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

#1510017Kofke，David A.给出分子如何相互作用的详细数学描述，很难预测由这些分子形成的宏观材料将如何表现。然而，这样的能力是非常有价值的，因为它为我们提供了一种强大的手段来理解、优化和控制自然和工程系统的行为。最可靠的技术是进行分子模拟，并在计算机上观察当许多分子虚拟相互作用时会发生什么。然而，这种方法也有一些缺点：它需要大量的计算机时间，这限制了可以使用的分子模型的类型，而且它产生的不是一个可以操纵的方程，而是需要进一步处理才能有用的数据，比如实验。在这个项目中进行的工作采取了完全不同的方法来解决这个问题。它通过系统地研究两个分子如何相互作用，然后是三个、四个等等，并以这种方式建立了一个描述宏观行为的理论上正确的方程。所得到的公式甚至可以比分子模拟更准确，但它有不同的限制，这与它所应用的温度和密度等状态条件有关。这个项目的目的是理解和克服这些限制，以便这种“团簇积分”方法能够取代分子模拟，成为理解和使用材料进行实际应用的一种强大和广泛使用的手段。这项工作沿着几个相辅相成的方向进行：(1)完善和扩展2013年文献中出现的一个重要算法。这被用来更好地计算项目所需的团簇积分；(2)探索估计非常高阶团簇积分的方法，并调查它们识别凝聚双节点密度的能力；(3)开发和应用加强已知临界标度的近似值。有证据表明，临界奇点阻碍了维里级数在临界点附近相当大范围的条件下的应用。通过近似式对奇异行为进行解析处理，使维里级数能够准确地定位汽液临界点，同时为周围区域提供一个大大改进的状态方程；(4)检验与焦耳-汤姆森效应有关的团簇系列；(5)将这些方法应用于实际感兴趣的流体系统。这项研究和相关活动的影响将从许多方面感受到。首先，这里开发的工具和理解可以帮助许多工艺流程的设计和操作，使制造和其他商业活动能够以更低的成本、更少的能源消耗和对环境的影响更安全地进行。将制作与这里研究的主题有关的教育工具，并将在网上传播用于实施我们开发的方法的开放源码软件。最后，这项研究背后的想法将被引入到本科生和研究生的课程中，以及为期两周的高中生年度研讨会的一部分。

#1510017Kofke, 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.