Linking dynamics and equilibrium thermodynamics: entropy scaling and density scaling of siloxane mixtures and other working fluids for Carnot batteries

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The top-down methodology ambitioned in the SPP requires accurate data on thermodynamic equilibrium and transport properties if high efficiencies are to be achieved. In inverse design, theoretically sound equations describing these properties are necessary to identify optimal working fluids and operating conditions. The development of predictive equations for transport properties has remained well behind that of equilibrium properties, such that it is the objective of the proposed project. In fact, the better availability of equilibrium property data and predictive equations makes exploring the link between transport and equilibrium thermodynamics compelling. Entropy scaling and density scaling, having isomorph theory as a background, will be addressed for modeling the shear viscosity and thermal conductivity of pure fluids and mixtures. One of the goals of this project is the elaboration of a trustworthy methodology and recommendations for the application of entropy scaling to transport property modeling. A critical evaluation of the available modifications of Rosenfeld’s pioneering work on entropy scaling theory based on studies of the siloxanes and their mixtures will be performed. Rosenfeld suggested that transport properties, when scaled with the appropriate physical dimensions, are an univariate function of the residual entropy. This project also lays a focus on the theoretical and methodological development of density scaling, since it, contrary to entropy scaling, does not require the availability of a Helmholtz energy equation of state. Preparatory work of the applicant showed that the use of a constant effective density scaling exponent, related to the fluid’s effective hardness, can transform the unique variable of density scaling into a univariate function of residual entropy. In this sense, a study of density scaling and its relationship with entropy scaling is proposed. This will require the use of model fluids and mixtures, based on the Mie potential, which allows for variation of the repulsive interaction. As a class of real fluids, the siloxane chemical family, linear and cyclic, as well as mixtures thereof will be studied. The choice of a chemical family will offer the possibility to investigate the link between model parameters and molecular structure, which is required for inverse design. In case of mixtures, emphasis will be put to mixing rules and to highly asymmetric mixtures, where the univariate behavior is expected to break down. Generally, molecular simulation techniques will be employed to obtain evenly distributed hybrid transport property data sets as well as residual entropy data. This project, conceived as a part of the SPP, includes a high level of collaboration with other partners. It is not limited to the development of transport property scaling schemes, but also includes the supply of equilibrium properties and the study of other fluids according to the specific needs of other SPP project partners.