207d

Neil H. Gray, The University of Akron, Chemical Engineering Dept., Akron, OH 44325-3906 and **J. Richard Elliott**, Chemical and Biomolecular Engineering, University of Akron, Akron, OH 44325-3906.

Previous reports have established that thermodynamic perturbation theory (TPT) can accurately characterize the thermodynamics of vibrating bond models of n-alkane chains, including vapor pressure and density. These molecular models are composed of hard sphere united atom sites with diameters of roughly 0.36 nm, bond lengths of 0.154 nm, and bond angles of 110°.^{1} The bonded interactions are defined by vibrating potential wells centered at 0.154 nm, 0.265 nm, and by an intramolecular diameter that controls how closely atoms can approach if they are more than two bonds apart, thus controlling the dihedral angle distribution.^{2} The bonded interactions apply to intramolecular sites that are seven or fewer bonds apart. The non-bonded interactions in this work are the same for intermolecular interactions or intramolecular interactions more than seven bonds apart. They are described by a sequence of four wells with varying depth, resembling steps in a staircase. The non-bonded interactions of CH3 are distinct from those of CH2, but the same potential models are transferred to chains of all lengths from C2 to C30. The simulations were performed at packing fractions ranging from 0.01 to 0.56. Each state point was simulated for 5 ns with 100 molecules. TPT decomposes the description of the molecular simulation results into a repulsive contribution (*A*0), and first and second order perturbations (*A*1, *A*2). Higher order perturbations are found to be negligible for packing fractions greater than 0.3. *A*0 is obtained by integrating the reference compressibility factor (*Z*0), which in turn is computed directly from the pressures simulated by molecular dynamics. *A*1 and *A*2 are computed by sums of distributions of sites within the simulated reference fluids.

Note that the TPT contributions are not necessarily computed with direct regard to the molecular connectivity. For example, the *Z*0 contribution is computed from the sum of all collisions, regardless of whether they are intramolecular or intermolecular collisions. Similarly, the *A*1 and *A*2 contributions are summed over site-site distribution functions that may involve sites on the same molecule as well as those on different molecules. For the *A*1 term, this includes only the non-bonded intramolecular interactions in addition to intermolecular interactions. The density dependence of the intramolecular *A*1 term has been investigated in this study. For the *A*2 term, we must recognize that there are both inter- and intra- molecular contributions to the pair correlations. For example, suppose *N _{ijm}* designates the number of

Keywords: Physical properties, molecular dynamics simulation, vapor pressure, density, phase equilibria, thermodynamic perturbation theory, intramolecular correlations, screening.

(1) Cui, J.; Elliott Jr., J. R. Phase Diagrams for Multi-Step Potential Models of n-Alkanes by Discontinuous Molecular Dynamics/Thermodynamic Perturbation Theory. J. Chem. Phys. 2002, 116, 8625.

(2) Unlu, O.; Gray, N. H.; Gerek, Z. N.; Elliott, J. R. Transferable Step Potentials for the Straight Chain Alkanes, Alkenes, Alkynes, Ethers, and Alcohols. Ind. Eng. Chem. Res. 2004, 43, 1788-1793.

(3) Elliott, J. R.; Gray, N. H. Asymptotic Trends in Thermodynamic Perturbation Terms. J. Chem. Phys. 2005, 123, 184902.

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