Pressure Virial Coefficients Research Articles

The reaction field in continuum models and molecular statistical theories of dielectric fluids

Abstract The first terms of the density expansion of the reaction field expressions in the molecular statistical theory, agree with the high temperature limit of the pressure virial coefficients for dipolar spheres and ellipsoids. Comparison is made between the reaction field expressions obtained from the continuum theory, simulated second pressure virial coefficients for ellipsoidal dipoles, and approximations which can be evaluated analytically using elementary methods. The classical expression fails particularly for oblate molecules. The analysis of the third pressure virial coefficient for hard sphere dipoles shows that the shielding of the dipole-dipole interaction by a third particle is overestimated in the Onsager model.

The second virial coefficient of quadrupolar dumbells

To study the effect of the shape of molecules on properties of polar fluids, the second pressure virial coefficient,B(T), of quadrupolar hard homonuclear dumbells is investigated both numerically and analytically. Convergence of the expansion ofB(T) about the hard dumbell reference is examined and a simple approximate analytic formula is derived which provides a good estimate ofB(T) for temperatures higher than the Boyle temperature,TB. BelowTB the examined expansion methods break down. Independently of the calculations ofB(T), an approximate analytic expression of the average Boltzmann factor of the model considered has been also derived.

The effect of molecular polarizability on the properties of fluids

We report a detailed study of the effect of polarizability (both isotropic and anisotropic) on the properties of dilute fluids and binary fluid mixtures. The properties studied include the second pressure and dielectric virial coefficients, the minimum pair interaction energy and structure, the radial distribution function and the structure factor. Our results show that polarizability makes a significant contribution to all the properties studied. The effect of polarizability becomes more important when mixture components have quadrupole moments of opposite signs. Anisotropy of polarizability in general is less important, except in the case of the second dielectric virial coefficient, or when the two molecules have quadrupoles of opposite signs. From the magnitude of these contributions, it also appears unlikely that effective models for dilute fluids can account for polarizability adequately, when it is not explicitly included in the potential model.

Analytical approximations to virial coefficients for pure and mixed systems

Analytic approximations, in the form of finite polynomial expansions in T -1, are given to the pressure virial coefficients of pure Lennard-Jones systems with strictly pairwise-additive potentials. Results are given through fifth order in both two and three dimensions. These analytic forms are combined in Pade approximants for the compressibility factor in three dimensions, and the critical constants found from them are in agreement with those obtained elsewhere; equally good agreement is found in the two dimensional case. Also reported are calculations of two- and three-dimensional third virial coefficients of mixtures of the heavier rare gases and simple molecules. The interactions are represented by single centre models, Lennard-Jones potentials which are shown to give mixed second virial coefficients in reasonable agreement with experimental values. The calculated and experimental third virials do not agree, but the inclusion of three-body interactions, through the triple-dipole and related terms, imp...

The effect of the anisotropy of the intermolecular potential on the second pressure virial coefficient of CH4

The effect of the anisotropy of the intermolecular potential energy on the second pressure virial coefficient of methane is studied. It is found that the largest contribution (≳50%) to the anisotropy correction arises from the short range repulsive potential. The most important long range contribution is due to the anisotropic dispersion potential, which involves the dipole–quadrupole polarizability A. Difficulties met in determining the magnitude of A from virial coefficient data are discussed.

Low density properties of a two dimensional dipolar fluid

Second and third pressure and dielectric virial coefficients are calculated for a two dimensional fluid of hard discs with embedded central point dipoles. These exact results are compared with the predictions of various integral equation theories based upon the hypernetted chain (HNC) approximation. The linearized (LHNC) equation gives poor pressure virial coefficients B p* and C p*, but good results for the dielectric coefficients B ε* and C ε*. The quadratic (QHNC) equation gives a good approximation to B p* and C p*, even for large values of the dipole moment μ*, but C ε* is very poor and is of the wrong sign for μ*2≳2·5. This failure is traced to the arbitrary neglect of rotational invariants other than 1, Δ(12) and D(12) in the eigenfunction expansion of the pair correlation functions h(12) and c(12) of the fluid. We also compute the critical point of the fluid. The critical constants are very different from those previously calculated in the mean spherical approximation (MSA).

Les coefficients du viriel de la constante diélectrique et de la pression des gaz imparfaits : mélange N2O–argon

Dielectric and pressure virial coefficients for six different mixtures of N2O–argon have been measured at 30.1 °C. The quadrupole moment of N2O calculated from the dielectric second virial coefficient of the mixture N2O–argon is 3.4 × 10−26 esu cm2. This value is identical to that obtained by Kirouac and Bose from the dielectric second virial coefficient of pure N2O. The good agreement confirms the model developped by Bose and Cole for quadrupolar molecules.

The third dielectric and pressure virial coefficients of dipolar hard sphere fluids

Approximate analytic expressions are generated for the third dielectric virial coefficient C e*, and the third pressure virial coefficient C p*, of a fluid of hard sphere dipoles.

Influence of the angle-dependent part of the dispersion forces on the thermodynamical and spectral properties of gaseous SF6

Analytical expressions for the electrostatic, dispersion and induction interaction between an octahedral molecule and an atom, a linear, tetrahedral, or octahedral molecule are deduced from previous work of the present authors concerning the tetrahedral molecules. This allows the calculation of the second pressure and dielectric virial coefficients, the spectral moments of the pressure induced far infra-red absorption band and the intermolecular mean squared torque for a gas of molecules belonging to the Oh group. Numerical applications to SF6 gas show that the anisotropic dispersion interaction contribution plays a dominant role in the virial coefficients but not in the spectral moments. It follows that the order of magnitude of the hexadecapole moment for SF6, previously determined by Rosenberg and Birnbaum from the spectral moments is practically unaffected by consideration of the anisotropic dispersion interaction. In contrast, the calculated values of the virial coefficients are modified significantl...

Three-body-potential contribution to the structure of krypton gas

The virial expansion for the inverse structure factor of a gas is known to involve coefficients which are a function of $q$ and $T$, and whose $q\ensuremath{\rightarrow}0$ limits are the usual pressure virial coefficients. The authors have made careful measurements of the structure factor of krypton gas using improved neutron-diffraction techniques at 15 densities between 0.25 and 6.19\ifmmode\times\else\texttimes\fi{}${10}^{27}$ ${\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{s}/\mathrm{m}}^{3}$ at $T=297$ K. The methods used are described, and the experimental errors are analyzed and found to be less than 1%. These data are compared to virial-expansion calculations based on the Barker et al. pair potential, to extract the first coefficient depending on the triplet potential. Some difference is found between this result and that predicted by the long-range triple-dipole (Axilrod-Teller) term.

Interactions of highly charged colloidal cylinders with applications to double-stranded.

AbstractThis paper presents new applications of the McMillan‐Mayer solution theory to dispersions of highly charged colloidal cylinders in monovalent salt solutions. The thermodynamic solution properties are given in terms of the virial expansions relating to a Donnan membrane equilibrium. General expressions are derived for the second Donnan pressure virial coefficient B2 and for the first two salt distribution coefficients A1 and A2. The effect of electric interactions is represented as an increased effective diameter dB or dA of the colloidal cylinder. This yields the simple excluded volume expressions B2 = πdBL2/4 and A1 = πdA2L/4 for hard cylinders of length L and diameter dB and dA, respectively. The coefficient A2 is derived from the dependence of B2 on the salt concentration.Computations are made for double‐stranded DNA in sodium chloride solutions with the DNA model developed in the preceding paper: a uniformly charged cylinder, with size and charge consistent with transport experiments, and surrounded by a Gouy double layer. In 1–0.005M sodium chloride solutions dB is found to vary from 29 Å to about 220 Å, and dA from 30 Å to about 170 Å, with little sensitivity to the uncertainties in the kinetic diameter d ≈ 24 Å and the experimental ζ potentials of DNA. Corresponding results predicted by the classical Donnan theory are 6–167 times too high for B2.Values of A2 are relatively small, in line with the expected rapid convergence of the virial expansion for the salt distribution. This is consistent with a phase transition from random to parallel orientation of the cylinders predicted first by Onsager for hard cylinders on the basis of B2, but not yet observed for DNA in simple salt solutions.

Dielectric and pressure virial coefficients of imperfect gases. VI. Analysis of results for CF3H and CFH3

The dielectric and pressure second virial coefficients of CF3H and CFH3 as measured by Sutter and Cole are reproduced to 5% by a model of pair interactions taking account of central forces, electrostatic interactions, and shape effects. Lennard-Jones 12–6 parameters from viscosity data of Casparian and Cole are used. To secure agreement, effects of molecular quadrupole moments of 4.5 and 2.3×10−26 esu and Buckingham and Pople shape factors −0.10 and +0.25 for CF3H and CFH3 are included. The latter are of proper sign and agree reasonably well with estimates from molecular models by Barnes and Sutton.

The statistical mechanics of non-spherical polyatomic molecules

Collision integrals and equilibrium pressure and dielectric second virial coefficients are calculated for a non-spherical m-6-8 model potential energy function. The results are applied in a correlation of the physical properties of carbon dioxide. It is shown that the inclusion of non-spherical contributions in the calculation of the collision integrals has a small but significant effect with respect to the accurate representation of data. The Mason-Monchick approximation that non-spherical molecules collide with fixed relative orientations is briefly discussed. Agreement between calculated and experimental values for the viscosity coefficient, the thermal conductivity coefficient, the second virial coefficients and the isotopic thermal diffusion factor is generally satisfactory.

Thermodynamic properties of organic oxygen compounds 32. Vapour pressure and second virial coefficient of propanal

The vapour pressure of propanal from 4 to 135 kPa was measured. The results, which were of only moderate accuracy because of decomposition of the sample, were combined with other published values for formulation of an equation to represent the variation of vapour pressure with temperature. Values of the second virial coefficient were calculated from measured enthalpies of evaporation by means of the equation and are compared with values for several related compounds.

Dielectric and pressure virial coefficients of imperfect gases: Hexadecapolar system

Dielectric and pressure virial coefficients of SF6 have been determined at 323.3, 348.3, and 373.9 K. Attributing the temperature dependent contribution of the second dielectric virial coefficient to dipole moments induced in one molecule by the hexadecapole moment of a second gives (5.40±0.7)×10−41 esu · cm4 for the molecular hexadecapole moment of SF6. The hexadecapole moment of SF6 derived from pressure second virial coefficients is (5.75±0.3)×10−41 esu · cm4.

Viscosities of polar gases by relaxation of capillary flow

A simple method is described in which capillary flow is measured by the exponential decay of capacitance difference of gases in two reservoirs connected to the ends of the capillary and viscosity is determined from the time constant. Results for Ar, CH3F, CHF3, and CH3CF3 in the temperature range 20–150°C are given, together with 12–6 potential parameters derived using the theory of Monchick and Mason. These parameters for the polar gases are believed to give a much better description of the central forces than parameters derived from pressure virial coefficients.

Dielectric and pressure virial coefficients of imperfect gases. Pure N2O

Dielectric and pressure virial coefficients of N2O have been measured at 6.5, 30.1, and 75.1 °C. The dipole moment and the polarizability determined from the first virial coefficient are, respectively, 0.18 D and 3.03 × 10−24cm3. In calculating the molecular quadrupole moment from the dielectric second virial coefficient, effects due to various interaction energy terms were taken into consideration. These energy terms are due to quadrupole-quadrupole interaction, dipole-dipole interaction, quadrupole-induced dipole interaction, reaction fields of induced moments, and anisotropic effects. Our experimental measurements lead to a molecular quadrupolar moment of 3.4 × 10−26 esu · cm2.

Analysis of the pressure virials and Clausius-Mossotti function for polyatomic gases

Statistical mechanical equations for the second pressure virial coefficient and the second and third dielectric virial coefficients for quadrupolar molecules are evaluated using the m -6–8 potential function. The results are compared with experimental data for nitrogen and fluorine. An approximate value for the quadrupole moment of fluorine is estimated. Agreement between theory and experiment is generally good.

Dielectric and Pressure Virial Coefficients of Imperfect Gases. V. Octopole Moments of CH4 and CF4

Dielectric second virial coefficients varying inversely with temperature have been determined by cyclic expansion measurements at 6.6, 49, and 100°C in the pressure range 1–100 atm. Attributing the temperature dependent contribution to dipole moments induced in one molecule by the octopole moment of a second gives 3.0× 10−34 and 4.4× 10−34 esu for the molecular octopole moments of CH4 and CF4.

Dielectric and Pressure Virial Coefficients of Imperfect Gases. III. CClF2H

Second dielectric and pressure virial coefficients at 50°, 100°, and 150° are reported, together with low-density dielectric results which give a dipole moment μ = 1.48 D and polarizability 5.3 × 10−24 cm3. The second virial data can be reasonably well fitted by a pair potential including a Lennard-Jones radial function, polarizable dipole interactions, and an anisotropic shape factor proposed by Buckingham and Pople, but difficulties in consistently accounting for these and other results for polar molecules are pointed out.