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.     

Two Hard Spheres in a Spherical Pore: Exact Analytic Results in Two and Three Dimensions

The partition function and the one- and two-body distribution functions are evaluated for two hard spheres with different sizes constrained into a spherical pore. The equivalent problem for hard disks is addressed too. We establish a relation valid for any dimension between these partition functions, second virial coefficient for inhomogeneous systems in a spherical pore, and third virial coefficients for polydisperse hard spheres mixtures. Using the established relation we were able to evaluate the cluster integral b ₂(V) related with the second virial coefficient for the Hard Disc system into a circular pore. Finally, we analyse the behaviour of the obtained expressions near the maximum density.     

Radial distribution function and second virial coefficient for interacting bosons

We have studied the radial distribution function and the second virial coefficient of interacting bosons. The second virial coefficient has been deduced theoretically and is in good agreement with experimental values. The third virial coefficient has been calculated from the experimental values of the pressure.     

Non-universal thermodynamics of a strongly interacting inhomogeneous Fermi gas using the quantum virial expansion

Within a quantum virial expansion, we investigate theoretically the violation of universal thermodynamics for a strongly interacting unitary Fermi gas trapped in a harmonic potential. The violation is caused by the existence and anisotropy of the trapping potential and a finite-range of the two-body interaction. We calculate the second virial coefficient by solving a two-fermion problem in 3D uniform harmonic traps, as well as in anisotropic traps. In the unitarity limit, the universal value of the trapped second virial coefficient is 1/4. We discuss in detail the non-universal correction to the second virial coefficient and to the equation of state.     

Molar volume for mixtures of methane with krypton,argon, ethane and carbon monoxide using the ISM equation of state

In this paper, an analytical equation of state (EoS) proposed by Ihm–Song–Mason (ISM) was employed to calculate the molar volume of mixtures of methane with krypton, argon, ethane and carbon monoxide. The best available pair interaction potential energy has been used to evaluate the second virial coefficients required by the ISM EoS. The calculated values of second virial coefficients were applied to the ISM EOS to predict the molar volumes for the above mentioned mixtures. Agreement with the experiment is excellent for all systems.     

Correlation of volumetric properties of binary mixtures of some ionic liquids with alcohols using equation of state

In our previous paper, we extended the Tao and Mason equation of state (TM EOS) to pure ionic liquids. Here we apply TM EOS based on statistical?Cmechanical perturbation theory to binary mixtures of ionic liquids. Three temperature-dependent quantities are needed to use the equation of state: the second virial coefficient, B ₂, effective van der Waals co-volume, b, and a scaling factor, ??. The second virial coefficients are calculated from a correlation that uses the normal boiling temperature and normal boiling density. ?? and b can also be calculated from the second virial coefficient by scaling. In this procedure, the number of input parameters, for calculation of B ₂, ??, and b reduced from 5 (i.e., critical temperature, critical pressure, acetric factor, Boyle temperature T _B, and the Boyle volume ?? _B) to 2 (i.e., T _bp and ?? _bp). At close inspection of the deviations given in this work, the TM EOS predicts the densities with a mean AAD of 1.69%. The density of selected system obtained from the TM EOS has been compared with those calculated from perturbed-hard-sphere equation of state. Our results are in favor of the preference of the TM EOS over another equation of state. The overall average absolute deviation for 428 data points that calculated by perturbed-hard-sphere equation of state is 2.60%.     

H-H and C-H coupling constants in neutral and protonated azines

New measurements are reported of the density dependent depolarization ratio for argon, krypton, xenon, methane and sulphur hexafluoride, and the results are analysed to provide values for the second and third depolarization virial coefficients. The relationships between the second depolarization virial coefficient, the zeroth moment of the two-body Rayleigh spectrum and the second Kerr virial coefficient are considered, and it is shown that they now provide consistent results for the collision-induced pair polarizability anisotropy. Former inconsistencies are attributed to insufficient allowance for the effects of three-body interactions. Calculations of the second and third depolarization virial coefficients based on the DID model and using the Maitland-Smith potential are in excellent agreement with the experimental results for argon, krypton and xenon.     

On the virial coefficients of the equation of state of a system of non-axial molecules

A thermodynamic perturbation theory in which all angle-dependent interactions are considered as a perturbation of the central potential is applied to calculate the second and third virial coefficients of a fluid composed of non-axial molecules. The influence of a large number of anisotropic pair- and three-body non-ādditive interactions has been considered. Experimental values have been used for the dipole moment, quadrupole tensor and for anisotropic polarizability. The parameters for the central Lennard-Jones (12-6) potential have been determined from the viscosity data. The relative contribution of each branch of pair and triplet interactions has been evaluated as a function of temperature for molecules possessing both the axial- and non-axial symmetries. It has been shown that the non-axial approximation is an improvement over the axial one. Theoretical results have been compared with the experimental data of CH₃OH.     

Evaluating virial coefficients for multicomponent mixtures: hard sphere mixtures and flexible chains

A new algorithm to compute the virial coefficients of multicomponent mixtures is proposed. The number of graphs that must be evaluated increases dramatically in a multicomponent mixture so that it becomes difficult to enumerate and compute all possible graphs. However, once all of them are known and evaluated, the virial coefficient of the mixture can be evaluated for any composition. If one is interested in the virial coefficient of a mixture of a certain composition, then a simpler approach can be followed. Starting from the graphs of a pure fluid, we assign a random chemical identity to each of the molecules of the graph. The probability of assigning a given chemical identity is taken from the composition of the mixture. In this way composition is treated as a random variable within the Monte Carlo procedure which determines the virial coefficient. The algorithm is checked by comparison with the virial coefficients of binary hard spheres mixtures which are well known. Good agreement is found. The procedure is then extended to multicomponent mixtures of hard spheres. Finally the procedure is applied to the determination of the virial coefficients of a flexible molecule. For flexible molecules the possible configurations of the molecules are treated as different components of the mixture. In this way we present what appears to be the first determination of the third and fourth virial coefficients of polymers in the continuum.     

Effect of crystal potential on electric field gradient calculations due to impurities in cubic metals

The electric field gradients caused by interstitial and substitutional point defects in f.c.c. metals have been studied. The perturbation on the host electron distribution has been calculated self-consistently using density functional formalism. The effect of strain caused by size difference between host and impurity atoms is treated in the point-ion model. The influence of the host potential on impurity perturbation is incorporated within the spherical solid approximation. The theory is applied to positive muon and mono-vacancy in Al and Cu hosts. The theoretical results are in good agreement with experiment and illustrate the importance of both strain and conduction electron contribution to the electric field gradient.     

Bound states and equation of state for nondegenerate quantum systems with short-range interactions

The influence of bound states on the second virial coefficient for systems with short-range interactions is investigated, and the equation of state is determined by different methods. The dissociation equilibrium between bound and free particles is discussed.     

Thermodynamics of the Stockmayer fluid in an applied field

The thermodynamic properties of the Stockmayer fluid in an applied field are studied using theory and computer simulation. Theoretical expressions for the second and third virial coefficients are obtained in terms of the dipolar coupling constant (λ, measuring the strength of dipolar interactions as compared to thermal energy) and dipole–field interaction energy (α, being proportional to the applied field strength). These expressions are tested against numerical results obtained by Mayer sampling calculations. The expression for the second virial coefficient contains terms up to λ⁴, and is found to be accurate over realistic ranges of dipole moment and temperature, and over the entire range of the applied field strength (from zero to infinity). The corresponding expression for the third virial coefficient is truncated at λ³, and is not very accurate: higher order terms are very difficult to calculate. The virial coefficients are incorporated in to a thermodynamic theory based on a logarithmic representation of the Helmholtz free energy. This theory is designed to retain the input virial coefficients, and account for some higher order terms in the sense of a resummation. The compressibility factor is obtained from the theory and compared to results from molecular dynamics simulations with a typical value λ = 1. Despite the mathematical approximations of the virial coefficients, the theory captures the effects of the applied field very well. Finally, the vapour–liquid critical parameters are determined from the theory, and compared to published simulation results; the agreement between the theory and simulations is good.     

Second virial coefficient of homonuclear two-centre Lennard-Jones molecules

A semiempirical expression based on numerical values of the second virial coefficient of the two-centre Lennard-Jones molecules and on the theoretical expression for hard dumbells is given. The resulting expression possesses the form developed formerly for the second virial coefficient of the Kihara non-spherical molecules and reproduces fairly well the correct limits at high temperatures. It allows the prediction of the second virial coefficient at reduced temperatures T*≧0·5.     

第二位力系数与体积关系的理论证明

用参数变换方法,研究了位形配分函数对体积的一次导数,得到了第二位力系数,从而证明了第二位力系数与体积无关,并对现有教材所给出的条件加以补充。     

Statistical mechanics of linear molecules I: Percus-Yevick and convolution-hypernetted-chain approximations

It is shown how the Percus-Yevick and convolution-hypernetted-chain approximations for dense fluids of linear molecules can be brought into practically applicable forms by using cartesian tensor formalism and pertubation theory. The possibility of expanding the intermolecular potential and the correlation functions is discussed in detail. Also, exact reductions for the Ornstein-Zernike relation in real space and for the Percus-Yevick equation are given. Some other approaches to the statistical mechanics of linear molecules are critically discussed. It is shown in particular, that the mean spherical model is an inconsistent type of perturbation theory. The necessary cartesian tensor formulae are given in appendices as well as formally exact expressions for the second virial coefficient and for the Fourier-transformed Ornstein-Zernike relation.     

Critical properties of non-spherical molecule fluids from the virial expansion

Critical constants of pure fluids (as important reference data in constructing vapour-liquid phase diagrams and basic input of various estimation methods) were determined for systems of non-spherical Kihara molecules; values of the critical temperature, density, compression factor and pressure of fluids composed of prolate and oblate molecules were evaluated from the fourth-order virial expansion. The second and third virial coefficients of the Kihara molecules were determined by applying the recently proposed method in which the effect of molecular core geometry and functional dependence of a pair interaction on the surface-surface distance are factorized and the former contribution determined from a formula for the corresponding hard convex body virial coefficient. The virial expansion for non-spherical Kihara molecules is applied to determine the critical constants of n-alkanes (methane to octane) and cyclic hydrocarbons (cyclopentane, cyclohexane, benzene and naphthalene); a fair agreement with experimental data was found.     

Interaction second virial co-efficient of polar-quadrupolar gas mixtures

The interaction second virial coefficient of a binary polar-quadrupolar gas mixtures of non-spherical molecules of arbitrary symmetry has been calculated for a set of unlike force parameters which is obtained from the force parameters for like interactions by using empirical combination rules. In the calculation the influence of anisotropic interactions has been considered. The relative contribution of each branch of interactions has been evaluated as a function of temperature. The theoretical results have been compared with the experimental data of CH₃F + N₂, CH₃F + CO₂ and CH₃Cl + CS₂. The agreement between theory and experiment is satisfactory.     

线型分子势能函数及第二维里系数计算

本文以两中心的Lennard—Jones（2CLJ）流体为研究对象,通过引入与温度相关的势能参数,提出了改进型的2CLJDQP势能函数模型。应用此模型计算了乙烷（C2H6）、六氟乙烷（C2F6）、氟甲烷（CH3F）、氯甲烷（CH3C1）、1,1,1-三氟乙烷（CH3CF3）、二氟乙烷（CH3CHF2）的第二维里系数,较...     

The intermolecular potential energy functions of krypton and xenon

The intermolecular potential energy functions for krypton and xenon have been determined using new semi-inversion techniques. These techniques, which have previously been applied to the data for argon, enable information about intermolecular forces to be obtained directly from second virial coefficient and gas viscosities measurements.     

Atomic interactions in neon and helium

The first two quantum corrections to the second virial coefficients of the Smith-Thakkar potential are calculated. Parameters for neon and helium, gases in which quantum effects are important, are then determined by fitting to semiempirical dispersion coefficients and experimental second virial coefficients. Viscosity coefficients for both gases and vibrational energy level spacings for the neon dimer are calculated as independent tests of the potentials. Overall agreement with experiment is excellent for neon and moderate for helium. The previously determined parameters for argon are found to be only very slightly perturbed by the inclusion of quantum corrections in the calculated second virial coefficients.