UNS: Detailed molecular-thermodynamic methods for high-precision calculation of condensation, criticality, and supercritical behaviors of fluids and fluid mixtures

#1510017 Kofke, David A. Given a detailed mathematical description for how molecules interact, it is difficult to predict how a macroscopic material formed from those molecules will behave. Yet such a capability is extremely valuable, because it gives us a powerful means to understand, optimize and control the behavior of natural and engineered systems. The most reliable technique is to perform a molecular simulation, and observe what happens when many molecules are made to interact virtually, on a computer. This approach has some disadvantages though: it takes a lot of computer time, which limits the type of molecular models that can be used, and instead of producing an equation that can be manipulated, it yields data, like an experiment, that requires further processing to be useful. The work performed in this project takes a completely different approach to the problem. It proceeds via a methodical examination of how two molecules interact, then three, four, etc., and in this manner builds a theoretically-correct equation that describes the macroscopic behavior. The resulting formula can be even more accurate than molecular simulation, but it has different limitations, which pertain to the state conditions such as temperature and density where it is applied. The aim of this project is to understand and overcome these limitations, so that this "cluster integral" approach can take its place alongside molecular simulation as a robust and widely-used means for understanding and using materials for practical applications. This work proceeds in several mutually reinforcing directions: (1) refining and extending an important algorithm that appeared in the literature in 2013. This is used to better enable calculation of cluster integrals needed for the project; (2) exploring methods to estimate very high-order cluster integrals, and investigating their ability to identify the condensation binodal density; (3) developing and applying approximants that enforce known critical scaling. Evidence suggests that the critical singularity hampers application of the virial series for a sizeable range of conditions in the vicinity of the critical point. Analytic treatment of the singular behavior via an approximant enables the virial series to locate the vapor-liquid critical point accurately, while providing a greatly improved equation of state for the surrounding region; (4) examining cluster series in relation to the Joule-Thomson effect; (5) applying the methods to fluid systems of practical interest. The impact of this research and related activities will be felt in many ways. First, the tools and understanding developed here can aid design and operation of many technological processes, allowing manufacturing and other commercial activities to be performed more safely, with lower cost, less energy usage, and reduced environmental impact. Educational tools will be produced relating to the topics studied here, and open-source software for implementing the methods we develop will be disseminated online. Finally, the ideas underlying this research will be introduced into curricula at the undergraduate and graduate levels, as well as part of an annual 2-week workshop for high-school students.