STATISTICAL ASSOCIATING FLUID THEORY FOR CHAIN MOLECULES WITH ATTRACTIVE POTENTIALS OF VARIABLE RANGE

A version of the statistical associating: fluid theory (SAFT) is devel oped for chain molecules of hard-core segments with attractive potenti als of variable range (SAFT-VR). The different contributions to the He lmholtz free energy are evaluated according to the Wertheim perturbati on theory. The monomer properties are obtained from a high-temperature expansion up to second order, using a compact expression for the firs t-order perturbation term (mean-attractive energy) a(1). Making use of the mean-value theorem, a(1) is given as the van der Waals attractive constant and the Carnahan and Starling contact value for the hard-sph ere radial distribution function in tens of an effective packing fract ion. The second-order perturbation term a(2) is evaluated with the loc al compressibility approximation. The monomer cavity function, require d for the calculation of the free energy due to the formation of the c hains and the contribution due to association, is given as a function of a(1). We analyse the equation of state for chain molecules with thr ee different types of monomer hard-core potentials with variable attra ctive range: square-well (SW). Yukawa (Y), and Sutherland (S). The the ory for the hard-con potentials can easily be generalised to soft-core systems: we develop a simple equation of state for Mie m - n potentia ls, of which the Lennard-Jones (LJ) 6-12 potential is a particular cas e, The equations of state, expressed in terms of reduced variables, ar e explicit functions of the reduced temperature, the packing fraction, the number of monomers segments forming the chain, and the parameter lambda which characterises thr range of the the attractive potential. The relevance of the last parameter in the application of the theory t o n-alkanes and n-perfluoroalkanes is explicitly shown with the SW exp ressions. An accurate description of the vapour pressure and the satur ated Liquid densities is obtained, with a simple dependence of the par ameters of the monomer potential on the number of carbons. The extensi on of our SAFT-VR expressions to mixtures is also presented in terms o f a simple expression for the mean-attractive energy for mixtures, bas ed on a straightforward generalisation of the theory for pure componen ts. (C) 1997 American Institute of Physics.