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.     

Thermophysical properties and collision-induced light scattering as a probe for gaseous helium interatomic potentials

Isotropic and anisotropic collision-induced light scattering spectra of helium gas at room temperature 294.5?K and at 99.6?K with the second pressure virial coefficients, second acoustic virial coefficients, viscosity and thermal conductivity have been used for deriving the empirical models of the pair-polarizability trace and anisotropy and the interaction potential. Theoretical zeroth and second moments of the binary spectra using various models for the pair-polarizabilities and interatomic potential are compared with the experimental values performed by Le Duff's group. In addition, third pressure virial coefficients, isotopic thermal factors, self diffusion coefficients, second virial dielectric constants and second Kerr coefficients calculated for these models are compared with experimental ones. The results show that these models are the most accurate models reported to date for this system.     

On the formal equivalence of the Frisch-Berne and Watts perturbation theories to evaluate transport coefficients

A system of hard spheres in contact with a structureless wall is considered. The potential between the wall and the particles is of Lennard-Jones type. The second, the third and the fourth three-dimensional virial coefficient of the adsorption isotherm are calculated. The result being that over an extremely large temperature range the two-dimensional virial treatment is a rather good approximation. Conclusions are drawn about the deviations from Henry's law and the coverage, which can be described by virial expansions. It is doubted whether, from experimentally determined virial coefficients, information about the potential between the adatoms can be extracted.     

On the quantum corrections to the virial coefficients of the equation of state of a fluid

The first quantum correction to the virial coefficients of the equation of state of a fluid is derived in the presence of a weak three-body potential ?(i, j, k). Results for the third and fourth virial coefficients are given. Representing the potential energy of interaction of a pair and a triplet, by the Lennard-Jones (12-6) model and the triple dipole dispersion potential model of Axilrod and Teller, the first quantum correction to the third virial coefficient is calculated for many values of T*. The theoretical result is compared with the experimental data of helium.     

On the Helmholtz Potential Metric: The Isotherm Length-Work Theorem

In this paper we introduce the Isotherm Length-Work theorem using the Helmholtz potential metric and the virial expansion of pressure in inverse power of molar volume. The theorem tells us what length of a thermodynamical system described by equation of state through virial expansion along isotherms actually is with such a metric. We also give explicit solutions for thermodynamic length along isotherms in the case of first, second and third order expansion     

On the gamma-type heterogeneity of adsorbing surface

The gamma-type distributions in adsorption energies of sites, subject to the Langmuir probability of occupancy, are analyzed with the aim to develop criteria for the reliability of estimates of the energy distribution from experimental adsorption data. For broad distributions this model leads to preferential occupation of sites with highest adsorption energies, which causes the breakdown of the virial expansion of adsorption isotherms. The resulting isotherms can be discriminated from simple Langmuir isotherms only for not too narrow distributions and the critical criterion is given. Finally, it is pointed out that experimental data do not allow to discern between a continuous and discrete distribution. All the conclusions can be generalized to other types of distribution in adsorption energies, including composite distributions.     

RESEARCH NOTE A method for predicting the virial coefficients of hard linear homonuclear molecules

This paper proposes a simple method for predicting the virial coefficients, up to the fifth, for hard linear homonuclear molecules. The method uses the virial coefficients for hard spherocylinders and hard linear tangent spheres to obtain the virial coefficients of linear fused hard spheres. The results are in very good agreement with the known values for the latter kind of molecules. Thus the method is suitable for predictive purposes when virial coefficients are not known, which makes it useful for the derivation of certain equations of state.     

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.     

Influence of heterogeneity on higher gas-solid virial coefficients

Using the virial formalism and the model of localized adsorption, an attempt is made to investigate the influence of heterogeneity on higher gas-solid virial coefficients.     

Density expansion of the magnetic susceptibility

The pressure of a system may be expanded as a power series in the density, whose coefficients are the virial coefficients. In this paper, the magnetic susceptibility of a $\text{spin}\text{-}\text{1}\text{2}$ fermion system is also expanded in powers of density. This process explicitly separates the temperature and density dependence of the magnetic susceptibility. The coefficients of this series are shown to be related to certain virial coefficients. The first (previously established) and second corrections to Curie's law are explicitly expressed in terms of second and third virial coefficients. These corrections to Curie's law are small for temperatures above 4K, but become important below that temperature. The first correction has been previously measured. Given a set of second and third virial coefficients, the importance of the second correction can be calculated immediately at any density of interest.     

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.     

Magnetic anisotropies of some aromatic molecules

A common method for the estimation of uncertainties introduced by surface and impurity effects into experimental measurements of virial coefficients is described. The sign and the amplitude of the second virial coefficient response to perturbation caused by adsorption of molecules on the internal surface of the vessel have been determined. It has been shown that the magnitude of the second virial coefficient distortion depends on such competing factors as adsorption-impurity perturbation parameter, mixture composition which has been corrected taking into account this perturbation, and the nature of the impurity expressed in terms of its second virial coefficient and of the solvent-impurity cross second virial coefficient. The character of the Lennard-Jones 12–6 potential parameters perturbation, caused by the adsorption-impurity effects, is determined using second virial coefficient data inversion technique. Numerical estimates are made for nitrogen, helium, argon, xenon, their binary mixtures, and also for krypton-sulphur hexafluoride gaseous mixtures.     

The influence of intermolecular interactions on the Kerr effect in gases

Expressions are derived for the second and third Kerr virial coefficients, B _K and C _K, of spherical top molecules in terms of irreducible cluster polarizabilities, and values are calculated using the dipole-induced dipole model for argon, krypton, xenon, methane, tetrafluoromethane, neopentane and sulphur hexafluoride. For mixtures of rare gases it is shown that the collision-induced dipole moment makes a negligible contribution to B _K. The effect of the choice of intermolecular potential function on the calculated second Kerr virial coefficients is also demonstrated. It is found that the predominant contributions to C _K arise from the pair polarizability, and that the triplet polarizability is only of minor importance.     

Universality in a 2-component fermi system at finite temperature

Thermodynamic properties of a Fermi system close to the unitarity limit, where the 2-body scattering length a approaches +/-infinity, are studied in the high temperature Boltzmann regime. For dilute systems the virial expansion coefficients in the Boltzmann regime are expected, from general arguments, to be universal. A model independent finite temperature T calculation of the third virial coefficient b3(T) is presented. At the unitarity limit, b3infinity approximately 1.11 is a universal number. The energy density up to the third virial expansion is derived. These calculations are of interest in dilute neutron matter and could be tested in current atomic experiments on dilute Fermi gases near the Feshbach resonance.     

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.     

Delta-function expansion of Mayer function with application to virial coefficients

The Mayer cluster integrals of a fluid with smooth, repulsive interactions are expanded in orders of a well-defined softness parameter. To first but not second order in softness, all virial coefficients are given by their hard-sphere forms with an effective diameter. A closed asymptotic expression is derived for the third virial coefficient which gives excellent results for the inverse power and exponential potentials.     

A note on the Percus-Yevick and hypernetted chain theories of adsorption: The second and third virial coefficients for a hard-sphere gas in contact with a wall with a soft surface layer

The first three virial coefficients of a new type in the density expansion of the adsorption isotherm for hard spheres in contact with a wall with a soft surface layer are calculated. The results are compared with those for hard spheres in contact with a hard wall.     

Statistical mechanics of linear molecules II: Density expansions,intermolecular potentials and virial coefficients

In the Percus-Yevick and convolution-hypernetted-chain equations obtained in the previous paper, a density expansion for the correlation functions is introduced. To first order in the density, the so-obtained equations are identical and exact. By solving these, the pair correlation functions for linear molecules are obtained explicitly to first order in the density and for arbitrary order in the potential perturbation expansion. From these, the second and third virial coefficients can be extracted for all orders. A generalized charge is defined and used to give generalized multipole expansions for the intermolecular potential. Explicit expressions for this potential model are given up to fourth order. It is shown how the correlation functions, and second and third virial coefficients can be obtained to fourth order for any intermolecular potential with the same perturbation structure.     

Equilibrium properties of hard non-sphere fluids

Derivation of the thermodynamic properties of fluids of hard non-spherical molecules of arbitrary symmetry is based on the decoupling approximation. Theoretical expressions are given and calculations made for the equation of state and virial coefficients for hard ellipsoids. These results are compared with Monte Carlo values and show fair agreement in all cases. The theoretical predictions for the equation of state for binary mixtures are compared with the Monte Carlo results for hard spheres and hard prolate spherocylinders. Theoretical expressions for the first order quantum correction to the free energy, pressure and virial coefficients are also given. The quantum effects increase with increase of density and with increase of anisotropy parameter.