A virial equation of state of associating systems based on wertheim's association theory
Kim, Hye Min
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An equation of state of a gas provides a mathematical relation among the pressure, volume, temperatures, and the number of moles. Many modifications of the perfect gas equation of state have been introduced and the virial equation of state (VEOS) is one of those. The great appeal of VEOS is the rigorous connection that it makes between the thermodynamic behavior and the molecular interactions, via these cluster integrals. VEOS performs well in describing the thermodynamic behavior of non-condensed non-polar molecular fluids. However, VEOS is not particularly effective at capturing the strong directional interactions of associating fluids. As an alternative to the virial equation of state (VEOS), a Wertheim equation of state (WEOS) is derived based on Wertheim's association theory and applied for the associating systems. Similar to VEOS, WEOS keeps molecular level detail, but by decomposing the intermolecular potential into association and non-association terms, it also captures the strong directional association of molecules via hydrogen bonding much more effectively than VEOS. The Mayer sampling Monte Carlo method is used to evaluate the cluster integrals that arise in the virial approach and the Wertheim approach. The effectiveness of Wertheim's multi-density formalism is verified with a simple Lennard-Jones model having one-, two-, and four-sites formed from conical square-well potential, and applied for three realistic models: the Gaussian charge polarizable model (GCPM) of water, and the improved OPLS-UA model and the new TraPPE-UA model for acetic acid. For GCPM water, we use a three-association-site model to represent 1 oxygen and 2 hydrogen sites and the multibody contributions are handled. For OPLS-UA and new TraPPE-UA acetic acid molecules, one-site and two-site models are examined and the flexible contributions are considered. We compare the pressures determined from various truncated WEOS to values from VEOS and from Monte Carlo simulation. The thermodynamic properties of associating systems obtained from WEOS converge much better to NpT simulation results compared to the conventional virial formalism.