(190t) Accurate Perturbation Theory for Chains of Soft-Core Attractive Segments of Arbitrary Softness

An improved equation of state for chains of spherical segments interacting through Mie potentials is presented and the thermodynamic properties are compared with Monte Carlo simulation data and experimental data for real chain molecule; vapour-liquid coexistence densities and vapour pressures as well as second derivative properties (heat capacities, isobaric thermal expansivities, and speed of sound) are examined. The equation is an improvement of that presented in previous work with the SAFT-VR approach [1]. The new approach is based on a rigorous use of the Barker and Henderson high-temperature expansion up to second order for the free energy of the monomer fluid. The radial distribution function of the reference monomer fluid, which is incorporated in the calculation of the chain properties is also calculated from a perturbation expansion up to second order. In the special case of the Lennard-Jones chains, the theory is seen to provide accurate estimates of the complete vapour-liquid diagram for chains up to 100 segments. We have also applied this new SAFT-VR equation of state to real substances (associating and non-associating) for which we show the importance of using a variable repulsive range through the Mie (inverse power law 1/rⁿ) potential to simultaneously describe vapour-liquid equilibrium and second derivative properties. Among these results we will place a particular focus on the effect of the softness of the potential to describe the anomalies in the thermodynamic properties of the fluid phases of water. The highly accurate representation obtained here for homonuclear chains, will be extended for heteronuclear molecules formed from Mie segments of different type by coupling the current development with the SAFT-gamma group contribution approach (previously developed for square-well potentials).[2]

References:

[1] Th. Lafitte, D. Bessieres, M. M. Piñeiro and J.-L. Daridon, J. Chem. Phys., 124, 024509 (2006).

[2] A. Lymperiadis, C. S. Adjiman, A. Galindo and G. Jackson, J. Chem. Phys. 127, 234903 (2007)