Prediction Of Second Virial Coefficients Research Articles

Ab initio study of the intermolecular potential energy surface for the ground electronic state of the O2–CO system and prediction of second virial coefficients

The intermolecular potential energy surface of complex pairing the ground electronic state of oxygen molecule $$ \left( {X^{3} \sum_{g}^{ - } } \right) $$ with carbon monoxide is calculated using the CCSD(T) method. The interaction energies obtained using the aug-cc-pVDZ and aug-cc-pVTZ basis sets are extrapolated to the complete basis set limit using the latest extrapolated scheme. The interaction energies were calculated by the supermolecular approach with the full counterpoise correction for the basis set superposition error. The effects of the orientation angle and dihedral angle on the stability of the system were studied by considering 1260 energy points of the O2–CO system. The results show that the interaction energy strongly depends on the orientation of two molecules. The second virial coefficients calculated using the potential energy surface are in good agreement with those obtained by the parameters of the Beattie–Bridgeman equation that regards the states of pure oxygen and carbon monoxide fluids.

An Improved Group Contribution Method for the Prediction of Second Virial Coefficients

Techniques most commonly used for the estimation of the second virial coefficients are based on the corresponding states principle. They are generally semiempirical correlating methods, and their validity is usually limited to nonpolar gases or to small polar molecules. In this paper, an estimation technique for the second virial coefficients based on a modified group contribution method is presented. This method can be applied to a wide range of organic compounds. In fact, the method depends on the knowledge of reduced temperature and acentric factor, and is based only on summing the products of the group contributions and their respective number of occurrences. Each group contribution is derived by analysis of the second virial coefficient data available in the literature.

Comparison of Neural Network and Empirical Models for Prediction of Second Virial Coefficients for Gases

In the paper, two tools are used for estimation of second virial coefficient for gases and the obtained results are compared with the experimental data. The first tool is the computer program for estimation of second and third virial coefficients for gases and gas mixtures from basic properties of components. The computer program incorporates two empirical methods, the Tsonopoulos method to estimate second virial coefficients for nonpolar to polar pure gases and gas mixtures, and the method of Orbey and Vera to estimate third virial coefficients for nonpolar pure gases and gas mixtures. The second tool is the artificial neural network model (ANN) for correlation and prediction of second virial coefficients for gases. The neural network model was developed with the training variables: critical temperature, critical pressure, critical volume, acentric factor, dipole moment and temperature with the learning method back propagation of errors according to the best prediction error. The target variable was the second virial coefficient of gas. The neural network model has architecture (6,10,4,1). The training error was 0.3%. The network predicts the second virial coefficient with the average prediction error of 1.3%. The second virial coefficients for twenty gases are estimated with both tools. The comparison of results with experimental data shows that the computer program based on empirical methods, and the neural network model are appropriate tools for second virial coefficient prediction for gases, but more accurate results are obtained with the neural network model which gives good predictions of second virial coefficients for every gas.

Equation of state and liquid-vapor equilibrium of polarizable Stockmayer fluids

In this work we develop the concept of an effective potential to obtain the equation of state of polarizable Stockmayer (PSM) fluids. This potential consists of a Lennard-Jones function with appropriate energy and distance parameters that depend on the reduced dipolar moment μ(∗) and polarizability α(∗). The approach deals accurately with polarizable SM fluids with μ(∗)≤2.0 and α(∗)≤0.1. However, prediction of second virial coefficients is reliable up to μ(∗)≤4.0. When the low-density sphericalized potential is used at moderate and large densities, the effect of the dipole-dipole attraction is overestimated in agreement with an effect previously found in the literature. This effect can be traced back to a frustration mechanism due to the interaction between three and more dipoles. We propose a model to account for this frustration effect and are able to reproduce the vapor-liquid equilibrium of polarizable SM fluids in agreement with simulated results from the literature. Molecular dynamics simulations were carried out to show that the effective SM fluid has a radial distribution function very close to that of the true SM system.

Prediction of thermodynamic properties of krypton by Monte Carlo simulation using ab initio interaction potentials

The vapor–liquid equilibria of pure krypton were calculated by Gibbs ensemble Monte Carlo simulation using two different ab initio pair potentials. One pair potential was obtained from coupled-cluster calculations, using the CCSD(T) level of theory and two successive correlation consistent basis sets, aug-cc-pVTZ and -pVQZ. The resulting pair potentials were extrapolated to obtain the basis set limit of the interaction energies. The second ab initio potential was taken from literature. It is shown that the coupled-cluster potential leads to a quantitative prediction of second virial coefficients, vapor pressures, and orthobaric densities, if Axilrod–Teller triple-dipole potentials are included in the simulations.

An extension of the group contribution model for thermodynamic and transport properties of dilute gases

Earlier work of the group contribution method presented by Oh and Campbell [Oh and Campbell, 1997] for prediction of second virial coefficients and dilute gas transport properties has been repeated with a new set of normal alkane second virial coefficient data (methane, ethane, propane, and normal pentane critically compiled by Dymond and Smith [1980], normal hexane recommended by Dymond et al. [1986], and the recommendation for normal butane, heptane and octane updated by Tsonopoulos and Dymond [1997]). This method has been extended to molecular linear gases (carbon monoxide, oxygen and hydrogen) and to alkanes-gases mixtures. The functional group parameters were revised from the simultaneous regression of second virial coefficient and viscosity data. Group parameters values (CH0, CH1, CH2, CH3, CH4, double-bonded CH1 double-bonded CH2, N2, and CO2 groups) and 8 binary group interaction parameters (kN2-CH0,GC,kN2-CH1,GC, kN2-CH2,GC, kN2-CH3,GC,;kCO2-CH0,GC,kCO2-CH1,GC,;kCO2-CH2,GC, andK CO2-CH3,GC were revised. New group parameter values are given for gases beyond those presented earlier (CO, O2 and H2) and 19 group binary interaction parameter ValueS (kN2-CH1D, GC,kN2-CH2D,GC;kCO2-CH1D,GCkCO2-CH2D,GC;kCO-CH1,GC,kCO2-CH2,GC,kCO-CH3,GC, kCO-CH1D,GC,kCO-CH2D,GC,kO2-CH0,GC,kO2-CH1,GC,kO2-CH2,GC,kO2-CH2,GC,kO2-CH3,GC,kH2-CH0,GC,kH2-CH1,GC, kH2-CH2,GC,kH2-CH3,GC,kH2-CH1D,GC,kH2-CH2D,GC are presented for hydrocarbon mixtures with gases. Application of the model shows that second virial coefficient data can be represented with results comparable to those obtained by Oh and Campbell [1997] and by the corresponding states method of Tsonopoulos [ 1974]. The accuracy of the model in viscosity and diffusion coefficient predictions of dilute gases is comparable to the methods of Lucas [1980] and of the Fuller method [Fuller et al., 1966].

An Equation of State for Associating Fluids

An equation of state (EoS) suitable for describing associating fluids is presented. The equation combines the simplicity of a cubic equation of state (the Soave−Redlich−Kwong), which is used for the physical part and the theoretical background of the perturbation theory employed for the chemical (or association) part. The resulting EoS (Cubic Plus Association) is not cubic with respect to volume and contains five pure compound parameters which are determined using vapor pressures and saturated liquid densities. Excellent correlations of both vapor pressures and saturated liquid volumes are obtained for primary-alcohols (from methanol up to 1-tridecanol), phenol, tert-butyl alcohol, triethylene glycol, and water. Moreover, excellent prediction of saturated liquid volumes may be obtained from parameters which have been estimated by regressing only vapor pressures. Finally, we suggest a method for reducing the number of adjustable parameters for alcohols to three while maintaining the good correlation of vapor pressures and saturated liquid volumes. We investigate the possibility of using the homomorph approach for estimating the EoS parameters and explain the problems observed. The estimated pure compound parameters have been tested in the prediction of second virial coefficients with satisfactory results.

Molecular dynamics simulation of water properties using RWK2 potential: From clusters to bulk water

The accuracy of the two-body potential of Reimers et al. (RWK2, 1982) for water was evaluated by molecular dynamics simulation. As a test of this potential's ability to describe microscopic properties, the predicted structure, binding energy, and vibrational frequencies of clusters of various sizes are shown to agree remarkably well with available measurements and results calculated from first principle methods. The reliability of the potential was further tested via molecular dynamics simulation of the properties of bulk water for a range of intensive parameters of geochemical interest. The simulated PVT properties, liquid structure, self-diffusion coefficients, vaporization enthalpy, and power spectra all agree within a few percent with experimental data. Compared to the more frequently used TIP4P potential, the RWK2 potential is more accurate in the prediction of second virial coefficients and vibrational spectra, but not less accurate in other properties studied here.

Comparison of light scattering of colloidal dispersions with direct force measurements between analogous macroscopic surfaces

The equilibrium force laws (force vs distance) between two macroscopic surfactant-coated mica surfaces separated by organic liquids have been determined. The aim was to ascertain whether directly measured forces are able to be employed in the prediction of second virial coefficients as obtained from light scattering experiments on analogous colloidal suspensions (i.e., spherical particles coated with the same surfactant and dispersed in the same medium). The quantitative agreement between the two independent measurements was excellent. This suggests that the interaction energy per unit area, which governs the physical properties of a bulk colloidal system, is indeed, the same as the equilibrium interaction energy per unit area of two macroscopic surfaces, for the systems investigated here. Such a correlation has been tacitly assumed in the past, and it is the first time that this assumption has been confirmed experimentally for any system.

Correlation of second virial coefficients by application of chemical theory and group contribution concept, part 1, pure substances

A correlation for predicting second virial coefficients of pure substances on the basis of the chemical theory has been developed for temperatures between 273 and 533 K. The parameters of the correlation reflect structural properties of the molecule and the contribution of functional (polar) groups. Thus, this method provides a prediction of second virial coefficients without specific parameters for individual substances. With the exception of chlorofluoro-compounds the correlation has been applied to almost all substances listed in the new data collection of Cholinski et al.. Calculated second virial coefficients agree with experimental data within experimental error. The new correlation can be extended to predict second cross virial coefficients.

Prediction of second virial coefficients from intrinsic viscosities in ternary polymer systems

AbstractDeviations in the determination of the unperturbed dimensions of polymers arising in ternary polymer systems (solvent (1)/solvent (2)/polymer) can be explained by the inaccurate use of an interaction parameter independent of polymer molecular weight. On this basis, a new formalism for the calculation of the second virial coefficient from intrinsic viscosity is proposed. This formalism was tested (and compared with well established formalisms) for all ternary polymer systems with simultaneous intrinsic viscosity and second virial coefficient data in the literature.

Prediction of second virial coefficients of organic compounds by a group contribution method

Prediction of second virial coefficients of organic compounds by a group contribution method

A simple potential model for linear symmetric molecules.

A simple molecular model is proposed for prediction of second virial coefficients of linear symmetric molecules. The intermodular potential is substituted by summation of the group-group interactions described by the Lennard-Jones 12-6 potential. The second virial coefficients of oxygen, carbon dioxide and ethylene predicted in the present study agree with the recommended values of IUPAC within 1% or 1cm3 mol-1 for wide temperature ranges. Furthermore, the prediction method proposed is compared with the intermodular potential model of Lennard-Jones and the corresponding state theory of Tsonopoulos. The present model is extended to mixtures straightforwardly without any binary parameter. The interaction second virial coefficients predicted by the model are in good agreement with observed data.

Second virial coefficient of ethane at 423.15K and prediction of second virial coefficients for normal alkanes.

Mesure par la methode de Burnett du 2eme coefficient viriel de l'ethane a 423,15°K. Determination des parametres potentiels du groupe methyl du modele OK pour la prevision des 2emes coefficients viriels de molecules symetriques lineaires. Application au calcul des 2emes coefficients viriels du propane et du butane et comparaison avec des donnees experimentales

A study of the volumetric and phase behavior of binary systems. Part III. P‐V‐T‐x data and second virial coefficients of propane‐perfluorocyclobutane mixtures

AbstractP‐V‐T‐x data for the propane‐perfluorocyclobutane system are reported in this paper. The data cover a temperature range from 329.4 to 397.7°K and a pressure range from 60 to 6920 kPa. The low pressure compressibility measurements were used to determine second virial coefficients of pure propane and pure perfluorocyclobutane and for seven of their mixtures. The prediction of second virial coefficients using an extended corresponding states principle is also reported. Excellent predictions of the second virial coefficients of both pure components and mixtures have been obtained using, in the case of mixtures, a binary interaction coefficient obtained from a study of the critical states of the system.

Prediction of second virial coefficients from intrinsic viscosities

AbstractOne of the most readily available characteristics of a polymer sample is its intrinsic viscosity in a particular solvent. This datum can often be estimated reasonably from a single relative viscosity measurement. A number of theories permit the calculation of the second virial coefficient of a polymer/solvent mixture given the intrinsic viscosity and polymer molecular weight. The intrinsic viscosity of the polymer under theta conditions is also needed, but this can be estimated, if necessary, from the molecular weight. This article compares the efficiencies of various alternative models for the prediction of second virial coefficients of a series of polymers and solvents. The most effective technique for this purpose first calculates the concentration‐dependent equivalent hydrodynamic volume of a solvated polymer coil. This value is used with a primitive statistical mechanical theory for virial coefficients of hard‐sphere suspensions to calculate the osmotic pressure or turbidity of the polymer solution. These simulated experimental values are fitted with a least‐squares line as in the real experiment, and the second virial coefficient is derived from the slope. The computations are relatively simple; the average deviation between observed and predicted virial coefficient was less than 16% for a variety of polymer types, molecular weights, and solvents.

Prediction of osmotic pressures of polymer solutions

AbstractA theory which has been developed to account for the effects of concentration on the equivalent hydrodynamic volumes of dissolved polymers has been combined with a statistical mechanical relation for the virial coefficients of dilute suspensions of rigid spheres. With a scaling factor for solvent goodness, osmotic pressures of polymer solutions can be predicted with good accuracy. The input parameters needed are the number‐average molecular weight of the polymer sample and its intrinsic viscosity in the solvent of interest, as well as its intrinsic viscosity under theta conditions. The intrinsic viscosities can be estimated with sufficient accuracy from tabulated Mark–Houwink coefficients. The model developed contains no adjustable parameters. Comparisons of predicted and reported experimental osmotic pressures are presented, and a method for prediction of second virial coefficients is described.

Prediction of second virial coefficients of mixtures from the principle of corresponding states

Values of the mixed virial coefficients B12 are predicted for twenty-eight mixtures where experimental values have been reported. McGlashan and Potter's reduced equation of state is used to calculate corresponding states values, Hudson and McCoubrey's combining rules being used for the mixed critical temperatures. A comparison is made between the experimental and predicted values, using both the Hudson and McCoubrey combining rule and the geometric mean rule for the critical temperatures. In the first six mixtures examined, which are a particularly good test of the procedure (because of differences in ionization potential and size of the two components), agreement is often obtained within the experimental error. In the case of the other twenty-two mixtures, sixteen are better represented by the new procedure.