Thermodynamics of the Stockmayer fluid in an applied field

Abstract

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 λ⁴, 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 λ³, 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.

Keywords:

• Stockmayer fluid
• applied field
• theory
• simulation

Acknowledgements

Ekaterina A. Elfimova and Philip J. Camp thank the Ural Federal University for supporting collaborative visits between the Edinburgh and Ekaterinburg groups.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. Original data from Mayer-sampling and molecular-dynamics simulations are available from http://dx.doi.org/10. 7488/ds/249

Additional information

Funding

Ekaterina A. Elfimovaand Alexey O. Ivanov gratefully acknowledge research funding from the Ministry of Education and Science of the Russian Federation [agreement no. 3.12.2014/K, contract no. 02.A03.21.0006]. Julien O. Sindt was supported by the Engineering and Physical Sciences Research Council (UK) through the provision of a studentship.