Discrete Modeling Approach for Cluster-Based Excess Gibbs-Energy of Molecular Liquids

The excess Gibbs-energy of a two-component liquid molecular mixture is modeled based on discrete clusters of molecules. These clusters preserve the three-dimensional geometric information about local molecule neighborhoods that inform the interaction energies of the clusters. In terms of a discrete Markov-chain, the clusters are used to hypothetically construct the mixture using sequential insertion steps. Each insertion step and, therefore, cluster is assigned a probability of occurring in an equilibrium system that is determined via the constrained minimization of the Helmholtz free energy. For this, informational Shannon entropy based on these probabilities is used synonymously with thermodynamic entropy. A first approach for coupling the model to real molecules is introduced in the form of a molecular sampling algorithm, which utilizes a force-field approach to determine the energetic interactions within a cluster. An exemplary application to four mixtures shows promising results regarding the description of a variety of excess Gibbs-energy curves, including the ability to distinguish between structural isomers.