Cross Virial Coefficients Research Articles

Density profiles of atoms in nano-tubes from an analytic method: hydrogen in a cylindrical pore

Knowledge of the structure of simple fluids in nano-tubes constitutes important information in many scientific and technical branches. Computer simulations and density functional theory (DFT) offer accurate but laborious results. We have proposed a simple analytical method to determine the background correlation function on the basis of the residual chemical potentials of a pair of interacting bodies and of the corresponding combined body. These potentials are obtained in terms of geometric quantities. In this paper we dealt with the combination rule for the geometric quantity Q; the harmonic mean rule was proposed and verified at low densities by calculating the third cross-virial coefficient, and by comparing calculated density profiles of the inhomogeneous systems of hard sphere–wall at higher densities. A slight improvement over the previous results were found. Next, we applied our analytic method to realistic systems of a simple molecule in the graphite cylindrical pore. Hydrogen (and carbon monoxide), interacting with carbon of the graphite via the modified LJ potential are considered and the density profile was determined taking into account only the soft-sphere interaction within Weeks–Chandler–Andersen approximation. The considered approach was found to yield a fair description of the realistic simple fluid–cylindrical pore system.

Extending the group contribution concept using kihara potential to perfluorinated n-alkanes C nF 2 n+2 ( n = 1–6) for estimating thermophysical properties

The concept of the group contribution using Kihara intermolecular potentials with a spherical core is extended to perfluorinated n-alkanes ( n = 1–6). The effective Kihara parameters for groups (CF 2, CF 3, CF 4) are estimated by fitting second virial coefficient B and dilute gas viscosity η together. The assumption of regarding CF 4 molecule as a single group is preferable to other two approaches based on the principle of group additivity: a combination of F–(CF 3) and CF 3–(F) groups; a single C–(F) 4 group and four F–(C) groups. Application of the model shows that second virial coefficients are represented with better results than those of the Tsonopoulos correlation, and are comparable to the correlation of Dymond's group and the Hohm correlation. Feasibility of the present method to calculate dilute gas viscosities is proved by comparison with the Lucas method, the Hohm correlation, the correlation of Yaws, and the Simsci Data Bank. Mixture property calculations of the model are enhanced by including binary group interaction coefficients k ij,gc, determined from second cross virial coefficient data, and are more reliable than other correlations for second cross virial coefficients and mixture viscosities. Prediction results of binary diffusion coefficients, not supplied to the parameter evaluations, are in significant agreement with experimental data and are compared well with values obtained by means of the Fuller method. Results studied here would be of use when extended to halogenated paraffins and their mixtures.

Crowding Induced Self-Assembly and Enthalpy-Entropy Compensation

We develop a general virial expansion to describe the influence of molecular additives on the equilibrium self-assembly of proteins or other supermolecularly assembling species M in solution. When specialized to high molar mass polymer additives, the cross-virial coefficient between the polymer and M, which dominates this effect, is found to vanish at a particular temperature T_{Theta} corresponding to an enthalpy-entropy compensation condition. Specifically, the increased stability of the assembled form of M, due to the modification of the entropy of the assembly by repulsive polymer-protein interactions, is progressively compensated by attractive interactions that alter the enthalpy of assembly.

Association and electrostatic steering of α-lactalbumin–lysozyme heterodimers

The salt and pH dependent association of hen egg white lysozyme with alpha-lactalbumin whey proteins has been studied using molecular level Monte Carlo simulations. A highly uneven charge distribution of alpha-lactalbumin leads to strongly ordered heterodimers that may facilitate the formation of structured, mesoscopic aggregates. This electrostatic steering gives rise to 80% alignment at 5 mM 1 : 1 salt which, due to screening, diminishes to 60% at 100 mM salt. The free energy of interaction minima, dominated by electrostatics, ranges between -9 kT at 1 mM salt to -2 kT at 100 mM (neutral pH). Calculated osmotic second virial cross coefficients indicate complexation in the pH interval 6-10. Multivalent ions are found to effectively destabilize the protein complex and, at constant ionic strength, the order is La(3+) > Ca(2+) > Mg(2+) > Na(+). Upon binding of calcium to alpha-lactalbumin both the interaction and orientational alignment with lysozyme are reduced due to induced changes in the whey protein charge distribution. This potentially explains the experimentally observed absence of supramolecular structuring for the calcium loaded holo alpha-lactalbumin. Where available, good agreement is found with experimental data.

A new combining rule for fluid mixtures

We present evidence for the regular behaviour of the Boyle temperature TB in gaseous binary mixtures of small molecules with negligible multipolar moments. We use this regularity to construct a new combining rule for the prediction of the cross interaction u12(r) in those mixtures. The combining rule gives TB of the cross interaction as the harmonic mean of the Boyle temperatures of the pure components. The validity of this harmonic rule is based on experimental data of 28 binary mixtures, whose TB have been obtained from experimental data of the cross virial coefficient B12(T). In determining TB we make use of non-conformal potentials that have been proven to represent very accurately the effective interactions of the molecules investigated. The new combining rule is used to give interaction parameters of several dozens of binary mixtures involving noble gases (Ne, Ar, Kr and Xe), diatomic molecules (N2, O2 and CO) and n-alkanes (from methane to n-octane). These interaction parameters lead to a prediction of cross virial coefficients B12(T) within experimental error. Electrostatic interactions, originating in permanent dipolar, quadrupolar, octupolar and hexadecapolar moments and exemplified by molecules of HCl, CO2, CF4 and SF6, depart from the regular non-polar behaviour.

The heat of mixing and second virial cross coefficient of water + oxygen and water + nitrogen

A vapour phase flow mixing calorimeter has been used to measure the heat of mixing H m E of (0.5H 2O + 0.5O 2)(g) and (0.5H 2O + 0.5N 2)(g) at the pressure p = 0.101325 MPa and at temperatures from (373.15 to 493.15) K. The H m E measurements were analysed using an association model for water in which the non-specific part of the interaction energy was calculated from the Stockmayer potential with the parameters ε/ k = 233 K, σ = 0.312 nm, and t ∗ = 1.278. The specific part of the energy was calculated from an equilibrium constant for the association of two water molecules K 298 K = 0.36 MPa −1 together with an enthalpy of association Δ H = −16.85 kJ · mol −1. The second virial coefficients of O 2 and N 2 were calculated from the Lennard-Jones potential. Cross coefficients B 12 were calculated from a combining rule containing an adjustable parameter ξ which is known to be satisfactory for mixtures of (water + hydrogen, or nitrogen, or argon, or methane). For all these mixtures the combining rule gives ξ = 0.99, and this value gives a good fit to the new H m E measurements on (water + nitrogen). For (water + oxygen) it was necessary to reduce ξ from 0.99 to 0.83 to fit the measurements. The values of B 12 for both mixtures are close to those obtained from measurements of the solubility of water in compressed oxygen or nitrogen, and confirm that B 12 for water–oxygen is less negative than that for water–nitrogen. This is in accord with recent theoretical calculations of the potential surfaces for water–oxygen and water–nitrogen.

High Concentration Formulations of Recombinant Human Interleukin-1 Receptor Antagonist: II. Aggregation Kinetics

At high protein concentrations (i.e., 50-100 mg/mL) and 37 degrees C, low solution ionic strength accelerates aggregation of recombinant human interleukin-1 receptor antagonist (rhIL-1ra). We have used a variety of physical and spectroscopic techniques to explain this observation. A population balance model was applied to a continuous mixed suspension, mixed product removal (MSMPR) reactor at steady-state to determine aggregate nucleation and growth rates. Nucleation rates increase at low ionic strength, while growth rates are unaffected. At low rhIL-1ra concentrations (i.e., <1 mg/mL), no conformational changes or differences in free energies of unfolding (DeltaG(unf)) were observed at 37 degrees C over the solution ionic strength range of 0.025-0.184 molal used for aggregation studies. However, increasing the protein concentration to 100 mg/mL shifts the rhIL-1ra monomer-dimer equilibrium significantly at low ionic strength to favor dimerization, which is reflected in subtle conformational changes in the circular dichroism and second-derivative FTIR spectra. In addition to a reversible dimer, an irreversible dimer forms by second-order kinetics during incubation at 37 degrees C. This noncovalent dimer does not significantly participate in further aggregation. The loss of native protein due to aggregation at 37 degrees C was third order in protein thermodynamic activity due to the rate-limiting formation of an aggregation-prone trimer. This trimer forms from irreversible attractive monomer-reversible dimer interactions, which were quantified using second osmotic cross virial coefficients. Lastly, the activity coefficient of rhIL-1ra estimated from aggregation rates is 50% higher at 100 mg/mL protein concentration than at 50 mg/mL, in close agreement with predictions from a hard-sphere model for activity coefficients.

Application of the group contribution concept to Kihara potential for estimating thermodynamic and transport properties: Part VI. Heavy globular molecules (SF 6, MoF 6, WF 6, UF 6, C(CH 3) 4, Si(CH 3) 4)

The group contribution concept using spherically symmetric Kihara intermolecular potential is applied to calculate second virial coefficient, dilute gas viscosity and diffusion coefficient for heavy globular molecules: sulfur hexafluoride SF 6, molybdenum hexafluoride MoF 6, tungsten hexafluoride WF 6, uranium hexafluoride UF 6, tetramethyl methane C(CH 3) 4, and tetramethyl silane Si(CH 3) 4. Kihara potential parameters are determined when second virial coefficient and viscosity data are satisfactorily fitted within experimental uncertainties. In the minimization procedure, each individual molecules itself is treated as a single functional group, namely molecular group, whereas functional groups (CH 0, Si 0, CH 3) are assigned to tetramethyl molecules (C(CH 3) 4, Si(CH 3) 4). Kihara potential parameters for molecular or functional groups (reduced core radius a*, fit parameters of the potential well depth α and β) are next used to estimate mixture properties: second cross virial coefficient, mixture viscosity, and binary diffusion coefficient. Mixture property predictions are notably improved by adding group binary interaction coefficient k ij,gc , which are determined by regressing second cross virial coefficient data. Application of the present method indicates that second virial coefficient data are represented with better results than those of the Tsonopoulos correlation, the correlation of Dymond's group, and the Zarkova and Hohm correlation. Feasibility of the present model to calculate dilute gas viscosity is proved by comparison with the Lucas method and the Zarkova and Hohm correlation. Prediction results of binary diffusion coefficient are in significant agreement with experimental data and are compared well with values obtained by means of the Fuller method.

Binary interaction parameter kij for calculating the second cross-virial coefficients of mixtures

The binary interaction parameters, k ij , of 119 mixtures were determined by fitting the second cross-virial coefficients of mixtures with correlations for pure compounds [L. Meng, Y.Y. Duan, L. Li, Fluid Phase Equilib. 226 (2004) 109–120; L. Meng, Y.Y. Duan, Fluid Phase Equilib., 258 (2007) 29–33] and classical mixing rules. The mixtures included nonpolar/polar (associated), polar/polar, quantum/nonpolar (quantum) binaries. Very simple correlations for k ij of H 2O/ n-alkane, CO/nonpolar and quantum/nonpolar (quantum) binaries were successfully developed. The results show that the present correlations can accurately predict the second cross-virial coefficients.

Intermolecular potential and second virial coefficient of the water-nitrogen complex

The authors construct a rigid-body (five-dimensional) potential energy surface for the water-nitrogen complex using the systematic intermolecular potential extrapolation routine. The intermolecular potential is then extrapolated to the limit of a complete basis set. An analytic fit of this surface is obtained, and, using this, the global minimum energy is found. The minimum is located in an arrangement in which N2 is near the H atom of H2O, almost collinear with the OH bond. The best estimate of the binding energy is 441 cm-1 (1 cm-1 approximately 1.986 43x10(-23) J). The extrapolated potential is then used to calculate the second cross virial coefficient over a wide temperature range (100-3000 K). These calculated second virial coefficients are generally consistent with experimental data, but for the most part the former have smaller uncertainties.

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.

A Simple Mixing Rule for the Deiters Equation of State: Prediction of Interaction Second Virial Coefficients and PVTx Properties of Binary Mixtures

The interaction second virial coefficients, B12, and PVTx behavior for the binary systems consisting of N2, CO2, CH4, C2H6, C3H8, and normal C4H10 are estimated by means of the Deiters equation of state (EoS). In this way a new combining rule based on the modified Lorentz–Berthelot combining rule is proposed for this EoS. The binary interaction parameters for these combining rules are calculated by fitting the expression for the interaction second virial coefficient derived from the Deiters EoS to the experimental cross virial coefficient data. The calculated B12 values from the optimized binary interaction parameters and Deiters EoS are in good agreement with experimental data. Also a van der Waals type mixing rule with the two binary interaction parameters kij and lij obtained from the experimental B12 values is presented for the Deiters equation of state, which is able to predict the volumetric properties of the above mixtures to a good degree of accuracy in the specified temperature and pressure range. Also it has been shown that the Deiters EoS has higher accuracy relative to the Peng–Robinson EoS for the prediction of the volumetric properties of the mixtures studied in this work.

Protein–polysaccharide interactions: The determination of the osmotic second virial coefficients in aqueous solutions of β-lactoglobulin and dextran

Solutions containing dextran and solutions containing mixtures of dextran + β-lactoglobulin are studied by membrane osmometry. The low concentration range of these solutions is considered. From the measured osmotic pressures the virial coefficients are obtained. These are analyzed using the osmotic virial coefficient of β-lactoglobulin solutions published earlier by us [Schaink, H.M., & Smit, J.A.M. (2000). Determination of the osmotic second virial coefficient and the dimerization of beta-lactoglobulin in aqueous solutions with added salt at the isoelectric point. PCCP, 2, 1537–1541]. The second cross-virial coefficient A 12 is found to be positive indicating a repulsive and probably mainly steric interaction between neutral in nature dextran and and practically uncharged β-lactoglobulin (pH=5.18). The measurements show that the β-lactoglobulin has only a small tendency to form multimers in the presence of dextran. The phase diagram of solutions of dextran+Whey Protein Isolate (appr. 60% β-lactoglobulin) is also presented. The McMillan–Mayer equation of state that considers only the second virial coefficients is found to be unreliable for the extrapolation up to the concentrations at which phase separation is expected.

Virial Coefficients from Burnett Measurements for the R23 + N2O System

This paper presents experimental results for the trifluoromethane (R23) + nitrous oxide (N2O) system, which has been chosen as a working fluid for low-temperature applications since it might be a valid option for the low-temperature stage in a cascade cycle. The thermodynamic properties of the binary mixture’s constituents are well known from the literature, but no experimental results have been published to date on the PVTx properties of this binary system. PVTx measurements were obtained for the binary R23 + N2O system for three isotherms (303, 323, and 343 K), performing 15 Burnett expansions in a range of pressures from about 4400 to 80 kPa. The second and third virial coefficients were derived from experimental results together with the second and third cross virial coefficients. The experimental uncertainties in the second and third virial coefficients were estimated to be within ±1 cm3·mol−1 and ±500 cm6·mol−2, respectively.

Determination of vapor pressure and solubility correlation of phenolic compounds in supercritical CO 2

New vapor pressure data for phenolic compounds (caffeic acid, ferulic acid, and p- and o-coumaric acids) were experimentally obtained and compared to values predicted by a group contribution method. A gas–liquid chromatography method was used to experimentally determine the vapor pressure since this method is reliable, reproducible and rapid. These vapor pressure data were then used to predict second cross virial coefficients of phenolic compounds in supercritical carbon dioxide (SC CO 2) using a method based on the residual chemical potential in terms of the virial coefficients and fluctuation theory. The solubility results obtained by this method were compared to those from two other correlations based on the regular solution theory and Chrastil equation. Good agreement was obtained with the correlations when compared to the experimental literature data on the solubility of phenolic compounds in SC CO 2.

An extension of the group contribution method for estimating thermodynamic and transport properties. Part IV. Noble gas mixtures with polyatomic gases

Earlier work on the group contribution method applied to Kihara potentials is extended to noble-polyatomic gas mixtures for the calculation of second virial cross coefficients, mixture viscosities and binary diffusion coefficients of dilute gas state using a single set of gas group parameters. Previously estimated parameter values for pure gas groups by our work [Oh, 2005; Oh and Sim, 2002; Oh and Park, 2005] were used. Assuming that noble-polyatomic gas mixtures examined are chemically dissimilar, a group binary interaction coefficient, kij, gc, was assigned to each interaction between noble-polyatomic gas groups, and 25 group binary interaction parameter values (kHe-H2, gc, kHe-N2, gc, kHe-CO, gc, kHe-CO2, gc, kHe-O2, gc, kHe-NO, gc, kHe-N2O, gc; kNe-H2, gc, kNe-N2, gc, kNe-CO, gc, kNe-CO2, gc, kNe-O2, gc; kAr-H2, gc, kAr-N2, gc; kAr-CO, gc, kAr-CO2, gc, kKr-O2, gc; kKr-H2, gc, kKr-N2, gc, kKr-CO, gc, kAr-CO2, gc; kXe-H2, gc, kXe-N2, gc, kXe-CO, gc, kXe-CO2, gc) were determined by fitting second virial cross coefficients data. Application of the model shows that second virial cross coefficient data are represented with good results comparable to values predicted by means of the corresponding states correlation. Reliability of the model for mixture viscosity predictions is proved by comparison with the Lucas method. And prediction results of binary diffusion coefficients are in excellent agreement with literature data and compared well with values obtained by means of the Fuller method. Improvements of the group contribution model are observed when group binary interaction coefficients are adopted for mixture property predictions.

An experimental study of PVTx properties in the gas phase for binary mixtures of HFC-161 and HFC-32

An experimental study of the pressure–volume–temperature–composition ( PVTx) properties in the gas phase for binary mixtures of ethyl fluoride (HFC-161) + difluoromethane (HFC-32) was conducted in the range of temperatures from 303.179 to 403.190 K, pressures from 1182.9 to 5918.2 kPa, densities from 0.5754 to 3.2174 mol dm −3, and compositions from 0.1597 to 0.8989 mole fractions of HFC-161. The measurements were performed with an isochoric cell apparatus. The uncertainties in the present work were estimated to be ±1.5 kPa for pressure, ±6 mK for temperature, and ±0.15% for composition. On the basis of the experimental PVTx property data, a truncated virial equation of state was developed for the binary HFC-161/32 system. This equation reproduced the experimental data in the gas phase within ±0.457% in pressure. The temperature dependence of the second virial coefficients, including the cross-virial coefficients for this system is also discussed.

Prediction of the second cross virial coefficients of nonpolar binary mixtures

The binary interaction parameter, k ij , of 268 nonpolar mixtures were determined from the database of second cross virial coefficients containing 1728 experimental data points by fitting the second cross virial coefficients with a new correlation for pure compounds [L. Meng, Y.Y. Duan, L. Li, Fluid Phase Equilib. 226 (2004) 109–120] and classical mixing rules. Regularity distributions were found for both n-alkane/ n-alkane binaries and fluorocarbon/fluorocarbon binaries. Correlations were developed following Tsonopoulos’ ideas [C. Tsonopoulos, Adv. Chem. Ser. 182 (1979) 143–162] with the quantity of binary compounds enlarged using Dymond's latest complication [J.H. Dymond, K.N. Marsh, R.C. Wilhoit, Virial Coefficients of Pure Gases and Mixtures, Subvolume B, Virial Coefficients of Mixtures, Series IV/21B, Landolt-Börnstein, 2002]. Correlations were also developed for inorganic/ n-alkane binaries using new k ij values. The predictions do not need any thermodynamic property parameters besides the carbon number. Comparisons with the existing correlations show that the present work is more accurate for nonpolar binary mixtures.

An extension of the group contribution method for estimating thermodynamic and transport properties. Part III. Noble gases

Earlier work on the group contribution method applied to the Kihara potential is extended to noble gases for the estimation of second virial coefficients, dilute gas viscosities and diffusivities with a single set of gas group parameters. Group parameters are determined when second virial coefficient and viscosity data of pure gases are satisfactorily fitted within the experimental uncertainties. Parameters for gas groups (He, Ne, Ar, Kr and Xe) are found to provide good predictions of mixture properties: second virial cross coefficients, mixture viscosities, and binary diffusion coefficients. Application of the model shows that second virial coefficient data are represented with good results comparable to the values by means of the corresponding states correlation. The reliability of the present model in viscosity predictions is proved by comparison with the Lucas method. Prediction results of diffusivity are in excellent agreement with literature data and compare well with values obtained by means of the Fuller method.

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, B b * , whose value is always assumed equal to unity. This value is then extrapolated to the experimental temperatures using only two empirical constants: K 1, a corrective multiplying factor of B b * 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 cm 3 mol −1 for the first and the second class and below 300 cm 3 mol −1 for the third class.