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Athermal Contribution to the Excess Entropy in the Long Chain Limit

J. Richard Elliott1, Neil H. Gray2, and Amir Vahid1. (1) Chemical and Biomolecular Engineering, University of Akron, Akron, OH 44325-3906, (2) Chemstations Inc., 2901 Wilcrest Drive, Houston, TX 77042

Mixtures of hydrocarbons have been simulated with discontinuous potential models to characterize the Helmholtz energy of the repulsive reference fluids (A0) as functions of density and composition. A previous study focused on methane, ethane, propane, n-butane, n-hexane, n-heptane, n-decane, and benzene.[1] Unfortunately, a slight inconsistency was encountered when the trend observed for these small molecules was extrapolated to the long chain limit. In the present work, we extend the analysis to methane with C10, C20, and C40 molecules of: nalkanes, ethyl-styrenes, and ethyl-propylenes. Compositions varied from 0.1 to 0.9 mole fraction for each binary mixture. Packing fractions varied from 0.3 to 0.5.

The goal of the present study was to develop a general strategy for interpolating the perturbation contributions between simulations of individual state points in order to facilitate usage of molecular simulation results in engineering applications. We find that the athermal entropy of mixing deviates significantly from ideality, but still follows the van der Waals mixing formula. This leads to an accurate characterization of the entropic contribution for mixtures of all sizes and shapes. A general rule is developed for predicting the athermal entropy of mixing based on knowledge of the volume ratios of the constituent molecules. The simulations are compared to several theories, including the MCSL theory for hard spheres,[2] the SAFT model,[3] and the Guggenheim-Staverman theory.[4]

Keywords: Thermodynamic properties, molecular simulation, polymers, entropy, mixtures, phase equilibria.

Reference:

1. Gray, N. H.; Elliott, J. R. In Quadratic Mixing in Perturbation Theory, AIChE Fall National Meeting, Austin, TX, 2004; Austin, TX, 2004; p 160e.

2. Mansoori, G. A.; Carnahan, N. F.; Starling, K. E.; Leland, T. W., Equilibrium Thermodynamic Properties of the Mixture of Hard Spheres. J. Chem. Phys 1971, 54, 1523-1525.

3. Chapman, W. G.; Gubbins, K. E.; Jackson, G.; Radosz, M., SAFT: Equation of State Solution Model for Associating Fluids. Fluid Phase Equilib. 1989, 52, 31.

4. Abrams, D. S.; Prausnitz, J. M., Statistical Thermodynamics of Liquid Mixtures: A New Expression for the Excess Gibbs Energy of Partly or Completely Miscible Systems. AIChE J. 1975, 21, 116.