Structure and thermodynamics of the one- and two-component square-well fluid

We suggest a new procedure for the quantitative description of the square-well (SW) fluid in the framework of the mean spherical approximation (MSA): At first, the direct correlation function inside the hard core (HC) has been expanded in polynomial series. Then, one obtains the analytical expression for the Fourier transform of the direct correlation function for an arbitrary HC pair potential using the MSA. Further, the SW pair potential has been included into this expression. As a result, one gets the analytical expressions for the structure factor and the isothermal compressibility of the SW fluid. For each set of the SW parameters, temperature, and atomic density, the coefficients of the expansion are determined numerically from the condition that the pair correlation function is zero inside the HC. During the determination of the coefficients, the pair distribution function is being computed. Besides, we numerically calculate the potential energy and pressure. Our results for the one-component SW fluid are in a good agreement with numerical results obtained in the literature from the Ornstein-Zernike equation solution within MSA. This fact allows us to hope that the generalization of this method to binary SW mixtures will be fruitful, so this generalization is given at the end of the article.