Modeling of Molecular Systems: Thermodynamics, Void Volumes, and Solid-Liquid Equilibrium
J.C. Rainwater, P.D. Beale (Univ. of Colorado), and S.G. Gay (Univ. of Colorado)
Objective: To develop a molecular theory of solid-liquid equilibrium (SLE) for pure molecular fluids and mixtures, including hydrocarbons, refrigerants, and polar fluids, and to develop techniques for modeling molecular systems in supercooled liquid, glassy, and amorphous states.
Problem: The complete description of a pure fluid or mixture requires knowledge of the fluid-solid boundary. Our SLE research to date indicates that molecular shape is important and that theories restricted to spherical molecules need to be generalized to nonspherical molecules. There exist methods to determine the thermodynamic properties of hard-sphere systems in terms of average void volumes and surface areas, which we are extending to elongated molecules.
Approach: For SLE, we have followed the approach of P.A. Monson of the University of Massachusetts. The molecule is modeled as a fused hard sphere assembly, for example, a homonuclear hard dumbbell for nitrogen or a heteronuclear dumbbell for methyl chloride. For the hard-body system, the solid free energy is determined in a computationally intensive manner by the method of Frenkel and Ladd, in which at least ten simulations must be performed. More theoretically, the free energy is calculated by the Lennard Jones-Devonshire cell model, from the free volume of a test molecule in a cage of fixed neighboring molecules on a lattice. The liquid free energy is obtained by simulation, and the phase boundary is determined by the double-tangent construction. At the end, mean-field attractive forces and dipole and quadrupole moments are added as perturbations. Free volumes and surface areas are monitored, and expressions are derived for the system pressure in terms of average free volumes and surface areas.
Results and Future Plans: After completion of our study of methyl chloride, we turned our attention to a fluctuating cell theory and the relationships between pressure and void properties for two-dimensional hard dumbbells. The fluctuating cell theory differs from the simple cell theory in that the positions of the cage molecules are allowed to fluctuate, and an average free volume is calculated. The fluctuating cell theory was expected to give better agreement with the results of the full Frenkel-Ladd calculation with multiple simulations than does the simple cell theory. We found this to be true for all hard dumbbells except when the bond length is very small, in the limit of a hard disk. In that limit, we recovered the earlier, counterintuitive discovery of Hoover et al. that the fluctuating cell theory gives poorer agreement than the simple cell theory. We have compared our earlier exact solution for void volumes in three dimensions of a hard-sphere system with a newly published, independent solution of the same problem by a group from Princeton and Bell Labs. Numerical results from the two solutions have been shown to be identical. An important remaining goal is to calculate free volumes of three-dimensional hard dumbbells semianalytically, where the spatial dimensions are integrated analytically and the two angular variables are integrated by polynomial quadruture. At present we have a robust algorithm for the semianalytical method, but it is slower than Monte Carlo. However, there are a number of possible ways of making the semianalytic method substantially faster, and these will be pursued. If successful, the method will allow for a fluctuating cell model in three dimensions with applications to plastic crystals and more complex molecules. Our first planned extensions are to triatomics with dipole moments, such as sulfur dioxide, and molecules that can be approximately modeled as three fused spheres, such as dimethyl ether and propane.
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Last modified: 21 February 2000