Lattice Gas Condensation and Its Relation to the Divergence of Virial Expansions in the Powers of Activity

  • M. V. Ushcats Taras Shevchenko National University of Kyiv, Admiral Makarov National University of Shipbuilding
  • L. A. Bulavin Taras Shevchenko National University of Kyiv
  • V. M. Sysoev Taras Shevchenko National University of Kyiv
  • S. Yu. Ushcats Admiral Makarov National University of Shipbuilding
Keywords: lattice gas, virial coefficients, reducible cluster integrals, activity, equation of state, condensation

Abstract

An efficient algorithm for the calculation of high-order reducible cluster integrals on the basis of irreducible integrals (virial coefficients) has been proposed. The algorithm is applied to study the behavior of the well-known virial expansions of the pressure and density in power series of activity up to very high-order terms, as well as recently derived symmetric power expansions in the reciprocal activity, in the framework of a specific lattice gas model. Our results are consistent with those obtained in other modern studies of the partition function in terms of the density. They disclose the physical meaning of the divergence that the mentioned expansions demonstrate in the condensation region.

References

M.V. Ushcats. High-density equation of state for a lattice gas. Phys. Rev. E 91, 052144 (2015).

https://doi.org/10.1103/PhysRevE.91.052144

M.V. Ushcats, L.A. Bulavin, V.M. Sysoev, S.J. Ushcats. Virial and high-density expansions for the Lee–Yang lattice gas. Phys. Rev. E 94, 012143 (2016).

https://doi.org/10.1103/PhysRevE.94.012143

M.V. Ushcats, L.A. Bulavin, V.M. Sysoev, V.Y. Bardik, A.N. Alekseev. Statistical theory of condensation – Advances and challenges. J. Mol. Liq. 224, 694 (2016).

https://doi.org/10.1016/j.molliq.2016.09.100

R. Balescu. Equilibrium and Nonequilibrium Statistical Mechanics (Wiley, 1975) [ISBN: 0471046000].

J.E. Mayer, M.G. Mayer. Statistical Mechanics (Wiley, 1977)

C. Feng, A.J. Schultz, V. Chaudhary, D.A. Kofke. Eighth to sixteenth virial coefficients of the Lennard-Jones model. J. Chem. Phys. 143, 044504 (2015).

https://doi.org/10.1063/1.4927339

M.V. Ushcats. Modified Lennard-Jones model: Virial coefficients to the 7th order. J. Chem. Phys. 140, 234309 (2014).

https://doi.org/10.1063/1.4882896

M.V. Ushcats. Communication: Low-temperature approximation of the virial series for the Lennard-Jones and modified Lennard-Jones models. J. Chem. Phys. 141, 101103 (2014).

https://doi.org/10.1063/1.4895126

A.J. Schultz, D.A. Kofke. Vapor-phase metastability and condensation via the virial equation of state with extrapolated coefficients. Fluid Phase Equilibria 409, 12 (2016).

https://doi.org/10.1016/j.fluid.2015.09.016

M.V. Ushcats. Virial coefficients of modified LennardJones potential. Ukr. Fiz. Zh. 59, 173 (2014) (in Ukrainian).

M.V. Ushcats. Modification of the Mayer sampling method for the calculation of high-order virial coefficients. Ukr. Fiz. Zh. 59, 737 (2014) (in Ukrainian).

M.V. Ushcats, S.J. Ushcats, A.A. Mochalov. Virial coefficients of Morse potential. Ukr. J. Phys. 61, 160 (2016).

https://doi.org/10.15407/ujpe61.02.0160

M.V. Ushcats, A.A. Gaisha. The fifth virial coefficient for the Sutherland, Morse, and Lennard-Jones potentials. Visn. Kharkiv Nat. Univ. 18, 67 (2013) (in Russian).

M.V. Ushcats, K.D. Evfimko. The sixth virial coefficient for the modified Lennard-Jones potential, Visn. Odessa Nat. Univ. 19 (1), 37 (2014).

M.V. Ushcats. Equation of state beyond the radius of convergence of the virial expansion. Phys. Rev. Lett. 109, 040601 (2012).

https://doi.org/10.1103/PhysRevLett.109.040601

M.V. Ushcats. ???????????. Visn. Kharkiv Nat. Univ. 17, 6 (2012).

M.V. Ushcats. Adequacy of the virial equation of state and cluster expansion. Phys. Rev. E 87, 042111 (2013).

https://doi.org/10.1103/PhysRevE.87.042111

M.V. Ushcats. Condensation of the Lennard-Jones fluid on the basis of the Gibbs single-phase approach. J. Chem. Phys. 138, 094309 (2013).

https://doi.org/10.1063/1.4793407

J. Groeneveld. Two theorems on classical many-particle systems. Phys. Lett. 3, 50 (1962).

https://doi.org/10.1016/0031-9163(62)90198-1

O. Penrose. Convergence of fugacity expansions for fluids and lattice gases. J. Math. Phys. 4, 1312 (1963).

https://doi.org/10.1063/1.1703906

E. Donoghue, J.H. Gibbs. Condensation theory for finite, closed systems. J. Chem. Phys. 74, 2975 (1981).

https://doi.org/10.1063/1.441420

T.D. Lee, C.N. Yang. Statistical theory of equations of state and phase transitions. II. Lattice gas and Ising model. Phys. Rev. 87, 410 (1952).

https://doi.org/10.1103/PhysRev.87.410

Published
2018-12-15
How to Cite
Ushcats, M., Bulavin, L., Sysoev, V., & Ushcats, S. (2018). Lattice Gas Condensation and Its Relation to the Divergence of Virial Expansions in the Powers of Activity. Ukrainian Journal of Physics, 62(6), 533. https://doi.org/10.15407/ujpe62.06.0533
Section
General problems of theoretical physics

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