Development of an Excess Gibbs-Energy Model

Excess Gibbs-energy models are the thermodynamic basis for the layout of thermal separation processes in the chemical and process industry, like distillation columns. Against the background of a change in resources towards biobased value chains, such models are being challenged by the need to describe more complex and/or oxygenated molecules. To contribute to this challenge, it is the scope of this research project to show new paths for the characterization of multi-component mixtures including complex molecules. Consequently, this project proposes to further develop a previously published excess Gibbs-energy model towards activity coefficients for chemical engineering applications. The novelty of the approach is that it a priori accounts for geometrical information about the possible arrangements of molecules in condensed phases by considering clusters of molecules as modeling basis. In this way, in particular compared to most state of the art quasichemical-based approaches, the usual decoupling of interacting surface segments from geometric restrictions is avoided and only geometrically feasible arrangements of molecules are considered, which in particular enables the distinction between isomeric configurations. The excess Gibbs-energy model as the starting point for this proposal was developed previously for clusters of dice-like molecules in a lattice. Its proposed further development comprises the improvement of the excess Gibbs-energy model itself by a different cluster construction, the combination of the model with a cluster sampling algorithm to provide cluster states for real molecules as model variables, and the application of the resulting model to Monte-Carlo data and a basic set of real two-component mixtures, to be compared to experimental data as well as established models.

Excess Gibbs-energy models are important tools to estimate properties and phase equilibria of fluid mixtures in the course of process engineering calculations, as they account for deviations of mixture behavior from the random mixing model. Goal of this project was to further develop a previously published excess Gibbs-energy model for artificial dice-like molecules towards real chemical components for chemical engineering applications, like phase equilibria. The peculiarity and novelty of the approach is that it's rigorously based on the use of the Shannon information as a synonym for thermodynamic entropy - something that has not yet been tried for the development of such models. To account for cooperative effects due to intermolecular interactions and size asymmetries, the concept is to use molecule clusters as modeling basis in order to a priori account for the three-dimensional geometrical information about the possible arrangements of molecules. This cluster based approach, considering interactions between four molecules (or three bonds, respectively), goes beyond established quasi-chemical models that are typically limited to pair-wise (one bond) interactions only. To determine the internal energies of such clusters, which represent the substance-specific input data for the thermodynamic model, a sampling procedure in the style of the PAC-MAC model, published by other authors, is used. This sampling, which was extended from molecule pairs to clusters, assumes that intermolecular interactions are described sufficiently accurately by a force field. The sampling provides a pool of geometrically possible clusters to the model, which combines these cluster energies with a probability distribution for the possible cluster states. The equilibrium distribution of these states is ultimately determined via minimization of the Helmholtz free energy of the system, as an analog to the 'maximum entropy principle' in information theory. From this equilibrium distribution, all bulk properties of the fluid, like the excess Gibbs-energy, are finally calculated. As a proof of concept, the model was exemplarily applied to selected two-component systems. A comparison with experimental data impressively demonstrates the applicability of the developed model to mixtures of different levels of complexity, including mixtures without association, mixtures in which cross-association takes place alone and mixtures in which both cross-association and self-association take place. Follow-up investigations are required to further develop the model to a fully predictive approach that reliably predicts cooperative effects from force field parameters alone. The project demonstrates that the use of Shannon information as thermodynamic entropy is a solid foundation for the development of models in the field of fluid phase properties, an approach that had scarcely been pursued before. This significant finding may motivate other groups to use this approach for other applications also. In this sense, the project results represent an important scientific advance in providing a link between information theory and thermodynamic modeling.