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378447 Real Chain Fluid Equations of State Derived from New Versions of Wertheim's Perturbation Theory

**ABSTRACT**

Modern molecular-based equations of state (e.g., statistical associating fluid theory SAFT type equations of state) typically involve a bonding term derived from a variation of Wertheim’s perturbation theory. The most commonly used expression for the bonding compressibility factor is derived from the primitive first-order perturbation theory (TPT1), which is based on the hard-sphere reference fluid and only involves nearest neighbor association interactions in clusters. The second-order perturbation theory (TPT2) is more accurate but is also more formidable because it requires an expression for the triplet interaction, which is generally unavailable. Another version, thermodynamic dimer perturbation theory (TPT-D) is also a first-order version based on the hard-dimer reference fluid. TPT-D has proven to be more accurate than TPT1 and more feasible than TPT2 (Marshall and Chapman, 2013).

The work presented in this paper is threefold and involves (1) improvement of the current “hard-sphere-plus-chain” TPT framework discussed above; (2) development of new TPT treatments for fluids including *attractive* interactions and (3) extension of the above theories to include molecular specificity (branched chain and linear molecules). First, regarding improvement of the current “state-of-the-art” TPT-D framework, we revisit the assumption of equality of successive pair correlation function derivatives ∂g_{HD}(s)∂h = ∂g_{HT}(s)∂h = ∂g_{HO}(s)∂h = … where g(s) is the pair correlation (radial distribution) function at contact value, h is the dimensionless molecular packing fraction and HD, HT and HO stand for hard-dimer, hard-tetramer, and hard-octamer respectively. Specifically, here we use molecular simulation data (Chang and Sandler, 1994) to reformulate the above derivative relationships. Moreover, we revisit the issue of the use of Chiew’s (1991) integral equation theoretical expression for g_{HD}(s) versus the use of an empirical fit of molecular simulation data for g_{HD}(s) versus h.

Secondly, concerning the introduction of new pair correlation functions into the theoretical development, we show that various intermolecular potential functions including Lennard-Jones, Square-Well, and Yukawa are capable of producing equations of state (EOS’s) for fluids including attractive interactions. Escobedo and de Pablo (1995) showed that the Generalized Flory Dimer (GFD) theory and TPT-D equations can be generalized into a common form and they obtained a highly accurate EOS for long athermal chains. Here, we investigate the feasibility of using their approach to obtain an accurate EOS for long *attractive* chain fluids. Finally, regarding molecular specificity, we employ the recently introduced approach used by Marshall and Chapman (2013) to distinguish between linear molecular effects versus effects from branching. Several practical examples including applications to both *model* and *real* hydrocarbon chain fluids are given to illustrate the points indicated above.

**REFERENCES**

Chang, J. and S. I. Sandler, *An Equation of State for the Hard-Sphere Chain Fluid: Theory and Monte Carlo Simulation*, Chem. Eng. Sci., **49**, 2777-2791 (1994).

Chiew, Y. C., *Percus-Yevick Integral Equation Theory for Athermal Hard-Sphere Chains. II. Average Intermolecular Correlation Functions*. Molec. Phys. **73**, 359-373 (1991).

Escobedo, F. A. and J. J. de Pablo,** ***Chemical Potential and Equations of State of Hard Core Chain Molecules*, J. Chem. Phys., **103**, 1946-1956 (1995).

Marshall, B. D. and W. G. Chapman, *Three New Branched Chain Equations of State Based on Wertheim’s Perturbation Theory*, J. Chem. Phys., **138**, 174109 (2013).

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