Journal of Physical Chemistry B, Vol.108, No.28, 10062-10070, 2004
First-order perturbative contribution to the compressibility factor of square-well fluids from Monte Carlo and integral equation theory
We have determined by Monte Carlo NVT simulations the zero- and first-order terms in the expansion of the compressibility factor of square-well fluids in the power series of the inverse of the reduced temperature for different densities and well widths. In addition, the values of the compressibility factor obtained from the perturbative expansion, truncated beyond the first-order term, are compared with those obtained directly by MC simulations performed on the SW system, which we reported previously (Largo, J.; Solana, J. R. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 2003, 67, 066112). The aim is to establish the limits of validity of this truncated expansion in terms of densities, temperatures, and potential widths. We have found that this approximation is very accurate for any value of the potential width, density, and temperature, except perhaps for small potential widths at very low temperatures. Moreover, the values of the first-order contribution are compared with those obtained from the Tang and Lu (Tang, Y.; Lu, B. C.-Y. J. Chem. Phys. 1994 100, 6665) perturbation theory based on the integral equation theory as well as with those from the Barker-Henderson perturbation theory. The aim is twofold: on one hand, to establish whether the pressure route used in the Tang-Lu theory provides better accuracy than the energy route used in the Barker-Henderson theory and on the other hand to determine whether the Tang-Lu theory, which is more complicated, is advantageous compared to the Barker-Henderson theory. We have found that the Barker-Henderson perturbation theory is advantageous compared to the Tang-Lu theory with regard to the calculation of the thermodynamic properties, whereas the contrary is true for structural properties.