A generic equation of state for liquid crystalline phases of hard-oblate particles

A generic equation of state (EoS) is developed for the hard cylindrical disc model to describe the isotropic phase of hard cut-sphere particles introducing a correction parameter to incorporate the negative contributions from higher-order virial coefficients. The isotropic–nematic–columnar phase diagram of hard cut-sphere fluids is investigated combining the new EoS with a scaled Onsager free energy for the nematic phase and an extended cell theory for columnar phase. By mapping the virial coefficients of an oblate spherocylinder on to those of the cylindrical disc (which are known algebraically), the new generic EoS is used to describe the isotropic and nematic phases of hard oblate spherocylinder particles. The predictions of the generic EoS are compared with available simulation data.     

Thermal effect and equation of state in solids

In the present paper, an attempt has been made to include the thermal effect into an isothermal equation of state using the Debye approximation representing volume as a function of pressure. The calculations are done in case of NaCl, CsCl, Mo, and W. The present calculations are in good agreement with the reported results.     

A perturbed hard-sphere equation of state extended to imidazolium-based ionic liquids

A perturbed hard-sphere equation of state (EOS) has been previously employed to predict pressure–volume–temperature properties of some ionic liquids (ILs) with phosphonium-, pyridinium-, and pyrrolidinium cations. In this work, we have extended the considered EOS to another class of ILs in compressed states. This class consists of 14 imidazolium-based ILs. The predicted densities were compared with those obtained from the experiment, over a broad pressure range from 0.1 to 200 MPa. From 1,122 data points examined for the aforementioned ILs, the total average absolute deviation was found to be 1.05%.     

Pressure dependence of melting temperature and shear modulus of hcp-iron

The pressure effects on melting temperature and shear modulus of hcp-iron have been studied based on the semi-empirical approach in the Debye model. The recent well-established pressure-dependent Grüneisen parameter has been applied to derive the analytical expressions of the Debye frequency, the Debye temperature, melting temperature and shear modulus which are of importance to geophysical implications. Numerical calculations have been performed for hcp-iron as functions of pressure up to the pressure of Earth's inner core. Our calculations are compared with those of previous experimental and theoretical data showing the good and reasonable agreements. The present results contribute to the database of high pressure melting, especially Earth's inner core boundary temperature, and could also be used to verify as well as analyze the future high pressure diamond-anvil cell experiments.     

Application of the Englert-Schwinger model to the equation of state and the fullerene molecule

The Englert-Schwinger model (ESM) is applied to two problems. One is the calculation of zero-temperature equation of state (EOS) of elements within the spherically symmetric Wigner-Sietz cell approximation. The other is to obtain the equilibrium radius of fullerene molecule using March’s approach [N. H. March, Proc. Camb. Philos. Soc. 48, 665 (1952)]. In each case, the results of the ESM are compared with those of Thomas-Fermi-Dirac (TFD) and Thomas-Fermi-Dirac-Weizsacker (TFDW) models. Zero-temperature equation of state calculations are done for Al and Cu. The results of the ESM show an enormous improvement over those of the TFD model. Also, the ESM is in good agreement with the TFDW model for compressions greater than 2. In the regime of validity of TFDW theory, i.e., compressions greater than 20 and 10 for Al and Cu, respectively, the deviations between the results of the two models are negligible. Hence, the ESM may be used in lieu of the TFDW model for EOS calculations. In the fullerene case, we have obtained the cohesive energy using the models assuming the radius obtained from accurate calculations of the fullerene molecule. We have also obtained the equilibrium radius predicted by each model. The results obtained show that the ESM results are not much of an improvement over the TFD results. This shows that the ESM cannot always improve the results of the TFD model and be a replacement for the TFDW model. However, as in the EOS case, it would give results in good agreement with TFDW results for properties that are dependent on the electron density at the outer reaches of the atom.     

凝聚态物质状态方程的一个数值模型

建立了凝聚态物质的一个三项式状态方程：以Faussurier平均原子模型为基础计算电子热压和电子热能;以Cowan模型为基础计算离子热压和离子热能;用基于实验数据的半经验拟合公式计算物质的冷压和冷能。用实验数据检验了用平均原子模型计算的平均电离度。将状态方程与Hugoniot关系式相结合,计算了Be和Al的冲击绝热曲线,结果充分地展现出电子在高温、高密度条件下的壳层结构效应。     

液相及固/液混合相区金属物态方程Grover模型存在的问题及修正

借助无序熵的概念, 直接推导出了液相金属的物态方程. 再利用固/液混合相区的熔化分数与其中固相、液相比体积之间的一般性关系, 替代了传统Grover模型中采用的熔化分数与温度成正比的近似条件, 得出更准确的固/液混合相区状态方程的表述形式. 修正后的物态方程解决了传统Grover模型中的固线、液线以及熔化线在P-T图上不一致的问题, 得到了更为符合物理事实的结果.     

从建立理想气体状态方程的两条途径谈焦耳定律是否独立

建立理想气体状态方程有两条途径,沿第一条途径焦耳定律是独立的,而沿第二条途径则焦耳定律不独立.     

The self-consistent average phonon equation of state for ionic crystals

The self-consistent average phonon (SCAP) approximation was successful in describing the thermodynamic properties of monatomic solids. This formalism was extended to ionic crystals (specifically sodium chloride) at two levels of approximation: (1) the phonon frequencies replaced by a single average frequency, and (2) the phonon frequencies replaced by two average frequencies corresponding to the usual acoustic and optic phonons. In order to compare with earlier calculations and with experiments various forms of the interatomic potential (with polarization neglected) were used. The SCAP calculation is in good agreement with experiment at low and medium temperatures but underestimates the high temperature thermal expansion. It is concluded that the SCAP formalism with polarization included should give a good approximation to the thermodynamic properties of simple ionic crystals over the entire temperature range.     

On a one-dimensional model for the three-dimensional vorticity equation

The one-dimensional model for the three-dimensional vorticity equation proposed by Constantin, Lax, and Majda is discussed. Some unsatisfactory points are examined, especially when the viscosity is introduced. A different model is suggested, which, while less solvable than the previous one, can be more strictly connected with the three-dimensional vorticity behavior. The study is of interest for the numerical treatment of the three-dimensional vorticity equation.     

Improved equation of state for ionic liquids using surface tension

The major objective of this work was the development of a reliable model to describe volumetric properties of ionic liquids (ILs). In this regard, we have applied the Ihm–Song–Mason equation of state (EOS) to some phosphonium- and imidazolium-based ILs. Three temperature-dependent parameters in the equation of state have been scaled based on the surface tension and the liquid density at room temperature. In order to improve the predictive power of the mentioned EOS for ILs, we have proposed using a simple modification. We have taken 1,228 experimental points to show the reliability of the improved EOS. The comparison of predicted densities with literature data over a broad range of temperature, 293–472 K, and pressures up to 200 MPa led to encouraging results. The average absolute deviation of calculated densities from literature values was found to be 0.75%.     

一种计算氩等离子物态方程的简单模型

将Thomas-Feimi统计模型电离势的数值结果进行函数逼近，给出一个便于近似数值求解的解析表达式和计算电离度的近似计算方法，计算了Ar元素LTE情况下的电离度和物态方程，结果与Saha模型的计算结果和实验结果符合较好.所提出的简单模型也适用于计算混合物物态方程，可以在电磁发射技术领域中的强电离等离子体中有广阔的应用前景. 关键词： 等离子体 物态方程 电离势 电离度     

基于Thomas-Fermi-Kirzhnits模型的物态方程研究

本文针对丝阵Z箍缩等高能量密度物理实验的数值模拟研究, 建立了一种适用温度、密度范围宽的三项式半经验物态方程. 三项式半经验物态方程包括零温自由能项, 电子热贡献项和离子热贡献项. 零温自由能项采用多项式拟合的方法确定. 多项式系数通过多项式计算的结果与高压缩比区域和压缩比为1时零温Thomas-Fermi-Kirzhnits模型计算的结果对应相等得到. 离子对物态方程的热贡献采用一种准谐振模型, 此谐振模型可以描述离子在固态相中的行为, 并且在高温度、低密度区域趋近于理想气体物态方程. 电子对物态方程的热贡献采用含温Thomas-Fermi-Kirzhnits模型计算. 利用所建立的三项式半经验物态方程计算了铝的等温压缩曲线, 并与实验数据做了对比. 给出了很宽温度、密度范围内铝的压强, 其数据与相应的SESAME数据库数据做了对比.     

Lattice QCD calculations for the physical equation of state

In this report we consider the numerical simulations at finite temperature using lattice QCD data for the computation of the thermodynamical quantities including the pressure, energy density and the entropy density. These physical quantities can be related to the equation of state for quarks and gluons. We shall apply the lattice data to the evaluation of the specific structure of the gluon and quark condensates at finite temperature in relation to the deconfinement and chiral phase transitions. Finally we mention the quantum nature of the phases at lower temperatures.     

A new global hydrogen equation of state model

Abstract

Simple statistical mechanics models have been assembled into a wide-range equation of state for the hydrogen isotopes. The solid is represented by an Einstein-Grüneisen model delimited by a Lindemann melting curve. The fluid is represented by an ideal gas plus a soft-sphere fluid configurational term. Dissociation and ionization are approximated by modifying the ideal gas chemical-equilibrium formulation. The T = 0 isotherm and dissociation models have been fitted to a new diamond-anvil isotherm and to laser-generated shock data. The main limitation of the model is in ionization at high compression.     

An equation of state contribution for dipolar and quadrupolar square-well fluids

A dipolar–quadrupolar contribution to the residual Helmholtz energy for a polar square well (a square well plus either a point dipole or a point quadrupole) fluid is developed based on the Padé approximation. Taking the square well system as reference, the contribution is formulated using an expansion for radial distribution function of the reference system. In addition to square well potential parameters the contribution depends only on dipole and quadrupole moments. This term is added as perturbation to a generalized equation of state for square well fluids. The results are then compared with the available simulation data in the literature. With the new equation obtained, it was possible to predict liquid–vapour equilibrium properties and critical properties of polar square well fluids more accurately than with available perturbation theories for multipolar square well systems. Application of the equation of state to a real dipolar (water) and a real quadrupolar (carbon dioxide) fluid indicated that the polar contribution greatly improved the predictions of saturation properties. Accurate prediction of critical properties for polar square well fluids remains as a challenge. This work can be useful in the development of better equations of state.     

A contribution to the equation of state of fluids at low temperatures based on thermodynamic Green's functions

In quantum statistical mechanics, the Green's function formalism provides an expression for the density of a fluid as a four-dimensional momentum-energy integral over the spectral function. This function can be expressed in terms of the complex self-energy of the single-particle excited states. By using the ladder diagram approximation, in a low activity limit at which Fermi-Dirac and Bose-Einstein distributions can be approximated by a Boltzmann distribution, the self-energy has been expressed in terms of the two-body scattering amplitude. Density and pressure can then be expressed in terms of the activity, the temperature, and the two-body scattering phase shifts. A complete numerical evaluation of these results has been made for the case of argon at 100K, represented by a hard-sphere plus square-well potential: results are presented for the complex self-energy, the density, and the pressure as a function of activity. The resulting equation of state is compared to experimental results represented by the Beattie-Bridgeman equation and good agreement is found for the gaseous part of the 100K isotherm. Furthermore, two simple analytic equations of state are derived from these expressions with additional (low-density) approximations, which resemble closely some of the equations obtained from the lattice gas theories.Work supported (in part) by the Defence Research Board of Canada, Grant No. DRB 9510-30, and by the Research Council of Texas A & M University.     

氩等离子体物态方程的TF简化模型

对于高温高压下氩等离子体的电离度和物态方程,本文给出了一种基于Thomas-Feimi(TF)统计模型的简化计算新方法:首先将TF模型电离势的数值结果进行函数逼近,给出一个便于数值求解的计算电离度的近似计算方法,并由此计算了局部热动平衡下的氩等离子体在10～1000 eV高温范围内的物态方程.计算结果与国外报道的其他几种理论模型的计算结果均符合很好,与实验值也吻合较好.本文所提出的简单模型也适用于计算混合物物态方程,可以在电磁发射技术领域中的强电离等离子体中有更为广阔的应用前景.