Quantum corrections to the thermodynamic properties of a two-dimensional fluid with hard-core potential

A simple theory, based on the physical interpretation of the reciprocal of activity, is developed to evaluate the thermodynamic properties of a two-dimensional fluid in the semi-classical limit. The theory is applied to calculate the quantum corrections to the equation of state and excess free energy of two-dimensional fluids, whose molecules interactvia hard-disc and square-well potential. It is found that the quantum effect increases with the increase of density and decrease of temperature.     

Perturbation theory for thermodynamic properties of a ν-dimensional square-well fluid

The Barker-Henderson perturbation theory is used for a ν-dimensional fluid with square-well potential. Analytic expressions are given for the equation of state, excess free energy per particle and internal energy. The numerical results are discussed. A significant feature is the increase of the thermodynamic properties with increasing dimensionality.     

Quantum corrections to thermodynamics of polar hard sphere fluids

The quantum corrections to the thermodynamic properties of polar hard sphere fluids and fluid mixtures are estimated taking into account the influence of dipole and quadrupole moments. Expressions are given for the second virial coefficient, free energy and pressure and results are given for different values ofμ* andϑ*. The first order quantum correction arises due to the translational contribution only. The quantum effect increases with density,μ* andϑ*. Numerical results are also estimated for binary mixtures of (i) hard spheres and dipole hard spheres and (ii) hard spheres and quadrupole hard spheres. The ‘excess’ free energy for dipole hard sphere binary mixture is also reported. It is found that the ‘excess’ quantum effect depends on the concentration and the particle diameter ratio and increases with increase ofμ* andϑ*.     

Thermodynamic properties of a two-dimensional square-well fluid

Analytic expressions for the thermodynamic properties of a classical two-dimensional square-well fluid and the first quantum correction to them are derived using the Barker-Henderson perturbation theory. Numerical results are reported. It is found that the quantum effect, which increases with increase of density, is largely determined by the hard-core and the attractive tail has a minor effect at high density.     

Perturbation theory of polar hard Gaussian overlap fluid mixtures

A perturbation theory of polar hard Gaussian overlap fluid mixture is discussed. Explicit analytic expressions for the second and third varial coefficients are given. Numerical results are estimated for the thermodynamic properties of quadrupolar hard Gaussian overlap fluid and fluid mixture. It is found that the excess free energy and internal energy depend on concentrationsc ₁,c ₂, molecular diameter ratioR, shape parameterK and the quadrupole momentsQ*₁,Q*₂.     

The statistical theory of the condensed system equation of state at high pressures

Abstract

One of the main problems in the statistical physics of condensed systems is the problem of the adequate equation of state to describe the thermodynamical properties of the substance in the wide range of pressure values. Here it is being solved by means of thermodynamic perturbation theory and the integral equations of the statistical theory of dense gases and liquids.     

Equilibrium theory of two-dimensional simple liquids

Using the Wigner-Kirkwood expansion and bare Lennard-Jones (LJ) (12-6) potential, an effectiveLJ potential is derived, which includes the quantum effects through the expressions of the effective diameter∂(T, λ) and well-depth (T, λ). We use theWCA perturbation theory to calculate the free energy and pressure for theLJ and effectiveLJ potentials. Simple analytic expressions are given for the reference system and the first order correction calculated. The results are quite good at high density. The quantum effects on the free energy and pressure are also discussed.     

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.     

The equation of state of the hard-disc fluid revisited

Some points about the search for analytical expressions for the equation of state of the hard-disc fluid are discussed in the light of the most recent advances in the field. New and accurate equations of state for this fluid are proposed.     

H_2+He流体混合物在部分离解区的物态方程

H2+He流体混合物在高温高压下由于氢的离解化学反应形成由H2,H,He三种粒子构成的混合体系,此时粒子间的相互作用较为复杂,离解能也会由于粒子间的这种复杂相互作用而降低.本文利用自洽流体变分理论来研究部分离解区H2+He流体混合物的高温高压物态方程,模型考虑了各种粒子间的相互作用及由温致和压致效应引起的离解能降低的自洽变分修正,并通过自洽流体变分过程对非理想的离解平衡方程求解得到粒子数密度分布,进而对自由能求导获得体系的热力学状态参量.计算结果与已有的冲击波实验数据、蒙特卡罗模拟及其他理论计算进行了比较.     

Thermodynamic properties of hard ellipsoid square-well fluid

The perturbation theory with non-spherical reference system is used for molecular fluid with angle-dependent square-well type potential. Simple analytic expressions are given for the thermodynamic properties such as the equation of state, excess free energy per particle, internal energy and internal heat capacity. The effects of anisotropy on the thermodynamic properties are discussed. The anisotropy effects increase with increase of density and decrease of temperature and depends on the anisotropy parameterx ₀.     

原子-辐射场相互作用系统量子统计力学的相干态表述

用Ｈｅｉｓｅｎｂｅｒｇ－ｗｅｙｌｅ（简称Ｈ－Ｗ）群直积ＳＵ（２）群上的相干态表述了原子－辐射场相互作用系统的量子统计力学,引入一个新定义的分布函数,将平衡态下密度矩阵的Ｂｌｏｃｈ方程转换成可分离变量的偏微分方程,给出了方程的形式解,算符和其平均值的表示。     

教学研究:介绍量子力学几个基本概念——兼答《关于量子几何相位的评注》中的几个主要问题

介绍了量子绝热定理的物理含义及成立的条件，认为有关主要献（Aharonov-Anandan,Bohm，孙昌璞等）的表述是正确的，而《关于量子几何相位的评注》^[1]（以下简称《评注》）相应的表述不完全正确。在此基础上，认为这些献和教材（R.Shankar)得出的涉及Berry绝热相位的一些论述（不含Berry绝热相因子的瞬时能量本征态不满足含时Schroedinger方程等）也是正确的，而《评注》的论述与此相反。《评注》认为只有γn(C)才是Berry相位。本作则倾向于把γn（t）叫做Berry绝热相位，而把γn（C）=γn（T）-γn（0）叫做几何相位（geometric phase)^[2]。     

Quantization of sine-Gordon solitons on the circle: Semiclassical vs. exact results

We consider the semiclassical quantization of sine-Gordon solitons on the circle with periodic and anti-periodic boundary conditions. The 1-loop quantum corrections to the mass of the solitons are determined using zeta function regularization in the integral representation. We compare the semiclassical results with exact numerical calculations in the literature and find excellent agreement even outside the plain semiclassical regime.     

On the study of fluid structure of tetrahydrofuran-n-butyric acid mixture by dielectric studies

The Kirkwood correlation factors g^eff and g_f, excess permittivity ε^E and excess free energy F^E of mixing for the binary mixture of n-butyric acid with tetrahydrofuran (THF) were calculated from the experimental dielectric data obtained at temperatures 303, 308, 313 and 318 K over the entire composition range. The value of g^eff decreases with increase in acid concentration and g_f is found to be greater than unity. At higher temperature, two maxima and two minima have been obtained for ε^E and F^E, respectively. These parameters are analyzed to obtain information about the complex formation through H-bond and dipolar orientation.     

Combined multi-level quantum mechanics theories and molecular mechanics study of water-induced transition state of OH~- + CO_2 reaction in aqueous solution

The presence of a solvent interacting with a system brings about qualitative changes from the corresponding gasphase reactions. A solvent can not only change the energetics along the reaction pathway, but also radically alter the reaction mechanism. Here, we investigated the water-induced transition state of the OH~- + CO_2→ HCO_3~- reaction using a multi-level quantum mechanics and molecular mechanics method with an explicit water model. The solvent energy contribution along the reaction pathway has a maximum value which induces the highest energy point on the potential of mean force. The charge transfer from OH~- to CO_2 results in the breaking of the OH~- solvation shell and the forming of the CO_2 solvation shell. The loss of hydrogen bonds in the OH~-solvation shell without being compensated by the formation of hydrogen bonds in the CO_2 solvation shell induces the transition state in the aqueous solution. The calculated free energy reaction barrier at the CCSD(T)/MM level of theory, 11.8 kcal/mol, agrees very well with the experimental value, 12.1 kcal/mol.     

On the statistical mechanics of rigid particles

In this paper, generalized functions are used in the configuration partition function for fluids composed of arbitrarily shaped, rigid particles. This leads to new expressions for the basic statistical thermodynamic functions and some equations that may be useful in developing approximate theories, such as the scaled particle theory, for such fluids. The results are applicable to a large class of arbitrarily shaped, rigid particles and reduce exactly to the usual hard-sphere expressions.     

关于二元混合物体系的偏摩尔吉布斯自由能的表达式

利用Gibbs-Duhem方程证明了偏摩尔自由能的一个计算公式.