Ab initio virial equation of state for argon using a new nonadditive three-body potential

An ab initio nonadditive three-body potential for argon has been developed using quantum-chemical calculations at the CCSD(T) and CCSDT levels of theory. Applying this potential together with a recent ab initio pair potential from the literature, the third and fourth to seventh pressure virial coefficients of argon were computed by standard numerical integration and the Mayer-sampling Monte Carlo method, respectively, for a wide temperature range. All calculated virial coefficients were fitted separately as polynomials in temperature. The results for the third virial coefficient agree with values evaluated directly from experimental data and with those computed for other nonadditive three-body potentials. We also redetermined the second and third virial coefficients from the best experimental pρT data utilizing the computed higher virial coefficients as constraints. Thus, a significantly closer agreement of the calculated third virial coefficients with the experimental data was achieved. For different orders of the virial expansion, pρT data have been calculated and compared with results from high quality measurements in the gaseous and supercritical region. The theoretically predicted pressures are within the very small experimental errors of ±0.02% for p ≤ 12 MPa in the supercritical region near room temperature, whereas for subcritical temperatures the deviations increase up to +0.3%. The computed pressure at the critical density and temperature is about 1.3% below the experimental value. At pressures between 200 MPa and 1000 MPa and at 373 K, the calculated values deviate by 1% to 9% from the experimental results.     

Thermodynamic studies of molecular interactions in aqueous alpha-cyclodextrin solutions: application of McMillan-Mayer and Kirkwood-Buff theories

Osmotic vapor pressure and density measurements were made for aqueous alpha-cyclodextrin (alpha-CD) solutions in the temperature range between 293.15 and 313.15 K. The experimental osmotic coefficient data were used to determine the corresponding activity coefficients and the excess Gibbs free energy of solutions. Further, the activity data obtained at different temperatures along with the enthalpies of dissolution (reported in the literature) were processed to obtain the excess enthalpy and excess entropy values for the solution process. The partial molar entropies of water and of alpha-cyclodextrin were calculated at different temperatures and also at different concentrations of alpha-CD. Using the partial molar volume data at infinite dilution, the solute-solvent cluster integrals were evaluated which yielded information about solute-solvent interactions. The application of McMillan-Mayer theory of solutions was made to obtain osmotic second and third virial coefficients which were decomposed into attractive and repulsive contributions to solute-solute interactions. The second and third osmotic virial coefficients are positive and show minimum at 303.15 K. The Kirkwood-Buff (KB) integrals G(ij), defined by the equation G(ij) = f(infinity)0 (g(ij)- 1)4pir(2) dr, have been evaluated using the experimental osmotic coefficient (and hence activity coefficient) and partial molar volume data. The limiting values of KB integrals, G(ij)(0) are compared with molecular interaction parameters (solute-solute i.e., osmotic second virial coefficient) obtained using McMillan-Mayer theory of solutions. We found an excellent agreement between the two approaches.     

Second virial coefficient of amylose acetate

The second virial coefficients of amylose acetate fractions have been determined at different temperatures and have been analyzed according to recent theories of second virial coefficient.     

Path-integral calculation of the third virial coefficient of quantum gases at low temperatures

We derive path-integral expressions for the second and third virial coefficients of monatomic quantum gases. Unlike previous work that considered only Boltzmann statistics, we include exchange effects (Bose-Einstein or Fermi-Dirac statistics). We use state-of-the-art pair and three-body potentials to calculate the third virial coefficient of (3)He and (4)He in the temperature range 2.6-24.5561 K. We obtain uncertainties smaller than those of the limited experimental data. Inclusion of exchange effects is necessary to obtain accurate results below about 7 K.     

Mayer-sampling Monte Carlo calculations of uniquely flexible contributions to virial coefficients

We present methods for computing contributions to the virial coefficients uniquely associated with molecular flexibility, and we demonstrate their use with application to the third, fourth, and fifth virial coefficients of united-atom models of linear alkanes and methanol belonging to the suite of transferrable potentials for phase equilibria (TraPPE-UA). We find that these uniquely flexible contributions are more difficult to compute than the remainder of the coefficient, especially for the conditions at which they appear to be most important. The significance of these contributions relative to the full virial coefficient grows with the number of sites (the size of the molecule), the number of molecules, and, to a certain extent, the temperature. The nature of the site-site interactions is of great importance: the significance of the uniquely flexible contribution at third and fourth order is orders of magnitude larger for TraPPE-UA methanol, which has Coulombic interactions, than for TraPPE-UA propane, which does not, even though both models have three sites per molecule and comparable bending potentials. While the uniquely flexible contribution of TraPPE-UA propane has a negligible impact on its third-order virial-equation-of-state estimate of the critical point, the uniquely flexible contribution of TraPPE-UA methanol increases this estimate of its critical pressure by about 5%.     

Second virial coefficients of Lennard–Jones chains

The second virial coefficients B₂ of Lennard–Jones chain fluids were calculated through Monte Carlo integration as a function of chain length m (up to 48 segments) and temperature. We found that at a fixed temperature the second virial coefficient decreases with chain length. At low temperatures, the virial coefficient changes sign from positive to negative as m increases. The simulation data also provide an estimate for the theta temperature T_Θ at which the attractive and repulsive interactions cancel each other for dilute solutions. It is found that the theta temperature T_Θ for Lennard–Jones chains with m>32 is 4.65 independent of chain length m. A comparison of simulated values of B₂ with those evaluated from two different perturbation theories for chain fluid shows that these approximate theories underestimate the second virial coefficients of Lennard–Jones chains.     

A virial coefficient interrelation for temperatures from about 1.0 to 2.7 times the critical temperature

An interrelation among the virial coefficients for temperatures between about 1.0 and 2.7 times the critical temperature is derived from the experimentally observed linearity of the temperature, T, versus the density, ρ, at constant K = (Z − 1)/ρ, where Z is the compressibility factor. This relates higher virial coefficients at a given T to the temperature dependence of the previous coefficients at that T.The experimental linearity of the constant-K (ISOK) lines is confirmed for nitrogen, from which accurate values of B and C, the second and third virial coefficients, are derived. The new interrelation is then used to find the fourth virial coefficient, D, for nitrogen in this T range (120–340 K).It is also shown that the Lennard–Jones 6,12 intermolecular potential does not obey this interrelation because its ISOK lines are not linear, and therefore it cannot represent the PρT behavior of nitrogen or other common gases.     

Generalised virial equation of state for natural gas systems

In this work we present a generalised virial equation of state for natural gas systems under custody transfer conditions. The model is based on corresponding states expressions for the second and third virial coefficients with argon as the reference fluid. These functional forms involve 12 adjustable coefficients. For the extension to mixtures we propose a one-fluid mixture model with binary interaction parameters in the combining rules for the mixture critical temperature and density. We obtained overall average absolute deviations (AAD) of 0.04 and 0.08% in pure-fluid compression factors and speeds of sound; AADs of 0.07 and 0.19% in compression factors and speeds of sound, respectively, of binary mixtures and AADs of 0.047, and 0.13% in natural gas compression factors and speeds of sound, respectively. These results compare favourably with equivalent calculations with other generalised virial coefficient models.     

A multisolute osmotic virial equation for solutions of interest in biology

The osmotic virial equation was used to predict osmolalities of solutions of interest in biology. The second osmotic virial coefficients, Bi, account for the interactions between identical solute molecules. For multisolute solutions, the second osmotic virial cross coefficient, Bij, describes the interaction between two different solutes. We propose to use as a mixing rule for the cross coefficient the arithmetic average of the second osmotic virial coefficients of the pure species, so that only binary solution measurements are required for multisolute solution predictions. Single-solute data were fit to obtain the osmotic virial coefficients of the pure species. Using those coefficients with the proposed mixing rule, predictions were made of ternary solution osmolality, without any fitting parameters. This method is shown to make reasonably accurate predictions for three very different ternary aqueous solutions: (i) glycerol + dimethyl sulfoxide + water, (ii) hemoglobin + an ideal, dilute solute + water, and (iii) bovine serum albumin + ovalbumin + water.     

The second virial coefficient of argon at low temperatures

We present experimental data of second virial coefficients of argon at temperatures of 77.3, 87.2 and 90.2 K. The results are in excellent agreement with theoretical values.     

Monte Carlo calculation of second and third virial coefficients of small-scale comb polymers on lattice

This paper reports the first computational estimation of the comb polymers' third virial coefficients. The number of the chains in the comb polymers range from 5 to 11. An algorithm that counts the contributing terms of the third virial coefficients in an accelerated manner is presented along with its efficiency dependence on the polymers' size. In addition, the second virial coefficients are estimated for the comb polymers and compared to previously reported results.     

Connection between the virial equation of state and physical clusters in a low density vapor

We carry out Monte Carlo simulations of physical Lennard-Jones and water clusters and show that the number of physical clusters in vapor is directly related to the virial equation of state. This relation holds at temperatures clearly below the critical temperatures, in other words, as long as the cluster-cluster interactions can be neglected--a typical assumption used in theories of nucleation. Above a certain threshold cluster size depending on temperature and interaction potential, the change in cluster work of formation can be calculated analytically with the recently proposed scaling law. The breakdown of the scaling law below the threshold sizes is accurately modeled with the low order virial coefficients. Our results indicate that high order virial coefficients can be analytically calculated from the lower order coefficients when the scaling law for cluster work of formation is valid. The scaling law also allows the calculation of the surface tension and equilibrium vapor density with computationally efficient simulations of physical clusters. Our calculated values are in good agreement with those obtained with other methods. We also present our results for the curvature dependent surface tension of water clusters.     

Higher-order virial coefficients of water models

We use the Mayer sampling method, with both direct and overlap sampling, to calculate and compare classical virial coefficients up to B6 for various water models (SPC, SPC/E, MSPC/E, TIP3P, and TIP4P). The precision of the computed values ranges from 0.1% for B2 to an average of 25% for B6. When expressed in a form scaled by the critical properties, the values of the coefficients for SPC water are observed to greatly exceed the magnitude of corresponding coefficients for the simple Lennard-Jones model. We examine the coefficients in the context of the equation of state and the Joule-Thomson coefficient. Comparisons of these properties are made both to established molecular simulation data for each respective model and to real water. For all models, the virial series up to B5 describes the equation of state along the saturated vapor line better than the series that includes B6. At supercritical temperatures, however, the sixth-order series often describes pressure-volume-temperature behavior better than the fifth-order series. For example, the sixth-order virial equation of state for SPC/E water predicts the 673 K isotherm within 8% of published molecular simulation values up to a density of 9 mol/L (roughly half the critical density of SPC/E water).     

Up to fourth virial coefficients from simple and efficient internal-coordinate sampling: application to neon

A simple and efficient internal-coordinate importance sampling protocol for the Monte Carlo computation of (up to fourth-order) virial coefficients ?B(n) of atomic systems is proposed. The key feature is a multivariate sampling distribution that mimics the product structure of the dominating pairwise-additive parts of the ?B(n). This scheme is shown to be competitive over routine numerical methods and, as a proof of principle, applied to neon: The second, third, and fourth virial coefficients of neon as well as equation-of-state data are computed from ab initio two- and three-body potentials; four-body contributions are found to be insignificant. Kirkwood-Wigner quantum corrections to first order are found to be crucial to the observed agreement with recent ab initio and experimental reference data sets but are likely inadequate at very low temperatures.     

Gaussian charge polarizable interaction potential for carbon dioxide

A number of simple pair interaction potentials of the carbon dioxide molecule are investigated and found to underestimate the magnitude of the second virial coefficient in the temperature interval 220-448 K by up to 20%. Also the third virial coefficient is underestimated by these models. A rigid, polarizable, three-site interaction potential reproduces the experimental second and third virial coefficients to within a few percent. It is based on the modified Buckingham exp-6 potential, an anisotropic Axilrod-Teller correction, and Gaussian charge densities on the atomic sites with an inducible dipole at the center of mass. The electric quadrupole moment, polarizability, and bond distances are set to equal experiment. Density of the fluid at 200 and 800 bars pressure is reproduced to within some percent of observation over the temperature range 250-310 K. The dimer structure is in passable agreement with electronically resolved quantum-mechanical calculations in the literature, as are those of the monohydrated monomer and dimer complexes using the Gaussian charge polarizable model water potential. Qualitative agreement with experiment is also obtained, when quantum corrections are included, for the relative stability of the trimer conformations, which is not the case for the pair potentials.     

Lateral intermolecular forces between biomembrane lipids in two dimensions: 1,2-dipalmitin at the heptane/water interface compared with phospholipids

The lateral interaction forces between phospholipids in two-dimensional arrays are fundamental to understanding membrane biophysics. In previous studies the related thermodynamic functions have been measured for spread phospholipid monolayers at the oil/water interface over a range of temperatures and densities, and the two-dimensional virial coefficients obtained. These coefficients have been computed from a model that emphasizes the head group zwitterion interactions. In this study we examine the contribution of the diglyceride portion of phospholipid molecules to the lateral intermolecular forces. Measurements of the heptane/water interfacial tension as a function of the concentration of 1,2-dipalmitoyl glycerol (DP) in the heptane were made over a range of low surface pressures at 25 degrees C. Infrared measurements on the DP solutions show that the solutions are ideal. The results are interpreted to give two-dimensional virial coefficients for the adsorbed monolayer. The second virial coefficient B2(T) for DP is +0.31 nm2/molecule, in marked contrast to the much larger positive values found for the corresponding phospholipids at the same interface and temperature, and clearly indicating an attractive component to the lateral potentials of mean force between pairs of DP molecules. The contribution of the diglyceride moiety to the pair potentials of the phospholipids thus appears to be minor but not negligible. The differences in the second virial coefficients for DP and the phospholipids are interpreted primarily in terms of the orientation of the ester carbonyl dipoles, also drawing on spectroscopic and diffraction evidence from related structures.     

Osmotic Coefficients of Aqueous Solutions of Some Poly(oxyethylene) Glycols at the Freezing Point of Solution

Summary. The freezing temperatures of dilute aqueous solutions of some poly(oxyethylene) glycols (PEG, HO–(CH₂CH₂O) _n –H, n varying from 4 to 117) were measured over a solute to solvent mass ratio from 0.0100 to 0.3900. The second and third osmotic virial coefficient (A ₂₂ and A ₂₂₂) of poly(oxyethylene) glycols in aqueous solution were determined. The molecular weight dependence of the second virial coefficient can be described by a simple relation A ₂₂=2×10^–5 M _n ^1.86, and the third virial coefficient is A ₂₂₂=0.038A ₂₂ ². The activity coefficients of the solute were calculated using the Gibbs-Duhem equation as applied by Bjerrum. From the osmotic and activity coefficients the excess Gibbs energies of solution, as well as the respective partial molar functions of solute and solvent and the virial pair interaction coefficients for the excess Gibbs energies were estimated. The second and the third osmotic virial coefficients are correlated with the Mc-Millan-Mayer virial coefficients.     

Osmotic Coefficients of Aqueous Solutions of Some Poly(oxyethylene) Glycols at the Freezing Point of Solution

The freezing temperatures of dilute aqueous solutions of some poly(oxyethylene) glycols (PEG, HO–(CH₂CH₂O) _n –H, n varying from 4 to 117) were measured over a solute to solvent mass ratio from 0.0100 to 0.3900. The second and third osmotic virial coefficient (A ₂₂ and A ₂₂₂) of poly(oxyethylene) glycols in aqueous solution were determined. The molecular weight dependence of the second virial coefficient can be described by a simple relation A ₂₂=2×10^–5 M _n ^1.86, and the third virial coefficient is A ₂₂₂=0.038A ₂₂ ². The activity coefficients of the solute were calculated using the Gibbs-Duhem equation as applied by Bjerrum. From the osmotic and activity coefficients the excess Gibbs energies of solution, as well as the respective partial molar functions of solute and solvent and the virial pair interaction coefficients for the excess Gibbs energies were estimated. The second and the third osmotic virial coefficients are correlated with the Mc-Millan-Mayer virial coefficients.     

Precision measurements of osmotic pressure in concentrated polymer solutions—II

Precision measurements of osmotic pressure have been carried out with several polymers (polystyrene, polymethylmethacrylate and polyvinyl acetate) in organic solvents. The concentration dependence of the osmotic pressure over a wide range of concentrations (up to 0·2 g/cm³) was established and the osmotic virial coefficients were evaluated. From the temperature dependence of the osmotic pressure, the partial molar heats and entropies of mixing were also determined. In the system polystyrene-cyclohexane, measurements were carried out near the θ-temperature; variation of the virial coefficients with temperature and molecular weight was studied. It was found that the conventionally defined θ-temperature is molecular weight dependent. At the θ-temperature, the third virial coefficient is positive and tends to a nonzero limit when the molecular weight tends to infinity.     

Computation of some thermodynamic properties of nitrogen using a new intermolecular potential from molecular dynamics simulation

A new pair-potential energy function of nitrogen has been determined via the inversion of reduced viscosity collision integrals and fitted to obtain an analytical potential form. The pair-potential reproduces the second virial coefficient, viscosity, thermal conductivity, self-diffusion coefficient, and thermal diffusion factor of nitrogen in a good accordance with experimental data over wide ranges of temperatures and densities. We have also performed the molecular dynamics simulation to obtain pressure, internal energy, heat capacity at constant volume, and self-diffusion coefficient of nitrogen at different temperatures and densities using our calculated pair-potential and some other potentials. The molecular dynamics of the nitrogen molecules has been also used to determine nitrogen equation of state in two (low and high) pressure ranges. Our results are in a good agreement with experiment and literature values.