Statistical theory of condensation — Advances and challenges

Ushcats, M. V.; Bulavin, L. A.; Sysoev, V. M.; Bardik, V.Yu.; Alekseev, Alexander N.

doi:10.1016/j.molliq.2016.09.100

Cited by 27 publications

(38 citation statements)

References 93 publications

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“…Although this function is not new (it was introduced by the Mayers themselves [1]), and its form is much simpler than that of the generating function in terms of irreducible integrals [4,5,6], it has not been used explicitly to derive the equation of state in terms of reducible integrals.…”

Section: Generating Function In Terms Of Reducible Integralsmentioning

confidence: 99%

“…All the equations mentioned above (in terms of the constant reducible as well as irreducible integrals) yield an essential discontinuity of density (the divergence to infinity) instead of the proper jump discontinuity. Although the main reason for such non-physical behavior is known in principle (it has been clearly stated in some researches [9,10,4]) the problem still remains absolutely unexplored in statistical theory.…”

Section: Introductionmentioning

confidence: 99%

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Equation of state for all regimes of a fluid: From gas to liquid

Ushcats

Bulavin

et al. 2018

Phys. Rev. E

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The study of Mayer's cluster expansion (CE) for the partition function demonstrates a possible way to resolve the problem of the CE non-physical behavior at condensed states of fluids. In particular, a general equation of state is derived for finite closed systems of interacting particles, where the pressure is expressed directly in terms of the density (or system volume) and temperature-volume dependent reducible cluster integrals. Although its accuracy is now greatly affected by the limited character of the existing data on the reducible cluster integrals and, especially, the absence of any information on their density dependence, a number of simple approximations indicate the qualitative adequacy of this equation in various regimes of a fluid: from gaseous to liquid states (including the transition region).

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Section: Generating Function In Terms Of Reducible Integralsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Equation of state for all regimes of a fluid: From gas to liquid

Ushcats

Bulavin

et al. 2018

Phys. Rev. E

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“…A new statistical approach has been proposed recently [1][2][3] for a wide range of lattice gas models, in which the "particle-hole" symmetry inherent in such models is used. For the general well-known virial equation of state (VEOS) [4,5]…”

Section: Introductionmentioning

confidence: 99%

“…the virial coefficients, for a variety of intermolecular interaction models [6][7][8][9][10][11][12][13][14]. However, modern researches [3,[15][16][17][18] testify that, at subcritical temperatures, the limit of applicability of VEOS (1) is a point, where the isothermal bulk modulus of the system vanishes, i.e. the value of density is determined by the equation…”

Section: Introductionmentioning

confidence: 99%

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

Ushcats¹,

Bulavin²,

Sysoev³

et al. 2017

Ukr. J. Phys.

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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. K e y w o r d s: lattice gas, virial coefficients, reducible cluster integrals, activity, equation of state, condensation.

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“…This activity, z G , is exactly the divergence point of the activity series, n 2 b n z n (and, therefore, the AVEOS series, nb n z n , b n z n , in accordance with the Cauchy-Hadamard theorem) [9,18,22,23,32].…”

mentioning

confidence: 96%

Evidence for a first-order phase transition at the divergence region of activity expansions

2018

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On the example of a lattice-gas model, a convincing confirmation is obtained for the direct relationship between the condensation phenomenon and divergent behavior of the virial expansions for pressure and density in powers of activity. The present study analytically proves the pressure equality for the low-density and high-density virial expansions in powers of density (in terms of irreducible cluster integrals or virial coefficients) exactly at the symmetrical points, where their isothermal bulk modulus vanishes, as well as for the corresponding expansions in powers of activity (in terms of reducible cluster integrals) at the same points (the points of their divergence). For lattice-gas models of arbitrary geometry and dimensions, a simple and general expression is derived for the phase-transition activity (the convergence radius of activity expansions) that, in particular, exactly matches the well-known phase-transition activity of the Lee -Yang model. In addition, the study demonstrates that Mayer's expansion with the constant (volume independent) cluster integrals remains correct up to the condensation beginning, and the actual density-dependence may be taken into account for the high-order integrals only in more dense regimes beyond the saturation point.

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Statistical theory of condensation — Advances and challenges

Cited by 27 publications

References 93 publications

Equation of state for all regimes of a fluid: From gas to liquid

Equation of state for all regimes of a fluid: From gas to liquid

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

Evidence for a first-order phase transition at the divergence region of activity expansions

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