The effect of steepness of soft-core square-well potential model on some fluid properties

The effect of repulsive steepness of the soft-core square well (SCSW) potential model on the second virial coefficient, critical behaviour (two- phase region and the position of critical point), and coordination number are investigated. The soft-core thermodynamic perturbation theory (TPT) presented by Weeks-Chandler-Anderson (WCA) recently developed by Ben-Amotz and Stell (BAS) has been used for the reference system, and the Barker-Henderson TPT for the perturbed system. The Barker-Henderson macroscopic compressibility approximation has been used for all order perturbation terms in which the second-order one is improved by assuming that the molecules in every two neighbouring shells are correlated upon the original assumption. By using the hard-sphere isothermal compressibility consistency for the radial distribution function (RDF), an analytical closed expression has been derived for the Helmholtz free energy function contained effective hard-sphere diameter. The accuracy of the model has been examined for the hard-core system, and an appropriate range found for the attractive width of the potential well (R), then the effect of steepness parameter on the critical quantities, coordination number, and the inversion temperature of the second virial coefficient, has been investigated qualitatively. The predicted results are in good agreement with the computer simulation data for the critical constants, and coordination number at the limit of the hard-core square-well potential model at least qualitatively, and for the attractive range 1.55 ≤ R ≤ 1.7, quantitatively. It was found that the steepness of the potential model has a marginal effect on the critical behaviour, and also every thermodynamic quantity at low and medium temperatures for which the molecular penetration is negligible, but since the penetration at high temperatures is significant, the role of the steepness of potential on the inversion temperature of the second virial coefficient and coordination number is highlighted.     

A simple and accurate equation of state for hard-disk fluids

A long-standing problem for hard-disk fluids is to find a simple and accurate equation of state. By observing the known updated virial coefficients from up to , we obtain an accurate empirical formula, with errors less than 0.5%. We further assume that the empirical formula is valid for all the virial coefficients. Using this assumption, we obtain a simple and accurate equation of state. In the density range 0<ρa²≤0.83, the predicted pressures are in good agreement with the simulation results. For 0<ρa²≤0.70, the errors are less than 0.007%. Even at ρa²=0.83, the error is only 0.5%.     

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.     

Heat capacities of the dipolar Yukawa model polar fluid

The Stockmayer fluid is often used to describe a polar fluid. The dipolar Yukawa (DY) fluid is also a useful model for such fluids and is convenient for theoretical applications. Here we use the mean spherical approximation (MSA) and perturbation theory (PT) to study the heat capacities of the DY fluid model of a polar fluid and compare these results with Monte Carlo simulations for this model polar fluid. We find that the DY fluid shows the same features as the Stockmayer fluid does; demonstrating the utility of the DY fluid and further finding that the MSA and PT approaches give reasonably accurate results for the heat capacity.     

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.     

Evaluation of thesscf andpy approximations for quadrupolar fluids

Two approximations, the single super chainf-expansion (sscf), and Percus-Yevick (py) approximation, are evaluated for a molecular fluid in which the molecules interact with a pair potential, that is the sum of Lennard-Jones and quadrupole-quadrupole parts at two values of reduced quadrupole moment. These results are compared with Monte-Carlo results. Except for the harmonic coefficienth (222;r), thesscf approximation seems to be quite accurate for the lower value of quadrupole moment but at higher valuespy approximation produces much better results except forh(220;r).     

Modified hypernetted-chain equation for the ground state of Bose fluids

Summary The modified hypernetted-chain equation is used to study the ground state of Bose fluids in the Jastrow approximation. We test the equation for different forms of the pair interaction and of the Jastrow pseudopotential and in all cases the energy of⁴He is given with an error not larger than 0.1 K at all densities. The effect of a triplet term in the wavefunction is also studied.

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Riassunto L'equazione integrale HNC modificata è applicata allo studio dello stato fondamentale di un fluido di Bose nell'approssimazione di Jastrow per diverse espressioni della interazione binaria e forme diverse della correlazione di Jastrow. In tutti i casi l'energia per⁴He è calcolata con un errore non superiore a 0.1 K a tutte le densità. Si considera inoltre l'effetto di una correlazione a tre corpi nella funzione d'onda.

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Резюме модифицированное уравнение цепочки используется для исследования основного состояния Ъозе-жидкости в приближении Ястрова. Мы проверяем уравнение для различных форм парного взаимодействия и псевдопотенциала Ястрова. Во всех случаях приводится энергия⁴He с погрешностью не более, чем 0.1 K для всех плотностей. Также исследуется влияине триплетного члена на волновую функцию.

     

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.     

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.     

An isothermal equation of state for solids

An isothermal equation of state (EOS) for solids, recently suggested by the authors in the realistic form, V/V₀=f(P), with relative volume as the dependent and the pressure as the independent variable, was shown to have an advantage for some close-packed materials in that it allows B′_∞=(∂B_s/∂P)_s(P→∞) to be fitted, and this is where the usual standard equations fail. In the present study, our EOS is applied to a number of inorganic as well as organic solids, including alloys, glasses, rubbers and plastics; varying widely in their bonding and structural characteristics, as well as in their bulk modulus values. A very good agreement is observed between the data and fits. The results obtained are compared with those from two well-known equations, expressible in the realistic form, proposed by Murnaghan and Luban. Further, the results are also compared with those from the widely used two- and three-parameter EOSs, expressible in the unrealistic form only, P=f(V/V₀), proposed by Birch—and also with those from the EOS model of Keane in which B′_∞ is explicitly expressed as an equation of state parameter. The results obtained from our model compare well to these EOSs. Our EOS, in general, yields the smallest mean-squared deviations between data and fits. The values of B′_∞calculated from our EOS are compared with those from Keane's model. Further, we have studied the variation of B′_∞with temperature using the experimental isotherms of Mo and W at 10 different temperatures ranging from 100 to 1000 K, and observed that the values of B′_∞ yielded by our model and that of Keane vary, as expected, within a narrow range. Furthermore, our EOS is applied to study the stability of the fit parameters with variation in the pressure ranges with reference to the isothermal compression data on Mo and W—and also to study the variation of isothermal bulk modulus with pressure, with reference to the ultrasonic data on NaCl and noted a very good agreement with experiment. In addition, our model is applied, with B₀ and B′₀ constrained to the theoretical values, to the five theoretical isotherms of MgO at 300, 500, 1000, 1500 and 2000 K obtained on the basis of a first principles approach—a good agreement is observed with the predictions, and the values of B′_∞ inferred at different temperatures tend to converge to a constant value.     

Exact equations of state for one-dimensional chain fluids

Using the isothermal-isobaric ensemble, exact equations of state are derived for three classical models of one-dimensional chain fluids. Each chain molecule is modeled by a series of linked sites which interact through nearest-neighbor bond potentials. In two of the models, the intramolecular bonds are modeled by infinitely deep square-well potentials, while in the third, the bonds are modeled by a harmonic potential. Intermolecular interactions are modeled by a hard-rod potential. Numerical results are presented for dimer and 8-mer fluids which illustrate the influence of chain length, well width and spring constant on the compressibility factor. The effect of adding an infinitely weak, infinitely long-ranged attractive interaction between the sites is also considered. The attractive tail induces a first-order phase transition of the gas-liquid type in all of the chain models. For certain values of the model parameters, however, two of the models show evidence of a second gas-liquid type transition, which appears to be associated with chain collapse.     

An alternative construction of the Percus-Yevick equation based on the equilibrium BBGKY hierarchy

The existing derivations of the Percus-Yevick equation are not readily extendable into the nonequilibrium domain. In particular, the elegant Percus functional construction relies on a test particle theorem which lacks an exact nonequilibrium generalization. We propose here a new construction which utilizes some elementary ideas of functional expansions together with the equilibrium BBGKY hierarchy of equations. Also, we feel this new construction provides fresh insight into the physical basis of the equilibrium Percus-Yevick equation.This research was supported in part by a grant from the Faculty Research Award Program of the City University of New York.     

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。     

Universal cubic equation of state and contact values of the radial distribution functions for multi-component additive hard-sphere mixtures

A universal cubic equation of state (UC EOS) is proposed based on a modification of the virial Percus-Yevick (PY) integral equation EOS for hard-sphere fluid. The UC EOS is extended to multi-component hard-sphere mixtures based on a modification of Lebowitz solution of PY equation for hard-sphere mixtures. And expressions of the radial distribution functions at contact (RDFC) are improved with the form as simple as the original one. The numerical results for the compressibility factor and RDFC are in good agreement with the simulation results. The average errors of the compressibility factor relative to MC data are 3.40%, 1.84% and 0.92% for CP3P, BMCSL equations and UC EOS, respectively. The UC EOS is a unique cubic one with satisfactory precision among many EOSs in the literature both for pure and mixture fluids of hard spheres.     

High-pressure equation of state for solid krypton from interatomic potentials

The pressure-volume isotherm for krypton at 300 K is evaluated by the Monte Carlo method using pair and three-body potentials. The pair potentials used are that of Aziz and Slaman and a slightly modified version of their potential which gives better agreement with high-energy scattering data. The three-body potentials considered are the Axilrod-Teller interaction and the first-order three-body exchange interaction as parametrized by Loubeyre. The results are compared with recent measurements at pressures up to 300 kbar and the implications of the comparison are discussed. The best agreement with experiment is found using the Axilrod-Teller interaction as the only many-body interaction, indicating that the three-body exchange interaction is to a large extent canceled by higher many-body interactions, at least in the highly symmetrical environment of the crystal.This paper is dedicted to Howard Reiss on the occasion of his 66th birthday.     

Neutron star equation of state in density dependent relativistic Hartree-Fock theory*

The equation of state of neutron stars is studied in the newly developed density dependent relativistic Hartree-Fock (DDRHF) theory with the effective interaction PKO1 and applied to describe the properties of neutron stars. The results are compared with the recent observational data of compact stars and those calculated with the relativistic mean field (RMF) effective interactions. The maximum mass of neutron stars calculated with PKO1 is about 2.45 M☉, which consists with high pulsar mass from PSR B1516+02B recently reported. The influence of Fock terms on the cooling of neutron stars is discussed as well.     

无限深方势阱本征值和本征态的三种求解方法

一维无限深方势阱模型是量子力学理想模型,经典教材中势阱的边界一般取得比较特殊.或关于坐标原点具有对称性,或势阱左边界位于坐标原点.本文首先展示了如何利用3种方法求解一维任意边界无限深方势阱能量本征值和对应的本征态,不同方法得到的结果彼此之间等价,讨论分析了这3种方法的推导结果,然后得到关于一维任意边界无限深方势阱能量本征值和本征态的通式,从中比较容易看出这两个物理量均与阱宽有关,并且本征波函数与边界值有关,最后将一维结果拓展到二维和三维任意边界无限深方势阱情况.     

Nuclear matter equation of state and σ-meson parameters

We try to determine phenomenologically the extent of in-medium modification of σ-meson parameters so that the saturation observables of the nuclear matter equation of state (EOS) are reproduced. To calculate the EOS we have used Brueckner-Bethe-Goldstone formalism with Bonn potential as two-body interaction. We find that it is possible to understand all the saturation observables, namely, saturation density, energy per nucleon and incompressibility, by incorporating in-medium modification of σ-meson-nucleon coupling constant and σ-meson mass by a few per cent.