Unified Framework of Multiscale Density Functional Theories and Its Recent Applications

Most chemical engineering processes involve complex multiphase fluid systems, and their evolution depends on the mechanism by which the inhomogeneous subsystems exchange information at different length scales. Whereas numerous theoretical methods with specific description accuracies have been developed for investigating physicochemical properties of various fluid systems, a unified theory that enables the investigation of mesoscale problems is still needed. Here, we introduce a unified framework of multiscale density functional theories (DFTs). With the same physical concept and mathematical framework four different versions of DFTs, covering quantum, atomic, molecular, and polymeric DFTs, are presented complemented with their illustrative applications at individual scales. In addition, the combinations of those DFTs with each other and with other conventional theories and simulation approaches are also discussed. Finally, general discussions on the up-to-date progress of DFTs and the expectations on their further extensions are given. The introduction of this unified framework of DFTs is expected to advance the theoretical study of mesoscale problems.