Divergence of activity expansions: Is it actually a problem?

Area of Science:

• Statistical Mechanics
• Thermodynamics
• Physical Chemistry

Background:

• Realistic interaction models (Lennard-Jones, Morse, etc.) are crucial for understanding molecular behavior.
• Virial expansions are used to describe the thermodynamic properties of gases and liquids.
• Understanding phase transitions, like condensation, is fundamental in physical sciences.

Purpose of the Study:

• To analyze the asymptotic behavior of virial expansions for pressure and density, considering high-order terms.
• To investigate the thermodynamic adequacy of these expansions in the divergence region.
• To provide a statistical explanation for the phenomenon of condensation.

Main Methods:

• Studied asymptotic behavior of virial expansions in powers of activity.
• Incorporated high-order power terms.
• Utilized known finite-order irreducible integrals and approximations of infinite irreducible series.

Main Results:

• The virial expansion behavior remains thermodynamically adequate even in the divergence region (subcritical temperatures).
• This behavior correctly predicts the onset of first-order phase transitions, showing density jumps.
• The study offers a statistical basis for the condensation phenomenon.

Conclusions:

• The high-order virial expansions provide a statistically adequate explanation for condensation.
• Further research on high-order cluster integrals and their density dependence is needed for a complete description of liquid and solid states.
• The findings contribute to a deeper understanding of phase transitions in molecular systems.