# RFA in Mathematica (FILES)

In this page you can find some files related to our work:
• Mathematica notebooks related to the rational function approximation (RFA) method for multicomponent mixtures of additive hard spheres
• Mathematica notebooks related to the rational function approximation (RFA) method for multicomponent mixtures of additive sticky hard spheres

As it's happily usual in science, you can use these notebooks freely; you only have to give credit to the author if you think this is suitable.

The rational function approximation (RFA) method allows us to obtain (approximate) analytical expressions for the radial distribution functions and structure factors in a multi-component mixture of additive hard spheres [S. B. Yuste, A. Santos and M. López de Haro, J. Chem. Phys., vol. 108, 3683 (1998) ] In this method, only contact values of the radial distribution function and the isothermal compressibility are required and thermodynamic consistency is easily achieved. The approach is simpler but yields equivalent results to the Generalized Mean Spherical Approximation. Calculations are presented in the next Mathematica programs for two binary and a ternary mixture at high density in which the Boublík-Mansoori-Carnahan-Starling-Leland equation of state is used.

Here we give three Mathematica 3.0 notebooks:

• The notebook alpha.nb allows us to obtain the parameter "alpha" that leads to thermodynamic consistency . The notebook alpha.ma is the Mathematica 2.2 version.
• The notebook rdf.nb gives the radial distribution function according to the RFA method. The Mathematica 2.2 version is rdf.ma
• The notebook sq.nb gives the structure factor. The version 2.2 is sq.ma.

The rational function approximation (RFA) method also allows us to obtain (approximate) analytical expressions for the cavity functions  and structure factors in a multi-component mixture of additive sticky hard spheres. [A. Santos, S.B. Yuste and M. López de Haro, J. Chem. Phys., vol. 109, 6814 (1998)].  In its simplest implementation, the method yields the Percus-Yevick approximation. In the next order,  only contact values of the cavity functions and the isothermal compressibility are required.

Here we give three Mathematica 3.0 notebooks:

• The notebook alphaSHS.nb allows us to obtain the parameter "alpha" compatible with prescribed values of the isothermal susceptibility and cavity functions at contact. The notebook alphaSHS.ma is the Mathematica 2.2 version.
• The notebook yr_Gs.nb allows us to evaluate the cavity function y_{i,j}(r) and the Laplace transform G_{i,j}(s) of  r*g_{i,j}(r)  according to the RFA method. The Mathematica 2.2 version is yr_Gs.ma
• The notebook ycon_chi.nb gives the contact value of the cavity functions and the isothermal susceptibility as prescribed by several approximations . The version 2.2 is ycon_chi.ma. 