(591d) Computational Cluster Methods for Development of Molecular-Based Equations of State: Beyond the Virial Equation

Thermodynamic models for bulk behavior are most effective and have greatest predictive power when they are developed with consideration of molecular phenomena. Methods based on computation of cluster integrals are attractive in this context because they can accommodate full molecular detail while providing simple formulas for the bulk behavior. The best-known such method is the virial equation of state (VEOS), which has a long history. It has been the subject of a number of studies that emerged after the development of the Mayer-sampling Monte Carlo method[1] for calculation of cluster integrals. The VEOS has well known limits, and it is worthwhile to consider other cluster-based formulations as a means to develop descriptions of the bulk via computation of cluster integrals.

Here we examine two such approaches. First we continue our previous work for associating systems. VEOS is not particularly effective at capturing the strong directional interactions of associating fluids. In our work we have considered instead Wertheim’s multi-density formalism for associating fluid systems. A Wertheim equation of state (WEOS) is derived based on Wertheim’s association theory[2, 3]. In previous work, the effectiveness of Wertheim’s multi-density formalism has been verified with a simple Lennard-Jones model having one-, two-, and four-sites formed from conical square-well potential[4]. In current work, we examine WEOS for two realistic models, the Gaussian charge polarizable model (GCPM) of water[5] and the improved TraPPE-UA acetic acid[6]. GCPM water is a polarizable model, so we need to extend the Wertheim treatment to handle such systems. We used a three-association-site model to represent 1 oxygen and 2 hydrogen sites. To describe the behavior of 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 GCPM water obtained from WEOS converge much better to NPT simulation results compared to the conventional virial formalism at both sub- and super-critical temperatures. We obtain similar improvement in WEOS over VEOS for acetic acid.

Second, we investigate the effectiveness of cluster-integral approaches for ionic solution. The long-range electrostatic force among ionic particles make the traditionally-defined virial coefficients diverge. To overcome this difficulty, Mayer[7] proposed a theory to generate cluster integrals via virial expansion of the Coulomb potential with the addition of an exponential factor, and then resummed the resulting integrals to attain convergence. These cluster integrals depend on ionic concentrations and can be conveniently used to estimate the thermodynamic properties, such as osmotic pressure and activity coefficients. We applied 1-1 restricted primitive model (RPM) to examine our approach. The 2nd order cluster integrals are reduced to single integrals because of spherical symmetry. While some researchers employed Fourier Transforms to calculate some 3rd order cluster integrals, we use Mayer-sampling Monte Carlo simulation together with Fast Fourier Transform to calculate all cluster integrals that have significant contributions to the properties up to the 4th order and thereby extend the range of concentration described by the theory. Comparison with simulation data for the same model is presented.

References

1.            J.K. Singh, and D.A. Kofke, Mayer Sampling: Calculation of Cluster Integrals using Free-Energy Perturbation Methods. Physical Review Letters, 2004. 92(22): p. 220601/1-220601/4.

2.            M.S. Wertheim, Fluids with highly directional attractive forces. I. Statistical Thermodynamics. Journal of Statistical Physics, 1984. 35(1): p. 19-34.

3.            M.S. Wertheim, Fluids with highly directional attractive forces. III. Multiple Attraction Sites. Journal of Statistical Physics, 1986. 42(3): p. 459-492.

4.            H.M. Kim, A.J. Schultz, and D.A. Kofke, Molecular Based Modeling of Associating Fluids via Calculation of Wertheim Cluster Integrals. Journal of Physical Chemistry B, 2010. 114: p. 11515-11524.

5.            P. Paricaud, M. Predota, A.A. Chialvo, P.T. Cummings, From dimer to condensed phases at extreme conditions: Accurate predictions of the properties of water by a Gaussian charge polarizable model. Journal of Chemical Physics, 2005. 122: p. 244511/1-244511/14.

6.            G. Kamath, F. Cao, and J.J. Potoff, An Improved Force Field for the Prediction of the Vapor-Liquid Equilibria for Carboxylic Acids. Journal of Physical Chemistry B, 2004. 108: p. 14130-14136.

7.            J.E. Mayer, The theory of ionic solutions. Journal of Chemical Physics, 1950. 18: p. 1426-36.