An improved method to predict second cross virial coefficients

A previous method of the author to calculate the second cross virial coefficients is re-considered to improve the reliability of the predictions and to reduce the number of empirical rules. The method is based on the reduced second cross coefficient at the normal boiling temperature, , whose value is always assumed equal to unity. This value is then extrapolated to the experimental temperatures using only two empirical constants: K₁, a corrective multiplying factor of and K, in an exponential term as a multiplying factor of temperature. To improve the reliability of the method, literature experimental data are grouped in three binary classes:

- non-polar or slightly polar fluids;

- at least one strongly polar fluid;

- strong interactions of the acid–base type.

Only the critical constants and the normal boiling temperature are required as input parameters.

Deviations of calculated results from experimental one are in the range 25–40 cm³ mol⁻¹ for the first and the second class and below 300 cm³ mol⁻¹ for the third class.     

Excess and interaction second virial coefficients for seven binary gaseous systems

Excess and interaction second virial coefficients have been measured over the temperature range 293–321 K for the systems He-N₂, He-CO₂, He-N₂O, He-CH₄, He-SF₆, He-CF₄ and Ar-SF₆. The excess second virial coefficients B_E are estimated to have an accuracy of 0.3 cm³ mol^?1.     

Calculation of the binary diffusion second virial coefficient

Calculations of the first density correction to the binary diffusion coefficient are presented for several mixtures. These calculations are based on the classical kinetic theory for mixtures developed by Bennett and Curtiss. The theoretical predictions agree well with experimental data.     

Fourth virial coefficients of asymmetric nonadditive hard-disk mixtures

The fourth virial coefficient of asymmetric nonadditive binary mixtures of hard disks is computed with a standard Monte Carlo method. Wide ranges of size ratio (0.05 ≤ q ≤ 0.95) and nonadditivity (-0.5 ≤ Δ ≤ 0.5) are covered. A comparison is made between the numerical results and those that follow from some theoretical developments. The possible use of these data in the derivation of new equations of state for these mixtures is illustrated by considering a rescaled virial expansion truncated to fourth order. The numerical results obtained using this equation of state are compared with Monte Carlo simulation data in the case of a size ratio q = 0.7 and two nonadditivities Δ = ±0.2.     

Second virial coefficients of polystyrene mixtures in 2-butanone

Variation of the second virial coefficient as a function of polymer composition for three pairs of polystyrene mixtures in 2-butanone has been studied using static light scattering. The results are better represented by the simple method of taking the geometric mean of the second virial coefficients of the separate polymer species rather than by the two-parameter theory. In one of the three combinations studied, the presence of a minimum in the second virial coefficient-composition plot supports similar observations by previous workers.     

The second and the third virial coefficients of athermal polymer solutions

The second and the third virial coefficients in the lattice model of athermal mixtures of molecules of different sizes are calculated. All computations have been done for two- and three-dimensional simple square and simple cubic lattices.     

Monte carlo calculations of second virial coefficients of chain molecules

Monte Carlo calculations have been performed for different types of chain molecules whose units interact through Lennard-Jones potentials. From the averaged Mayer function, we have evaluated the intermolecular two-body cluster integral, obtaining results for second virial coefficients. We have investigated the following points: a) the site modelization of alkanes by comparison of our results with gas phase data of different linear and branched alkanes and their mixtures. b) the prediction of interpenetration factors for flexible linear and star polymer chains in a good solvent (or excluded volume conditions). c) the determination of the theta point for a model of flexible polymer chains and the comparison of data for finite chains with theoretical predictions.     

Collision cross sections, pressure-broadening coefficients and second virial coefficients for the acetylene-argon complex: experiments and calculations on a new potential energy surface

Integral cross sections and pressure-broadening coefficients have been measured by molecular beam scattering and by high-resolution infrared spectroscopy, respectively, for the acetylene-argon system. A new potential energy surface (PES) is proposed to describe structure and dynamical properties of this prototypical weakly bound complex. The PES has been parametrized exploiting a novel atom-bond pairwise additive scheme and has been fitted to the experimental data. Calculations of the scattering cross sections (both differential and integral), pressure-broadening, and second virial coefficients have been performed using both the present and also the most recent ab initio PES available in the literature. Analysis of the new experimental data indicates that the anisotropy of the interaction in the well region should be larger than that obtained in ab initio calculations. This is also in line with previous spectroscopic results.     

Gas phase PVT properties and second virial coefficients of dimethyl ether

Dimethyl ether (DME) is an important chemical material and gets more and more attention as a clean alternative fuel and refrigerant nowadays. The gas phase PVT properties of dimethyl ether were measured using the Burentt-isochoric coupling method in the temperature range of 328–403 K with two Burnett expansions at 383 and 403 K. A total of 126 experimental points have been obtained. The experimental measurement uncertainties were estimated to be within ±10 mK for temperature and ±0.7 kPa for pressure. The second virial coefficients along 16 isotherms were derived using the present data.     

Hydrophobic interactions and osmotic second virial coefficients for methanol in water

A recent theory of the hydrophobic effect together with a simple model for an alcohol molecule is used to calculate the osmotic (McMillan-Mayer) second virial coefficientB ₂ for methanol dissolved in water. We use this calculation to study the validity of common arguments that try to draw microscopic structural information from experimental virial coefficient data. In disagreement with many workers, we find that the hydrophobic interaction between hard spheres in water is attractive and that its strength diminishes as temperature is raised. Models that have come to the opposite conclusions have neglected complications inherent to real solutes such as the role of the hydroxy groups in affecting the correlations between the apolar portions of neighboring alcohols. The calculations reported here indicate that this neglect is a poor approximation for methanol. Our calculations also show that osmotic virial coefficients are sensitive to subtle details in the potentials of mean force. Therefore, slowly varying (e.g., dispersion) interactions may also contribute significantly to the values of these coefficients without significantly changing the solvent structure near the solute molecules.     

An extended correlation for second virial coefficients of associated and quantum fluids

The empirical correlation developed in a previous paper is extended to hydrogen bonding and quantum pure compounds. The calculations of the second virial coefficients only require additional parameters, the reduced dipole moment for the associated compounds (alcohols, amines, water) and reduced de Broglie wavelength for the quantum compounds (H₂, D₂, T₂, ³He, He, Ne). The results agree well with experimental data.     

Intermolecular potential energy surface and second virial coefficients for the water-CO2 dimer

A five-dimensional potential energy surface is calculated for the interaction of water and CO(2), using second-order M?ller-Plesset perturbation theory and coupled-cluster theory with single, double, and perturbative triple excitations. The correlation energy component of the potential energy surface is corrected for basis set incompleteness. In agreement with previous studies, the most negative interaction energy is calculated for a structure with C(2v) symmetry, where the oxygen atom of water is close to the carbon atom of CO(2). Second virial coefficients for the water-CO(2) pair are calculated for a range of temperatures, and their uncertainties are estimated. The virial coefficients are shown to be in close agreement with the available experimental data.     

Correlation of the mutual diffusion coefficients of binary liquid mixtures

A correlative UNIDIF model for the mutual diffusion coefficients of binary liquid mixtures is developed using statistical thermodynamics and the absolute reaction rate theory. In this model, a mole fraction average of the logarithm of the pure-component limiting diffusion coefficients is taken as a reference term. The model expresses the excess part of the diffusion coefficient relative to this reference term in a form similar to that of a UNIQUAC equation which comprises two parts due to the combinatorial and residual contributions. The combinatorial part depends on the molecular sizes and shapes. The residual part includes two binary interaction parameters, which are obtained from data regression, for each binary mixture. Mutual diffusion coefficients of nonpolar+nonpolar, nonpolar+polar and polar+polar fluid mixtures are correlated in this study. Optimal binary interaction parameters are presented. Correlation results using the UNIDIF model for mutual diffusion coefficient are satisfactory and are superior to those from other methods.     

Equations of state for fluids: empirical temperature dependence of the second virial coefficients

In this paper, an empirical dependence of the second virial coefficients is derived from equations of state. The second virial coefficient B2 is found to be a linear function of 1/T1+beta, where T is the temperature and beta is a constant and has different value for different substances. Excellent experimental supports to this relationship are reported for nonpolar fluids, polar fluids, heavy globular molecule fluids, and quantum fluid He-4.     

Velocity cross correlations in binary mixtures of simple fluids

The velocity cross correlation integrals $$D_{{\text{ab}}}^{\text{J}} = (N/3)\mathop \smallint \limits_{\text{o}}^\infty< {\text{v}}_{{\text{1a}}} ({\text{t}}) \cdot {\text{v}}_{{\text{2b}}} (0) > {\text{dt,}} {\text{a}} {\text{ = }} {\text{1,2;}} {\text{b}} {\text{ = }} {\text{1,2}}$$ can be estimated from the intradiffusion coefficients D ₁ ^° and D ₂ ^° at each mole fraction x₁ of component 1 on the basis of the exact relations among the Onsager phenomenological coefficients together with an assumed equation relating the joint diffusion coefficients D _ab ^J . The results from several such equations are compared with experimental data and with similar results derived by Hertz in a different way to represent the behavior of f _ab ≡D _ab ^J x _b in ideal reference systems. In some cases the agreement with experimental data for relatively ideal systems is even better than given by Hertz's results. For greater accuracy in predicting the D _ab ^J from D _a ^dg data one would need a prediction of the limiting value of D _aa ^J at x_a=0 for a=1,2. Presently known theory does not give a basis for estimating this limit reliably.     

Ab initio intermolecular potential energy surface and second pressure virial coefficients of methane

A six-dimensional potential energy hypersurface (PES) for two interacting rigid methane molecules was determined from high-level quantum-mechanical ab initio computations. A total of 272 points for 17 different angular orientations on the PES were calculated utilizing the counterpoise-corrected supermolecular approach at the CCSD(T) level of theory with basis sets of aug-cc-pVTZ and aug-cc-pVQZ qualities. The calculated interaction energies were extrapolated to the complete basis set limit. An analytical site-site potential function with nine sites per methane molecule was fitted to the interaction energies. In addition, a semiempirical correction to the analytical potential function was introduced to take into account the effects of zero-point vibrations. This correction includes adjustments of the dispersion coefficients and of a single-parameter within the fit to the measured values of the second virial coefficient B(T) at room temperature. Quantitative agreement was then obtained with the measured B values over the whole temperature range of the measurements. The calculated B values should definitely be more reliable at very low temperatures (T<150 K) than values extrapolated using the currently recommended equation of state.     

Corrected formula for first quantum corrections to second virial coefficients for non-spherical molecules

The formulas of Wang Chang, commonly used to calculate quantum corrections to the second virial coefficient for anisotropic interactions, are found to contain an error. A simple, correct formula, valid for any like or unlike combination of atoms and molecules of complexity up to and including symmetric tops, is given.     

Methane-water cross second virial coefficient with quantum corrections from an ab initio potential

We present our calculations of the cross second virial coefficient (B12) and of a related quantity, phi 12 = B12-TdB12/dT, for the methane-water system in the temperature range T = 200-1000 K. These calculations were performed using one of the ab initio potentials developed in previous work [Akin-Ojo and Szalewicz, J. Chem. Phys. 123, 134311 (2005)]. Quantum corrections of order variant Planck's over 2pi(2) were added to the computed classical values. We have estimated the uncertainties in our computed B12 and phi 12(T). This allowed evaluation of the quality of the experimental data to which we compare our results. We also provide an analytical expression for B12(T) as a function of the temperature T obtained by fitting the calculated values. This formula also predicts values of phi12(T) consistent with the directly calculated values.