Values Of Second Virial Coefficient Research Articles

A hard-core Exp-6 intermolecular potential function for determining virial coefficients of pure nonpolar and slightly-polar molecules

In this work, we have applied the hard-core term to the Exp-6 intermolecular potential function, in order to obtain a more realistic model for determining the values of second virial coefficients of nonpolar and slightly-polar gases. The second virial coefficients of 24 nonpolar and slightly-polar gases of quite differing natures, including hydrocarbons from the alkane, alkene, and aromatic families, as well as non-hydrocarbons such as carbon dioxide, were calculated using the proposed hard-core Exp-6 intermolecular potential function. The results showed that this integrated approach significantly improves the Exp-6 model, bringing it closer to reality. The average errors in calculated second virial coefficients, over the 564 data points considered, is just 1.5%. In addition, the third virial coefficients of non-polar or slightly-polar gases can be accurately predicted using this proposed potential function. For example, the AAD% of the predicted third virial coefficients of 327 data points corresponding to 11 gases by the proposed model is 50.5%, which is much smaller than the AAD% of the original Exp-6 (80.6%), Lennard-Jones (94.3%) and Kihara (73.5%) models.

Probing Uranium(IV) Hydrolyzed Colloids and Polymers by Light Scattering

Tetravalent uranium readily undergoes hydrolysis even in highly acidic aqueous solutions. In the present work, solutions ranging from 0.4 to 19 mM (total U) concentration (1<pH<4) are carefully investigated by light scattering technique with special emphasis on polymerization leading to colloid formation. The results clearly indicate that the concentration has significant effect on particle size as well as stability of colloids. With increasing concentration the size of colloids formed is smaller due to more crystalline nature of the colloids. Stability of colloids formed at lower concentration is greater than that of colloids formed at higher concentration. Weight average molecular weight of the freshly prepared and colloidal polymers aged for 3 days is determined from the Debye plot. It increases from 1,800 to 13,000 Da. 40–50 atoms of U are considered to be present in the polymer. Positive value of second virial coefficient shows that solute-solvent interaction is high leading to stable suspension. The results of this work are a clear indication that U(IV) hydrolysis does not differ from hydrolysis of Pu(IV).

Static and dynamic light scattering studies on dilute polyrotaxane solutions

Static and dynamic light scattering measurements were performed for dilute polyrotaxane solutions in different types of solvent systems, i.e. dimethylacetamide (DMAc) or dimethylformamide (DMF) containing 1-6 wt% lithium chloride (LiCl), 1 M aqueous sodium hydroxide (NaOH) and dimethylsulfoxide (DMSO). No aggregation of the polyrotaxane in DMF/LiCl was confirmed in the present study. Radius of gyration of the dissolved polyrotaxane was largest in NaOHaq., followed by values in amide solvents/LiCl and that in DMSO, and was probably dominated not by Coulombic repulsion but by the mutual affinity between solvent and polyrotaxane. Ratio of radius of gyration to hydrodynamic radius suggested the flexible random-coiled conformation in DMSO and relatively more extended, semi-flexible ones in amide solvents/LiCl and NaOHaq. The obtained values of second virial coefficient and weight average molecular weight seemed to be affected by a potential change in differential refractive index increments, caused by selective macrocationization or ionization.

Molar volume for mixtures of methane with krypton, argon, ethane and carbon monoxide using the ISM equation of state

In this paper, an analytical equation of state (EoS) proposed by Ihm–Song–Mason (ISM) was employed to calculate the molar volume of mixtures of methane with krypton, argon, ethane and carbon monoxide. The best available pair interaction potential energy has been used to evaluate the second virial coefficients required by the ISM EoS. The calculated values of second virial coefficients were applied to the ISM EOS to predict the molar volumes for the above mentioned mixtures. Agreement with the experiment is excellent for all systems.

Protein crystallization: Contribution of small angle X-ray scattering (SAXS)

Small Angle X-ray Scattering (SAXS) experiments together with crystallization experiments have shown the importance of studying macromolecular associations and interactions involved in nucleation and crystal growth mechanisms. In the study by SAXS of Bovine pancreatic trypsin inhibitor (BPTI) and Aspergillus flavus Urate oxidase (UOX) in crystallization conditions, we characterize the crystal growth unit, which is a decamer in the case of BPTI and a tetramer in the case of UOX. We study interactions in solution, showing that salt, added alone to small protein solutions, is efficient to induce attractive interactions leading to crystallization, whereas for large proteins, the addition of non absorbing polymers is necessary to induce attractive interactions, which are characterized by negative values of second virial coefficient (A 2 ).

Effect of decane or sodium decanoate on the thermodynamics of globular protein solutions

The elucidation of the effect of decane or sodium decanoate (models of the nonpolar or polar lipids) on the molecular parameters and thermodynamic properties of proteins has been carried out in binary (protein-solvent) and ternary (protein-protein-solvent) aqueous solutions. Ovalbumin and 11S globulin, globular proteins of well-known structure, were considered. Light-scattering data manifest protein association in aqueous medium under the influence of both decane and sodium decanoate. Association of protein molecules in aqueous medium is higher under the influence of the nonpolar decane molecules. The thermodynamic parameters for different types of pair interactions in the systems ( the second virial coefficients) were estimated from static light-scattering data in the binary and ternary aqueous solutions of biopolymers without and with decane or sodium decanoate. The values of the second virial coefficients obtainedfrom binary solutions exhibit high thermodynamic affinity of protein associates formed under the influence of decane or sodium decanoate for aqueous medium. Maximal thermodynamic affinity of the protein associates for the solvent was observed in the case of the polar sodium decanoate added to the proteins. The values of the cross second virial coefficients obtained from ternary solutions indicate that the addition of the nonpolar decane molecules to the proteins increases the strength of the thermodynamically unfavorable interactions between protein molecules that are different in nature. On the other hand, the addition of polar sodium decanoate to the proteins leads to a decrease in the thermodynamically unfavorable protein-protein pair interactions in aqueous medium. The influence of the decane or sodium decanoate on the conformational state of the proteins in aqueous medium was characterized by differential scanning microcalorimetry. The data obtained manifest significant changing of the conformational stability of the protein globule under the influence of decane or sodium decanoate. The character of this influence strongly depends on the nature of both the low-molecular-weight organic compounds and the proteins studied.

Calculation of second virial coefficients and gaseous viscosities of the refrigerants HFC-32 (CH2 F2), HFC-23 (CHF3), and HCFC-22 (CHC1F2)

The second virial coefficients of refrigerants HFC-32 (CH2F2), HFC-23 (CHF3), and HCFC-22 (CHC1F2) have been correlated on the bisis of site site model potential and have been compared with experimental results. The molecular interactions consisted of repulsion dispersion and electrostatic parts. From the site site potentials adjusted to the experimental second virial coefficients, spherically averaged potentials have been determined and a subsequent calculation of gaseous viscosity has been carried out. Agreement between measured and calculated values of second virial coellicients and gaseous viscosity is satisfactory. Calculated values of second virial coefficients and gaseous viscosity beyond available experimental data, therefore. can be assumed as a reliable extrapolation to lower and higher temperatures.

Improved results for the potential parameters of methyl and methylene obtained from second virial coefficients of n-alkanes

Second virial coefficients of n-alkanes have been evaluated using the rotational isomeric state model. Methyl and methylene groups have been modelled as lennard-Jones (12–6) sites differing in size and in energy well depth. The parameters have been chosen to reprdoce experimental values of second virial coefficients of a number of n-alkanes in a broad range of temperatures. The new proposed parameters improve the description of the experimental data with respect to our previous work (López Rodríguez, A., Vega, C., Freire, J. J., and Lago, S., 1991, Molec. Phys., 73, 691). Moreover, differences in the fitted size and well depth of the methyl and methylene groups appear now as physically reasonable.

Thermodynamic properties of dichloromethane gas

Virial coefficients, derived from an analysis of precise P-V-T data, form a basis for the determination of thermodynamic properties and the force constants of appropriate intermolecular potential models. An earlier work reports experimental P-V-T measurements for dichloromethane gas from about 350 to 510 K along with compression factors and second virial coefficients. This study presents revised values of second virial coefficients and the following other derived quantities (the figure in parentheses indicates the estimated percent uncertainty): (i) third virial coefficients (2-20); (ii) Stockmayer (12-6-3) force constants; (iii) thermodynamic properties (0.2-0.5 up to 10 atm, increasing to 5 at 30 atm and above); and (iv) fugacity coefficients.

ChemInform Abstract: The Second Virial Coefficient of 3‐Center Lennard‐Jones Molecules and Its Relation to 1‐ and 2‐Center Molecules.

The second virial coefficients of homonuclear three-centerLennard-Jones molecules are calculated with various parameters of the isosceles triangle connecting the three sites. A special effort is made to establish the reducedBoyle temperaturesT B and the values of the second virial coefficients atT/T B=0.3 for the sake of comparison with one- and two-centerLennard-Jones molecules. It is shown that it is possible to find parameter values of the interaction potential of one- and two-centerLennard-Jones molecules which give very similar values of second virial coefficients forT/T B≥0.3, and the equivalence conditions are established. These conditions might not only give a basis for a microscopic scaling of state variables, but also some restrictions for the validity of the group contribution concept.

The second virial coefficient of 3-centerLennard-Jones molecules and its relation to 1- and 2- center molecules

The second virial coefficients of homonuclear three-centerLennard-Jones molecules are calculated with various parameters of the isosceles triangle connecting the three sites. A special effort is made to establish the reducedBoyle temperaturesT B and the values of the second virial coefficients atT/T B=0.3 for the sake of comparison with one- and two-centerLennard-Jones molecules. It is shown that it is possible to find parameter values of the interaction potential of one- and two-centerLennard-Jones molecules which give very similar values of second virial coefficients forT/T B≥0.3, and the equivalence conditions are established. These conditions might not only give a basis for a microscopic scaling of state variables, but also some restrictions for the validity of the group contribution concept.

Light Scattering from Copolymer Solutions

AbstractA new type of copolymer from para‐aminobenzoic acid and 6‐aminohexanoic acid was obtained by reacting the monomers in four different mole ratios. The polycondensation was carried out at 80d̀C with triphenyl phosphite as the initiator in N‐methyl‐2 pyrrolidone/pyridine mixture. The molecular weights of unfractionated and fractionated samples were determined by light scattering techniques in solvents of varying refractive index. From the values of second virial coefficient it is concluded that the solvent power for copolymer increases with increasing aminohexanoic acid mole fraction in the case of dichloroacetic acid and trifluoroacetic acetic acid while in dimethyl acetamide it decreases.

Mixture virial coefficients for the Hamann-Lambert model for globular molecules

The Hamann-Lambert model for globular molecules using Lennard-Jones 12- 6 potential functions for the atomic interactions has been used to obtain second virial coefficients for CH4, CF4, SF6, SiF4, CMe4, SiMe4, and the mixtures CH4-CF4, CH4-SF6, CH4-CMe4, CH4-SiMe4, and CF4-SF6. Additive third virial coefficients have been computed where experimental data are available. Of the 18 parameter sets needed for the 12-6 interactions in the above molecules and their combinations ten were obtained by a least-squares fitting process using experimental values of second virial coefficients, five were obtained from combining rules, and the remaining three from sources independent of virial coefficient data. The computed values of the virial coefficients agree well with the experimental data although in the case of the third virial coefficients improved agreement would be obtained if some form of non-additivity could be allowed for.

Graft polymers from poly(vinyl chloride) and chlorinated rubber

AbstractGraft polymers from poly(vinyl chloride) (PVC) and chlorinated rubber (CIR) with side chains of poly(methyl methacrylate) (PMMA), poly(methyl acrylate) (PMA), or poly(ethyl methacrylate) (PEMA) were synthesized. For this purpose, a vinyl monomer was polymerized in the presence of small quantities of PVC or CIR with benzoyl peroxide as catalyst. The graft polymers were separated from both homopolymers by precipitation with methanol from methyl ethyl ketone solutions of the reaction products and the grafting efficiency was calculated. The graft polymers were characterized by infrared spectra, elemental analysis, NMR, and osmometric or light‐scattering determinations. From the results it is concluded that the PVC or CIR molecules contain side chains of PMMA, PMA, or PEMA. The graft polymers showed higher molecular weights, and the values of second virial coefficient for these polymers were much different from those of the starting polymers.

Second virial coefficients of some argon-hydrocarbon mixtures and their comparison with chromatographic values

New measurements of the interaction second virial coefficient (B 12) of some mixtures of argon with various low molecular weight hydrocarbons are presented. Recently, several workers have proposed and examined methods of measuring B 12 by means of high-pressure gas chromatography, and these argon mixtures have been measured, primarily, in order to provide a comparison with those results obtained chromatographically. Although experimental error is still quite high (due mainly to lack of accurate values for second virial coefficients of the pure hydrocarbons), the agreement is good and the GLC results appear to be reliable.

Isotopic Thermal-Diffusion Factor for Krypton

The isotopic thermal-diffusion factor α0 for krypton has been determined over a temperature range of 242° to 643°K. An artificial mixture of krypton isotopes containing about 14% 82Kr and 10% 86Kr was utilized in this study in conjunction with a 10-tube swing separator, α0 being obtained from the concentration changes in these two isotopes only. A least-squares fitting procedure yields potential parameters α=16.1±0.6, and ε/k=244°±13°K for the exponential-six potential model. Further least-squares fitting with viscosity data gives rm=3.88±0.02 Å. Satisfactory agreements have been obtained, between experimental data and values calculated according to the present potential, for coefficients of diffusion and thermal conductivity. The calculated values for second virial coefficient from this potential, however, shows rather poor agreement with the experimental values.

Second Virial Coefficient of Polyelectrolytes. I

The second virial coefficient of polyelectrolytes at the limit of zero polymer concentration was studied using an interionic interaction theory based on a spherical model for macro-ions. A formulation of the polyelectrolyte—polyelectrolyte interaction parameter β22 is presented. A simple relation for the Donnan equilibrium, which was originally found with a rod-like model, and which is related to the simple electrolyte—polyelectrolyte interaction parameter β23 is discussed. It is shown, for poly(sodium phosphate)—sodium bromide—water system, that the second virial coefficient, which is given as a function of β23 and β22, can be described satisfactorily with two adjustable parameters, the dimension of macro-ions R and its polymer concentration dependence ∂R/∂n2. From the observed value of second virial coefficient, ∂R/∂n2 is found to be positive at the limit of zero polymer concentration, in contrast to the negative values of the derivative at higher concentrations. The polymer concentration dependence of the osmotic effect is shown to be consistent with a positive value for ∂R/∂n2.

Second Virial Coefficient for the Spherical Shell Potential

Values of the second virial coefficient for the three-parameter spherical shell potential are tabulated over wide ranges of temperature and shell size. The potential, which is not new, results from the interaction of two spherical surfaces having uniform distributions of Lennard-Jones (6–12) sites. An objective comparison is made between the tabulated values and the literature values for second virial coefficients, from which the potential parameters for twenty compounds are determined. Generally, the spherical shell potential generates a better fit than does the parent Lennard-Jones potential. The potential parameters found are in good agreement with expectations based upon density and interatomic distance data.

Colligative properties of polyelectrolyte solutions. VI. Donnan membrane equilibrium

AbstractThe Donnan membrane equilibrium of a linear polyelectrolyte solution was studied, using sodium polyvinyl alcohol sulfate as the sample and sodium chloride as the diffusible salt. Simultaneous measurements of membrane potential, sodium and chloride ion activities, sodium chloride distribution, osmotic pressure, and viscosity were carried out. The measurements of membrane potential and ionic activities gave consistent results which could be accounted for by the Donnan theory. The second virial coefficient, which was found to be much lower than the ideal Donnan term, was examined according to Scatchard's theory. It was found that while the theory gave a good qualitative explanation to the experimental results, it could not be used for quantitative discussion. For quantitative examination of the experimental second virial coefficient, the value of second virial coefficient was calculated from the assumption that osmotic pressure is proportional to the difference of the sum of solute activities on both sides of membrane, and was found to be nearly equal to the observed value.