A topological theory of phase diagrams for multiphase reacting mixtures

Residue curve maps are an effective way of representing phase equilibria in non-ideal multicomponent mixtures. In this representation the phase equilibrium surfaces are replaced by an equivalent flow of trajectories of a vector field. The flow is characterized by a set of singular points that correspond to the pure components and azeotropes present in the mixture. It is shown that the patterns in these maps for reaction mixtures obey a global constraint arising from a topological invariant for the manifold on which they are defined. This constraint is in the form of an integer equation that phase diagrams must obey in addition to the Gibbs phase rule. The main advantage of the method is that certain global statements can be made about the structure of reactive phase diagrams, independently of the details of phase equilibrium data or models.