Pressure Virial Coefficients Research Articles

Line shapes of isotropic and depolarized CILS spectra of neon: Interaction potential and pair polarizability

The present work proposes three interaction potentials between two gaseous neon atoms and applies them to the study of models representing the anisotropy and trace of the induced pair polarizability tensor. The proposed empirical interatomic potentials for the gaseous Ne-Ne interaction are developed by fitting the Improved Lennard-Jones (ILJ), Modified Tang-Toennies (MTT) and Barker et al. (BFW) potentials simultaneously to the spectroscopic and transport properties over a wide temperature range. The validity of the proposed interatomic potentials is verified by comparing the calculated and experimental second pressure virial coefficient over a wide temperature range. In addition to this, the results show satisfactory accordance between the experimental and calculated vibrational energy levels using the deduced pair potential parameters compared to those reported for neon gas. These comparisons exhibit acceptable accuracy when the present work potential parameters are inserted to reproduce the transport and thermo-physical properties, besides the spectral moments and the spectral line-shape intensities for neon gas. The isotropic and depolarized collision-induced light scattering (CILS) spectra are produced and analyzed as functions of the potential considered. They exhibit sensitivity to both the attractive part of the potential and the short-range values of the polarizability anisotropy or mean at intermediate and high frequencies. Mean and anisotropy are deduced directly from spectral line shapes using a new inversion method.

Three-body potential and third virial coefficients for helium including relativistic and nuclear-motion effects.

The non-additive three-body interaction potential for helium was computed using the coupled-cluster theory and the full configuration interaction method. The obtained potential comprises an improved nonrelativistic Born-Oppenheimer energy and the leading relativistic and nuclear-motion corrections. The mean absolute uncertainty of our calculations due to the incompleteness of the orbital basis set was determined employing complete-basis-set extrapolation techniques and was found to be 1.2%. For three helium atoms forming an equilateral triangle with the side length of 5.6 bohr - a geometry close to the minimum of the total potential energy surface - our three-body potential amounts to -90.6 mK, with an estimated uncertainty of 0.5 mK. An analytic function, developed to accurately fit the computed three-body interaction energies, was chosen to correctly describe the asymptotic behavior of the three-body potential for trimer configurations corresponding to both the three-atomic and the atom-diatom fragmentation channels. For large triangles with sides r12, r23, and r31, the potential takes correctly into account all angular terms decaying as r-l12 r-m23 r-n21 with l + m + n ≤ 14 for the nonrelativistic Born-Oppenheimer energy and l + m + n ≤ 9 for the post-Born-Oppenheimer corrections. We also developed a short-range analytic function describing the local behavior of the total uncertainty of the computed three-body interaction energies. Using both fits we calculated the third pressure and acoustic virial coefficients for helium and their uncertainties for a wide range of temperatures. The results of these calculations were compared with available experimental data and with previous theoretical determinations. The estimated uncertainties of present calculations are 3-5 times smaller than those reported in the best previous works.

Theory of Weakly Polydisperse Cytoskeleton Filaments.

Cytoskeleton filaments have the extraordinary ability to change conformations dynamically in response to alterations of the number density of actins/tubulin, the number density and type of binding agents, and the electrolyte concentration. This property is crucial for eukaryotic cells to achieve specific biological functions in different cellular compartments. Conventional approaches to biopolymers’ solution break down for cytoskeleton filaments because they entail several approximations to treat their polyelectrolyte and mechanical properties. In this article, we introduce a novel density functional theory for polydisperse, semiflexible cytoskeleton filaments. The approach accounts for the equilibrium polymerization kinetics, length and orientation filament distributions, as well as the electrostatic interaction between filaments and the electrolyte. This is essential for cytoskeleton polymerization in different cell compartments generating filaments of different lengths, sometimes long enough to become semiflexible. We characterized the thermodynamics properties of actin filaments in electrolyte aqueous solutions. We calculated the free energy, pressure, chemical potential, and second virial coefficient for each filament conformation. We also calculated the phase diagram of actin filaments’ solution and compared with the corresponding results in in vitro experiments.

Ultra-accurate thermophysical properties of helium-4 and helium-3 at low density. I. Second pressure and acoustic virial coefficients

The second pressure and acoustic virial coefficients of helium-4 and helium-3 are computed employing an accurate ab initio potential from the literature. The fully quantum-mechanical formulations are derived for second acoustic virial coefficient, which are not available in the literature. The uncertainty of our calculated values is quantified and evaluated based on the potential inaccuracy. For helium-4, our theoretical values are in excellent agreement with the best measurements and a recent ab initio calculation. Our estimated uncertainty is at least five times smaller than the previous best determination. For helium-3, systematic errors are detected for the widely accepted ab initio data and our new results are probably more reliable. The computed values of this work are given in the supplemental materials over a wide temperature range between 1 and 10 000 K, which are useful especially for primary temperature metrology.

The cubic-plus-association equation of state for hydrofluorocarbons, hydrofluoroolefins, and their binary mixtures

Hydrofluorocarbons, hydrofluoroolefins, and their mixtures are widely used as working fluids in energy systems. Weak hydrogen bond exists in these fluids and thus contribute to their thermodynamic properties. In this work, we account for the contribution of the weak hydrogen bond by tailoring the cubic-plus-association (CPA) equation of state (EoS) and its parameter fitting procedure. Overfitting to the liquid properties is avoided by introducing the saturated vapor density into the fitting objective function. The EoS is extended to binary mixtures using the van der Waals mixing rules and Elliot combining rule in which process solving the cross-association fraction is reduced from an equation set consisting of 4 nonlinear equations to a single nonlinear equation. The performance of the present model is investigated in terms of the vapor-liquid equilibria (VLE) and volumetric properties of 15 pure fluids and 40 binary mixtures using fitted and zero binary interaction parameter, and is compared with the reference data, a CPA EoS that uses the traditional parameter fitting procedure, the Soave-Redlich-Kwong (SRK) EoS, and a volume-translated SRK EoS. The present model (including the EoS and fitting procedure) accurately reproduces the vapor pressure, density, and second virial coefficient for the pure fluids and binary mixtures, and is the only valid model among the investigated models for both the VLE and the volumetric properties in both liquid and vapor phases. The contribution of the association term to the pressure is also shown in the temperature-density diagram, presenting a similar behavior as that in water in which the effect of the hydrogen bond is comparatively more pronounced.

Evaluation of second osmotic virial coefficients from molecular simulation following scaled-particle theory

ABSTRACTWe report a scaled particle theory-based method for evaluation of second osmotic virial coefficients from molecular simulations of dilute species in solution. In this method, we evaluate the work associated with growing a cavity in solution that is perfectly permeable to the solvent but is completely impermeable to the solutes, thereby establishing an osmotic stress between the cavity interior and exterior. Extrapolating our results to determine the solute concentration in contact with a cavity with an infinite radius, we are able to evaluate the solute osmotic pressure and second osmotic virial coefficient. A finite size correction is introduced to account for the impact of effectively concentrating the solutes in the periphery of the simulation box with increasing cavity size. We demonstrate the utility of the proposed method by evaluating second osmotic virial coefficients for methane in water as a function of temperature. The approach proposed here provides a physically transparent route for calculation of second osmotic virial coefficients by direct interrogation of simulation configurations without having to explicitly evaluate the long-range integral over solute-solute correlations required following McMillan-Mayer theory.

Accurate virial coefficients of gaseous krypton from state-of-the-art ab initio potential and polarizability of the krypton dimer.

We have developed a new krypton-krypton interaction-induced isotropic dipole polarizability curve based on high-level ab initio methods. The determination was carried out using the coupled-cluster singles and doubles plus perturbative triples method with very large basis sets up to augmented correlation-consistent sextuple zeta as well as the corrections for core-core and core-valence correlation and relativistic effects. The analytical function of polarizability and our recently constructed reference interatomic potential [J. M. Waldrop et al., J. Chem. Phys. 142, 204307 (2015)] were used to predict the thermophysical and electromagnetic properties of krypton gas. The second pressure, acoustic, and dielectric virial coefficients were computed for the temperature range of 116 K-5000 K using classical statistical mechanics supplemented with high-order quantum corrections. The virial coefficients calculated were compared with the generally less precise available experimental data as well as with values computed from other potentials in the literature {in particular, the recent highly accurate potential of Jäger et al. [J. Chem. Phys. 144, 114304 (2016)]}. The detailed examination in this work suggests that the present theoretical prediction can be applied as reference values in disciplines involving thermophysical and electromagnetic properties of krypton gas.

Thermodynamic Studies of Ionic Interactions for the Drug Ranitidine Hydrochloride in Aqueous Solutions at 298.15 K

In the present communication, we report the activities and activity coefficients of a model drug, ranitidine hydrochloride (RT·HCl) in aqueous solutions at 298.15 K. These calculations are based on the experimental measurements of densities and osmotic coefficients of RT·HCl in aqueous solutions as a function of concentration of the drug at 298.15 K. The density data have been used to obtain apparent and partial molar volumes at finite concentrations as well at infinite dilution and the experimental osmotic coefficient data are used to determine the activity and mean ionic activity coefficients of solute and solvent, respectively. The activity data have been processed to obtain the mixing and excess Gibbs energy changes as well as to obtain the osmotic pressure and osmotic virial coefficient of the drug. The variation of osmotic coefficient (ϕ) and ln γ ± as functions of concentration are studied; we observed a negative deviation from the limiting law in solution. The values of critical micelle concentration (cmc) and aggregation number (n) are estimated by applying the pseudo-phase separation model to the ϕ data. The data have been examined by applying the McMillan–Mayer theory of solutions and Pitzer approach for aqueous ionic solutions. The results are interpreted in terms of hydrophobic stacking interactions, structure making/breaking effects (kosmotropic/chaotropic effects) and cation–cation, cation–anion-cation attractions in aqueous solutions.

An equation of state for the isotropic phase of linear, partially flexible and fully flexible tangent hard-sphere chain fluids

A new equation of state is developed that accurately describes the isotropic phase behaviour of linear, partially flexible and fully flexible tangent hard-sphere chain fluids and their mixtures. The equation of state is based on the equation of state of Liu and Hu [H. Liu and Y. Hu, Fluid Phase Equilibr. 122, 75 (1996)] for fully flexible chain fluids. The effect of molecular flexibility is described by a pure-component parameter that is introduced in the theory at the level of the cavity correlation function of next-to-nearest neighbour segments in a chain molecule. The equation of state contains a total of three adjustable model constants. The extension to partially flexible- and linear chain fluids is based on a refitting of the first model constant to numerical data of the second virial coefficient of partially flexible and linear tangent hard-sphere chain fluids. The numerical data were obtained from an analytical approximation for the pair-excluded volume. The other two parameters were adjusted to molecular simulation data for the pressure of linear tangent hard-sphere chain fluids. For both, pure component systems and mixtures of chains of variable flexibility, the pressure and second virial coefficient obtained from the equation of state, are in excellent agreement with the results from Monte Carlo simulations. A significant improvement to TPT1, TPT2, generalised Flory-dimer theory and scaled particle theory is observed.

Kerr and Cotton–Mouton effects in atomic gases: a quantum-statistical study

Theory of the birefringence of the refractive index in atomic diamagnetic dilute gases in the presence of static electric (Kerr effect) and magnetic (Cotton–Mouton effect) fields is formulated. Quantum-statistical expressions for the second Kerr and Cotton–Mouton virial coefficients, valid both in the low- and in the high-temperature regimes, are derived. It is shown that both virial coefficients can rigorously be related to the difference of the fourth derivatives of the thermodynamic (pressure) virial coefficient with respect to the strength of the non-resonant optical fields with parallel and perpendicular polarisations and with respect to the external static (electric or magnetic) field. Semiclassical expansions of the Kerr and Cotton–Mouton coefficients are also considered, and quantum corrections up to and including the second order are derived. Calculations of the second Kerr and Cotton–Mouton virial coefficients of the 4He gas at various temperatures are reported. The role of the quantum-mechanical effects and the convergence properties of the semiclassical expansions are discussed. Theoretical results are compared with the available experimental data.

Multiproperty empirical isotropic interatomic potentials for CH4–inert gas mixtures

An approximate empirical isotropic interatomic potentials for CH4–inert gas mixtures are developed by simultaneously fitting the Exponential-Spline-Morse-Spline-van der Waals (ESMSV) potential form to viscosity, thermal conductivity, thermal diffusion factors, diffusion coefficient, interaction second pressure virial coefficient and scattering cross-section data. Quantum mechanical lineshapes of collision-induced absorption (CIA) at different temperatures for CH4–He and at T=87K for CH4–Ar are computed using theoretical values for overlap, octopole and hexadecapole mechanisms and interaction potential as input. Also, the quantum mechanical lineshapes of collision-induced light scattering (CILS) for the mixtures CH4–Ar and CH4–Xe at room temperature are calculated. The spectra of scattering consist essentially of an intense, purely translational component which includes scattering due to free pairs and bound dimers, and the other is due to the induced rotational scattering. These spectra have been interpreted by means of pair-polarizability terms, which arise from a long-range dipole-induced-dipole (DID) with small dispersion corrections and a short-range interaction mechanism involving higher-order dipole–quadrupole A and dipole–octopole E multipole polarizabilities. Good agreement between computed and experimental lineshapes of both absorption and scattering is obtained when the models of potential, interaction-induced dipole and polarizability components are used.

Activity and Activity Coefficient Studies of Aqueous Binary Solutions of Procaine, Lidocaine, and Tetracaine Hydrochloride at 298.15 K

Osmotic coefficient and density measurements are reported for the aqueous solutions of three hydrochloride salts of local anesthetical drug compounds, procaine (PC·HCl), lidocaine (LC·HCl), and tetracaine (TC·HCl) at 298.15 K and at ambient pressure. The experimental osmotic coefficient data are used to determine the activity and mean ionic activity coefficients of solute and solvent, respectively. The activity data have been processed to obtain the mixing and excess thermodynamic properties, such as Gibbs free energy (which has been studied as a function of drug concentration), as well as to obtain the osmotic pressure and osmotic virial coefficients of the drug compounds. The mean ionic activity coefficients of the ions decrease with the increase in drug concentration. The results of mixing and excess free energy changes do not show abrupt changes. These results are examined from the point of view of premiceller (associative) equilibria and the occurrence of critical micelle concentration (cmc). A discussion is presented on the basis of aggregation of cations, and the aggregation numbers of 2, 1.56, and 6 are obtained for PC·HCl, LC·HCl, and TC·HCl, respectively, in the solution phase, applying the pseudophase separation model. An application of the McMillan–Mayer theory of solutions to the data is made. It is noted that overall second virial coefficients are small and negative for the drug molecular salt, whereas it is positive for nonelectrolyte contribution. All of these are examined on the basis of structural characteristic of molecules and electrostatic and hydrophobic interactions.

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.

Thermophysical Properties of Dilute Hydrogen Sulfide Gas

New, simple, and practical correlations for shear viscosity, self-diffusion coefficient, bulk viscosity, and thermal conductivity of hydrogen sulfide in the limit of zero density are provided, together with a correlation for the second pressure virial coefficient. The correlations are based on the values of thermophysical properties generated from a highly accurate, fully quantum-mechanical, ab initio potential energy surface. The validation of the computed values of thermophysical properties against the rather scarce experimental data demonstrates an excellent agreement with the most accurate data sets. The analysis undertaken indicates that the correlated values provide the most reliable, accurate, and internally consistent representation of thermophysical properties of hydrogen sulfide. The correlations extend over the temperature range (180 to 2000) K. The behavior of each transport property is represented by an independent correlation of the appropriate effective collision cross section as a function of temperature, while the behavior of the second pressure virial coefficient is directly represented as a function of temperature. The uncertainty of the proposed transport property correlations varies from ± 0.4 % for the shear viscosity in the temperature range (300 to 700) K to ± 5.0 % for the bulk viscosity. The uncertainty of the second pressure virial coefficient correlation is estimated to be of the order of ± 1 cm3·mol–1 at temperatures above 400 K, decreasing to ± 30 cm3·mol–1 at 180 K.

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.

An empirical multi-parameter anisotropic intermolecular potential, collision-induced absorption and predicted collision-induced light scattering spectra for CF 4–He

An approximate anisotropic intermolecular potential for the interaction of CF 4 with He is developed by simultaneously fitting the Exponential Morse-Morse-Morse-Spline-van der Waals (EM3SV) potential form to high energy beam results, interaction pressure virial coefficients, diffusion coefficients, mixture viscosity and thermal conductivity. The collision-induced absorption spectrum of this system at 213 K has been calculated using the empirical models of the induced dipole moment and the interaction potential. Theoretical zeroth, first and second moments of this spectrum using various models for the induced dipole moment and interatomic potential are compared to the experimental values. Also, with this potential and with a suitable model for the anisotropy, the lineshape calculations have been used to predict a reasonable experimental spectrum of the induced light scattering. The results show that these models of the potential, the induced dipole moment and the induced anisotropy are the most accurate models reported to date for this mixture.

Calculations of the thermophysical properties of binary mixtures of noble gases at low density from ab initio potentials

Interaction potentials determined ab initio from quantum mechanics were used to calculate the thermophysical properties of six binary mixtures of noble gases: helium–neon, helium–argon, helium–krypton, neon–argon, neon–krypton and argon–krypton. From the ab initio potentials, the second pressure virial coefficient, the binary diffusion coefficient and the thermal diffusion factor were computed for the considered binary mixtures at low density in the temperature range 100–5000 K employing well-established formulas in statistical thermodynamics and the kinetic theory of dilute gases. In all cases, while not as good as that for pure noble gases, close agreement between experimental data and the theoretically calculated values shows that ab initio potentials are reliable for the calculation of accurate thermophysical properties of binary mixtures of noble gases over a wide temperature range.

Ab initio intermolecular potential energy surface and thermophysical properties of hydrogen sulfide

A six-dimensional potential energy hypersurface (PES) for two interacting rigid hydrogen sulfide molecules was determined from high-level quantum-mechanical ab initio computations. A total of 4016 points for 405 different angular orientations of two molecules were calculated utilizing the counterpoise-corrected supermolecular approach at the CCSD(T) level of theory and extrapolating the calculated interaction energies to the complete basis set limit. An analytical site-site potential function with eleven sites per hydrogen sulfide molecule was fitted to the interaction energies. The PES has been validated by computing the second pressure virial coefficient, shear viscosity, thermal conductivity and comparing with the available experimental data. The calculated values of volume viscosity were not used to validate the potential as the low accuracy of the available data precluded such an approach. The second pressure virial coefficient was evaluated by means of the Takahashi and Imada approach, while the transport properties, in the dilute limit, were evaluated by utilizing the classical trajectory method. In general, the agreement with the primary experimental data is within the experimental error for temperatures higher than 300 K. For lower temperatures the lack of reliable data indicates that the values of the second pressure virial coefficient and of the transport properties calculated in this work are currently the most accurate estimates for the thermophysical properties of hydrogen sulfide.

Ab initio pair potential energy curve for the argon atom pair and thermophysical properties for the dilute argon gas. II. Thermophysical properties for low-density argon

A recent argon–argon interatomic potential energy curve determined from quantum-mechanical ab initio calculations and described with an analytical representation [B. Jäger, R. Hellmann, E. Bich, and E. Vogel, Mol. Phys. 107, 2181 (2009); 108, 105 (2010)] was used to calculate the most important thermophysical properties of argon governed by two-body interactions. Second pressure, acoustic, and dielectric virial coefficients as well as viscosity and thermal conductivity in the limit of zero density were computed for natural argon from 83 to 10,000 K. The calculated values for the different thermophysical properties are compared with available experimental data and values computed for other argon–argon potentials. This extensive analysis shows that the proposed potential is superior to all previous ones and that the calculated thermophysical property values are accurate enough to be applied as standard values for the complete temperature range of the calculations.

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.