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Binary Collision Density in a Non-Ideal Gas as a Function of Particle Density, Collision Diameter, and Temperature

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Abstract

Using molecular dynamics simulations, binary collision density in a dense non-ideal gas with Lennard-Jones interactions is investigated. It is shown that the functional form of the dependence of collision density on particle density and collision diameter remains the same as that for an ideal gas. The temperature dependence of the collision density, however, has a very different form at low temperatures, where it decreases as temperature increases. But at higher temperatures the functional form becomes the same as that for an ideal gas.

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References

  1. Moelwyn-Hughes, E.A.: Physical Chemistry, 2nd edn. Pergamon Press, New York (1961)

    Google Scholar 

  2. Tolman, R.C.: Statistical Mechanics with Applications to Physics and Chemistry, pp. 241–243. Chemical Catalog Company, New York (1927)

    MATH  Google Scholar 

  3. Silbey, R.J., Alberty, R.A.: Physical Chemistry. Wiley, New York (2001)

    Google Scholar 

  4. de Lima, E.F., Ho, T.S., Rabitz, H.: Laser-pulse photoassociation in a thermal gas of atoms. Phys. Rev. A 78, 063417 (2008)

    Article  ADS  Google Scholar 

  5. Akkelin, S.V., Hama, Y., Karpenko, I.A., Sinyukov, Y.M.: Hydro-kinetic approach to relativistic heavy ion collisions. Phys. Rev. C 78, 034906 (2008)

    Article  ADS  Google Scholar 

  6. Itakura, K., Morimatsu, O., Otomo, H.: Shear viscosity of a hadronic gas mixture. Phys. Rev. D 77, 014014 (2008)

    Article  ADS  Google Scholar 

  7. Gaspard, P., Gilbert, T.: Heat conduction and Fourier’s law by consecutive local mixing and thermalization. Phys. Rev. Lett. 101, 020601 (2008)

    Article  ADS  Google Scholar 

  8. Sentoku, Y., Kemp, A.J.: Numerical methods for particle simulations at extreme densities and temperatures: weighted particles, relativistic collisions and reduced currents. J. Comp. Phys. 227, 68466861 (2008)

    Article  MATH  Google Scholar 

  9. Dunkel, J., Hänggi, P.: Relativistic Brownian motion: from a microscopic binary collision model to the Langevin equation. Phys. Rev. E 74, 051106 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  10. Dunkel, J., Hänggi, P.: Relativistic Brownian motion. Phys. Rep. 471, 1–73 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  11. Peano, F., Marti, M., Silva, L.O.: Statistical kinetic treatment of relativistic binary collisions. Phys. Rev. E 79, 025701(R) (2009)

    Article  ADS  Google Scholar 

  12. Mohazzabi, P., Helvey, S.L., McCumber, J.: Maxwellian distribution in non-classical regime. Phys. A 316, 314–322 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  13. Mohazzabi, P., Schmidt, J.R.: Maxwellian relaxation of elastic particles in one dimension. Am. J. Phys. 79, 861–866 (2011)

    Article  ADS  Google Scholar 

  14. Silbey, R.J., Alberty, R.A.: Physical Chemistry. Wiley, New York (2001)

    Google Scholar 

  15. Liboff, R.L.: Kinetic Theory, 2nd edn. Wiley, New York (1998)

    MATH  Google Scholar 

  16. Miandehy, M., Modarress, H.: Equation of state for hard-spheres. J. Chem. Phys. 119, 2716–2719 (2003)

    Article  ADS  Google Scholar 

  17. Kittel, C.: Introduction to Solid State Physics, 7th edn. Wiley, New York (1996)

    MATH  Google Scholar 

  18. Gould, H., Tobochnik, J.: An Introduction to Computer Simulation Methods, vol. 8, 2nd edn. Addison-Wesley, New York (1996)

    MATH  Google Scholar 

  19. Haile, J.M.: Molecular Dynamics Simulation. Wiley, New York (1992)

    Google Scholar 

  20. Reference [17], p. 23

  21. This is because the fraction of total volume occupied by the hard spheres is \(\displaystyle \frac{\pi n}{6}\)

  22. Gould, H., Tobochnik, J.: An Introduction to Computer Simulation Methods, 2nd edn. Addison-Wesley, New York (1996)

    MATH  Google Scholar 

  23. Herzfeld, K.F., Smallwood, H.: In: Taylor, H.S., Glasstone, S. (eds.) A Treatise on Physical Chemistry, vol. II, 3rd edn, p. 37. Van Nostrand, New York (1951)

  24. Strictly speaking, \(-\epsilon \) is the potential energy of the system of two particles. However, without loss of generality, we can assume that particles \(i\) and \(j\) have, respectively, \(-\epsilon \) and zero potential energies

  25. Pathria, R.K.: Statistical Mechanics. Pergamon Press, New York (1972)

    MATH  Google Scholar 

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Correspondence to Pirooz Mohazzabi.

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Mohazzabi, P. Binary Collision Density in a Non-Ideal Gas as a Function of Particle Density, Collision Diameter, and Temperature. J Stat Phys 169, 362–373 (2017). https://doi.org/10.1007/s10955-017-1868-x

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  • DOI: https://doi.org/10.1007/s10955-017-1868-x

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