Admiral Makarov National University of Shipbuilding, 9 Geroyev Stalingrada Avenue, Mykolayiv 54025, Ukraine.
Taras Shevchenko University of Kiev, 2 Academic Glushkov Avenue, Kiev 03680, Ukraine.
Phys Rev E. 2017 Dec;96(6-1):062115. doi: 10.1103/PhysRevE.96.062115. Epub 2017 Dec 13.
For realistic interaction models, which include both molecular attraction and repulsion (e.g., Lennard-Jones, modified Lennard-Jones, Morse, and square-well potentials), the asymptotic behavior of the virial expansions for pressure and density in powers of activity has been studied taking power terms of high orders into account on the basis of the known finite-order irreducible integrals as well as the recent approximations of infinite irreducible series. Even in the divergence region (at subcritical temperatures), this behavior stays thermodynamically adequate (in contrast to the behavior of the virial equation of state with the same set of irreducible integrals) and corresponds to the beginning of the first-order phase transition: the divergence yields the jump (discontinuity) in density at constant pressure and chemical potential. In general, it provides a statistical explanation of the condensation phenomenon, but for liquid or solid states, the physically proper description (which can turn the infinite discontinuity into a finite jump of density) still needs further study of high-order cluster integrals and, especially, their real dependence on the system volume (density).
对于包含分子吸引力和排斥力的实际相互作用模型（例如 Lennard-Jones、修正 Lennard-Jones、Morse 和方阱势），已经研究了压力和密度的维里展开式在活性幂次下的渐近行为，考虑了高阶幂次的功率项，基于已知的有限阶不可约积分以及最近的无限不可约级数的近似值。即使在发散区域（亚临界温度下），这种行为在热力学上仍然是充分的（与具有相同不可约积分的维里状态方程的行为相反），并且对应于一级相变的开始：发散给出了在恒定压力和化学势下密度的跳跃（不连续性）。一般来说，它提供了对凝聚现象的统计解释，但对于液体或固体状态，物理上适当的描述（可以将无限不连续性转化为密度的有限跳跃）仍然需要进一步研究高阶团簇积分，特别是它们对系统体积（密度）的实际依赖性。
