Thermodynamics of the Stockmayer fluid in an applied field

Ekaterina A. Elfimova, Alexey O. Ivanov, Julien O. Sindt, Philip J. Camp*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The thermodynamic properties of the Stockmayer fluid in an applied field are studied using theory and computer simulation. Theoretical expressions for the second and third virial coefficients are obtained in terms of the dipolar coupling constant (λ, measuring the strength of dipolar interactions as compared to thermal energy) and dipole–field interaction energy (α, being proportional to the applied field strength). These expressions are tested against numerical results obtained by Mayer sampling calculations. The expression for the second virial coefficient contains terms up to λ<sup>4</sup>, and is found to be accurate over realistic ranges of dipole moment and temperature, and over the entire range of the applied field strength (from zero to infinity). The corresponding expression for the third virial coefficient is truncated at λ<sup>3</sup>, and is not very accurate: higher order terms are very difficult to calculate. The virial coefficients are incorporated in to a thermodynamic theory based on a logarithmic representation of the Helmholtz free energy. This theory is designed to retain the input virial coefficients, and account for some higher order terms in the sense of a resummation. The compressibility factor is obtained from the theory and compared to results from molecular dynamics simulations with a typical value λ = 1. Despite the mathematical approximations of the virial coefficients, the theory captures the effects of the applied field very well. Finally, the vapour–liquid critical parameters are determined from the theory, and compared to published simulation results; the agreement between the theory and simulations is good.

Original languageEnglish
Number of pages12
JournalMolecular Physics
Issue number23
Early online date29 Jun 2015
Publication statusPublished - Jun 2015


  • applied field
  • simulation
  • Stockmayer fluid
  • theory


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