# Statistical associating fluid theory for chain molecules with attractive potentials of variable range

Alejandro Gil-Villegas, Amparo Galindo, Paul J. Whitehead, Stuart J. Mills, George Jackson, Andrew N. Burgess- Physical and Theoretical Chemistry
- General Physics and Astronomy

A version of the statistical associating fluid theory (SAFT) is developed for chain molecules of hard-core segments with attractive potentials of variable range (SAFT-VR). The different contributions to the Helmholtz free energy are evaluated according to the Wertheim perturbation theory. The monomer properties are obtained from a high-temperature expansion up to second order, using a compact expression for the first-order perturbation term (mean-attractive energy) a1. Making use of the mean-value theorem, a1 is given as the van der Waals attractive constant and the Carnahan and Starling contact value for the hard-sphere radial distribution function in terms of an effective packing fraction. The second-order perturbation term a2 is evaluated with the local compressibility approximation. The monomer cavity function, required for the calculation of the free energy due to the formation of the chains and the contribution due to association, is given as a function of a1. We analyse the equation of state for chain molecules with three different types of monomer hard-core potentials with variable attractive range: square-well (SW), Yukawa (Y), and Sutherland (S). The theory for the hard-core potentials can easily be generalised to soft-core systems: we develop a simple equation of state for Mie m−n potentials, of which the Lennard-Jones (LJ) 6-12 potential is a particular case. The equations of state, expressed in terms of reduced variables, are explicit functions of the reduced temperature, the packing fraction, the number of monomers segments forming the chain, and the parameter λ which characterises the range of the the attractive potential. The relevance of the last parameter in the application of the theory to n-alkanes and n-perfluoroalkanes is explicitly shown with the SW expressions. An accurate description of the vapour pressure and the saturated liquid densities is obtained, with a simple dependence of the parameters of the monomer potential on the number of carbons. The extension of our SAFT-VR expressions to mixtures is also presented in terms of a simple expression for the mean-attractive energy for mixtures, based on a straightforward generalisation of the theory for pure components.