Modeling of Fluids and Interface via Synthesis of Integral Equations and Mayer-Sampling Cluster Integral Calculations

0854340 Kofke Intellectual Merit. This project aims to develop and apply methods for calculating cluster integrals that appear in statistical mechanical theories of fluids. The primary method used is the Mayer sampling approach that was developed and refined in prior work. The present work is focused on the calculation of virial coefficients, and has two general thrusts. First, the project aims to improve methods for calculating these coefficients. Efforts here consider better characterization of the temperature dependence, more efficient grouping of the clusters to minimize the computational effort, and use of approximate integral equation closures to reduce the magnitude of the necessary Mayer sampling integrals and thereby reduce the error in their calculation. The second project goal is to study the performance and improve the application of the virial treatment in characterizing fluid phases. The aim is to better characterize the convergence of the virial series, and determine how it may be applied to approximately locate vapor liquid critical points, particularly as applied to mixtures. The work also looks to develop reformulations or approximants that can improve the range of application of the virial series. Broader Impact. Advances from this research have intrinsic potential for broad impact in chemical thermodynamics. The ability to rapidly move from a molecular model to its macroscopic properties can facilitate the formulation of molecular models that are better able to characterize fluid phases. This in turn can yield truly predictive capabilities in material properties over a useful range of conditions, given only molecular specifications and thermodynamic state. The results of this research would thus produce an enabling technology that can lead to progress in other fields in many unforeseen ways. At a minimum, this research will eliminate the need to ever perform a molecular simulation of a vapor phase or supercritical material, instead permitting a much more efficient and accurate characterization through a molecular based virial treatment. This capability can be useful for diverse applications, such as characterization of gas-phase molecular clustering, or phase equilibria calculations performed in the Gibbs ensemble, or study of solute partitioning in supercritical fluids; notably, all of these capabilities are important to energy and environmental applications. Several special forms of dissemination are performed to ensure that this work is readily adopted by others. Graphically oriented software applications are developed and made available via the web. Different versions of this software are, respectively, designed to: (1) permit the user to generate clusters meeting particular specifications, in a form suitable for use by his or her own computer codes, or simply for presentation pictorially for instruction or contemplation; (2) calculate cluster integrals and virial coefficients for arbitrary potentials using the methods being developed in the project; and (3) identify pure fluid and mixture critical points given values of the virial coefficients.