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Analytical Evaluation of Second Virial Coefficient Using Sutherland Potential and Its Application to Real Gases

Year 2018, Volume: 18 Issue: 1, 83 - 89, 30.04.2018

Elif Somuncu

Abstract

A simple and efficient analytical formula for the calculation of second virial coefficient over Sutherland
potential is derived. The compute conclusions of the second virial coefficient determined for
Sutherland potential are compared with calculations of second virial coefficient using Lennard-Jones
(12-6) potential and Exp-6 potential. The accuracy of the analytical formula is tested by application to
molecules Kr, Xe,Ne and Ar . The results of the calculations for wide temperature range show
excellent agreement with the data existing in the literature.

Keywords

Second virial coefficient Sutherland potential Thermodynamics

References

  • Abdulagatov, A. I., Kaplun, A. B., Meshalkin, A. B., Abdulagatov, I. M. and Stepanov, G. V., 2002. Second Caloric Virial Coefficients for Real Gases and Combined Spherical Symmetric Potential for Simple Molecular Interactions. Journal of Chemical Thermodynamics, 34, 2049–2072.
  • Deszczynski, M., Harding, S. E., Winzor, D. J., 2006. Negative Second Virial Coefficients as Predictors of Protein Crystal Growth: Evidence From Sedimentation Equilibrium Studies that Refutes the Designation of Those Light Scattering Parameters as Osmotic Virial Coefficients. Biophysical Chemistry, 120, 106 – 113.
  • Fender, B. E. F. and HalseyJr, G. D., 1962. Second Virial Coefficients of Argon. Krypton. and Argon‐ Krypton Mixtures at Low Temperatures. Journal of Chemical Physics, 36, 1881.
  • Garberoglio, G., Moldever, M. R. and Harvey, A. H., 2011. Improved First-Principles Calculation of the Third Virial Coefficient of Helium. Journal of Research NIST, 116, 729-742.
  • Garberoglio, G., Jankowski, P., Szalewicz, K., and Harvey, A. H., 2012. Second Virial Coefficents of 2 H and its isotopologues from a six-dimensional potential. Journal of Chemical Physics, 137, 154308- 154319.
  • Gibson, W. G., 1981. Third Virial Coefficient for Quantum Hard Spheres: Two-Point Padé Appraximants for Direct and Exchange Parts. Journal of Statistical Physics, 26, 333-346.
  • Glasser, M. L., 2002. Second virial coefficient for a Lennard-Jones (2n-n) system in d dimensions and confined to a nanotube surface. Physics Letters A, 300, 381-384.
  • Graben, H. W., Present, R. D., 1964. Third Virial Coefficient for the Sutherland ,  Potential. Reviews of Modern Physics., 1025-1033.
  • Gradshteyn, I. S., Ryzhik, I. M., 1965. Exponential Integrals. Tables of Integrals. Series and Products. Acedemic, London. 1-1762.
  • Hirschfelder, J.O., Curtiss, C. F., Bird, R. B., 1954. Molecular Theory of Gases and Liquids. USA Jonh Wiley & Sons. 1-931.
  • Hostettler, H. U., Bernstein, R. B., 1959. Comparison of Exp-6, L-J (12.6) and Sutherland Potential Functions Applied to the Calculation of Differential Scattering Cross Sections. Journal of Chemical Physics, 31, 1422-1423.
  • Hutem, A. and Boonchui, S., 2012. Numerical Evaluation of Second and Third Virial Coefficients of Some Inert Gases via Classical Cluster Expansion. Journal of Mathematical Chemistry, 50, 1262-1276.
  • Kaplan, I. G., 2006. Intermolecular Interactions: Physical Picture, Computational Methods and Model Potentials. Jonh Wiley & Sons, 183-200. Kihara, T., 1953. Virial Coefficiens and Models of Molecules in Gases. Review of Modern Physics, 25, 831-843.
  • Konowalow, D. D. and Hirschfelder, J. O., 1961. Intermolecular Potential Functions for Nonpolar Molecules. Physics of Fluids, 4, 629-635.
  • Levi, D., M. Llano, D., 1975. Closed Form of Second Virial Coefficient for Sutherland Potential. Journal of Chemical Physics, 63, 4561-4562.
  • Mamedov, B. A. and Somuncu, E., 2014. Analytical Treatment of Second Virial Coefficient over Lennard-Jones (2n-n) Potential and its Application to Molecular Systems. Jounal of Molecular Structure, 1068, 164-169.
  • Mamedov, B. A. and Somuncu, E., 2015. Accurate Calculation of Second Virial Coefficient of the Exp-6 Potential and Its Application. Physica A, 420, 246-257.
  • Mason, E. A. and William, E. R., 1954. The Intermolecular Potentials of Helium and Hydrogen. Journal of Chemical Physics, 22, 522- 535.
  • Mayer, E. J. and Mayer, M. G., 1948. Statistical Mechanics. John Wiley &Son, New York, 277- 294.
  • McQuarrie D. A., 1973. Statistical Mechanics. Harper & Row, New York, 222-245.
  • McCarty, M., Babu, .S.V.K., 1970.First Quantum Corrections to Second Virial Coeffiicent of Stockmayer Gas. Journal of Physical Chemistry, 74, 1113-1115.
  • McQuarrie, D. A. and Simon, J. D., 1997. Physical Chemistry: A Molecular Approach. University Science Books Sausalito Calfornia, 49-82.
  • Meng, L. and Duan, Y. Y., 2006. Site-Site potential function and second virial coefficients for linear molecules. Molecular Physics, 104, 2891-2899.
  • Mi, J., Tang, Y., Zhong, C., 2008. Theoretical Study of Sutherland Fluids with Long-Range, Short-Range, and highly Short-Range Potential Parameters. Journal of Chemical Physics, 128, 054503- 054510.
  • Mohammadi, A., Saadatabadi, A. R., Khanpour, M., 2012. Second Virial Coeffiecients of Exp-6 Chains: A Monte Carlo Simulation. Chemical Physics, 397, 26–33.
  • Oh, S. K., 2010. Extending the Group Contribution Concept Using Kihara Potential to Perfluorinated n-alkanes   2 2 1 6 n n C F n    for Estimating Thermophysical. Fluid Phase Equilibria, 288, 87-95.
  • Pathria, R. K., 1996. Statistical Mechanics. Second Edition, Elsevier Press, 299-340.
  • Prausnitz, J. M., Lichtenthaler, R. N., Azevedo, E. G. de, 1999. Fugacities in Gas Mixtures.Molecular Thermodynamics of Fluid Phase Equilibria. Prentice-Hall, New Jersey, 123-211.
  • Ramos-Estrada, M., Tellez-Morales, R., Iglesias- Silva, G. A., Hall, K. R., 2004. A generalized correlation for the second virial coefficient based upon the Stockmayer potential. Latin American Applied Research, 34, 34-41.
  • Reif, F., 1965. Fundementals of Statistical Mechenics and Thermal Physics. McGraw-Hill, New York.1- 333.
  • Vargas, P., Munoz, E., Rodriguez, L., 2001. Second Virial Coefficient for the Lennard-Jones Potential. Physica A, 290, 92-100.
  • Vega, C., McBridge, C., Menduina, C., 2002. The Second Virial Coefficient of the DipolarTwo Center Lennard-Jones Model. Physical Chemistry Chemical Physics, 4, 3000-3007.
  • Widom, B., 2002. Statistical Mechanics: A Concise Introduction for Chemists. Cambridge Universty Press.1-1322.

Year 2018, Volume: 18 Issue: 1, 83 - 89, 30.04.2018

Elif Somuncu

Abstract

References

  • Abdulagatov, A. I., Kaplun, A. B., Meshalkin, A. B., Abdulagatov, I. M. and Stepanov, G. V., 2002. Second Caloric Virial Coefficients for Real Gases and Combined Spherical Symmetric Potential for Simple Molecular Interactions. Journal of Chemical Thermodynamics, 34, 2049–2072.
  • Deszczynski, M., Harding, S. E., Winzor, D. J., 2006. Negative Second Virial Coefficients as Predictors of Protein Crystal Growth: Evidence From Sedimentation Equilibrium Studies that Refutes the Designation of Those Light Scattering Parameters as Osmotic Virial Coefficients. Biophysical Chemistry, 120, 106 – 113.
  • Fender, B. E. F. and HalseyJr, G. D., 1962. Second Virial Coefficients of Argon. Krypton. and Argon‐ Krypton Mixtures at Low Temperatures. Journal of Chemical Physics, 36, 1881.
  • Garberoglio, G., Moldever, M. R. and Harvey, A. H., 2011. Improved First-Principles Calculation of the Third Virial Coefficient of Helium. Journal of Research NIST, 116, 729-742.
  • Garberoglio, G., Jankowski, P., Szalewicz, K., and Harvey, A. H., 2012. Second Virial Coefficents of 2 H and its isotopologues from a six-dimensional potential. Journal of Chemical Physics, 137, 154308- 154319.
  • Gibson, W. G., 1981. Third Virial Coefficient for Quantum Hard Spheres: Two-Point Padé Appraximants for Direct and Exchange Parts. Journal of Statistical Physics, 26, 333-346.
  • Glasser, M. L., 2002. Second virial coefficient for a Lennard-Jones (2n-n) system in d dimensions and confined to a nanotube surface. Physics Letters A, 300, 381-384.
  • Graben, H. W., Present, R. D., 1964. Third Virial Coefficient for the Sutherland ,  Potential. Reviews of Modern Physics., 1025-1033.
  • Gradshteyn, I. S., Ryzhik, I. M., 1965. Exponential Integrals. Tables of Integrals. Series and Products. Acedemic, London. 1-1762.
  • Hirschfelder, J.O., Curtiss, C. F., Bird, R. B., 1954. Molecular Theory of Gases and Liquids. USA Jonh Wiley & Sons. 1-931.
  • Hostettler, H. U., Bernstein, R. B., 1959. Comparison of Exp-6, L-J (12.6) and Sutherland Potential Functions Applied to the Calculation of Differential Scattering Cross Sections. Journal of Chemical Physics, 31, 1422-1423.
  • Hutem, A. and Boonchui, S., 2012. Numerical Evaluation of Second and Third Virial Coefficients of Some Inert Gases via Classical Cluster Expansion. Journal of Mathematical Chemistry, 50, 1262-1276.
  • Kaplan, I. G., 2006. Intermolecular Interactions: Physical Picture, Computational Methods and Model Potentials. Jonh Wiley & Sons, 183-200. Kihara, T., 1953. Virial Coefficiens and Models of Molecules in Gases. Review of Modern Physics, 25, 831-843.
  • Konowalow, D. D. and Hirschfelder, J. O., 1961. Intermolecular Potential Functions for Nonpolar Molecules. Physics of Fluids, 4, 629-635.
  • Levi, D., M. Llano, D., 1975. Closed Form of Second Virial Coefficient for Sutherland Potential. Journal of Chemical Physics, 63, 4561-4562.
  • Mamedov, B. A. and Somuncu, E., 2014. Analytical Treatment of Second Virial Coefficient over Lennard-Jones (2n-n) Potential and its Application to Molecular Systems. Jounal of Molecular Structure, 1068, 164-169.
  • Mamedov, B. A. and Somuncu, E., 2015. Accurate Calculation of Second Virial Coefficient of the Exp-6 Potential and Its Application. Physica A, 420, 246-257.
  • Mason, E. A. and William, E. R., 1954. The Intermolecular Potentials of Helium and Hydrogen. Journal of Chemical Physics, 22, 522- 535.
  • Mayer, E. J. and Mayer, M. G., 1948. Statistical Mechanics. John Wiley &Son, New York, 277- 294.
  • McQuarrie D. A., 1973. Statistical Mechanics. Harper & Row, New York, 222-245.
  • McCarty, M., Babu, .S.V.K., 1970.First Quantum Corrections to Second Virial Coeffiicent of Stockmayer Gas. Journal of Physical Chemistry, 74, 1113-1115.
  • McQuarrie, D. A. and Simon, J. D., 1997. Physical Chemistry: A Molecular Approach. University Science Books Sausalito Calfornia, 49-82.
  • Meng, L. and Duan, Y. Y., 2006. Site-Site potential function and second virial coefficients for linear molecules. Molecular Physics, 104, 2891-2899.
  • Mi, J., Tang, Y., Zhong, C., 2008. Theoretical Study of Sutherland Fluids with Long-Range, Short-Range, and highly Short-Range Potential Parameters. Journal of Chemical Physics, 128, 054503- 054510.
  • Mohammadi, A., Saadatabadi, A. R., Khanpour, M., 2012. Second Virial Coeffiecients of Exp-6 Chains: A Monte Carlo Simulation. Chemical Physics, 397, 26–33.
  • Oh, S. K., 2010. Extending the Group Contribution Concept Using Kihara Potential to Perfluorinated n-alkanes   2 2 1 6 n n C F n    for Estimating Thermophysical. Fluid Phase Equilibria, 288, 87-95.
  • Pathria, R. K., 1996. Statistical Mechanics. Second Edition, Elsevier Press, 299-340.
  • Prausnitz, J. M., Lichtenthaler, R. N., Azevedo, E. G. de, 1999. Fugacities in Gas Mixtures.Molecular Thermodynamics of Fluid Phase Equilibria. Prentice-Hall, New Jersey, 123-211.
  • Ramos-Estrada, M., Tellez-Morales, R., Iglesias- Silva, G. A., Hall, K. R., 2004. A generalized correlation for the second virial coefficient based upon the Stockmayer potential. Latin American Applied Research, 34, 34-41.
  • Reif, F., 1965. Fundementals of Statistical Mechenics and Thermal Physics. McGraw-Hill, New York.1- 333.
  • Vargas, P., Munoz, E., Rodriguez, L., 2001. Second Virial Coefficient for the Lennard-Jones Potential. Physica A, 290, 92-100.
  • Vega, C., McBridge, C., Menduina, C., 2002. The Second Virial Coefficient of the DipolarTwo Center Lennard-Jones Model. Physical Chemistry Chemical Physics, 4, 3000-3007.
  • Widom, B., 2002. Statistical Mechanics: A Concise Introduction for Chemists. Cambridge Universty Press.1-1322.
There are 33 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Elif Somuncu

Publication Date April 30, 2018
Submission Date December 14, 2016
Published in Issue Year 2018 Volume: 18 Issue: 1

Cite

APA Somuncu, E. (2018). Analytical Evaluation of Second Virial Coefficient Using Sutherland Potential and Its Application to Real Gases. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 18(1), 83-89.
AMA Somuncu E. Analytical Evaluation of Second Virial Coefficient Using Sutherland Potential and Its Application to Real Gases. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. April 2018;18(1):83-89.
Chicago Somuncu, Elif. “Analytical Evaluation of Second Virial Coefficient Using Sutherland Potential and Its Application to Real Gases”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 18, no. 1 (April 2018): 83-89.
EndNote Somuncu E (April 1, 2018) Analytical Evaluation of Second Virial Coefficient Using Sutherland Potential and Its Application to Real Gases. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 18 1 83–89.
IEEE E. Somuncu, “Analytical Evaluation of Second Virial Coefficient Using Sutherland Potential and Its Application to Real Gases”, Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 18, no. 1, pp. 83–89, 2018.
ISNAD Somuncu, Elif. “Analytical Evaluation of Second Virial Coefficient Using Sutherland Potential and Its Application to Real Gases”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 18/1 (April 2018), 83-89.
JAMA Somuncu E. Analytical Evaluation of Second Virial Coefficient Using Sutherland Potential and Its Application to Real Gases. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2018;18:83–89.
MLA Somuncu, Elif. “Analytical Evaluation of Second Virial Coefficient Using Sutherland Potential and Its Application to Real Gases”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 18, no. 1, 2018, pp. 83-89.
Vancouver Somuncu E. Analytical Evaluation of Second Virial Coefficient Using Sutherland Potential and Its Application to Real Gases. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2018;18(1):83-9.