Predicting mixing free energy using mutual ghosting

The excess free energy of mixing Delta G(ex) governs the phase behavior of mixtures and controls material properties. It is challenging, however, to measure Delta G(ex) in simulations. Previously, we developed a method that combines molecular dynamics (MD) simulations with thermodynamic integration along the path of transformation of chains to predict the Flory Huggins interaction parameter chi for polymer mixtures and block copolymers. However, this method is best applied when the constituent molecules of the blends are structurally related. To overcome this limitation, we have developed a new method to predict Delta G(ex) for mixtures. We perform simulations to induce phase separation within a mixture by gradually weakening the interaction between different species. To compute Delta G(ex) we measure the thermodynamic work required to modify the interactions and the interfacial energy between the separated phases. We validate our method by applying it first to equimolar mixtures of labeled and unlabeled Lennard-Jones (LJ) beads, and labeled and unlabeled benzene, which results in good agreement with ideal solution theory. Then we compute the excess free energy of mixing for equimolar mixtures of benzene and pyridine, using both united-atom (UA) and all-atom (AA) potentials. Our results using UA potentials predict a value for Delta G(ex) about four times the experimental value, whereas using AA potentials gives results consistent with experiment, highlighting the need for good potentials to faithfully represent mixture behavior.