Modification of a new potential model used for calculation of the second virial coefficient and zero density transport properties

Abstract

A new hard-core potential model was recently used to calculate thermodynamic properties of some model fluids, including equilibrium properties, such as compressibility factor and internal energy. A Lennard–Jones (LJ) like potential has been used to modify the repulsive part of the potential. The modified potential contains five parameters, namely, α, R, ε, σ, and σ_HS. The parameter α is the tail of the attractive branch whose value changes from zero to one. In this work, we have chosen α = 1 to make the potential continuous at separation r = Rσ, where the parameter R is the well width. R lies in the range 1.2 to 2.5, and R = 1.3 was found to be the best value for all real gases studied. The parameter ε is the well depth of potential function, and σ is the separation at which the potential function is zero. σ_HS is the effective hard sphere diameter, which depends on temperature and an additional parameter. Using statistical mechanics along with the Boltzmann factor criterion (BFC) for the effective hard sphere diameter, an analytical expression has been derived for the reduced second virial coefficient in terms of the reduced temperature. Fitting experimental data to expression derived for the second virial coefficient, the potential parameters ε and σ are obtained. Since this potential is spherical (depending only on distance), three types of species are chosen, namely Ar and He (monoatomic), N₂and O₂ (diatomic), and methane (spherical molecule), to show how appropriate this potential model is for them. This model predicts an inversion temperature for the second virial coefficient (temperature at which the second virial coefficient pass through a maximum) at , where T ₁ is the inversion temperature, and T_B is the Boyle temperature. The predicted value is better than that of the L–J model (for which ). The maximum percentage deviation of the second virial coefficient is about 2%, except around the Boyle temperature. Then the transport properties of the fluids at the zero density limit, including viscosity, thermal conductivity, and self-diffusion coefficients, are calculated using the same values of the potential parameters. Maximum percentage deviation of transport properties at the zero density limit is about 3% for viscosity (except for Ar, with 5%), about 2.5% for thermal conductivity (except for N₂ and Ar, at 8 and 5%, respectively), and about 8% for the self-diffusion coefficient. In comparison with experimental data, the modified potential model gives more accurate results than those obtained from the hard-core and modified hard-core potential models, especially at high temperatures.

Acknowledgements

We would like to thank M. Nahali for use of his computer programs to calculate the collision integrals, and are grateful to the Sharif University of Technology research council for financial support.