范德瓦耳斯气液状态方程纵横谈

首先强调了范氏方程是气液系统的状态方程,范氏方程可以很好地说明物质气态和液态的相互转变．分析了焦-汤效应,简述了气体的液化与低温的获得．     

Equation of state of a supercritical fluid based on the Ornstein-Zernike equation

A numerical modeling of the thermodynamic properties of a fluid is performed using the method of integral equations. The predictions are compared with the results of MC and MD simulations. The problem of stability of the numerical solution is examined. The methods for correcting the correlation functions and for estimating their uncertainties are proposed.     

An equation of state for alkali metals

Semi-empirical equations of state based on Lindemann's law have been developed to determine the pressure (P) dependence of the melting temperature (T_m) of Li, K, Rb and Cs. The basic inputs are Grüneisen parameter and the bulk modulus. T_m–P variations exhibit maximum melting temperature with concave downwards. The maximum in T_m for Cs is found to occur at pressure of 2.2 GPa whereas for Li, K and Rb it falls in the range of 7–9.5 GPa. The predicted values of T_m as a function of pressure, based on the present empirical relation, fit quite well with the available experimental data. The empirical relation can also be used to extrapolate T_m at higher pressure from the values available at lower pressures.     

范德瓦耳斯和他的状态方程

在物理学发展史上，范德瓦耳斯对气—液流体系统做了开创性的研究工作，建立了人类历史上第一个既能反映气、液各相性质，又能描述相交和临界现象的状态方程。范德瓦耳斯的理论成就和研究方法对热力学、统计力学和低温物理学的发展产生了重要而深远的影响。文章系统探讨了范德瓦耳斯方程产生的历史背景、科学意义和局限性，讨论了范德瓦耳斯的理论和方法对当代物理学的启发意义。     

Infrared photodetectors based on graphene van der Waals heterostructures

We propose and evaluate the graphene layer (GL) infrared photodetectors (GLIPs) based on the van der Waals (vdW) heterostructures with the radiation absorbing GLs. The operation of the GLIPs is associated with the electron photoexcitation from the GL valence band to the continuum states above the inter-GL barriers (either via tunneling or direct transitions to the continuum states). Using the developed device model, we calculate the photodetector characteristics as functions of the GL-vdW heterostructure parameters. We show that due to a relatively large efficiency of the electron photoexcitation and low capture efficiency of the electrons propagating over the barriers in the inter-GL layers, GLIPs should exhibit the elevated photoelectric gain and detector responsivity as well as relatively high detectivity. The possibility of high-speed operation, high conductivity, transparency of the GLIP contact layers, and the sensitivity to normally incident IR radiation provides additional potential advantages in comparison with other IR photodetectors. In particular, the proposed GLIPs can compete with unitravelling-carrier photodetectors.     

Analysis of the critical line network for the van der Waals equation at the van Laar point

The density-density plot of the critical lines of the van der Waals equation at the van Laar point is analyzed through its algebraic properties. It is shown that this curve is an irreducible expression of the fifth degree of genus one. In addition, we show the topology of the second branch, i.e., theT=0 solution, which will interact with the first branch as soon as the energy parameters are slightly different from the van Laar values. Finally, we analyze the behavior of the van der Waals equation near the point at which liquid-liquid separation takes place.     

论范德瓦尔斯a和b参数与温度的关系

范德瓦尔斯方程中a、b参数是否与温度相关,不但不同文献中的说法互不相同,而且有同一文献前后的结论相互矛盾.本文分析了这个令人迷惑的问题.在热力学中a和b参量被处理为与温度无关,它仅仅在临界点附近有效并可以把范德瓦尔斯方程表述为对应态定律;在更加广泛的温度区间a、b参量和温度有关,但是范德瓦尔斯方程却丧失了其独特性.统计...     

A theoretical study of van der Waals neon trimer using Faddeev equations

The properties of two- and three-atomic clusters of neon are studied. Based on the Faddeev differential equations in the total angular momentum representation, we have calculated the lowest binding energies for the neon trimer. The results obtained are compared with previous published results     

Remarks on the Gibbs adsorption equation and the van der Waals,Cahn-Hilliard theory of interfaces

The common statements of the Gibbs adsorption equation, and a phenomenological theory of interfaces (van der Waals, Cahn-Hilliard theory), are summarized, and then two remarks are made. The first is that only certain identifications of the local energy and entropy densities are admissible in the phenomenological theory if it is to be consistent with the adsorption equation. The second is a generalization to any of the relative adsorptions Γ_i(j) in a c-component system, of a microscopic interpetation that Leng, Rowlinson, and Thompson recently gave to Γ₂₍₁₎ in a one-component system, where 2 and 1 refer to the densities of energy and matter, respectively.     

On the generalization of the Van der Waals equation of state for mixtures

For pure fluids, the dependence of the Van der Waals parameter a on the temperature and density have been examined. The Van der Waals equation of state with an accurate hard-core part and temperature- and density-dependent parameters a_ij has been applied to fluid mixtures. The calculated p^E and V^I are compared with experimental data for AN₂ at 1–120 atm.     

论范氏气体方程和理想气体状态方程的关系

一般认为范氏气体方程在大体积极限下和理想气体状态方程一样.不过理想气体还要求满足焦耳定律等,也就是内能对体积的偏导数为零.由于内能对体积的偏导数可以化为物态方程的一阶导数,是否能在状态方程一阶导数这一层次上也要求范氏方程的大体积极限和理想气体一致就值得探讨.结果表明:如果在一阶导数层次上比较,范氏气体方程在大体积极限下不能再回复到理想气体.推广范氏方程让范氏系数依赖于温度,可以得到实际气体在大体积极限下的一个渐近形式.     

Nonclassical behavior of the van der Waals gas

The partition function of the van der Waals gas is represented by a functional integral which is evaluated by summing the value of the integrand over its absolute and all of its secondary maxima. This leads to a one-to-one correspondence with the Ising model with nearest-neighbor interactions only. Whereas the classical behavior of the van der Waals gas is due to the absolute maximum in function space, the nonclassical behavior is shown to derive from the combined contribution of all the secondary maxima. The relation of this work to inverse range expansions and to the droplet model of condensation is discussed.     

A comment on the common one-dimensional derivation of the van der Waals forces

In many physical text-books a simple one-dimensional model is used to derive the characteristic 1/R ⁷-dependence of the attractive van der Waals forces. We show that this calculation is wrong. The long range forces in this simple model are not attractive but repulsive proportional to 1/R ⁶. Only a three-dimensional calculation yields the correct behavior.     

Generic van der Waals equation of state for polymers, modified free volume theory, and the self-diffusion coefficient of polymeric liquids

In this paper, a molecular theory of self-diffusion coefficient is developed for polymeric liquids (melts) on the basis of the integral equation theory for site-site pair correlation functions, the generic van der Waals equation of state, and the modified free volume theory of diffusion. The integral equations supply the pair correlation functions necessary for the generic van der Waals equation of state, which in turn makes it possible to calculate the self-diffusion coefficient on the basis of the modified free volume theory of diffusion. A random distribution is assumed for minimum free volumes for monomers along the chain in the melt. More specifically, a stretched exponential is taken for the distribution function. If the exponents of the distribution function for minimum free volumes for monomers are chosen suitably for linear polymer melts of N monomers, the N dependence of the self-diffusion coefficient is N⁻¹ for the small values of N, an exponent predicted by the Rouse theory, whereas in the range of 2.3?lnN?4.5 the N dependence smoothly crosses over to N⁻², which is reminiscent of the exponent by the reptation theory. However, for lnN?4.5 the N dependence of the self-diffusion coefficient differs from N⁻², but gives an N dependence, N^−2−δ(0<δ<1), consistent with experiment on polymer melts in the range. For polyethylene δ≈0.48 for the parameters chosen for the stretched exponential. Because the stretched exponential function contains undetermined parameters, the N dependence of diffusion becomes semiempirical, but once the parameters are chosen such that the N dependence of D can be successfully given for a polymer melt, the temperature dependence of the self-diffusion coefficient can be well predicted in comparison with experiment. The theory is satisfactorily tested against experimental and simulation data on the temperature dependence of D for polyethylene and polystyrene melts.     

On the van der Waals interaction of carbon nanocones

Based on the continuum Lennard-Jones model, the van der Waals interaction of two concentric and eccentric carbon nanocones with different or identical sizes are investigated in this paper. Also, on the basis of classical mathematical modeling techniques, a new semi-analytical solution is given to evaluate the van der Waals potential energy and interaction force distributions of two concentric carbon nanocones. Finally, a universal potential energy is presented for the carbon nanocones.     

Thermodynamic Curvature of the Binary van der Waals Fluid

The thermodynamic Ricci curvature scalar R has been applied in a number of contexts, mostly for systems characterized by 2D thermodynamic geometries. Calculations of R in thermodynamic geometries of dimension three or greater have been very few, especially in the fluid regime. In this paper, we calculate R for two examples involving binary fluid mixtures: a binary mixture of a van der Waals (vdW) fluid with only repulsive interactions, and a binary vdW mixture with attractive interactions added. In both of these examples, we evaluate R for full 3D thermodynamic geometries. Our finding is that basic physical patterns found for R in the pure fluid are reproduced to a large extent for the binary fluid.     

A study of basis set imbalance effects on the calculation of intramolecular potentials for van der Waals systems

The effects of using different basis sets have been investigated in the study of the intermolecular potential (IMP) of Ne₂, a prototypical van der Waals system. A balancing effect on the strength of the IMP was observed, whereby basis set inclusion of diffuse atom centred polarization functions (ACPFs) in conjunction with bond functions, at the expense of compact ACPFs, resulted in an overestimated IMP, while the opposite situation resulted in an underestimated IMP. Recent proposals made for monitoring the saturation of the SCF total atomic energy [10] and SCF interaction energy [11] are shown to be insufficient criteria with which to judge whether a basis set predicts an underestimated repulsive contribution to the interaction energy at the MP4(SDTQ) level, and hence whether a basis set predicts an overestimate in the IMP. The observations result in an unresolved ambiguity in choosing an appropriate basis set for larger van der Waals systems, where one is forced to make major concessions in basis set quality and where one does not have the experimental results with which to ‘guide’ the competing balance between the above basis functions.     

Raman scattering study of two-dimensional magnetic van der Waals compound VI_3

The layered magnetic van der Waals materials have generated tremendous interest due to their potential applications and importance in fundamental research. Previous x-ray diffraction(XRD) studies on the magnetic van der Waals compound VI_3, revealed a structural transition above the magnetic transition but output controversial analysis on symmetry. In this paper we carried out polarized Raman scattering measurements on VI_3 from 10 K to 300 K, with focus on the two Ag phonon modes at ～ 71.1 cm~(-1) and 128.4 cm~(-1). Our careful symmetry analysis based on the angle-dependent spectra demonstrates that the crystal symmetry can be well described by C_(2h) rather than D_(3d) both above and below structural phase transition. We further performed temperature-dependent Raman experiments to study the magnetism in VI_3. Fano asymmetry and anomalous linewidth drop of two Ag phonon modes at low temperatures, point to a significant spin–phonon coupling. This is also supported by the softening of 71.1-cm~(-1) mode above the magnetic transition. The study provides the fundamental information on lattice dynamics and clarifies the symmetry in VI_3. And spin–phonon coupling existing in a wide temperature range revealed here may be meaningful in applications.