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.     

Second virial coefficient for the dipolar hard sphere fluid

The dipolar hard sphere fluid is a useful model for a polar fluid. Some years ago, the second virial coefficient, B(2), of this fluid was obtained as a series expansion in the inverse temperature or (dipole strength) by Keesom. Little work on this problem seems to have been done since that time. Using a result of Chan and Henderson for the spherical average of the Boltzmann factor of this fluid, more complete results are obtained for B(2). The more complete results are more negative than the Keesom series, as one would expect, but his expansion is remarkably accurate. This method can be used to obtain the second virial coefficient of the dipolar Lennard-Jones (Stockmayer) or dipolar Yukawa fluids.     

On the third virial coefficient for the alkali metal vapours

Theoretical calculations of the third virial coefficient for the pure components of all alkali metal vapours have been carried out using recently reported potential energy surfaces for the doublet and quartet states in which the interaction of three ²S ground-state atoms may evolve. The discrepancy between the theoretical and available experimental estimates for those coefficients is pointed out.     

Various contributions to the osmotic second virial coefficient in protein-water-cosolvent solutions

An analysis of the cosolvent concentration dependence of the osmotic second virial coefficient (OSVC) in water-protein-cosolvent mixtures is developed. The Kirkwood-Buff fluctuation theory for ternary mixtures is used as the main theoretical tool. On its basis, the OSVC is expressed in terms of the thermodynamic properties of infinitely dilute (with respect to the protein) water-protein-cosolvent mixtures. These properties can be divided into two groups: (1) those of infinitely dilute protein solutions (such as the partial molar volume of a protein at infinite dilution and the derivatives of the protein activity coefficient with respect to the protein and water molar fractions) and (2) those of the protein-free water-cosolvent mixture (such as its concentrations, the isothermal compressibility, the partial molar volumes, and the derivative of the water activity coefficient with respect to the water molar fraction). Expressions are derived for the OSVC of ideal mixtures and for a mixture in which only the binary mixed solvent is ideal. The latter expression contains three contributions: (1) one due to the protein-solvent interactions B2(p-s), which is connected to the preferential binding parameter, (2) another one due to protein/protein interactions (B2(p-p)), and (3) a third one representing an ideal mixture contribution (B2(id)). The cosolvent composition dependencies of these three contributions were examined for several water-protein-cosolvent mixtures using experimental data regarding the OSVC and the preferential binding parameter. For the water-lysozyme-arginine mixture, it was found that OSVC exhibits the behavior of an ideal mixture and that B2(id) provides the main contribution to the OSVC. For the other mixtures considered (water-Hm MalDH-NaCl, water-Hm MalDH-(NH4)2SO4, and water-lysozyme-NaCl mixtures), it was found that the contribution of the protein-solvent interactions B2(p-s) is responsible for the composition dependence of the OSVC on the cosolvent concentration, whereas the two remaining contributions (B2(p-p)) and B2(id)) are almost composition independent.     

Interdependence of enthalpic and entropic contributions to the second osmotic virial coefficient

The interdependence of the enthalpic contribution A_{2, H} and the entropic contribution A_{2, s} to the second osmotic virial coefficient for a given polymer-solvent system has been investigated from the experimental and the theoretical point of view. Experimentally, the following common facts were observed for various systems at temperatures and pressures below the critical values for the solvent. Both the isobaric and isothermal dependences can be approximated over relatively wide ranges of A_{2, H} by linear relations with a slope deviating only slightly, but in a characteristic manner from a value of ?1. When the temperature is increased at constant pressure one moves along an isobar towards higher A_{2, H}; when the pressure is increased at constant temperature, one moves along an isotherm in the opposite direction, i.e., towards lower A₂, _H. Theoretically this behavior can be described in a qualitative manner, starting from a relation derived by Patterson and Delmas on the basis of the Prigogine corresponding-states theory. The reasons for the lack of quantitative agreement are discussed.     

Classical and quantal calculations of the dimerization constant and second virial coefficient for argon

Summary Computations of the second virial coefficient and thermodynamic equilibrium constant for the dimerization of argon are reported. These are based on accurate analytic representations of the Ar-Ar interaction energy. Calculations have been made using classical and quantal statistical mechanics and for the second virial coefficient the JWKB series as well.     

Polystyrene in cyclopentane: Dilute solution properties from the upper critical to the lower critical solution temperature

Dilute solutions of polystyrene in cyclopentane are studied with four narrow-distribution polymer fractions ranging in molecular weight from 1.6 × 10⁵ to 1.8 × 10⁶. Light scattering (total intensity) and viscosity measurements cover a temperature range spanning both “theta” temperatures: the limiting upper critical solution temperature (19.6°C) and the limiting lower critical temperature (154.5°C). Within experimental uncertainty, chain dimensions are the same at the two theta temperatures. Correlations among second virial coefficients, mean-square molecular radii of gyration, and intrinsic viscosities, are analyzed. Temperature and molecular-weight dependences are correlated satisfactorily in terms of the excluded-volume parameter z that is central to the “two-parameter” theories of dilute solution behavior. The data can also be correlated in the framework of the newer renormalization theories.     

A generalized expression for the ratio of the critical temperature to the critical pressure with the van der Waals surface area

Using an extensive database of experimental critical properties for heavy compounds, which have been compiled mostly from recent literature sources, it is shown that the ratio T_c: P_c (critical temperature over critical pressure) can be expressed in terms of the van der Waals surface area (Q_w), which is readily available for any compound from the group contributions of Bondi (given also in UNIFAC tables). The proposed correlation is based on the hole theory of Kurata and Isida for n-paraffin liquids, which is mathematically equivalent to Flory's theory of polymer solutions. The method is suitable for medium to high molecular weight compounds with unknown critical constants. For example, if only one of the two critical constants is available, then the proposed generalized equation offers a useful rapid procedure for the estimation of the other critical property for use in corresponding states, and other relevant applications where knowledge of the critical properties is required. Furthermore, the T_c: P_c method can be used in many cases for identifying the most suitable among the existing group contribution methods for estimating the critical properties of heavy and complex compounds for which experimental values are, very often, not available.     

Thermodynamic study of poly(N-vinyl caprolactam) hydration at temperatures close to lower critical solution temperature

The lower critical solution temperature of aqueous solutions of poly(N-vinyl caprolactam) falls in the 305–307 K range and depends on the molecular weight of the polymer. The thermodynamic functions of mixing at 298 K have been calculated from measurements of vapor pressures and heats of dissolution and dilution. Partial Gibbs energy, partial enthalpy, and partial entropy of mixing were negative over the entire range of composition. Increasing temperature resulted in a decrease in the exothermal character of mixing. Excessive heat capacity values, calculated from the dependencies of enthalpy of mixing on temperature, were positive over the entire composition range. Heat capacity of dilute solutions was measured at 298 K and partial heat capacity of poly(N-vinyl caprolactam) at infinite dilution was shown to be positive. The data obtained point out the hydrophilic and hydrophobic hydration of poly(N-vinyl caprolactam) in aqueous solutions. Hydrophobic hydration dominates at temperatures close to binodal curve. As a result, the mutual mixing of the polymer with water is decreased and phase separation takes place.     

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.     

Volumetric properties of aqueous solutions of amino acids from the singular to critical temperature

The partial volume -V ₂ ⁰ of amino acids in aqueous solution is assumed to be zero for T = 227 K (singular temperature) and T= T _c (critical temperature). The literature data for -V ₂ ⁰(T) of ten amino acids at 278–328 K are reproduced by the two-parameter equation with a standard deviation of 0.06–0.16 cm³/mol. Only for asparagine and tryptophan the standard deviation exceeds 0.3 cm³/mol. In the case of glycine and alanine, the relation -V ₂ ⁰(T) in the high temperature range is obtained. -V ₂ ⁰ is divided into contributions (?-H ₂ ⁰/?p) _T and —T·(?-S ₂ ⁰/?p) _T . Their dependence on the temperature and amino acid nature is discussed. Positive values of ?-C ₂ ⁰/?p) _T characterize amino acids as water structure breakers; however, the differentiation of compounds by this feature is not successful. The behavior of amino acids in aqueous solutions is compared with the behavior of urea.     

A method for experimental determination of the temperature dependence of relaxation times in dielectrics

A new method is suggested for the experimental determination of the dependence of the relaxation times on the temperature in dielectrics for which the time–temperature superposition principle is valid. The method makes possible the determination of this dependence for a separate relaxation process (for instance, for the β-relaxation process) over a wide temperature range by means of comparatively simple mathematical operations which are only slightly sensitive to experimental errors. Two or more discharge-current curves, measured with temperatures increasing in an arbitrary way with time, are used for this purpose.     

A general procedure for obtaining wave functions obeying the virial theorem

The virial theorem for molecules is shown to have two different forms, one employing the energy gradient the other involving the Hellmann–Feynman force. While the former VT can be fulfilled by a uniform scaling of the basis set, the latter cannot be satisfied in certain basis sets, and can give unrealistic results in others. The scaling procedure is applied to molecules at nonstationary points on the potential energy surface and it is found that energy components can change substantially, especially at short bondlengths, while the change in total energy is small. The effects on molecular properties are also small.     

A systematic formulation of the virial expansion for nonadditive interaction potentials

A new formulation of the virial expansion for a classical gas is derived without the restriction to pairwise-additive interaction potentials. Explicit expressions up to the eighth virial coefficient, suitable for numerical evaluation, are given in the form of integrals over sums of cluster diagrams. Compared with previous approaches, the number of cluster diagrams increases more moderately with increasing order of the virial coefficient. Thus, the new formulation should be particularly useful for the computation of high-order virial coefficients.     

A Mass-spectrometric study of propionaldehyde oxidation in the negative temperature coefficient region

The oxidation of propionaldehyde has been investigated in a 1-L Pyrex reactor at total pressures of 50–120 torr and temperatures 553–713 K. Detection of reactants and products was principally by molecular beam mass spectrometry, although certain species could only be measured by gas-chromatographic analysis. At 553 K the yield of water was ～83% of the propionaldehyde consumed, leading to the conclusion that OH is the principal chain carrier near the beginning of the negative temperature coefficient region. Many oxygenated organics (CH₂O, CH₃CHO, C₂H₅OH, C₂H₅O₂H, CH₃O₂H) and C₂H₄ are formed during the oxidation process. These oxidation products are consistent with the important role of O₂ addition to C₂H₅ radicals at 553 K followed by subsequent reactions of the C₂H₅O₂ radical. As the temperature is increased, the product concentrations smoothly change to a much simpler distribution in which C₂H₄, H₂O₂, and CO are the dominant products.     

An analytical expression for the variation of the vapour pressure of liquids with temperatures up to critical conditions

In development of previous observations, the author proposes a four-constant equation which accurately reproduces the vapour pressures of liquids from about 0.04 mm to critical conditions. The equation holds for: (a) a variety of substances ranging from hydrogen and the lowest inert gases through non-polar and polar organic compounds and (b) fused salts and liquid metals to the upper limits of vapour pressures available. It satisfactorily accounts for infection points, and correlates previous work on entropies of vaporisation in terms of an aspherical factor.Of the four constants, one is universal and a second nearly so; below about 5 atm therefore, the equation reduces to one containing only two specific constants. The theoretical significance of the latter equation is discussed in terms of a free-volume theory of the liquid state.     

A new three-parameter viscosity-temperature equation for saturated liquids from the triple point to the critical point

A new simple viscosity-temperature equation with only three adjustable parameters is proposed that is valid over the entire saturated liquid curve for a chemically diverse set of compounds. This equation can incorporate the correct near-critical behavior and satisfies the need for a reliable equation for fitting and predicting the viscosity of saturated liquids. It reproduces data within the experimental uncertainty over the entire saturated liquid region. Compared with the previous viscosity-temperature equations, the new equation not only more accurately correlates experimental data but also more effectively extrapolates values from the usual range in which data are available both to the critical point and to the triple point.