state are 6.63% and 12.19%, respectively.     

磁电双层膜层间耦合的弹性力学研究

基于磁致伸缩相与压电相的本构方程,应用弹性力学模型,简要介绍了如何推导自由状态的磁电双层膜纵向、横向磁电(ME)电压系数. 并采用相应的材料参数计算了La_07Sr_03MnO₃-Pb(Zr,Ti)O₃ (LSMO-PZT),Tb_1-xDy_xFe_2-y(TDF)-PZT双层膜中的磁电电压系数,具体分析了其与压电相 关键词： 磁电效应 双层膜 TDF LSMO PZT     

Equilibrium properties of hard non-sphere fluids

Derivation of the thermodynamic properties of fluids of hard non-spherical molecules of arbitrary symmetry is based on the decoupling approximation. Theoretical expressions are given and calculations made for the equation of state and virial coefficients for hard ellipsoids. These results are compared with Monte Carlo values and show fair agreement in all cases. The theoretical predictions for the equation of state for binary mixtures are compared with the Monte Carlo results for hard spheres and hard prolate spherocylinders. Theoretical expressions for the first order quantum correction to the free energy, pressure and virial coefficients are also given. The quantum effects increase with increase of density and with increase of anisotropy parameter.     

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.     

Equation of state in the quasi-classical approximation

An approximate equation of state is considered that contains a correction for electron-gas inhomogeneity in the exchange-correlation and kinetic energies in the quasi-classical approximation. The problem of finding the model parameters satisfying the condition P=0 has been solved for metals at a normal density. The results of numerical solution of the model equations are presented for degrees of compression. The values of the quasi-classical parameter determining the approximation accuracy are found. The results are illustrated by the dependences on the degree of compression plotted in the range ρ/ρ₀=1–10⁶ and by the spatial dependences. Our approach to construction of the equation of state provides for a quite simple but sufficiently accurate approach to the experimental values of the model parameters. Moreover, the proposed model gives much more self-consistent information as compared to conventional approximations. In particular, the ionicity is calculated for an increase in the density. The model equation can also be used instead of the well-known effective bound-electron potential approximation.     

A Monte Carlo model for determination of binary diffusion coefficients in gases

A Monte Carlo method has been developed for the calculation of binary diffusion coefficients in gas mixtures. The method is based on the stochastic solution of the linear Boltzmann equation obtained for the transport of one component in a thermal bath of the second one. Anisotropic scattering is included by calculating the classical deflection angle in binary collisions under isotropic potential. Model results are compared to accurate solutions of the Chapman–Enskog equation in the first and higher orders. We have selected two different cases, H₂ in H₂ and O in O₂, assuming rigid spheres or using a model phenomenological potential. Diffusion coefficients, calculated in the proposed approach, are found in close agreement with Chapman–Enskog results in all the cases considered, the deviations being reduced using higher order approximations.     

Thermal expansion coefficient of ternary liquid mixture using hard sphere models and Flory’s statistical theory

The coefficients of thermal expansion (α) of ternary liquid mixtures of heterocyclic compounds viz., pyridine/quinoline with phenol in benzene have been evaluated at 308.15, 318.15 and 328.15 K, respectively. A comparative study of thermal expansivity using different models for hard sphere equation of state and Flory’s statistical theory has been made. The computed values of thermal expansivity are compared with the experimental results. The excess values of thermal expansivity have also been computed and utilized to discuss the existence and strength of intermolecular interactions in the ternary liquid system under investigation.     

Effects of powder flowability on the alignment degree and magnetic properties for NdFeB sintermagnets

The magnetic powders for sintered NdFeB magnets have been prepared by using the strip casting (SC), hydrogen decrepitation (HD) and jet milling (JM) techniques. The effects of powder flowability and addition of a lubricant on the alignment degree and the hard magnetic properties of sintered magnets have been studied. The results show that the main factor affecting powder flowability is the aggregation of magnetic particles for powders in a loose state, but it is the friction between the powder particles for powders that are in a compact state. The addition of a lubricant with suitable dose can slightly prevent the congregating of powders, obviously decrease the friction between the powder particles, improve the powder flowability, and increase the alignment degree, remanence and energy product density of sintered magnets. Mixing a suitable dose of lubricant and adopting rubber isostatic pressing (RIP) with a pulse magnetic field, we have succeeded in producing the sintered NdFeB magnet with high hard magnetic properties of B_r=14.57 KG, _jH_c=14.43 KOe, (BH)_max=51.3 MGOe.     

Self-diffusion and density of liquid hexafluorobenzene as a function of pressure and temperature

Measurements of self-diffusion coefficients to pressures of 2000 bar? 1 bar ≡ 10⁵ N m^-2. and densities to 2600 bar, except where limited by freezing, have been made for liquid hexafluorobenzene C₆F₆ at eight temperatures from 15°C to 150°C. The N.M.R. spin echo technique was used for the self-diffusion measurements, and the densities were determined with a densitometer of the bellows-slidewire type. The density data have been fitted satisfactorily to a modified form of the Tait equation, and the self-diffusion results were reproduced by a polynominal in pressure for each isotherm.

Several models of transport in liquids were evaluated. All models depend sensitively upon a quantity ν-ν₀, the difference between the specific volume of the liquid and that of a hypothetical dense solid. The free volume model describes the data only if ν₀ is allowed to depend upon pressure. The hard sphere model failed to describe our results for C₆F₆ at temperatures above 70°C even when the effective hard sphere diameter was treated as an adjustable parameter.     

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.